JHEP02(2020)174 E Springer January 7, 2020 February 9, 2020 : February 27, 2020 : : , Received Accepted Boris J

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JHEP02(2020)174 e Springer January 7, 2020 February 9, 2020 : February 27, 2020 : : , Received Accepted Boris J. Kayser, Published e [email protected] , Published for SISSA by https://doi.org/10.1007/JHEP02(2020)174 Patrick J. Fox, d [email protected] , [email protected] e , Andr´ede Gouvˆea, . a,b,c 3 [email protected] , 1912.07622 and Jennifer L. Raaf The Authors. e c Beyond Standard Model, Neutrino Physics

One proposed component of the upcoming Deep Underground Neutrino Ex- , [email protected] Fermi National Accelerator Laboratory, Batavia, IL 60510, U.S.A. E-mail: [email protected] Lexington, KY 40506, U.S.A. Department of Physics, UniversityBerkeley, of CA California, 94720, U.S.A. Northwestern University, Department of2145 Physics Sheridan & Road, Astronomy, Evanston, IL 60208, U.S.A. Center for Neutrino Physics,Blacksburg, Department VA of 24061, Physics, U.S.A. Virginia Tech, Department of Physics and Astronomy, University of Kentucky, b c e d a Open Access Article funded by SCOAP charge of the final state particles leads to theseKeywords: bounds. ArXiv ePrint: physics possibilities studied are searchesStandard for dark Model vector hypercharge bosons mixing group,the kinetically leptophilic Standard with Model the vector Higgs bosons,Model boson, dark neutrinos. and scalars heavy We mixing neutral demonstratethese with leptons that scenarios. that the We mix illustrate MPD with how can the the extend ability Standard existing of bounds the MPD in to most measure of the momentum and periment (DUNE) near detectortime projection complex chamber: is the a Multi-Purposepotential multi-purpose, Detector of (MPD). magnetized, the We explore gaseous MPD, thesitive argon focusing new-physics to on new scenarios physics in thanparticles which a that the liquid are argon MPD produced detector, is in/near specifically significantly the searches more beam for sen- target semi-long-lived and decay in the MPD. The specific Abstract: Jeffrey M. Berryman, Kevin J. Kelly Searches for decays of newMulti-Purpose particles near in Detector the DUNE JHEP02(2020)174 43 39 45 4 5 12 47 37 3 7 6 41 16 10 21 24 34 39 23 – i – 36 28 3 31 8 10 30 14 20 19 40 33 7 26 16 13 1 7.3.3 Expected DUNE MPD sensitivity 7.4.1 Final7.4.2 states with unobservable lepton Final number states with only charged particles 7.2.1 Relevant and irrelevant decay channels 7.3.1 Backgrounds7.3.2 for relevant HNL decay Existing channels limits 3.3.1 Three-body decays 7.4 Deducing the nature of the HNL — Dirac vs. Majorana 7.2 Decays of Heavy Neutral Leptons 7.3 Sensitivity to Heavy Neutral Leptons 6.1 Dark Higgs6.2 boson production Dark Higgs6.3 boson decays Backgrounds and sensitivity 7.1 Production of Heavy Neutral Leptons 5.1 Production5.2 of leptophilic gauge bosons Decays of5.3 leptophilic gauge bosons Sensitivity to leptophilic gauge bosons 4.1 Dark photon4.2 production Dark photon4.3 decay channels and Backgrounds lifetime 4.4 Dark photon sensitivity 3.2 Focusing of3.3 charged mesons Particle flux at the DUNE near3.4 detector Signals of decays in the Multi-Purpose Detector 2.2 Particle thresholds2.3 and reconstruction capabilities Particle signatures2.4 in the multi-purpose Background detector rates from the neutrino beam 3.1 Production of charged and neutral mesons 2.1 Experimental parameters and assumptions 7 Heavy Neutral Leptons 5 Leptophilic gauge bosons 6 Dark Higgs boson 4 Dark photon 3 Simulation details Contents 1 Introduction 2 DUNE near detector complex JHEP02(2020)174 ] 1 ], 5 , 29 4 – 25 56 ] (ArgonCube) of the detector. 3 ], millicharged parti- ] will use liquid argon 55 1 volume 21 – 6 – 1 – of the detector. For new physics searches that rely on particles ] for a more thorough summary of beyond-the-Standard-Model ], but is foreseen to include a modular LArTPC [ 30 2 mass 53 ]. The next generation of neutrino experiments will undoubtedly be able to 31 , ], and exotic interactions among the Standard Model (SM) neutrinos [ 24 24 – 22 In most new physics searches at neutrino facilities, the dominant backgrounds for the Beyond DUNE’s nominal mission to perform precision measurements of neutrino prop- The MiniBooNE-DM search avoided this issue by diverting the proton beam into a beam dump, allowing 1 For the DUNE nearvolumes, detectors, but the their LArTPC different and densities MPD imply will that have their roughly targetneutrino-related the masses backgrounds same will to be active differ significantlydedicated by smaller experimental a than run in factor for beam-on aoperation searches. new of This physics DUNE. strategy search. requires a What we propose here is parasitic with the standard signals of interest ariseThese from scale interactions with of the neutrinosscattering in from the the detector, the beam signalsignal rate with is rates the also in proportional detector. to searches the for detector novel mass. particle However, decays scale as the active to name a fewsearches (see ref. in [ neutrino experiments).the experimental collaborations, Several leading of tointerest these stringent [ limits scenarios on have the been newinterrogate physics these investigated scenarios and by of other new physics scenarios with increased precision. erties and neutrino oscillations, both itsof near new and physics. far Recently, detectors interest willgrown, in serve as using with powerful neutrino proposals probes detectors to tocles search search [ for for new physics dark has matter/dark sectors [ particles produced in neutrino interactions.although The not LArTPC component identical ofprecision the to measurements near the of detector, neutrino far oscillations.momentum-analyze detector, particles The MPD’s exiting is main the critical purposein LArTPC, is to reducing but to systematic it the track uncertainties will and DUNE for also the mission play oscillation an of analysis. important making role currently under design [ with a spectrometer(MPD). immediately The downstream, MPD called will the(HPTPC) consist Multi-Purpose surrounded of a Detector by high-pressure an [ The gaseous HPTPC electromagnetic argon has calorimeter, time the projectionmuch all same lower chamber situated nuclear density, allowing target within this as a detector ArgonCube magnet. to and more the finely far resolve the detectors details but of has low-energy a 1 Introduction The upcoming Deep Undergroundtime Neutrino projection Experiment (DUNE) chambers (LArTPCs) [ at its far detector site. The near detector facility is A Meson production details andB beam energy Derivation comparison of charged meson decays into leptophilic vector bosons 8 Conclusions JHEP02(2020)174 is H contain provides 7 – is the U(1) 3 describes a 4 is a coupling µν 5 0 F µ while , we describe the DUNE N . details a search for dark 2 (1.1) 4 , or S , µ Kinetic Mixing; Gauge Coupling; , V , , 0 µν Scalar Portal; F Neutrino Portal , we explore the capability of the MPD to ]: the vector, scalar, and neutrino portals. 7 39 – 2 – Vector Portal Vector Portal – 32 , 6 0 N µν is the lepton doublet. The parameter SM µ is a vector current made out of SM fermion fields, ) HS F J † L µ µν H SM LH µ 0 V F ( J , µ 2 | S | H † H explores the capability to search for heavy neutral leptons (HNLs) that 7 explains a search for a dark scalar particle that mixes with the SM Higgs boson; 6 In this work, we show that the DUNE MPD will have exceptional capacity to search The remainder of this paper is organized as follows. In section As a guiding principle of which new physics searches to study, we focus on the three We propose using the DUNE MPD as a detector for the decays of new particles within for new physics infinalized, a we variety use of this aspect scenarios.the of Near the With Detector MPD the suite. to DUNE advocatethe While for Near added the its Detector capabilities LArTPC inclusion design could of in searchpossibility the not the for of MPD final yet these design discovering allow new new for for physics physics. a scenarios, considerable increase in sensitivity and the section and section mix with the SMdetermine, neutrinos. if a Also heavy innature neutral section and lepton therefore whether is neutrinos discovered, are whether Dirac lepton or number Majorana is fermions. violated in capabilities and expected backgrounddetails rates of the of simulation interestthe techniques for specific we new the use physics MPD. throughout searchesvector for Section our bosons which studies. we that advocate: mix Sections search section kinetically for with vector bosons the that SM are hypercharge coupled group; to section various combinations of lepton flavor number; might also be connectedmanuscript, to we other will new explore the particles,of capabilities such each of as of the an these DUNE MPD types extended in of dark searching new sector. for particles. the InNear decays this Detector complex and the MPD. We also provide details regarding the measurement Here, the new physics particleshypercharge are field represented strength, by the Higgs scalar doublet,with mass and dimension 1. These new particles are interesting in their own right, but they a standalone detector, will be able to outperform therenormalizable LArTPC. portals toEach the portal SM consists [ renormalizable of operator a constructed new outSM particle of fields: Lorentz- or and mediator gauge-invariant combinations that of couples to SM particles via a consequently be, roughly, a factor of 50 larger thanits in active the volume LArTPC. for preciselycharge this reconstruction, reason. as Additionally, theallow well excellent for as tracking these ability searches the to and particle-identification be capability, further optimized. of For the decays of MPD new will particles, the MPD, as of 50. In searches for decaying particles, the signal-to-background ratio in the MPD will JHEP02(2020)174 , we +z A protons 22 584 m

10 axis represents × z (1 t) DUNE HPTPC 47 . DUNE MPD ECAL/Magnets (1 579 m 2

= 574 m corresponds to the z (50 t) DUNE LArTPC ] for more detail regarding the 43 Distance from Target (not to scale) Distance from Target – 574 m 40 earth – 3 – = 579 m corresponds to the front of the multi-purpose 230 m z Decay Volume Decay + π − π 0 protons strike the target each year. Unless otherwise stated, we η π = 0 m corresponds to the front of the target,

z Target 10 × Magnetic Focusing Horns Magnetic Focusing z = 0 m provides a schematic of the features of the DUNE target and near detector 47 . 1 we assume that the protons in the LBNF-DUNE beam have 120 GeV of energy, . Schematic layout of the DUNE beam, target, and near detectors. The 120 GeV Proton Beam Figure Some projections of DUNE operation include the possibility of an upgraded beam (roughly twice the 2 energy SM neutrinos, havediscuss also the been impact considered of by different the beam collaboration. configurations on In our appendix number results, of which protons is ona marginal. target per constant year) number thatoperation of can time protons operate with on in such the an target upgraded second per beam. half year, of the so experiment. our We ten-year assume projection is equivalent to a shorter and that 1 assume data collection of equal(“reverse time horn in neutrino current”) (“forward modes. horn Inon current”) and general, target) antineutrino we will of assume totalnotably ten data years the collection possibility in of our the analyses. beam protons Different having beam 80 GeV configurations, of most energy or focusing higher 2.1 Experimental parametersHere and we assumptions specify theincluding the exact beam experimental setup, parameters magnetic focusing that horns,Beam: we and assume the detectors. in our simulations, beam strikes a targetfocusing and horn that system. thereach The particles the focused boundaries emerging of particles from the traversedetector decay the volume a hall are target decay is assumed enter volume; to positioned a comeis any downstream to occupied magnetic particles of rest by and that the raw decay. decay earth. The volume near and the space between them complex, including the protonthe beam experimental target, hall. decay volume, WeDUNE direct and Experiment. the the reader layout of to detectors refs. in [ hall of interest for this work. The figure is not drawn to scale. We consider that the proton detector. The masses listed with the two detector components are2 the expected fiducial masses. DUNE near detectorIn complex this section, we outline our assumptions for the setup of the DUNE Near Detector Figure 1 the beam direction; front of the liquid argon near detector, and JHEP02(2020)174 ]. 5 and π ) produced in 0 S ), we assume the K ] for more detail. 3 , ], this corresponds 0 L 44 45 for clarity. We note , K 1 , 5 , ] for more detail. η , we include the magnetic 4 2 , 3 0 π we assume a total distance of 230 m 7 MeV for electrons, muons, and protons, . – 4 – ]. 44 ) and neutral mesons ( s D 8 MeV, and 3 the liquid argon near detector has a width (transverse to , . the Multi-Purpose Detector (MPD) is a magnetic spectrom- D 8 tons (1 ton fiducial). See refs. [ . is largely similar for muons and pions, we take their kinetic 14 MeV, 1 . consistent with simulations performed by the DUNE collaboration, we dE/dx 5 T central field. The axis of the cylinder is perpendicular to the beam di- . First, we focus on the energy thresholds for which a charged particle would leave a The HPTPC operates at a pressure of 10 atmospheres, leading to a total mass of argon , specifically. Short-lived ( a track. Accordingto to kinetic the energies continuous-slowing-down of approximationrespectively. 0 [ These values assumeenergy a deposition pressure ofenergy 10 thresholds atm to in be the the gaseous same. argon. These values Since are the listed in table In this subsection, weHPTPC, discuss as various well thresholds as required theWe capability for make of particle use measuring identification charge of in and the distinguishing the information pairs in of ref. particles. [ track long enough to be identified. We assume that 2 cm is a reasonable length to identify in the gas TPCParameters of associated to roughly the 1 detectionin of the charged next particles subsection. in the gaseous argon are2.2 given Particle thresholds and reconstruction capabilities symmetry axis of the detector isuniform aligned apparent with detector the thickness direction for ofa all the incoming beam, muon particles. since tagger this The interleaved leadsWe possibility to with discuss of a the how including such ECAL a is muon under tagger exploration impacts our by results the wherever collaboration relevant. [ Multi-Purpose Detector: eter with a cylindricalits high-pressure heart. gaseous argon The time HPTPCelectromagnetic projection has calorimeter a chamber diameter (ECAL) (HPTPC) of and at magnet 5 the m with HPTPC+ECAL and 0 system a is lengthrection. situated of However, 5 inside for simplicity, m. a when simulating It our is signals surrounded (see by section an Liquid argon near detector: the beam direction) ofThe 7 fiducial m, mass a of height the of near 3 detector m, is and 50 a t length of (in argon. the beam See ref. direction) [ of 5 m. K our simulations are not deflected by the magneticDecay focusing volume horns. andbetween near the detector target distance: andLArTPC the is 574 end m of from the the target, decay and pipe, the wherever front of relevant. the MPD The is front 579 of m the from the target. assume three aluminum focusingon horns the that polarity produce of toroidalcharged the magnetic particles applied fields. current, that Depending theembedded are horns within produced the focus first in horn. eitherfocusing the As collisions explained effects positively in of on or detail the in the negatively section momentum protons distributions with of a long-lived, graphite charged mesons target — Focusing horns: JHEP02(2020)174 ]) 5 (10) GeV of energy, O 7% level if they exceed . 8 8 7 14 . . . . 1 1 3 0 – 5 – ) for each track enable this detector to distinguish dE/dx Kinetic Energy Threshold (MeV) − − − p /µ /π /e + + + e µ π Particle ]. 40 lists the types of signals that are expected for the new physics processes . Expected thresholds for track identification in gaseous argon, operated at 10 atm. 2 Table We assume that transverse momenta are measured at the 0 Table 1 some of the possible decay channels.with Finally, the the decaying high-energy particles proton-beam-target areleading produced interaction associated to and decay will products have (produced with in several neutrino GeVvariable each. interactions) with which will In signal have contrast, events can lower much be of energy, distinguished. the giving background another kinematical escape the ECAL). With theoutside addition the of ECAL, a more muon tagger separation (currently power under would consideration be [ achieved. discussed in later sections,oppositely along charged pairs with of leptons links or toto hadrons whose the those reconstructed target. tracks sections. should The point reconstructed In back invariant general, mass will the provide signals another are handle for identifying to distinguish among theespecially tracks if left they by come heavierundergoing to optimization, particles but a (pions, in stop its muons,itself, current within kaons, this state ECAL protons), the it should is gas have some only(2) volume. ability one pions to interaction separate that The length interacting punch thick. ECAL pions through from By design (all (1) muons muons is and and currently roughly 30% of pions will punch through and In the HPTPC, energy depositedsensitive in pads the form at of each ionization(energy) deposited is end per sampled of unit by length the a ( electrons plane cylindrical of from detector. charge- heavier particles The for characteristics a of large the range charge of particle momenta, and some ability signatures studied throughout thisopposite work signs) will emerging include from atassuming a least that common particle two vertex. has charged a particles Events very (with with high only energy, could one2.3 be charged more particle, difficult to Particle charge-identify. signatures in the multi-purpose detector 1 GeV. Below 1 GeV, weis assume expected them to to be be measured efficient at anda the vertex accurate. 1% will level. Two be particles Charge identified with as identification For opposite two separate the charges tracks emerging once purposes from they of areparticle/negative-particle separated this by pairs, more work, than unless 1 this cm. Furthermore, the corresponds there vertex to is nearly is no perfect very ambiguity separation close in of to positive- the a charge detector assignment. boundary. Nearly all experimental that these are farnear lower detector than [ the thresholds for particle identification in the liquid argon JHEP02(2020)174 represents the . Dark Higgs Dark Higgs Dark Higgs , , , X (10 cm). Far more 4 O decay point. Given the 0 π New Physics Models Heavy Neutral Leptons Heavy Neutral Leptons Heavy Neutral Leptons Heavy Neutral Leptons Heavy Neutral Leptons arise from photon conversions. The Leptophilic Gauge Boson Leptophilic Gauge Boson Leptophilic Gauge Boson invariant mass. Backgrounds to the , , , 0 − e π + e (10 meters); approximately 12% of photons , it is not possible to distinguish muons from c pairs will typically be of much lower energy O Dark Photon Dark Photon Dark Photon ]. For different search channels throughout this – 6 – − e 46 + , e 44 in the LArTPC than in the HPTPC. − e Features + e Direction, Energy Direction, Energy Direction, Energy Invariant Mass, Direction Invariant Mass, Direction Invariant Mass, Direction Invariant Mass, Direction Invariant Mass, Direction of photons in the gas is 3 0 alone in the HPTPC. With the addition of the ECAL (and potentially ]), some fraction of the pions will be distinguishable by their hadronic ∓ ∓ π 5 π ρ 0 − ∓ − − − e µ µ e µ /π /µ /µ + + + + − ∓ ∓ e µ π νe νe ρ νµ π + dE/dx → → Signal π e → e → → . Expected decay signatures of new physics processes. In the left column, lists the expected number of neutrino-related events for scattering on argon for a X X → X → X X → 3 X X Neutral pions are only visible in the HPTPC if the photons from the pion decay For momenta above a few hundred MeV/ In the HPTPC, possible background pairs of X This is in contrast with the LArTPC, where the conversion distance of photons is 3 (meters)-long photon conversion length, rarely (about 1% of the time) will both photons photons can fake the signal of 2.4 Background rates fromTable the neutrino beam variety of different interaction types [ to a common vertex, allowingnew reconstruction physics of processes the are expectedto to be produce small, multiple since pions theMultiple background and processes pion have would production need no inadditional other vertex standard activity activity, neutrino at which is the interactions detectable neutrino is down interaction generally to vertex. accompanied very low by energies in the HPTPC. convert. Most of theproduce time, the signals photons with willO a reach the shower ECAL, axis where thatconvert they within will points the convert back gas. and to Ifbefore one the converting, then photon the converts in energy the depositions gas in and the the two subdetectors other will reaches still the point ECAL back sections of this paper.trino interactions Backgrounds in could the then gas,with arise in no from which other a standard visible muon charged-current and particles,the neu- a but target pion these to of would be opposite still considered charges need background are to to produced point signals back discussed in in the this direction paper. of beam direction. We discuss backgrounds of this nature inpions detail via in section a muon tagger [ interactions. We discuss the capability of distinguishing muons and pions in the relevant conversion distance produced by standard beamthe neutrino ECAL. interactions However, in these thethan converted gas the signal will pairs convert considered before in reaching this paper and they will infrequently correlate with the Table 2 new physics particle decaying. JHEP02(2020)174 . -scattering µ 7.3.1 ν and pair — per year of 4.3 + π − µ (10%) of the time. Therefore, O 3 4 5 5 5 6 ) that decay leptonically, leading 10 10 10 10 10 10 × × × × × × K charged-current events in one year of 98 89 96 47 17 64 ...... µ 5 1 1 4 5 1 , depending on the mode of operation) and ν µ ν π or µ – 7 – ν when operating in neutrino mode, or vice versa Number of events per ton-year µ ν inclusive inclusive 0 0 π π CC Total NC Total CC Total NC Total e e µ µ Event class ) of this type of background event — a ν ν ν ν CC NC 5 . This allows for focusing of positive (forward horn current) or — assuming one ton of fiducial mass. Charged-current µ µ with respect to 6 1 ν ν (10 µ 10 O ν × 64 . . Expected number of neutrino-related events scattering on argon (liquid or gas) assuming pairs, then this background could be further reduced using the kinematic information As an example, consider the total number of − µ + at the near andcontamination far of detectors. In orderfor antineutrino to mode), produce focusing a hornsas purer are beam depicted utilized (i.e., immediately in one downstreamnegative figure of with (reverse the a horn target, smaller current) mesons. Forward (reverse) horn current corresponds to an into BSM particles. 3.1 Production ofThe charged and general neutral strategy mesons produce of a large DUNE, flux of while chargedto mesons operating (mostly a as large a flux of neutrino SM beam neutrinos experiment, (mostly is to particles that then decay intoDUNE beyond-the-Standard-Model target. (BSM) particles We atthe will or direction be near and interested energy the in spectrum,particle in the to order flux reach to of determine thedetails the the of DUNE probability BSM simulating for MPD particles, the a and both given production decay BSM in of inside terms SM it. of particles (predominantly In mesons) this that section, decay we discuss the capabilities, etc. We will discuss these techniques in detail3 in sections Simulation details All of the new physics scenarios studied in this work rely on simulating the flux of SM other detectable hadronic activity at thewe interaction vertex) naively expect data collection in the MPD.µ If, for example, weof were the searching charged for particles, a information signal regarding that the consists hadronic of system, particle identification or could otherwise be misidentified asto our infer desired the signal). total We number will of use these background estimated events rates foroperation each — search. 1 on argon will lead to the production of a single charged pion along with the muon (and no Table 3 1 t of fiducial mass and 1 year of datawork, collection. these events can contribute as background (assuming they have the right kinematics JHEP02(2020)174 6 (3.1) − 10 ], which − s Pythia8 D × 46 6 . 1 provides more ) are unaffected 6 A s − D 10 + s , D × 2 , respectively. . D 1 5 ), on the other hand, are 0 6 S K 19 and . − K 0 4 10 − and D × 0 L 19 0 . . K 0 6 π 2 y p | ]. 6 + z 33 − η . p 2 x | 0 51 p 10 , + q D × 50 9 0 [ . 7 – 8 – . π 2 ≡ 3

z T (with operation in neutrino mode), as a function of p p −

16 . Fluka K 0 ], simulating 120 GeV protons on target and using the in the left panel and 47 [ + 24 Fluka Species . ] and K 0 Mesons/POT decay 49 , z and 4 − . 48 2 π [ Pythia8 ) and charged mesons that decay promptly ( 7 0 S + . option to generate mesons. In doing so, we obtain the overall rate of π 2 K , Geant4 as the four-momenta at decay, assuming they don’t hit the boundaries of the 0 L Geant4 K depicts the normalized differential decay rates of the long-lived charged mesons , 2 0 π . Average number of neutral mesons produced per proton-on-target assuming 120 GeV . Average number of charged mesons produced per proton-on-target assuming 120 GeV Species Pythia8 Figure The average numbers of different charged and neutral mesons produced per proton on We will explore scenarios in which the flux of a new particle is produced via de- Mesons/POT extracted from the longitudinal distance by the focusing horns, so,with in our simulations, we usedecay the volume. lab-frame Long-lived four-momenta obtained chargedsubject mesons to (namely, the effects ofmesons, we the use focusing output horns. from themakes For DUNE the use Beam distributions Interface of Working of Group the (BIWG) [ long-lived charged 3.2 Focusing of chargedThe mesons quantities we explicitly requiremomenta in at order production tomesons but simulate ( meson instead decays their are four-momenta not their at four- the time of decay. Neutral target (POT), assuming a 120 GeV beam,also are allows listed in us tables tobe obtain of the interest lab-frame indetails simulating four-momenta the of of flux the this of outgoing differentbeam simulation mesons, new results. as particles. which well will Appendix as comparisons between 80 GeV and 120 GeV proton meson production from the primarytotal proton meson interaction; this flux procedure asmary underestimates it interaction the neglects scatter secondary inmoderately production or conservative. when near mesons the produced target. in Our the results pri- may then be interpreted as “antineutrino” modes henceforth. cays of charged orwe neutral use the mesons. software ‘‘SoftQCD:all’’ To simulate the production rate of a given meson, Table 5 protons. enhancement of the (anti)neutrino flux, so we will refer to the modes as “neutrino” and Table 4 protons. JHEP02(2020)174 , + η , K 0 10 π + − — this + − π π K K z than that | 1 distributions z T , while those characterizes p p 2 + | | − z K T p p 1 10 | − . As discussed, we 10 , the longitudinal po- × 1 | 3 z T − p are similar to those in p | decay 10 2 with the right panel of s z − | ∼ 3 D 10 z T p p | ∼ | z T distributions than for the and determine the position of p p and 3 | − − 10 π distributions (red), D depicts the normalized differential − vs. 3 4 π − + 2 1 2 1

10 Pythia8 − − 10

| 10 10

z T ) ( Γ /p p d illustrates several eﬀects of the focusing

Γ 1 d , figure 2 2 250 – 9 – . Instead, the bulk of decays of the anti-focused, + − + − 2 π π K K − 200 10 in this case) lie near simulations of charged meson transport through the DUNE , as a proxy for how well-focused the corresponding mesons for a subset of the unfocused species — namely, − | | ∼ z π distributions (blue), | z T 150 p p z T /p | + p p T | π [m] p Fluka | 100 decay and z 50 (left). 2 distributions (purple). This figure is for operation in neutrino mode, in which Geant4 = 0 and point towards the near detector. We clearly see two effects here 0 − 230 m, corresponding to the end of the decay pipe. Mesons that reach the T . The distributions for promptly decaying K p ≈ 0 S 50 4 1 2 3 K ] using . Decay distributions of long-lived charged mesons as determined by the DUNE collabo- − − − − −

and we choose not to display them. Comparing ﬁgure , the bulk of decays of the unfocused mesons lie near

distributions: pions are focused more eﬃciently than kaons.

10 10 10 10

dz decay −

]

[m 3 2

z 1 Γ 1 d − In contrast to the right panel of figure , and K 0 L surface, see figure of the focused mesons liewrong-sign near mesons (specifically simulate the production oftheir neutral decay mesons according using toinsist the that proper any lifetime meson of that the reaches meson the and end its of simulated the energy. decay pipe We decays at rest at the rock decay rates as aK function of figure figure how well-focused a givenwould meson have is at the— first, time the of distribution itsof of decay the the — negatively positively a charged charged ones, perfectlygreater mesons as separation, focused peaks the due at meson former to smaller arevs focusing, focused. between Also, the we observe that there is a horns. First, we seeis that because the they positively arelarger charged the mesons distances. focused tend Secondly, mesons, to wenear and decay also at travel see larger through a theend peak horns of of and the decays beam for decay pipe all pipe to four will distributions stop located and decay at rest. In the right panel, (green), and positively charged mesons are focused. in the right panel. The left panel of figure Figure 2 ration [ focusing horns. The leftsition panel of presents the decay decay. distributionsand The in right longitudinal terms panel momentum, of presents decayare. distributions in In terms both of the panels, ratio we of transverse show JHEP02(2020)174 ), we (blue), 2 0 ) of the π (with masses x, y, z distributions for X − π )], the flux of new 2 / + π , and rad 2 4 S − , 10 1 + − S π π (10 O 1 0 0 L S K K 1 − 10 | z T into particles p p | 2 0 − P , except for unfocused neutral mesons: π η 10 2 – 10 – 3 − 10 4 − 2 2 1 1

10 − − 10

| 10 10

z T

) ( Γ /p p d

(purple). We include the focused/unfocused

Γ 1 d 0 S , respectively); we will be interested in the lab-frame kinematics of K X m , and 2 S (green), and m 0 L , . Identical to the right panel of figure 1 K S m We are interested in decays of parent mesons into both two- and three-body final , P (red), 3.3.1 Three-body decays In some cases, webody are decay. interested in Here the weConsider discuss production the the of three-body assumptions a decay made particlem of in that a these comes situations particle from and a their three- validity. states. The two-body kinematicsthe may three-body kinematics be is solved less easilybody straightforward. in decays We discuss the in our the parent recipe next rest for handling subsection. frame; three- however, particles is highly dependentof on our features assumption such that as thehave the (effectively) detector boost is reduced of coaxial the the withcompensated solid parent the in angle meson. beam our by direction Because signal roughly (seetwo event 20%. effects section rates will by This approximately the lower cancel. longer acceptance effective will depth be of the detector; these the four-momenta of theparent’s relevant daughter(s). rest These frame four-momenta backmeson are decay to boosted location, from the we the labMPD. can The frame. determine fraction whether of Combined thegeometrical produced BSM with acceptance particles particle the that of will position pass the passthe through ( through DUNE detector. the the near near detector. A detector careful Since defines it treatment the has of a this small effect solid is angle [ critical for 3.3 Particle flux atOnce the the DUNE parent near distributionparticle(s) detector has of been interest obtained, at webasis the must by determine DUNE Monte-Carlo the near flux simulating detector. of the This the rest-frame is BSM decays done of on a the particle-by-particle parent particle to obtain Figure 3 η comparison in grey solid/dashed lines. JHEP02(2020)174 N . (3.2) 2 X 50 m + determine 225 . 0 40 (right). The X 2 2 X 4 S 1 m S [GeV] − 30 X 2 [GeV] → 2 S E ) . ]. These three energy m P 2 , assuming three different . 0 (acc X 20 52 + N E 0 1

0 2 S

π 60 40 20 80 PDF + rest frame) according to three m is a heavy neutral lepton (see µ rest frame. For concreteness, we 10 + N + − → K K 2 P + 0 m 4 4 4 4 4 0 K 2 P 10 10 10 10 10 m × × × ×

4 , where

in the

5 4 3 2

det . X

N ) R < R

( N

2 X ) det (at . 0 N m π distributions (for simplicity, we concentrate on . 50 + – 11 – + X + µ 2 K 2 S → /dE is considered to be spin-0, so the angular distribution m 40 Γ + d + P at the front face of a detector located 579 m from the original 1 K 2 S N m [m] 30 produced in the decay ) . N − 2 P (at det 20 m R v u u t , and to show that the dependence is fairly small. As an illustrative 10 X ≤ must lie in the range /dE is not monoenergetic in that frame. Kinematics dictates that the rest-frame 0 Γ (CM) X 5 5 5 5 5 0 d X X E 10 10 10 10 10 . Distributions of = 200 MeV. The three distributions are ﬂat (blue), piecewise-linear (red), and the true ) with a mass of 200 MeV. × × × ×

≤ 7

N 4 3 2 5 X N m X Our goal in this subsection is to investigate the dependence of our analysisWe on simulate the the three-body decay (isotropic in the production point. Of those that have pass through the face of the MPD, we display their energy (i.e., its energy and whether it is pointing in the direction of the detector). In all of the m + (b) piecewise linear, symmetricenergy about distribution the for middledistribution HNL probability of production, density the functions as energy aredecays depicted described range, are in simulated and in using the (c) the inset ref.operation focused of the [ during figure true neutrino mode only), and we determine (1) the spatial distribution of choice of example, we focus onsection the decay different energy distributions: (a) flat between the energy endpoints (200 MeV to 225 MeV) Beyond this, different interactionthe structures shape governing of the the decay differential width of the outgoing particleshowever, is isotropic inenergy of its rest-frame. In contrast to two-body decays, displays the spatial distribution of K distribution in the right figure. X scenarios we consider in this work, Figure 4 probability density functionstake for the energydistribution of (green) if this is a three-body decay producing a heavy neutral lepton. The left panel JHEP02(2020)174 (i.e., those N , we see that the particles that pass ), we will focus on 4 ], where the liquid and 53 N 7.4 10 m. The standard model neutrino ∼ R , the blue curves correspond to the flat 4 – 12 – . 7 – ) are relevant, we apply them. We will discuss how the kinematic 4 5 m). In all panels of figure . 2 1 < = 579 m (the front face of the MPD), as measured from the center of the The right panel depicts the energy distribution of accepted ) depicts the results of the simulations. The left panel depicts the radial dis- z . 4 4 (at det R We will also be specifically focused on the decay products’ kinematics when discussing Of interest are quantities such as the energy of visible particles and opening angles Figure As an aside, we note that the radial distribution peaks at 4 distribution. Such kinematic informationlepton number can is provide violated, an and interesting we handle will into exploit whether it whenflux peaks possible. at muchgaseous lower radii. argon near Using the detectorstypes DUNE-PRISM may of near move searches. detector off-axis concept up [ to 36 m could allow for further optimization of these such feature. disentangling different new physicsnewly-discovered HNL scenarios. is a Inthe Dirac particular, lab-frame or when Majorana decay discussing product fermion whether (see energies a section as a proxy for the new particle’s rest-frame decay quantities will allow forinstance, an any improved new search particle for thatto these decays an completely new visibly, electron-positron particles, suchonce pair, where as the a relevant. will total dark four-momentum produce For photon ofgood decaying decay the separation final-state products particles of with is signal reconstructed. an from This invariant background allows mass since for peak the latter is not expected to have any the kinematics of the final-statein particles. detail in All sections of these are model dependent andbetween discussed different particles that leave aeffects track in (see the MPD. table When any threshold or efficiency 3.4 Signals ofWe decays are, in in the general, Multi-Purpose interestedDUNE Detector in MPD. the After event determining rates thedetermining of flux the different of associated decays a of given probability new new for particles particle a at in decay the the of MPD location interest and to occur, we also simulate match fairly well, whereon the this piecewise-linear evidence, distribution whendecay prefers simulating products three-body higher are decays, flat energies. in wetions the here, assume Based phase this the space simplified distributions of analysissensitivities. of the suffices, the final-state especially particle when energy. it comes For our to ambi- estimating detector energy distribution, the red correspondcorrespond to to the the piecewise-linear true distribution,flat energy and and true distribution. the distributions green both Inthat tend the the to left agree acceptance panel in fractionThe terms of in of piecewise-linear figure radial distribution simulating distributions, tends these so towe two we prefer see expect scenarios larger that should radii. the be Similarly, energy in largely distributions the similar. of right accepted panel, events for the flat and true distributions through the MPD. tribution at beam axis. with at the location of the MPD, and (2) the energy distribution of the JHEP02(2020)174 ], The 62 (4.1) , 5 61 , 20 characterizes produced via depends upon 0 ε ε A . Should the dark and χ ], NuCal [ 0 µν F 60 , µ 0 A 0 µ . Thus, any dark photon that A χ 0 . 2 m A 4 ], Orsay [ 2 2 − M 59 < – 10 + 0 A 56 0 µν ε < F with field strength < M µν and couples to the SM via the dark photon , as well as production from the continuum 0 0 ]). In this section, we focus on searching only 0 χ F A ε 2 m γA – 13 – 55 , − 17 0 µν into F η µν 0 F and 1 4 , many new physics search strategies utilizing neutrino de- 0 , we explore the possibility that a new vector boson exists in 1 π 5 L ⊃ − ]; we will be interested in ). Such dark matter can be fermionic or scalar, and current and , are forbidden, i.e., χ 54 2 4.1 . Dark photons produced in these ways have energies of several GeV. 0 → , such decays may lead to long-lived dark photons. This is the region of 0 ε ppA A ] — have probed a similar region of parameter space in this fashion. is the mass of the dark photon → 57 0 ] provides a thorough review of searches for dark photons and existing constraints. A pp 63 M Previous experiments — among them, E141 [ As discussed in section . The kinetic mixing term is a renormalizable operator and the size of Ref. [ 5 µν kinetic mixing parameter. Forthe the decays DUNE of MPD, light weprocess mesons will be interested in The DUNE MPD will be sensitive to regions of parameter space for which the lab-frame and E137 [ main differences between thedistance various between experiments the is targetdetector the where region. the production dark mechanism The photonswhere and it interplay are the will between produced be these best and suited the means to instrumented search each for experiment a particular has combination a of dark sweet photon spot mass and dark photon, is produced on-shell willkinetic only mixing decay into SMparameter particles. space in Depending which on we the are strength interested of for this the study. dark photon, or amatter dark then travels photon to thatat the decays detector the promptly and neutrino into scatters, nearexotic dark depositing detector signatures energy matter (typically have that pairs. been scattering can proposedfor off be The [ the nuclei measured dark dark or photon electrons,photon without although be requiring more part the of existence a of larger dark sector matter, containing dark matter, we require that decays of the introduced in eq. ( future neutrino experiments arespace in capable which of the dark probingand matter well-motivated is antiparticles a regions in thermal of relic, thetypically symmetric parameter early between calls dark for universe. matter the particles dark The matter search to strategy be adopted produced in in these meson proposals decays either via an off-shell how it is generated [ tectors have been proposed,sectors. specifically One in particular searches intenselyin for studied which dark new dark matter physics matter and model, is associated charged due under dark to U(1) its simplicity, is one where the strength of kineticF mixing with the SM hypercharge gauge-group, with field strength In this section andnature. section Here, we will focusto on SM the fermions case only inso-called through which dark this kinetic photon vector mixing boson — with acquires interacting the small via SM couplings the U(1) vector hypercharge portal, group — the 4 Dark photon JHEP02(2020)174 0 φ π (4.3) (4.4) (4.2) ) and allows 0 , and A 0 0 , E A # , leading to − ), the ratio 0 ppA 2 4 ω ]. The pro- A p 4.3 H E → M ( 2 ! 62 p is the fraction of , at center-of-mass and ) = 12 GeV. The 4 p pp 2 z m z , with momentum ρ is 14 0 m p ]. N H 0 − 2 . A E decay, we estimate (a) 2 65 = 2 p 3 0 z (1 γA 0 z m , s . 0 according to the detector − ) 2 2 γA 2 m A 3 0 2 T 2 T + 2 p 2 into m A M 41%. Given the spectra of p → 0 . . z, p 2 M A m ' ( − m 2 800 MeV [ + M 1 H ba and 4.4 s H 2 p 2 p w ≈ z ) = 39 √ m 2 2 0 m , and provide our estimates for the

ε ) A 2 ) 2 2 γγ 0 ) 2

M A z × 4.3 ) → ) M z − ( η with SM vector mesons is the proton mass. In eq. ( is the transverse momentum of the outgo- − 0 γγ ,N p 1 A T (1 + (1 F → p m z – 14 –

, the bremsstrahlung process z 2 0 ) m ) 0 )( . We simulate the production of these as described A s s − z ( η ( 2 that are produced in the direction of the detector, one ) , and − pN pN , here limited by 2 p z 0 0 σ σ and 823% and Br( (1 A ), where A m ) = Br( . − 0 z 0 2 ) is the photon splitting function, z = M z π 2 T 0 +2 γA 2 T A + is the initial proton incoming momentum, that reach the HPTPC detector and (b) the energy spectrum (100 m) or longer, where decays at the location of the MPD φ, zP z, p 0 0 ) = 98 N → ( O 1 + (1 2 A P 2 A sin " ba d dzdp m γγ is M ) over the appropriate range of w T ) 0 z → Br( A EM 4.4 0 φ, p πH α − 2 π 2 , and ε ) encodes the mixing of the s cos T + (1 4.3 ) = ], Br( ) is the cross section of a proton hitting a target nucleus is its energy, , p 2 T . The branching ratio of a given neutral meson s 2 T , is close to one for the energies and masses of interest here. The form factor, 0 0 p ( 64 p A flux that reaches the detector, as described in section 3 A E 0 E z, p pN = E p ( ( σ A produced in the DUNE target and the kinematics of , 0 m ba H , in eq. ( η ≡ To determine the number of In addition to meson decays into A w 0 ,N = 2 1 A s F an enhancement in dark photon production when must integrate eq. ( and of total cross sections, evaluated at the two energies of interest, where energy squared ing the proton’s initial momentum transferredis to an the azimuthal longitudinal angle. momentum of The the double-differential production rate is us to probecalculation larger of values the of duction production rate in is thisp expressed process in is terms described of in properties refs. of [ the outgoing From ref. [ and the fraction of produced of the For the DUNE MPD, theof neutral dominant mesons, production specifically mechanismin for section dark photons is the decay will be optimal. Inphotons this in section, the we parameter discuss spacebackgrounds the of for production interest for and searches the decay ofDUNE DUNE mechanisms MPD MPD. this of sensitivity We dark type discuss to the these in associated dark section photons4.1 in section Dark photon production decay length of the JHEP02(2020)174 , η 5 (4.5) (4.6) 9] and ) from . 0 , 4.3 400 MeV, 1 . . [0 flux due to 0 0 ∈ A A z M enters the detector decays, and the green 0 . We assume ten years 10 0 η , e.g., A . As explained above, A | ) are valid. 2 meson mass. In figure T ε M p ρ 4.4 | ] focuses on detectors with . | . protons per year. The red curve T 0 and 67 ) is only valid in certain limits, p , , | z 1 21 . , ) and ( ) is satisfied. We include these . The peak in the bremsstrahlung 0 ppA 0 4.4 10 66 det A , A 4.3 θ 4.5 → × 2 14 M ,M p 47 pp . that traverse the HPTPC in 10 years of sin m 0 0 1 A − 2 [GeV] A 0 10 0 A M A M – 15 – − E 0 2 A ], where the prediction is that the − = 1; this flux scales with p 0 E ], the form of eq. ( 67 0 ε 2 0 − , the blue line displays those from Mixed Dark Photon ,E ppA γA 0 0 < 10 γA 68 − , that travel towards the DUNE Multi-Purpose Near Detector, π A → → 2 T 0 → 0 62 p π η pp A ,E p E ]. In contrast, here, we transform the variables of eq. ( Kinetically 3 ) are satisfied and thus eqs. ( − 14 18 17 21 20 19 10 . Note that this relationship holds regardless of the detector’s solid

] or SeaQuest [ 4.6

10 10 10 10 10

0 A

. yr 10 / /ε

N meson decay. This is in contrast with projections for this process at, − 2 = 1, and a beam luminosity of 1 66 ). In these variables, the requirement that the η ε 10 2 T 800 MeV comes from enhanced mixing near the × , p ) and ( 0 ' 4 A 0 displays the expected number of 4.5 ≈ A E is half the angular size of the detector, as viewed by the target. For the DUNE produced via decays of 5 ( . . 0 M . Expected number of A det det → 1 GeV for SHiP [ θ θ ) < Figure T 2 | T z, p p curve for we see that theto bremsstrahlung production process via (green)for is instance, comparable, SHiP even [ at decays is an order of magnitude or so larger than that from bremsstrahlung. This difference Some of theserestrictions restrictions in are our automatic calculationwhich and once eqs. ( only eq. include ( contributions to the fluxoperation from at regions DUNE, in normalizedbremsstrahlung production to allows us to reach larger angle, and we advocateprocess. for As its explained use inrequiring whenever refs. considering [ dark photon production in this ( leads to the constraint where MPD, geometry. The majoritya of much the larger existing solidtraditional literature angle approach is [ (as to viewed integrate over from| a the specific range beam of target) than we consider here. The Figure 5 a distance of 579of m beam from operation, the productiondisplays target, as a functiondisplays those of produced mass in the bremsstrahlung process JHEP02(2020)174 ], 69 The (4.8) (4.9) (4.7) 6 ratio, through R hadrons. For 0 2 A → M 0 = A into each final state . . s 0 ) 0 A 0 2 2 ` A at 2 A m , and M R 2 M − , the partial width is = µ − . ` s + ( 1 + . + 5 µ ` R 1 GeV). We reproduce the partial 0 ) 2 ` → × 2 may contribute for high center-of- A − . 0 ) m 0 µ 0 ). Other factors, especially the boost 4 M A − 0 A A + µ A , µ − hadrons consists largely of the final state + M − hadrons) 1 → e µ /M → . This mechanism could increase sensitivity, + 0 → 0 → s e 0 0 − → 2 A qq A e − 0 A into hadron pairs, we rely on the e M → + A M – 16 – 0 e + 0 2 ( e = (1 GeV A ( A σ s 15 100 m, we can use these widths to determine the σ α ε : into hadrons is related to flux, as seen in figure 0 − 1 3 0 0 hadrons. All of the backgrounds we discuss here come ≡ , more complicated final states exist (see, e.g., ref. [ ≈ A 0 10 A A ) A s → M ) = ≈ ( cτ 0 . M − 2 R ` A ε 6 + hadrons) = Γ( ` → → of mass , and 0 0 0 − A A in figure A µ Γ( 0 2 GeV — we do not include this in our calculations, and expect that it + Γ( A µ & M 0 → A 0 here for clarity. For decays into lepton pairs M A 0 , A − e + masses of interest, the decay channel e . However, depending on 0 , modify this relationship slightly. 0 Since we are interested in Direct production of dark photons via − A In addition to these backgrounds, there will be many events where a neutrino scatters off material in → π 6 A 0 + from neutrinos in thesignal DUNE comes beam from scattering a decaying off particle an (that argon originated nucleus in in orthe ECAL/magnet near the (which, the HPTPC. together, have target), aenter compared mass the of to gas roughly TPC. 400to tons), These be and entering particles vetoed particles from using those could timing interactions contribute and as fiducialization. background, Further which study are, is in required. principle, able of 4.3 Backgrounds In this section weA discuss the expected background rates for the different search channels Combining these expressions, we displayas the a branching function fraction of of expected parameter range forthat which the DUNE’s event sensitivity rate is peaks maximized. for We find, roughly, The partial width of In order to express the partial width of the π for a discussion of the differentwidths decay of channels for the proton parton density functions for but only for would not affect the sensitivity we present here. 4.2 Dark photonWe decay consider channels three and decay lifetime modes of SeaQuest, and has a significantlylarger smaller geometrical solid acceptance angle for than theDUNE, either. bremsstrahlung resulting This process in leads a relative to to comparable a meson relatively decays for mass energy proton collisions. However, such a calculation requires robust knowledge of is due to the fact that the DUNE near detector is much further from its target than SHiP or JHEP02(2020)174 , 0 0 π π + Ar + pair, with a ν events in ten − e 5 → + 10 e × produced in coherent 10 + Ar 0 ν π events. The third require- 4 10 × 1 pairs if the following occur: − into different final states of interest as a e 0 + (green), and hadronic final states (orange). A e decay will be pointing in the direction of 1 − 0 − [GeV] µ 0 π 10 + A µ M decay, one is either missed by the ECAL, or is, – 17 – 0 π ) events. This also includes ) events (for the exposure we consider) may be dras- − − 0 6 µ e 2 π + + − are coming from nuclear emission, they will be emitted e µ hadrons (purple), 10 0 (10 → → → π − 0 0 0 O e A A A + e → 3 − 0

1 2 1

10 − − A

→ events are expected per ton-year of exposure. We expect that the

10 10 0 ) X A Br( with no significant hadronic activity. As for the second requirement, : ]. 0 0 0 A π 69 : the dominant background for this channel is π M − e ) NC + 5 e decay. This reduces our background sample to 2 (10 . The branching ratio of the dark photon → O 0 γγ The other photon converts in the gasThe (which converted occurs photon’s for electromagnetic roughly showerdirection 12% is consistent of identified with photons). as the an direction from the target/decay pipe. No other hadronic activity occurs at theOf vertex the of two the photons neutrino comingfor interaction. from some reason, not attributed to a common vertex with the second photon. A • • • • → 0 π ment, that the otheroccur photon in converts 12% in ofestimate the events the — gas probability this that TPCthe a brings (before target. photon our reaching Because from background most the down of ECAL) to the will 2400 events. Finally, we neutrino-related background of tically reduced by the requirementsevents listed above. will Specifically, have we detectable expectenergy that hadronic above 80% activity of 5 MeV) NC (atyears, in least will the one be MPD. charged NC Thiswe particle estimate means with (conservatively) that that kinetic only the DUNE 20%, MPD or will 2 miss 10% of photons coming from In all, the outgoing charged particles point back to the target toi.e., greatly neutral-current reduce single-pion background rates. (NC production, where the recoilingclass target may is be too misinterpreted as low-energy signals to with be only observable. Events of this Figure 6 function of mass Adapted from ref. [ a light neutrino scattering off a heavy nucleus, so we can take advantage of the fact that JHEP02(2020)174 ] ) π 70 , the − e neutrino + e can be ap- − µ − (around 10% (50) events. + e → ]. Overall, we 7 µ O + 0 e 70 , where the elec- A 0 → A 01% of photons will . 1 event in ten years. 0 M A < ), then we still have ad- invariant mass, where the 0 7 A events in the MPD (we obtain − e will have zero invariant mass. Ad- + charged-current-single-pion (CC1 e − µ e ν + e ) increases this to 0.1% (2.6%). Given all ◦ (5 angular cut turns out to be too optimistic. signal, there will be an irreducible background ◦ ◦ – 18 – − ) events per ton-year. The authors of ref. [ e 5 . + e we consider these two channels in the same category 1 (10 ] (likely consisting of alternating layers of scintillator conversion to 5 → O γ 0 angular cut, this is a background rate of , (20) neutrino trident A ◦ O γγ → hadrons: 0 π → faking the being the only visible particles in the final state: neutrino trident 0 ] estimate 0 A − π e 71 + , e and 70 − µ + µ Finally, we note that the same angular cuts discussed regarding In addition to If such a conservative cut is required (perhaps to retain a signal from decays down- The Multi-Purpose detector will be more sensitive than the LArTPC to smaller amounts of hadronic → 7 0 expect that ten signal events willafter constitute considering a that significant our excess over signalbackground background, events events especially will will share be a smoothly common distributed in that variable. activity due to its lower thresholds, see table and a high-density material like steel) that will further reduce pion/muon misidentification. plied here — when a muonrarely and be a in pion the fake thisthan direction signature, of when the the trying direction beam. of to the reduce This pair will allows the very for backgrounds even to further neutrino background trident reduction events [ our search as well (roughly 1%surrounding of the background HPTPC events will survive). have Weapproximately moderate also 70% ability note to of that identify the charged charged ECAL a pions pions positive will vs. identification muons interact of — hadronically thoseconsidering that in adding do the a interact. ECAL, muon Additionally, allowing the tagger for DUNE [ collaboration is events, with anexplored expected a similar rate set of of signalstrident and events in backgrounds, focusing the DUNE on the LArTPCby search near a for detector (where ratio therejection background of techniques, rates including the are the larger fiducial rejectionof of mass background events events survive with in this hadronic cut), each activity and a detector). variety of kinematical cuts They that would apply discussed to certain background kinematics should be differentetc.) from and our should signature not (in contribute sizably terms to ofA the invariant search mass, proposed direction, here. as they share the same background, predominantly matical separations may be exploited if a 1 of events with events. Refs. [ this by scaling their LArTPC projections to the mass of the HPTPC) in ten years. Their stream of the beamditional target, handles such to aselectron/positron separate that pair signal discussed will from in havetron/positron background. an pair section from invariant mass Forditionally, consistent these the background with decay electrons/positrons willenergy, tend where to the have lower signal (around electrons/positrons 500 MeV) will have several GeV of energy. These kine- beam direction (the angular resolution ofpass the this gas cut. TPC), then A roughlyof more 0 these conservative considerations, cut we of expectEven 1 an with optimistic a background very rate conservative of 5 nearly isotropically. If we require that the angle of the photon is within 4 mrad from the JHEP02(2020)174 for 2 ε ] and from 62 – 10 56 , or hadrons shown in − µ Mixed + µ − 1 , , but in those regimes, existing − 0 e A + , a total of 10 decays are expected e Dark Photon 15 , these events should be roughly 40% 0 − for a given amount of data collection. A 10 vs. kinetic mixing parameter squared 2 0 E137 ε ≈

NuCal 1 A Kinetically − [GeV] 2 M ε 0 10 A . and 0 M – 19 – A mass 0 M

100 evts . A

Orsay ] in shaded gray. These regions correspond to a total

≥ that reach the DUNE MPD, we calculate the expected 0 72 2 A 10 evts − 300 MeV and E141

DUNE 10 ≥ ≈ SN1987A 0 . Searching for the correct combination of different final states decays in the DUNE MPD after ten years of data collection, in blue A − , we assume 100% efficiency in identifying particle/antiparticle 0 e

DUNE M A + 7 e 3 − 8 18 20 10 12 14 16 10 − − − − − − −

decays as a function of 10 10 10 10 10 10 ε 2 0 A , we display the regions where we expect at least 10 (blue) and 100 (red) such . Regions of parameter space of 7 . For instance, if decays and 60% 6 In producing figure − µ + can also improve thedark capabilities photons of from a those search of for the dark other photons, new physics andpairs scenarios — disentangle we this signals approximation discuss of likely in breakslimits later down are sections. for more lighter powerful than the DUNE MPD search for dark photons. emission during Supernova 1987A [ number of decays beingof 10 decay, or one 100 must — includefigure in the order branching to fraction determinein into ten the years. number According of toµ a the branching certain fraction type of Given the energy spectrum of the number of In figure decays, assuming ten yearsof of this data parameter collection. space constrained In by addition, E141, we Orsay, show NuCal, the and excluded E137 region [ which we expect 10(red). (100) Currently excluded regions are in grey. 4.4 Dark photon sensitivity Figure 7 JHEP02(2020)174 ], ). to 67 5.1 (5.1) V ] 89 , gauge boson . Hence, even β 83 β , L range. This com- 63 − nor 14 dx, α ], and SeaQuest [ − # as [ α L 2 2 66 10 mass) is well below the q q αβ ) ) g − x x V 16 − − is the four-momentum of the − µ (1 (1 10 q ], SHiP [ x x ≈ − − 74 , 2 β and α ε 2 ` 2 ` 73 α m m " , associated with gauging the difference is emitted on-shell due to this mixing, so gauge coupling V β V M L ) log , as the detectors associated with these pro- 2 x − ε – 20 – − α will have a visible decay channel. L (1 µ . x of mass for similar mass dark photons. 4 m 1 2 0 , will couple directly to neutrinos or charged leptons V ε Z production through neutral meson decays and for β 8 L 2 V αβ π − 2 eg in section α 0 − ]. A L 88 . This coupling means that the gauge boson will be produced in ) = – β 2 to represent a leptophilic gauge boson in this section, to contrast with the purely q ), is related to the 75 ( V [ and the SM photon is induced at one loop via SM particles that are , new vector bosons may also interact with the SM if they are gauge 4.1 τ αβ and 4 V ε , α e, µ is the mass of charged lepton with flavor = α . In the limit where the momentum transfer (i.e., the that is mixed with the SM photon. This contribution is in addition to any kinetic gauge bosons lighter than 2 ` β 2 V τ , m V L M α We are interested in situations in which a The leptophilic gauge boson Overall, we find that the DUNE MPD will be able to extend sensitivity to a dark photon We use the symbol − ≡ 8 µ 2 L q kinetically-mixed dark photon boson mixing that might bethe present bare in kinetic the mixing UVThis Lagrangian. is kinetic zero mixing From and now allowsdecay on, that for to we the a will effective pair assume mixing of that charged is leptons determined that by are eq. not ( in either generation as defined in eq. ( where between lepton numbers in generations charged meson decays through finalcharged state leptons, bremsstrahlung if and can kinematicallymixing decay accessible. between to neutrinos In and charged addition under both to SM this hypercharge and direct the coupling, new U(1). kinetic This loop-induced kinetic mixing, baryon/lepton number between two generations, thenWe no expect additional fermions that are DUNE necessary. new will symmetry have is the leptophilic, strongestwith and sensitivity therefore to focus such on new the physics when case the of a While the dark photoncussed couples in to section the Standardbosons Model of purely a via newmetry kinetic group should mixing, under be as which dis- SM. anomaly some SM free, However, if particles which SM are often fields charged. requires are Such charged extending a in the gauge a field sym- vectorlike fashion, content for of instance the differences of FASER/SHiP) would be much moretors boosted are than those then produced sensitivethat at to DUNE. DUNE dark These is detec- sensitive photons to with smaller relatively shorter proper5 lifetimes, meaning Leptophilic gauge bosons in the sub-GeV mass regimeplements for other kinetic future mixing experiments, in such the which as will FASER [ be sensitiveposals to are larger significantly values closer of produced to in their this production type targets. of If environment, dark then photons those exist produced and at are CERN (for detection at JHEP02(2020)174 is V (5.2) (5.3) (red), ) as a µ . 5.1 L − will apply 5.3 e 4 L . Assuming . Which of these 8 B may be emitted in 10 V τ µ τ L L L − − − e e µ L L L 1 , (green). The change of behavior . ! τ α β α may be radiated in charged meson 2 ` 2 ` 2 ` L . In addition, m m 1 m 2 − V V − 8 −

µ 10 M β L 2 ` log [GeV] m 2 V 2 π αβ 2 M αβ π − – 21 – eg 12 2 10 eg ) and ﬁgure (blue), and −→ 5.1 −→ − τ 3 − αβ L . In the opposite limit, where the momentum transfer (or for the three diﬀerent leptophilic gauge bosons: ε αβ 10 ε − . We provide our sensitivity estimates in section V 2 αβ (relative to the gauge coupling squared) given by eq. ( e g M 2 ) | L 3 (green). Here, we assume the only contribution to the kinetic mixing 5.2 ε | − τ 4 − L 10 2 3 4 5 6 1 1

− − − − − −

−

| −

10 10 10 10 10 10 (red),

αβ αβ

/g ε µ

4 2 2 . µ L − L V − (10 e L ≈ O 2 . Kinetic mixing | (blue), and τ αβ ε L | With any kinetic mixing, the production processes discussed in section ) is much larger than both of the charged lepton masses, − V e decay signatures in section 5.1 Production ofIn leptophilic gauge addition bosons to thedecays with production final-state via leptons. kinetic The greatest mixing, abundance of these will be from charged pion here, suppressed according todecays eq. involving ( charged leptonsprovide and a derivation neutrinos of by theprocesses being branching is ratio most radiated relevant for depends in such onflavor(s) the decays how of strong in final interest. the appendix kinetic state; We mixing discuss is, we the as production well as mechanisms the in lepton the following, and then the We show the kinetic mixingproduced for each on-shell, leptophilic we U(1) show symmetry thesquared in kinetic for figure mixing squared relativeof to the the loop new integral gauge at coupling particle thresholds is apparent. and M lighter of the two charged lepton masses, the kinetic mixing becomes a constant, Figure 8 function of vector bosonL mass is from the massivemodel standard photon and model fermions generating a loop process connecting the standard JHEP02(2020)174 e → m and − e π across π . m is larger (and the V We show 8 = V ) and orange V µ 9 µ V ν 200 MeV) are ν π M mass range, see µ ≈ µ V V → → M 10 displays the expected K π = 1, assuming ten years νV νV 9 ± ± ` ` ppV γV 2 eµ γV → g . The features apparent in → and → → ± → ± 0 8 K π pp π η in orange), as well as neutral- V e 1 ν mass, as depicted figure K over most of the e V τ L → , we derive the branching ratios of these 5 GeV. Thus, despite the small kinetic − B e π ∼ < 1 − production; the decays involving electrons, traveling towards the DUNE MPD as a function L [GeV] bremsstrahlung). 10 V V V V M M – 22 – ppV in purple and in green. These rates assume that there is only for in blue) via loop-induced kinetic mixing, as well as → µ , since the kinematic threshold will be 2 π ) η 2 pp L V − ppV µ . In appendix 10 ]. V /m → α − gauge bosons e ν 91 production mechanisms (mostly near , e µ α m pp , albeit at a suppressed rate. Figure L ` 90 µ L − γV m → e in red and 3 − L 0 − 15 14 13 12 21 20 19 18 17 16 → 10

. The diﬀerences in production rate between neutrino and antineutrino modes,

10 10 10 10 10 10 10 10 10 10

eµ

V N . yr 10 / /g η

9 /K 2 gauge boson, the processes m vector boson, charged meson decays to electrons are chirally suppressed decay), and green ( µ π = τ η L and L V − passing through the DUNE MPD, normalized to − M e e assuming ten years of data collection, and equal run time in neutrino and antineutrino V ppV L L V . The number of , and is larger than ( → M allows for searches of heavier 8 V For a For a pp ). Dot-dashed lines display expected number due to processes relying on kinetic mixing — red decay), blue ( e We sum over the two different charges of meson decays, as well as the different final state leptons 9 ν , in generating figure 0 K π mixing, the processes dependingall on masses. kinetic Specifically, mixing we dominate note the that the production loop-suppressed of process µ due to the focusing of charged mesons, is negligible. reflections of the variation of the kinetic mixing with while production via charged mesonThe loop-induced decays with kinetic final-state mixing muons isfigure rely largest on for kinetic mixing. of data collection withcontributions from equal charged run mesons timemeson ( contributions in ( neutrino andthe bremsstrahlung antineutrino process modes. loop-induced kinetic mixing, atthe the rate depicted in figure equivalent kaon decays) willhowever, contribute are to helicity suppressed relativee to those involving muons.rather than Production via number of and kaon decays, three-body decays. The ratethe for final-state lepton these mass three-body [ decays is proportional to the square of Figure 9 of mass modes. Solid lines display expected( number due to charged meson( decays — purple ( JHEP02(2020)174 , V V π ), or from (5.4) (5.5) β V or M α ), is 4.7 gauge boson. Here, , the proton-proton via the small kinetic . ρ τ 10 α − 2 ` 2 L V e γV m γV − M + 4 → e µ bremsstrahlung), purple ( → 0 π η L − 1 ppV s 1 → ! . depicts the expected number of α V V 2 ` 2 µ V pp ν traveling towards the DUNE MPD as a π M ± m 10 M µ ppV 2 , assuming such a decay is kinematically 12 V 2 αβ → − β → g 1 ` ± produced for a − π pp [GeV] 1 + + β gauge bosons as a function of mass 10 ` V

V ) = τ . Figure M ν L → V – 23 – ν V π e − M V decay), green ( ν e → 12 τ V V 2 αβ µ V L η e e ν e ν g gauge bosons 2 ν V ± L ± − and ± e µ decays via loop-induced kinetic mixing. Specifically, we e τ 10 Γ( → − α → → L decays to muons). ), causes the meson production mechanisms to final states → V ) = ` − ± ± ± 8 − α + α − K K π e ` ` gauge bosons that may decay into e K K + α L L τ ` → L 3 → decay), blue ( V − gauge bosons will decay to pairs of neutrinos (flavor − 15 14 13 12 21 20 19 18 17 16 10 0

µ V

π 10 10 10 10 10 10 10 10 10 10

depicts the number of eτ

V N . yr 10 / /g ). Dot-dashed lines display expected number due to processes relying on

assuming ten years of data collection, and equal run time in neutrino and L L 2 Γ( V 11 − K M α L . The number of Finally, figure ) and orange ( π When relevant, we also consider will be interested in we sum over the flavors. The decay width, assuming massless neutrinos, is The decay into charged leptons, similar to those of dark photons in eq. ( 5.2 Decays ofAt leptophilic tree gauge bosons level, pairs of charged leptons accessible. Since we will not be able to observe neutrinos emerging from the decays of the small kinetic mixing (figure containing muons to dominategauge boson as mass long is asbremsstrahlung close they process to are causes 770 MeV kinematicallykinetic significant and mixing. production, accessible. it even can When mix with the with the the small SM loop-induced than the helicity-suppressed passing through the DUNE MPDvarious for channels. Figure 10 function of mass antineutrino modes. Solid( lines display expected numberkinetic due mixing to — charged red mesondecays ( to decays muons), — and purple orange ( JHEP02(2020)174 . 5 − 10 × 2 ≈ ) − e . The resulting + αβ e ]. Over the region eε 63 → 10 final state, we choose → V γV − bremsstrahlung). γV e and found that it should αβ → → + g 0 4 e π η ppV → V V 1 µ µ ν ν ± pp ± µ µ ppV → → traveling towards the DUNE MPD as a → ± ± ). For the K π pp ] recently explored the impact of a light V 11 – 89 1 − [GeV] 9 10 V M final state in section – 24 – 100 MeV, the invariant mass would be significantly harder − ) with the replacement e τ − decay), and green ( + 1 5.5 gauge bosons η 2 e L − ∼ τ 10 L − − gauge bosons decaying this way is Br( µ µ τ L L L at the time of big bang nucleosynthesis occur. Large values of 3 − . − decay), blue ( µ eff 15 14 13 12 21 20 19 18 17 16 10 0

10 10 10 10 10 10 10 10 10 10

µτ π V

N . yr 10 / /g ). Dot-dashed lines display expected number due to processes relying on assuming ten years of data collection, and equal run time in neutrino and 2 final states within the DUNE MPD. In all cases, we assume ten years V K M − µ + µ is 100%. 5 are disfavored by measurements of big bang nucleosynthesis, however this is . The number of . 0 10 or gauge boson on the cosmological history of the universe, and found that for certain & − τ e L We reproduce existing limits from experimental searches from ref. [ + eff ) and orange ( We note that for invariant masses of − e N 10 µ π relativistic species ∆ ∆ true only when data are analyzed under particular cosmologicalto assumptions. reconstruct No than for existing larger invariant masses. iments (E141, Orsay, andelectron E137 scattering providing via the the exchange strongest ofcoming constraints), the from new as the gauge well boson TEXONO as (with experiment).L the neutrino- Ref. strongest constraints [ combinations of masses and gauge couplings, large contributions to the number of effective for which greater thanWe three discussed or the greater backgrounds to thanbe a ten background-free. signal As eventsefficiency are with expected the in dark ten photon years. search, we assumeof here parameter space that we the are detector interested in, these are largely from electron beam dump exper- Here we present theto expected sensitivity ofof DUNE data to collection leptophilic and gaugewith equal bosons the run production decaying time ratesto in depicted show neutrino in regions and figures of antineutrino parameter modes space (in (the agreement gauge boson mass and the new gauge coupling) mixing. This width isbranching given fraction for by eq. ( 5.3 Sensitivity to leptophilic gauge bosons Figure 11 function of mass antineutrino modes. Solid( lines display expected numberkinetic due mixing to — charged red meson ( decays — purple JHEP02(2020)174 . → 10 0 A indicates , with the µe µ g L 2 MeV exists. gauge bosons, − τ and . 1 MeV, and will be e L , where we expect V ]. V > gauge bosons with L 4 − M V − µ M 94 e , L M L 10 71 1 − for . e 4 L and µ − µτ µ g 10 L gauge bosons. The region in red L > µ − L − e µτ g e − L E137 e 1 − L L 10 . As stated above, the existing literature V [GeV]

gauge bosons for ones. Our expected DUNE MPD sensitivity, . TEXONO . Orsay V τ τ – 25 – M L L 3 evts 10 evts 2 − − gauge bosons is the possible explanation for the long-standing ≥ E141 ≥ − 10 µ τ are nearly identical to those from e L L L τ ]. This solution requires − 200 MeV, where decays into muons modify the lifetime DUNE DUNE µ L 93 L ≈ , − V e 92 , L M 84 3 , − 7 8 4 5 6 10 − − − − −

, 10 10 10 10 10 µe g 80 , we expect the three event contour to represent the MPD sensitivity , is slightly weaker, due to the reduced production discussed cf. figure 4.3 13 displays our expected DUNE MPD sensitivity to Cosmological constraints should exist for gauge bosons but not 12 11 . Expected sensitivity at the DUNE MPD to µ 2) anomaly [ L − g in section − e The existing limits on Figure − One key theoretical motivation of L e 11 + probed by neutrino trident interactions in the DUNE LArTPC Near Detector [ shown in figure This results in the expectedexisting sensitivity limits. being slightly weaker than, but comparable to, the muon ( than the existing limitsthe below existing this literature mass limits either, as and we include expect a they dashed wouldonly black extend. line exception to being extend near of fairly well. For comparison,presents existing sensitivity limits that is are nearly depicted asunlikely in powerful to as grey. improve electron on We beam them. seeat dump here experiments, This existing but that is experiments it not DUNE leads is terribly todoes surprising a not since display large electron limits flux below bremsstrahlung of roughly 2 MeV — we expect that DUNE is no more powerful but no such analysis exists in the literature. Likewise,masses no between 1 analysis MeV for and 1(ten) GeV. signal For points events inside are thee blue expected. (red) region, Given more than the three discussion regarding backgrounds for Existing limits in this parameterour space extrapolation are of in existing grey. limits. The dashed line for small laboratory measurements constrain sensitivity. Figure 12 (blue) indicates more than ten (three) signal events expected in ten years, a background-free search. JHEP02(2020)174 τ L − µ mixing, L indicates . Here, we V eτ g both in the − 14 unsuppressed. − ρ µ and − + µ V µ + M µ → 1 V τ L gauge bosons. The region in red τ L − gauge bosons in figure e − τ e may decay into 1 E137 − L L to decay upstream of both detectors, L 10 V − V µ L

[GeV] TEXONO Orsay V due to the kinetic-mixing-suppressed branching

. . — we encourage a more detailed study of this – 26 – M − e 2 14 − 3 evts + E141 10 evts e 10

≥ ≥ →

DUNE V DUNE 3 − , the bremsstrahlung process is enhanced due to production. At this mass, 7 8 4 5 6 ρ 10 − − − − −

10 10 10 10 10 m V eτ g gauge bosons in this region of parameter space. As discussed around ≈ τ V L M − (1) signal event with ten years of data collection. We indicate the region µ O L . Expected sensitivity at the DUNE MPD to , for ], and we emphasize that the DUNE MPD approach would be the first terrestrial 11 89 Lastly, we depict the expected sensitivity to the SM is via a renormalizable operator. In the previouscouple sections, to we the discussed Standarda sensitivity Model result to via of semi-long-lived kinetic ascenarios vector mixing are new bosons with a gauge subset that the symmetrynew of SM under the particles hypercharge commonly-studied may which group renormalizable be some or dark added SM sector as to fermions portals, the where are SM charged. and the Those interaction between the dark sector and MPD and the LArTPC,could as enhance the well overall as DUNE sensitivitygauge allowing in bosons the this in region, completely allowing for new searches areas for of parameter space. 6 Dark Higgs boson We find that forto a observe very narrowin range which of this parameter occurs space,region in the of green parameter DUNE space in MPD forbackgrounds figure may future to expect work, such specifically a in search. determining the However, neutrino-related combining searches for fraction to electrons. Regardless,ref. [ such a searchsearch is for complementary to thefigure limit derived in leading to significant Existing limits in this parameterour space extrapolation are of in existing grey. limits. The dashed line for small are hindered in such a search for Figure 13 (blue) indicates more than ten (three) signal events expected in ten years, a background-free search. JHEP02(2020)174 π ϕ (6.1) → K interacts with the to acquire a vacuum ϕ ϕ 1 . and τ , the couplings to the SM evt . − L 2 5 H µ | + decaying preferentially into the ϕ ) expected. In grey, the region for µ | − − 2 → ϕ e ]. In green is the region of parameter and | occurs after electroweak symmetry V µ + 89 H 4 ϕ e 1 | (1) − L O λ 10 → and V with the H L ⊃ [GeV] V or , π π – 27 – M gauge bosons at the DUNE MPD. The region in red − τ µ 2 − L + ϕ, 10 (1) signal events, see text for further discussion. 2 − | 5 , µ . O

. µ 0 − H L e | >

3 evts . + δ to electrons and muons, up to kinematic eﬀects. For a dark eﬀ

. e ≥ and SM particles proceeds through the SM Higgs bosons, so 0 N ∆ A ϕ 12

DUNE 10 evts → L ⊃

≥ , as the free parameters. may yield ϕ 3 ϕ − 7 8 4 5 6 − 10 − − − − − M

10 10 10 10 10 µτ g + µ → mass, 5 at the time of big bang nucleosynthesis [ . V ϕ 0 > and the SM Higgs boson may mix. . Expected sensitivity to eff ϕ N , and the When considering new vector bosons in sections A second portal option is the Higgs portal, where a new scalar carries any charge, SM or new-physics related. For this study, they are phenomenologically equivalent, The second option is more common in the literature — the first is super-renormalizable, but forbidden ϑ 12 ϕ and the decay modes are heaviest final state available. if as long as characterizes the kinetic mixing betweenroughly the equivalent decays SM of and newHiggs, U(1) the coupling gauge between bosons.couplings This are led related to to SMproduction particle mechanisms masses, to and favor arein situations therefore the hierarchical. involving following heavy This subsections. quarks, will drive which In we particular, will the discuss dominant production modes are expectation value. This mixing may behowever, expressed we in choose terms of to Lagrangiansin parameters. use Here, the phenomenological mixing parameter, which wewere denote given as by the electric charge of the SM particle, reweighted by the parameter that In the case of the firstbreaking, operator, mixing while between for the second operator mixing requires both which ∆ space for which SM via one of two operators Figure 14 (blue) indicates more than ten (three) signal events ( JHEP02(2020)174 , 0 L t W K = , for ] (6.3) (6.4) (6.5) (6.6) (6.2) i ϕ 97 – 95 ,   is [ mesons in the is 246 GeV is the ϕ V 2 i B ≈ couples via mixing m , , ∗ v id ϕ ! ! V 0 L 0 . 2 π 2 π 2 K 2 K ) u,c,t m m m X m = ϑ. i xy , , 2 2 0 L 2 + 2 , which has a small branching ϕ ϕ v 2 K 2 K 2 ϕ sin y . Because 3 M M 0 boson and top quark introduces π 2 m m ϕ π + due predominantly to its smaller ! 16

x 2 2 b W ϕ 1 2 ϕ ϕ → ), given by contributions with a 2( m . On the other hand, mesons lighter M K S + ϑ ρ ϑ ρ 6.2 − K − 2 2 A 7 9 2 meson into a strange meson and a 2 1 y γ sin sin

B + 3 3 − 7 2 . − − -meson production is not negligible at DUNE, . 5 2 π x – 28 – S D 10 10 m ' K will be suppressed by elements of the CKM matrix × × 12 GeV. ) 1 + + ϕ ϕ 2 ≈ ϕ p s 2 K s 1 2 X M m ) = 7 ) = 2 √ is larger than for − ϕ ϕ decay into a light meson and a dark Higgs → -meson production at DUNE is too small to be competitive produced via decays of other mesons. In comparison with L ) = 0 2 K π B B π K K ϕ m ], we may write the branching fractions of interest as x, y → ( → Br( 7 ϕ 18 0 L 100 ρ 1 – γ K K   95 meson decay into Br( are both negligibly small. Here, and throughout, Br( 2 K v D 2 m ] γ ), the branching fraction of a ϑ ) is a dimensionless function, ], among others, discuss the production of 100 6.4 meson. However, and x, y 100 ( – = sin )–( B : the one-loop penguin diagram involving a 1 ϕ , is [ γ ρ 95 couplings, which are large. While ϑ 6.3 M K t One may also consider Following refs. [ The matrix element for is the − While this branching fractionDUNE is target relatively large, is thethan extremely production kaons small, are rate produced see of in appendix abundance. However, branching fractions of interest, such as total width. We disregardfraction the due contribution to from the large total width of eqs. ( small where The branching fraction for contribution comes fromboson the and third a loop term involvingthe in up-type contribution quarks. eq. from The the ( largest top contribution quark. will come when where vacuum expectation value of the neutral component of the Higgs ﬁeld. The dominant contributions of and the bottom-quark Yukawa coupling. Theϕ meson with the largest branching fraction into with existing experiments, since Refs. [ with the SM Higgs scalar, itsto production will heavy be quarks. largest inand processes At that allow DUNE, for couplings theϕ dominant contribution comes from the decays of 6.1 Dark Higgs boson production JHEP02(2020)174 0 L ϕ − in K K − K 1 and , and − + -produced K 0 K L , K would have an + 1 − K ϕ 10 live long enough to decay at rest, and a 0 L 0 ϕ from [GeV] ϕ L ϕ − + 0 ϕ K π K π ϕ that have their momentum π in neutrino mode, M 2 coming from ϕ − → → → + . 10 + − 0 ϕ L -produced K π K K K 0 L = 1. Solid (dashed) lines are for ) and determine the number of m K ϑ − 2 6.4 3 Dark Higgs Boson − , while kaon focusing is not the main K 15 17 16 10

∓

10 10 10

ϕ . yr 5 ϑ/ sin / N π 2 ) and ( > m that are produced in a given decay and 0 π 6.3 ϕ m of dark Higgs particles as a function of their mass − – 29 – ϕ 1 0 L . The dominant sensitivity at the DUNE MPD K ϑ 2 and defocus m sin as π 9 ϕ 1 − − directed towards the DUNE MPD as a function of their mass M 10 ϕ distribution is unaﬀected by focusing and the distinction between Dark Higgs [GeV] 0 L ϕ ϕ ϕ ϕ − + 0 K π π π M 2 − → → → 10 + − 0 L K K K , we present the fraction of 3 15 − , are as small as 10 1 2 3 1 10 − − −

. Left panel: acceptance fraction

νϕ 10 10 10 ϕ , and is because a significant fraction (roughly 25%) of e 0, the acceptance fraction of the focused distribution ( 15 With this information about the direction of travel of the dark Higgs, we simulate the In figure → → . The acceptance fraction is defined as the fraction of all produced , assuming five years of data collection in both neutrino mode (solid lines) and antineutrino particles from these decays that pass through the DUNE MPD, assuming five years of ϕ ϕ ϕ reach the rock atvery the small end fraction of of the the isotropic DUNE decay products beam are decay pointing pipe. in the Those directiondecays of with the the MPD. branching fractionsϕ from eqs. ( larger; DUNE is designed topriority focus of the experiment.acceptance fraction we Na¨ıvely, somewhere expect between thatare the neither the focused focused and nor defocusedfigure unfocused. distributions, as This they is not the case, as evident by the green line in worthy of note. Reversingmode the nearly perfectly horn interchanges current thedecays and acceptance — switching fraction dashed from of lines neutrinoM are to coincident antineutrino withantineutrino solid mode) lines is of almost, theanalyzing but opposite decays not of color. quite, charged pions double instead In that of the charged of kaons, limit the this ratio defocused would distribution. be significantly If π then, will come from kaon-related production of dark Higgs bosons. are traveling in the direction of the MPD when they are produced. Several features are neutrino (antineutrino) mode, anddecays, blue, respectively. red, The andneutrino/antineutrino modes, green and lines so indicate allow there for is reaching no larger corresponding values dashed of green line. Figure 15 M pointing in the direction ofnumber the of DUNE MPD dark at Higgs theM time particles of their production.mode Right (dashed panel: lines). expected We scale the number of particles to sin JHEP02(2020)174 ]. (6.9) (6.7) (6.8) 102 (6.13) (6.10) (6.11) (6.12) . 2 | ) 2 ϕ are unaffected by , 0 M L 2 π ( F K G 2 . | s ]. For the mass range of π 2 π 2 ϕ 2 / 96 m 3 M ), we follow the discussion 101 4 . s, is related to the strangeness 2 ϕ + θ 2 ` b are extracted from derivatives 2 − )] ϕ F M s d ( m 1 ∆ ( M 4 b G π iπκ s )) + , . − s ϑ 13 ) ( ) s 2 2 1 s ψ are given by Γ , and ) + ∆ b ∆ πv sin Γ s 2 ` + 2 + b ϕ b ( 3 ϕ 16 394 MeV. m π , (1 + ) + θ M ϑ ) + κ κ s b [Γ ≈ ( ) is defined as s 2 2 ( s 7 9 0 − 2 π ψ ( π ψ s 1 + 1 ) = sin m – 30 – πv ψ . To estimate 0 m 2 8 ϕ ) + π s ππ (1 + 0 − decays, respectively. Because M ( (1 + π 2 π π 0 log L 0 1 + L s F θ → distribution also extends to slightly larger masses, as K κ m , dimensionless, and differ in definition from those in ref. [ d 2 9 → K ) = G m 0 ϕ L − ϕ 2 π 2 π ` K ) = ) = ) = ) = F m + s s s s 2 ` , and ( ( ( ( , the decay widths of − π π π π − π G s → θ Γ 16 ∆ 2 ) = 2Γ( K m ϕ 2 = 0. The dimensionless parameter , − , but below a few GeV, the width to mesons is hard to determine 5 GeV, the only meson decay open is to a pair of pions. This decay π + s Γ( π . < ) = + 0 K s m ϕ π ( . ψ M → ϕ , 354 MeV whereas is the (dimensionless, in contrast with some results in the literature) tran- ϕ ϕ M , the invariant mass-squared of the outgoing pion pair: | ≈ s ) Γ( . Here, solid (dashed) lines indicate (anti)neutrino mode, and blue, red, and 2 ϕ ], which we now briefly outline. This transition amplitude may be expressed, π M 15 ( m 102 G − | Note that these quantities are, like K 13 content of the pion. Finally, the function In these formulae, the dimensionfulof quantities the form factors at At next-to-leading order in chiral perturbation theory, of ref. [ in the limit offunctions isospin of conservation, in terms of three independent form factors, which are Here sition amplitude for the process For masses above 2 due to strong QCD effectsinterest and here, the effects of mesonwidth resonances can [ be expressed in terms of a hadronic matrix elements as, 6.2 Dark Higgs bosonFor very decays light of figure green lines indicate the focusing horns, there isand no antineutrino distinction between modes. this productionm The mechanism for neutrino data collection in both neutrino and antineutrino mode. This is depicted in the right panel JHEP02(2020)174 , ) 8 − 16 flux = 0, , and ϕ 2 ∆ , − = 10 Γ ϑ θ, b 2 6 GeV is a kinematic . 2 / 1 = 2 ) decay is dominated as a function of mass become kinematically Γ ϕ /s 8 1 b 2 π − ππ , m , where, for a particular 2 4 − → 4 = 10 M = 2m − ϕ π ϕ ϑ decay are so hierarchical. For 2 (1 7 GeV are kinematically forbidden, this

Mϕ = 2mµ ϕ . ≡ and − = 500 MeV, relative to the leading- 1 κ − − µ ϕ 10 = 2 µ + as a function of its mass in ﬁgure + µ M θ µ ϕ b → [GeV] 09, ϕ . ϕ M ], this leads to an enhancement of the partial – 31 – = 0 ). 8 2 − − 102 10 , here we expect nearly every event to be in a single F d − 6.12 = 10 µ ϑ + 2 )–( µ sin 6.10 → 0 decay in the detector becomes signiﬁcantly more likely. A ]. This leading order result is obtained by setting 3 ϕ − 8 6 4 2 1 12 10 10

10 10 10 10

103

10 10 ϕ cτ [m] ] extracts the relevant parameters from measurements of pion-pion scat- . As discussed in ref. [ ) = 0 in eqs. ( 2 s 400 MeV, the lifetime is of order of the distance between the DUNE target ( , we may safely consider the expected backgrounds in the DUNE MPD to − 102 ϕ − , or pion pairs and argued that, especially when utilizing the invariant mass − , we discussed the possible backgrounds for searches of final states involving and 40% being µ − = 130 MeV is the pion decay constant and . Rest-frame lifetime of a dark Higgs with mixing sin 4 , one expects a certain ratio of different final states, such as 60% of events being + µ − 0 e µ π + 3 GeV A . + F µ e M , In contrast to the dark photon scenario studied in section Instead of depicting branching fractions of different final states as a function of mass, − = 3 = 0, and . We label the points at which the decays → e ϕ 0 F + ∆ mass A search channel because thelighter individual dark partial Higgs/vector bosons widths where for strategy decays into will not allow us to disentangle the two hypotheses. Secondly, because the e peak of be small. Thepractically signal identical to for that ahere for dark two a possible Higgs dark ways scalar photon of decaying decaying disentangling into the into charged two charged hypotheses. leptons. leptons We will discuss appear roughly 200 and the MPD, meaning a 6.3 Backgrounds andIn sensitivity section we choose to presentkeeping instead in the mind total that, given lifetime itsby of hierarchical the couplings heaviest to allowed SM final fermions, is state. significantly For longer light than masses, the the lifetime distance (assuming to sin the DUNE near detector. For masses between tering. In ourb calculations, we use width into pions by a factororder of approximately result 4.4 from at ref.d [ M accessible for clarity. where factor. Ref. [ Figure 16 JHEP02(2020)174 ], ] of as a 105 0 21 A and ϕ comes from decays 0 1 A ]. A recent study [ Belle / 99

depicts in blue (red) regions

LHCb →

L −

` ` π K

+ 0 0 17

]) to measure diﬀerent portions

− µ µ CHARM .

E949 / E787

100 evts

spectrum should be less focused than − e e CHARM . + , ﬁgure

≥ 0 ϕ A 1

10 evts − [GeV] ]. We also include a limit from searches for Dark Higgs Boson

DUNE 10 ≥ versus mixing between the dark and SM Higgs ϕ X a factor of a few weaker than those anticipated M ϕ + 104 π ϑ , M – 32 –

E949 DUNE 2 / → 99 + , E787 K 97 ) in ten years of data collection at DUNE. For comparison, SN1987A parameter space. ππ ϑ 2 − 2 9 3 5 7 , or 11 13 10 − − − − − −

−

10 10 10 10

10 10 sin ϑ 350 MeV, improving on the BNL search and CHARM for this wide

µ 2 + − vs. sin µ , ϕ parameter space for which we expect at least ten (one hundred) total − M ϑ e 2 + parameter space where one expects more than 10 (100) dark Higgs scalar decays in e ϑ . Region of the dark Higgs mass 2 vs. sin one. One proposal for the DUNE Near Detector Complex is that the liquid and ϕ We see here that the DUNE MPD will allow for an improvement on current limits Combining the fluxes and the decay width of ϕ M the window still openconsiderations of between supernova searches luminosity from ofthe Supernova sensitivity this 1987A of Fermilab’s type [ short baseline (displaceddark neutrino Higgs decays) detectors models (e.g., and projects ICARUS bounds and limitsat on SBND) from sin to DUNE. charged kaons decaying to atranslated charged into pion and an invisible particle, reported inbetween ref. roughly [ 20 range of masses. A DUNE MPD search may also allow us to comprehensively search in function of how off-axison- the and near off-axis, detector making is, it and possible search to for distinguish such the aof different shape new when physics hypotheses. operating decays (into existing limits are depicted in grey [ is coming from decaysof of neutral mesons both (or chargedthe continuum and processes), neutral the kaons,gas where TPCs move offof axis the (the neutrino DUNE-PRISM spectrum. proposal In [ principle, one can calculate the distribution of Figure 17 bosons sin the DUNE MPD, inexcluded. blue (red). In grey is the region of parameter space currently experimentally JHEP02(2020)174 15 N 7.2 ]). (7.1) , and 3 We are 106 , ν 2 14 , ν , we discuss 1 ν discusses how, 7.3 7.4 ] and our work is different for 106 considered here and section , the neutrino weak-interaction while the lighter three states have N N, N . Finally, section N 2 matrix elements, are constrained by αN | M U αi τN + U U in our work and figure 5 of ref. [ | i ν 26 αi , or U 2 has mass – 33 – 3 | , 2 , , and N µN X =1 U i | 25 , , = 2 | 1 GeV, when the HNLs can be produced by the same 24 α ν eN . U | N ] simulated HNL fluxes by reweighting the well-studied light neutrino fluxes M as a heavy neutrino or a heavy neutral lepton (HNL). 106 . N can be written as linear combinations of the neutrino mass eigenstates τ . The latter, along with the is nonzero for a given analysis. ] focused on connecting such HNLs to the origin of the light neutrino 3 is a Dirac or Majorana particle, hence whether lepton-number symmetry , ν . Furthermore, the same parameters allow for a variety of decay modes µ discusses the production channels for , m τN 106 N 2 αN , ν ] recently explored the DUNE near detector’s sensitivity to HNLs in great e decays that could be detected in the DUNE MPD. In section ,U U 7.1 : ν , m . The fourth mass eigenstate 106 1 N µN ,N m 3 ,U , ν e, µ, τ 2 Ref. [ Section Here, we refer to eN Such gauge-singlet fermions which mix with light neutrinos areWe often also referred emphasize to that the as simulation “sterile of neutri- HNL production in ref. [ are Majorana or Dirac fermions. U , ν = 14 15 1 at the DUNE near detectorresults hall, agree where validates we the simulate two HNL different fluxes approaches. from the parent mesons. The fact that the or Majorana particles. nos.” We avoid thisoscillations. terminology, as it often refers to mixingthe that bulk coherently of modifies results the — active ref. neutrino [ and did not separateless, them our for results the(specifically, and sake for theirs, of example, background when figures Whereas reductions, asking ref. as similar [ we questions,masses, do. are we choose Neverthe- qualitatively a equivalent different lens and focus on diagnosing whether such HNLs are Dirac if such an HNL weremine detected whether in DUNE, measurementsis of the violated decay in products nature. could deter- detail. Their analysis utilized the combined decay volume of the LArTPC and the MPD, of discusses backgrounds associated with each signal andpling present to the expected the sensitivity SM for via HNLs cou- nonzero decay pipe and are stilland heavy enough decay to rates decayparameters into of charged SM such particles. HNLs Thefor are production the governed HNLs, byallow depending the us on to weak the search interactionscouples HNL for and to HNLs mass. only the in one the mixing These charged DUNE lepton production MPD. flavor and For at simplicity, decay a we time, mechanisms will i.e., consider we that will assume that at most one neutrino oscillation experiments. ThisN setup allows for the possibility that interested in 1mechanisms MeV — meson and lepton decays — as the light neutrinos in the DUNE target and ν α masses In this section, weSM consider gauge the interactions. existence Assuming of thesethey are new not couple, fermions charged at under that any the are otherelectroweak renormalizable not gauge symmetry level, symmetries, charged to under breaking, lepton the eigenstates for doublets one and the new Higgs fermion doublet. After 7 Heavy Neutral Leptons JHEP02(2020)174 , , ) ) 2 | N N + x, y + (7.3) (7.2) eN e ( . The µ U (where | N ρ → → 7.4 + `N + produced in π D , → , ! ∗ . N τ 2 ) 2 m N + W e m ) — we direct the M xy 0 , → π relative to light neutrino + α 7.2 0 2 m 2 ` y → qq m m ) and the two- and three- + + that, when produced, are

s x via via K N D N , 2( , assuming five years of data ρ mesons can also be produced N N N will depend on which coupling N − discusses how we simulate the + B enhancement 2 2 decay right-handed. M | e 3 y N , and 2 + | 2 + αN → m ) D 2 U for the approximations made in our x αN + , x U 3 | − K − | , 1 K 1 + (1 , ). Section N x p + ) N e π ν , the most dominant channels for every possible + 2 – 34 – for HNLs that couple only to electrons via + α e ) N ` → 0 y is a Dirac or Majorana fermion in section + π + e − → π N x → + → ( m + + s − D K y stemming from this decay; we will discuss this and how it , + N N x displays the expected number of + ) = Br( e ] for details. See section 0 N 18 decays, discussed in some detail below. + α ] have explored the possibility of HNL production in fixed-target K ` ) = prefers to emerge from the two-body s ) is the two-body branching fraction into SM neutrinos, and 112 ) is considered — we discuss each case in turn below. In general, we , → ν N 111 → D ) can be greater than one, indicating helicity x, y – + α ( + τN ` + 111 N x, y U D m This function is ( ρ and , → 106 N , ρ 16 N + Br( , or + D m 66 e are partons) may be considered. Additionally, , 0 µN 0 π production processes of interest are as follows. For simplicity, we focus our discus- q 52 U , considered. Figure The meson decays considered are The possible decay channels resulting in a flux of For large enough beam energy, the direct production of → N Note that eN N and + 16 U D M traveling in the direction of the MPD asproduction, a where the function of the sion on positivelychannels charged in mesons neutrino decaying, modetineutrino which mode. at would DUNE. be The the charge-conjugated processes dominant dominate production in an- affects the determination of whether expressions for three-body decaysreader are to more refs. complicated [ three-body than decay simulations eq. and ( their validity. Production with electron coupling: These decays are isotropicpolarization in asymmetry the of rest frame of the parent meson. We also calculate the where Br( is a function thatsuppression. accounts for the available phase space in the decay, including helicity protons on target, however, HNL production from both of these channels is( negligibly small. express the two-body meson decay branching fractions into body decays. Wetwo-body also include secondary production from the decaysq of in the target, contributing further to HNL production. Given that DUNE uses 120 GeV Refs. [ experiments such as DUNEmechanisms are in leptonic decays some of detail. mesons,or either via three-body In two-body decays decays such (such (such as ageneration as of scenario, relevant mesons the (in relevant this production case, 7.1 Production of Heavy Neutral Leptons JHEP02(2020)174 , N N 10 10 + 6 here. 6 − µ − mesons 6 = 0 − = 0 = 10 s = 10 = 0 = 0 → 2 2 2 | | 2 | 2 2 . The | | | D eN µN τN eN µN τN + U U U N | | | U U U | | | 1 = 10 1 + K µ 2 , | N eN → + U | µ mesons (orange). For + s N N 1 0 0 1 N N − s 0 [GeV] 0 − N N K N N K D [GeV] 10 − − − + + + N N K → N N K N 10 D e e e e e e N − − − + + + , µ µ µ µ µ µ M M → → → → → → + traveling toward the DUNE → → → → → → N + − + − + − s s π Antineutrino Mode + − + − + − s s . Again, we separate HNL Antineutrino Mode D D D D D D + D D D D D D N µ mesons (green), and 0 2 19 2 N − N 0 0 − N N K 0 N π 0 10 N π traveling toward the DUNE MPD as D N N 10 N π − − + + N π N − + N e e e e − − + + e e − + µ µ . Different meson-decay contributions µ µ µ N µ → → → → 6 → → → → → → → + − + − → → − + − + − + − + − π π K K K K π π K K K K + 3 D 3 − = 10 − 10 , 10 2 mesons (green), and | 10 10 N 6 6 + − eN D − µ U – 35 – | . Different meson-decay contributions are indicated 0 = 0 = 0 = 10 = 10 = 0 as in the electron-coupled channel, we consider = 0 6 2 2 2 π | 2 | 2 | 2 | | | − eN µN τN eN µN τN U U U = +1 (assuming lepton number is a good quantum U U U | | | | | | → 1 1 L = 10 + 2 | D , assuming five years of data collection in neutrino mode (left) , µN N U N 1 | 1 − [GeV] − M + [GeV] is nonzero. The list is as follows: 10 N 10 N µ 2 M M | Neutrino Mode Neutrino Mode → µN , assuming five years of data collection in neutrino mode (left) or antineutrino U + | N 2 2 − − D 1. Dashed curves indicate three-body decays. M 10 10 , − N = + L µ . Number of electron-coupled heavy neutral leptons . Number of muon-coupled heavy neutral leptons 0 3 3 − π − 8 6 4 16 14 12 10 6 4 8 10 14 12 10 16

10 10 10

10 10 10 10 10 10 10

yr 5 / N

. 10 10 10 10

N yr 5 / N . → + Production with muondecays coupling: when only K flux from each ofproduction these in neutrino contributions mode is (left depicted panel) in from antineutrino figure mode (right panel). collection in (anti)neutrino modeFor for all the production left mechanisms, (right)charged the panel. meson darker into color We take an correspondsnumber), HNL to where the with the lighter decay color ofHNL corresponds a with to positively a negatively charged meson decay into an mode (right). Weby have different fixed colors:each pions meson, (red), darker kaons colorsnegatively-charged (blue), indicate meson positively-charged decays. meson Dashed decays, curves indicate where three-body fainter meson colors decays. indicate Figure 19 a function of mass or antineutrino mode (right).are We indicated have by fixed (orange). different colors: For each pionscolors meson, indicate (red), darker negatively-charged kaons meson colors decays. (blue), indicate Dashed positively-charged curves meson indicate three-body decays, meson where decays. fainter Figure 18 MPD as a function of mass JHEP02(2020)174 . . , , τ 6 N − 20 Nπ + τ = 10 → flux for → is larger, 2 τ | N τ + ν τN D + U | : τ decays (purple). τ τ decays. Here, we m mass. Because the leptons: s τ 10 τ 6 − D/D represents the = 0 = 10 = 0 2 2 2 | | | -produced HNLs corresponds 20 , it will be able to decay into eN µN τN τ U U U N | | | traveling toward the DUNE MPD 1 − + M N NX NX . Because these decays involve the → → 2 + − | τ τ decays are sufficiently prompt that the τN . τ 1 U − leptons, figure | [GeV] 10 N N N and its branching fraction into τ − + ` ` M produced in two-body . The number of – 36 – mesons (orange), and secondary D → → µ µ + − s s s τ D D D lastly, we list the meson decays in which HNLs are Nν decays; see the orange and green curves in figure 2 Neutrino or Antineutrino Mode − D → mesons or 10 N N . These decays provide sensitivity to significantly heavier − + τ ` ` and subsequent D , 20 → → e s decays on their own — nearly up to the e + − s D D is heavier than Nν , assuming five years of data collection. We have fixed s 3 D/D ] give the partial widths of HNL decays of interest. For a given − N D mesons (green), → 4 3 6 5 at least one charged lepton D/D

10 10 10 10

τ N 5yr)] (5 N/ [ N D 113 , , , we determine the available decay channels, the total rest-frame lifetime Nρ N 112 , → M . Because 52 τ . Number of tau-coupled heavy neutral leptons N , + and τ 2 | NK Refs. [ → decays contribute more than αN + → s s -coupled HNL than U fully invisible or swamped byand backgrounds. will combine We classify their these branchingstates decay fractions/decay are channels widths those as for with irrelevant simplicity. Our relevant final | 7.2 Decays of Heavy NeutralDepending Leptons on the flavora to variety which of an final HNL states. couples and At the DUNE MPD, several of these final states will either be magnetic horns focus neither.τ We consider theto the following purple decays curves of inτ figure focusing has no effectfive on years of the data collection in either neutrino or antineutrino mode. lepton, we need onlyD consider decays of mesonsD with mass greater than We also consider decaysassume of that secondary both the Dark colors indicate positively-charged particle decays,particle where decays. faint ones indicate negatively-charged Production with tauproduced coupling: when the only nonzero coupling is Figure 20 as a function ofThe mass expected rateare is unaffected independent by ofby the which different focusing mode colors: magnets. the beam The is different operating meson-decay in; contributions all are parent indicated particles JHEP02(2020)174 . + 3 ν π − µ , or 2 → ν produced is a Dirac , , 1 N N would exist, − ν . We include N µ + N + than if it were + ρ π 2 − | − e νµ µ 10 αN is nonzero at a time. → → U | → | τN N we assume U | into different final states as a 17 = +1 particle N L , and | ,N ,N 1 + µN + ) have lepton number +1 and their U α + K νµ | ` , − − | e e [GeV] eN → → N U | M is a Majorana fermion so that lepton number is – 37 – 1 decays − N . + + 10 is more common, rendering comparisons between our results π ρ − − e e Irrel N ,N − + ,N − + − µ µ e = 0 = 0 6= 0 + e + . K + − 2 2 2 − | | π | + νe νe νµ e coupled HNL − eN µN τN is one of the three light neutrino mass eigenstates, 7.4 νe e − U U U e | | | 2 ν − → → 1 2 3 1

. The grey curve is a collection of decays considered to be irrelevant, as 10 − − −

→ N 10 10 10 N N Br( ) X N : M in our simulations. would be forbidden. If − N π + Relevant . The branching ratio of an electron-coupled HNL µ is nonzero: is a Dirac particle. When presenting sensitivities, • | is a Dirac particle, and only gives the decays for the → N and its branching fractions into channels of interest. We list the decay channels of eN N If HNLs are Dirac particles so that lepton number is conserved, then the N In the literature, assuming Majorana U N | 17 and existing limits a little more indirect. Of course, in practice,that this daughter neutrino will notthe be decays of observed. This list also assumes If 7.2.1 Relevant andIn irrelevant creating decay the channels following listthat of only possible one decays, we of have theIn continued mixing the to matrix list, assume elements for the simplicity daughter violated, then both decayswhen would occur, each withfermion, the which same corresponds rate toa as a that Majorana more for fermion. conservative reachMajorana We to HNLs will lower in section discuss the nuances of the differences between Dirac and interest for each coupling below. from positively charged mesondecays decay must (along conserve with leptonbut number. For instance, the decay Figure 21 function of its mass described in the text. of JHEP02(2020)174 , 0 , νη, νφ νφ. νη − µ + → → → ρ → + − νµ µ − 10 → → µ + ,N νµ 0 → νπ νω, N νη,νφ N νη, νω, N → → → → → → background from incoming beam ,N ,N into different final states as a function 1 0 + + π N νe K − − µ µ ,N [GeV] ,N → → ,N + ,N N 0 0 0 ,N M ντ 0 νπ νω, N νπ νρ − – 38 – e νρ 1 ,N decays − → → → → + . + − π ρ 10 e → → − − + µ µ Irrel νe ,N ,N − − + − → − µ e µ + 6= 0 = 0 = 0 K e + + + 2 2 2 π − | | | + N νe νe νµ µ ,N coupled HNL ,N − 0 eN µN τN 0 ,N − 0 µ νe U U U ν, N ν, N µ | | | ν, N 2 3 νη 3 νρ − channel will have a large NC 3 νη → → 1 2 3

10 − − − 0

→ → →

→ →

→ → 10 10 10 N N Br( ) X N : : : νπ : : N N N N N N → . The grey curve is a collection of decays considered to be irrelevant, as described N N Irrelevant Irrelevant Relevant Irrelevant Relevant M is nonzero: is nonzero: . The branching ratio of a muon-coupled HNL • • • • • | | τ N µN We expect all of the decays we deemed irrelevant to be background-dominated; for U U | | instance, the If If Figure 22 of its mass in the text. JHEP02(2020)174 is for pair 2 | 2 | − e αN + αN e U | U | -trident events are 10 − e and mixing + e N . However, as discussed in M − − N µ e + + pair will neither point perfectly νe νµ Irrelevant decays background events is very small − − 1 e into different final states as a function e + + e N e ). The different relevant channels are , we do not present any branching fractions τ 23 [GeV] N > m M N – 39 – M couples to the SM via coupling only to electrons 1 − 10 N cannot be accurately reconstructed, meaning that this In the DUNE MPD, roughly 20 this final state is relevant regardless of which N 18 = 0 6= 0 = 0 : 2 2 2 ), and taus (figure | | | − coupled HNL eN µN τN e − U U U 22 τ | | | + 2 decay channels. We also discuss existing limits in this parameter −

1 2 3 1

νe 10 − − −

→ N

10 10 10 ). Additionally, even though the neutrino carries away momentum, the Br( ) X N 4 → display the branching fractions into the relevant and irrelevant decay 23 N – . The grey curve is a collection of decays considered to be irrelevant, as described N 21 M . The branching ratio of a tau-coupled HNL ), muons (figure , the expected number of neutrino-related 4 21 Figures This is true even if the signal events are produced along the decay pipe (in contrast to in the target, as 18 in the beam directionsection nor reconstruct the invariantfor mass ten of years of data collection. was relevant in section We will discussbackgrounds. each of ourSearches relevant for decaynonzero channels and in will contribute turn,cause nontrivially of to and the the final-state resulting their neutrino, sensitivity of the associated each reconstructed coupling. Be- Here we discuss the sensitivitythe as different a possible function ofspace the and HNL how mass DUNE will be able to7.3.1 improve on them. Backgrounds for relevant HNL decay channels (figure in color withbranching corresponding fractions labels, sum to where 1 the for all irrelevant masses, curves,7.3 are which in enforce grey. Sensitivity that to the Heavy Neutral Leptons neutrinos. Additionally, sincein all general irrelevant the decays invariant mass haveanalysis of handle at is least not one available to outgoing distinguish neutrino, signal fromchannels background. under the assumptions that Figure 23 of its mass in the text. Becausein we this do region. not consider any JHEP02(2020)174 + − ), N ρ µ + pair + π µ − − e µ + → µ . This final . Additional N 0 2 mass. There- | π and other new + N αN π N U | s decay to photons , this signal channel 0 − π µ and + µ N . We expect that 10 signal , these decays are expected (100) background events in M 4 − are a statistically significant system to reconstruct the e O decaying to + 0 − + π e νe ρ + + π → νe N → N scattering as a background for π as with 1000 events expected in the liquid argon TPC. – 40 – the remainder of our relevant channels consist of and the direction of the total final-state particle ∼ : CC1 will result in the − e is the only coupling between the HNL and the SM; N ν µ + ρ + αN − U νe µ like the dark photon search with or → : charged-current backgrounds with single pion emission where − µ + N ν µ µ , we compare the sensitivity reach of the DUNE MPD against 2 + lifetime, and therefore its probability of decaying in the detector, − | N νe νµ αN ]. This rate, and the kinematics of such events, may be predicted in a system would have an invariant mass peak corresponding to the U | → → 71 + , π 0 70 N N π − with two particles in the final state, one being the charged lepton and the other µ N interactions between the HNL andparticles SM modify particles the or interactionsin between a nontrivial way. should still be withinbackgrounds a significantly. degree or so of the direction of the beam, allowing us to reduce neutrino-related 7.3.2 Existing limits For each nonzero existing limits. We assumeHNL that production and decay are then completely determined by For instance, the channel state would be relativelywhich easy deposit to their reconstruct. energymass; in In the the the ECAL, DUNE allowing MPD, the mass of interest. Asstatistically with significant here. most other relevant channels, we expect 10 signal events to be being a charged meson.scattering While backgrounds (for certain instance, channels willthe have invariant relatively mass large reconstruction neutrino-related momentum of will allow formeson significant that background decays within suppression. the detector Channels volume with may allow a for more final-state distinguishing signatures. 20 signal events, insteadin of this 10 channel. events, will correspond toSearches a for statistically two-body significant final sample decays states: of the pion is misidentifiedreconstructed to the be dark photon afore, mass; muon. we here, would they In will not theinvariant mass, not expect case reconstruct as of to the we the findten would dark years a for of photon, a peak data dark the on collection photon. with top the We of DUNE expect MPD. a For smooth this reason, background we in expect the that at least pion as an electron orwould muon. the background Particle reduction identification strategies would discussedevents help in will reduce section correspond this to background, a as statistically significantSearches sample for in these channels. will be competing against data-driven way by using theTherefore, sample we of expect thatsample for 10 ten signal years events of of data collection. Searches for to have very low backgrounds, mostly associated with the misidentification of a charged also expected [ JHEP02(2020)174 ] 2 | 124 αN U ], and | 131 175 MeV - of interest, ∼ ] proposed a N ] provide con- M 139 ]. Measurements 136 105 . For simplicity, we [ ], CHARM [ µν ], or the proposed SHiP at PSI [ 7.3.1 130 → and the number of signal µN 144 . For a given K , ]. Recently, precise measure- -coupled HNL via double-bang ] rates and spectra; ref. [ N τ ] contributes limits for 400 MeV 74 → 7.2.1 M 124 , the strongest constraints come π 135 N 123 ], JINR [ , M ) have allowed for improved limits for 110 122 µ [ ] that is stronger than any existing ones ν + µ eν 134 2 GeV, the strongest constraints come from → → – 41 – ], T2K [ & + ] provide the most stringent constraints for the ] proposed a search using atmospheric-produced π π N ]. For larger 129 133 138 ] and searches for , M between roughly 150 MeV and 450 MeV, we include a )/Br( ] and N 124 128 e 126 , ν ]. These last three limits are slightly weaker than those M + 121 e – decays provide constraints for masses between roughly 70 MeV 125 140 → 114 µν ]. For + ], PS191 [ π → ]. 126 ] and DELPHI [ K , 127 ]. The existence of such HNLs can also be investigated in the NA62 ]. Recently, ref. [ , decay [ N 146 141 ], the forthcoming FASER experiment [ 125 , 143 β 137 ]; however, no such analysis has yet been performed by the collaboration. -coupled HNL, the NuTeV experiment [ M ] and lepton universality measurements [ e 109 145 ] experiments. Above factories could also reanalyze data to search for such HNLs using kinemati- 142 133 2 GeV. The Brookhaven E949 experiment provides constraints in the Michel decay spectrum [ B 132 30 MeV, the strongest constraints come from searches for deviations from pre- 60 MeV [ . µ . . N As discussed above, in determining the number of signal events for a given point in HNLs that couple purely to the tau are relatively less constrained. Existing searches For muon-coupled HNL, many of the same probes apply. In addition to the probes Existing limits for electron-coupled HNL come from a variety of probes. For M N N 300 MeV region with precision measurements of the decay a combined search forsensitivity all than kinematically-accessible what channels we would present. lead to slightly greater parameter space, and therefore theDirac DUNE fermion. MPD If sensitivity, it we were assume a that Majorana the fermion, HNL then is its a total decay width would be a factor We present the expected sensitivityat of the a DUNE time. MPD assumingevents only The deemed one statistically search nonzero significant channelsshow is are only the as as search discussed channels listed which inof drive in channels the section section overall that sensitivity dominate at DUNE the — others the for collection some range of Current cal arguments [ experiment [ experiment [ 7.3.3 Expected DUNE MPD sensitivity discussed above. from CHARM [ mass ranges of interest. IceCubesignatures could [ have sensitivity to straints at low and 175 MeV [ HNL that cansimilar travel search to using and IceCube.ported decay a inside Moreover, the constraint Super-Kamiokande MicroBooNE in and collaboration ref. ref. has [ [ recently re- discussed for . ∼ of the BEBC [ DELPHI [ ments of the ratioM Br( preliminary limit from thein NA62 this experiment range. [ M dicted nuclear provides a thoroughical review assumptions, of see constraintsfrom also on the [ heavy PIENU neutrinos [ under minimal theoret- JHEP02(2020)174 ∓ 19 µ (red), νe (blue); − − → e µ + N + νe νe N/ 10 → → . Most notably, in (orange). Three of N = 0 = 0 N N (red), 2 2 | | DELPHI − M − or ρ e µN τN — + + + U U e | | µ νe 24 −

1 →

. We highlight the sensitivity

→ BEBC / CHARM νe

N (orange). As with the electron-

N PS191 / T2K → M

∓

, compared to those from CHARM NA62 ρ or N/ 2 N | + µ ρ eN −

(orange). Each channel corresponds to ten → | 1 e PIENU − (red); [GeV] ∓ N ρ 10 → − N e e + N channel (which should produce a relatively clean – 42 – M νe → ∓ π . See text for more detail. ∓ N → − ∓ µ e ∓ e π ρ + ± 2 N/ N ± ± − νe νe e e 7.3.1 →

PIENU (purple), and 10 / N, → → → → ∓ N π (purple); and N N N N coupled HNL

TRIUMF µ − π , we will explore how a discovered HNL could be diagnosed to be − → + e e (purple), and 3 N 7.4 − ∓

4 6 8 2 1

→ 10 12

10 π − − − −

− − |

10 10 10 10

e N 10 10

U , depicts the expected DUNE MPD sensitivity if the HNL couples to the depicts the expected DUNE MPD sensitivity to an electron-coupled HNL 2 (blue), → or ∓ 25 24 + . Expected sensitivity of the DUNE MPD to an electron-coupled HNL, assuming ten e N π ]. In section − N/ e νµ 106 Figure Figure This assumes the HNL is longer-lived than the distance to the detector. → → 19 muon. The channelsN of interest arecoupled similar HNL, in to the those absence ofHNL in a discovery, will figure searches in improve the on DUNE existing MPD for limits a for muon-coupled a wide range of is constrained by existingthe limits absence (shown of in a grey) discovery, the signal for in some the range DUNE of MPD)and will BEBC, improve limits by on roughly an order of magnitude. assuming ten years of dataThe collection channels with included equal here time are N in neutrino and antineutrino modes. these search channels are sensitive to regions of the parameter space that lie beyond what of two larger, leading to twiceThe as difference many signal in events sensitivity forref. under a [ given the point Dirac in parameter andDirac space. Majorana or Majorana. assumptions was explored in Figure 24 years of data collectionis (equal a time Dirac in fermion. neutrino(blue), and Specific antineutrino decay modes), channels assumingsignal are that events, considered: as the discussed HNL in section JHEP02(2020)174 ], ], − − e µ + + 141 109 νe νµ (orange). (red) and → → ∓ ρ − N N , we have no e ], NA62 [ µ τ + 10 → 143 νe > m N = 0 = 0 → 2 2 DELPHI | | N N/ . See text for more detail. eN τN N M U U | | factories [ 7.3.1

-coupled HNL at the DUNE B

BEBC /

CHARM τ

PS191 / T2K 142 (purple), and →

. We discuss this search channel and ∓ µN K E949 π − e

µ + 1 KEK − [GeV] νe → 10 N N →

– 43 –

M N/ N

→

µN π ] searches do not have much sensitivity. This same ∓ − ∓ e ∓ e and a charged meson. The DUNE MPD sensitivity π ρ ± + 2 133 (blue), ± ± − µN νe νµ µ µ ∓ τ 10 e → → → → → π N N N N νµ PSI coupled HNL → − N µ is assumed to be the HNL produced in association with a positively displays the expected sensitivity to 3 − N/ N 4 6 8 2

1 10 12 26

− − − −

− − driven by the search for ]. Such searches would be complementary in probing this gap with the

10 | 10 10 10

10 10 µN

U N (red),

144 2 (green). Due to background considerations discussed above, the . M − e − . Expected sensitivity of the DUNE Multi-Purpose Near Detector to a muon-coupled + µ 7.4 + νe νµ → Finally, figure N → In that case, when and FASER [ DUNE MPD. 7.4 Deducing the natureAbove, of we assumed the that HNL HNLs — are Dirac Dirac vs. fermions Majorana and that lepton number is conserved. curve corresponds to 20channel will signal provide events. aand more a In powerful combination of the constraint both than absence channelswhere will existing of allow the CHARM us a CHARM to constraints search and discovery, for [ window DELPHI tau-coupled the can HNL [ be in a probed, window as discussed above, by IceCube [ MPD. Because no productionaccess mechanism to exists any for finalto HNLs a states tau-coupled with with HNLneutrino is and independent antineutrino of modes howthe the since magnetic data the focusing collection productionN horns. time mechanisms is are divided The not between two impacted channels by we display are to low-mass how an HNL decaying inin this section way could be diagnosed to be a Dirac or Majorana fermion Figure 25 heavy neutral lepton, assuming tenmodes). years of data collection We (equal assumeN/ time in that neutrino the and antineutrino HNLEach channel is corresponds to a ten Dirac signal events, fermion. as discussed in Specific section decay channels are considered: JHEP02(2020)174 or + π − µ → 10 N , the green region − produced via pos- µ = 0 = 0 + 2 2 N | | νµ eN µN U U | |

DELPHI that perfect charge/particle 1 7.4.2 -coupled heavy neutral lepton, assum- , the red region encompasses parameter τ = 1, its decays always contain nega- − e L + 1 νe − (green), compared against existing limits from [GeV] 10 − N µ + – 44 – M CHARM νµ − → − µ e + + 2 N − ], Majorana HNLs also diﬀer from Dirac ones in their νe νµ N/ 10 148 → → ]. For the ﬁnal state – N N 133 coupled HNL 146 ) and those with only charged particles, where the total lepton 0 − (red) and τ νπ 3 − − e

4 6 8 2 → 1 +

10 12

10 − − − −

− − |

| νe

10 10 10 10

10 10

τN

U → 2 or ] and DELPHI [ , with equal probability. Since the magnetized DUNE MPD has charge- and N − − . Expected sensitivity of the DUNE MPD to a e 141 π N/ + + µ νe We explore the potential of determining whether HNLs that are discovered by DUNE As explored in refs. [ → → these different spectra could be distinguished. are Dirac or Majoranawith unobservable fermions. lepton number Two dueN classes to the of presence HNL of final a neutrino states in are the considered: final state those (e.g., decay kinematics. When thewill HNLs in general are have produced a netdecay in polarization, angular weak-interaction potentially distributions. meson leading to decays, Differentdifferent asymmetry they rest-frame decay-product in angular energy their spectra distributions rest-frame in will the be lab frame. reflected in Even with a charge-blind detector, itively charged mesonN decay may thenparticle-identification decay, capabilities, for it will instance, beof able into to decay search either into for these differences finalidentification between are states. the rates not We required will to show perform in this section analysis. indicates twenty signal events, due to background considerations. See text for morecharged detail. lepton and havingtively its charged own leptons lepton or number then neutrinos. they On will the also other violate hand, lepton if number HNLs in are Majorana their decays, fermions, i.e., the Figure 26 ing ten years ofmodes data is collection irrelevant). (howchannels this We time assume is that apportionedCHARM the between [ HNL neutrino and isspace antineutrino a for Dirac which ten fermion. signal events We are show expected, whereas sensitivity for to the the final state JHEP02(2020)174 , is = N N for N 0 N M νπ → for will produce N 0 27 = 350 MeV. We νπ and N , with the opposite that an extremely 0 → 0 M νπ N 27 νπ decays when the DUNE → − N K ]. In contrast, for Dirac decay to 148 [ and N + N K ]. However, the DUNE beam is not energies. neutrinos, including the light ones, are 148 0 π all ). is a Majorana particle would have far-reaching ∓ – 45 – π energies as they travel to the detector. We note 20. It is apparent in figure N When simulating the HNL decays, we assume they for a Majorana HNL. In principle, the distributions − µ , we expect this channel to have a large background N 0 20 10 → ∼ νπ energy distributions are depicted in figure is a Dirac fermion, the 7.2.1 , are Majorana particles, the decays N 0 → is a Majorana particle, its exchange will lead, via mixing, s in the rest frame of π N N 0 N consider, for instance, the decays π N ] explored this decay channel as a possible means of distinguish- : 0 148 is maximally anisotropic [ νπ 0 → νπ N → N lab-frame energies and angles relative to the beam direction are different between The authors of ref. [ These resulting lab-frame If the neutrinos, including Because of leptonic mixing, if we can establish experimentally that an HNL 0 The results of this analysis in antineutrino mode are qualitatively equivalent. π 20 corresponding to boost factorslarge of sample of eventssample (even to neglecting distinguish background between events) Dirac would and be Majorana required HNLs. toing use Dirac this from Majorana HNLs in a toy scenario. Our analysis differs from theirs in two and so determine the lab-frame distribution of 350 MeV; the Majoranadepicts (Dirac) the hypothesis lab-frame results distribution arethat of depicted the in HNLs red are (blue). highly boosted; The inset most of them have energies between 5 and 10 GeV, For concreteness, we explore thedetermine kinematics the of flux such (and decays polarization)facility assuming is of operated HNLs in from neutrinoare mode. either Majorana (i.e.,or the Dirac decay (i.e., products the are decay emitted products isotropically are in emitted the anisotropically rest in the frame) rest frame) fermions, an isotropic distribution of the decay a perfect environment forparticles such in the searches beam. — Evenanisotropy, since will if there hinder the will separation between be the some Majorana and contamination Dirac of fermion hypotheses. of these two hypotheses; abe large distinguished. enough sample For of illustrativealthough, decays as purposes, could discussed we allow in explore these section from this distributions neutral-current decay events. to channel in detail here, indicate whether the HNL isstate’s a lepton Dirac number, or one Majorana must fermion. rely exclusively InsteadSearches on of for kinematic identifying information. the final a Dirac HNL, and the decay ticles. Thus, establishing thatimplications. an HNL 7.4.1 Final statesIf with unobservable there lepton are number to SM determine neutrinos the in state’s total the lepton final number, state and of counting these an events HNL will decay, not then readily it is not possible a Majorana particle, thenMajorana it particles. will For, followto if that diagrams thatthese give mass Majorana eigenstates masses have to Majorana masses, all it the follows neutrino that mass they will eigenstates, be and Majorana once par- number may be measured (e.g., JHEP02(2020)174 , 0 are and νπ , this N N 0 → νπ decays, in N as a function N 0 4, significantly ] explored this νπ − 30 106 20 couples only to the and 0 N νπ 15 25 . Ref. [ N Neutrino Mode , instead of either one or the . Scenarios in which are significantly less boosted, 0 N, N Neutrino Mode 10 [GeV] frame distribution N νπ − N, N 20 and E Lab 5 Dirac Majorana rest frame) as in the decay N N ). Compared to the final state 0 [GeV] 15

0 3 2 1 . . .

0 0 0 0 PDF , we showed that the DUNE MPD is sensitive 26 π E – 46 – 7.3 10 with boost factors between, roughly, 2 N in section 5 : − energies prior to their decay. e = 350 MeV + N N M νe 0 are not as discrepant (in the 1 0 3 2 . . .

0 0 0

π →

0 dE

N N − [GeV

] ) or only to the tau (ﬁgure

= 350 MeV. The red line depicts this distribution for Majorana

dN 1 1 energy, assuming operation in neutrino mode at the DUNE MPD. For all cases N N 0 25 . This is particularly true for the scenarios in which rest-frame decay is isotropic. The blue line depicts this distribution for Dirac π M − ] considered a flux of e . Expected distribution (area normalized) of HNL decays to N + 148 νe We conclude from this that, if DUNE discovers an HNL that is produced predominantly → decays, in which the rest-frame decay is maximally anisotropic. The inset shows (black) the number, its kinematics aredecay different in for more Dirac detail. andDirac/Majorana Majorana We anticipate that,such Majorana because the vs. Dirac relativeenvironment. fermion angular We leave differences distributions a would for more be detailed difficult study to of these measure three-body in decays the to DUNE future work. Searches for to a large region of currentlyN unexplored parameter space by searching formuon the decay (figure channel has significantly lower background. While it suffers from having unidentifiable lepton from charged kaon decay, then suchthe beam-neutrino environments intrinsic are nature not ideal ofgenerated for from the studying only HNL one mass chargewould of be in kaon, significantly more the and propitious. in final which We leave state the the study of such scenarios to future work. ination is not veryin significant. ref. Second, [ and morelower importantly, than the what toy would analysis occuryield performed for predicted a energy 350 MeV distributions HNL that at are DUNE. substantially More more strongly difficult boosted to HNLs distinguish. N lab-frame distribution of main ways. First, we consideredother. the We decays did, of however, both determine that the impact of this wrong-lepton-number contam- Figure 27 of lab-frame we consider which the JHEP02(2020)174 10 -coupled . The left µ ). This is 1 Both Modes N A in neutrino M 1 - and ∞ − [GeV] e 10 N = +1. Obviously, (for each different M L 2 N − = +1 directed toward -coupled HNL. For each 10 M τ L coupled HNL are identified, the lepton − and appendix τ 3 − 4 10 -(right) coupled HNLs. When 10 400 MeV for the τ & 1 N M Neutrino Mode Antineutrino Mode Both Modes 1 − [GeV] and their charges 1 in equal abundance — the measured ratio 10 N presents the ratios in neutrino mode (blue) − M -(center), and = 2 28 µ – 47 – − = +1 reaching the MPD to the number of HNLs 10 L coupled HNL -coupled HNL, and right is for L − µ 1 would be diverted away. Then, using measurements µ 3 − − -(left), 10 e -coupled one. = are notable. First, the expected ratio typically deviates 10 τ L = +1 and 28 L 1 ) mesons, where negatively charged mesons are produced in more s D 1 / − [GeV] 10 D N M 1, assuming the HNL are Dirac fermions, as a function of the mass 2 − − 10 1 also reaching the MPD. In a perfect world, this ratio is Neutrino Mode Antineutrino Mode Both Modes , we calculate the ratio of two fluxes as a function of coupled HNL -coupled HNL, center is for − e − . Expected ratio of heavy neutral lepton decays with lepton number +1 to those with 20 e 3 – − =

1 2 2 1

10 − − 10

10 −

10 10 1) = L ( /N +1) = L ( N 18 L Several features in figure Assuming the HNLs are Dirac fermions, and using the production rates depicted in from 1 more in neutrino modefavorable. than in This antineutrino mode, is making not suchover a because measurement the more of other; the itfrequently ability in of is the the simply beam beam than becausenot to negatively true positively charged focus for ones charged heavy one (see ( light polarity table mesons of mesons are produced more and antineutrino mode (red)the for distinction between neutrino andparticles antineutrino are modes unfocused), is we irrelevant usewould (because decay purple the as lines. parent if they Ifwould have HNLs be were 1. Majorana fermions, then they figure coupling): the number ofwith HNLs with mode and 0 in antineutrino mode. Figure experiment operating in neutrino modea would detector produce and HNLs any with HNLsof with charge/kinematics, one could deducean that experiment the like decaying DUNE HNLsantineutrino is have contamination not exists perfect; in neutrino even mode, with and the vice light versa. neutrinos, a certain level of 7.4.2 Final statesIn with the only charged previous particles number subsection, is we unobservable due focused towith on the only decay presence charged of modes particles SMnumber where, in neutrinos. will if which We particles be now the explore determined. final-state final states In lepton a perfect world, assuming HNLs are Dirac fermions, an panel is for panel, the blue (red)to line corresponds the to two operation operationscenarios in and modes (anti)neutrino for overlap mode. all (purple masses The lines) in results the for associated Figure 28 lepton number JHEP02(2020)174 − 1), π is a + − µ 1) for N = − L events (at = and ( ∓ + L N π π − µ µ 7 − 10 , both neutrino and → N 4 = +1 or 10 M N 3% CL . 1) after performing these L = +1) and 68 95% CL 99% CL − coupled HNL L − ( = , µ 3 N L ). The Dirac hypothesis can be ( ≈ 3 = +1 ones. Additionally, the ratio 28 /N 10 L = 250 MeV N M ) or Majorana fermion (where the ratio = +1) 2 | 8 L − Expected Dirac Ratio 28 µN ( 10 expected U is approximately 20% and this is the largest | N N 2 ∓ – 48 – 1, to determine whether the detected HNL is a 10 π − 1 HNLs than µ − = = L → N = 20 , we perform a number of pseudoexperiments where we expected 2 | L (few). Even with perfect event-by-event identification of N O µN 10 U | increases, so does the expected number of events, and it becomes 1 assuming perfect lepton-number-identification, as a function of the = +1 or 2 − | = 250 MeV muon-coupled HNL. Here, we simulate data assuming L 9 µN N − 1

1 U

10 − 10

− M

10 1) = L ( /N +1) = L ( N . For a given for a displays the result of this procedure assuming five years of data collection in , fewer than one or two events are expected, and this procedure should not be used. 2 = 250 MeV. We calculate the expected number of | 9 2 | − 29 . Expected ability to measure the ratio of HNL decays with lepton number +1 to N µN µN 10 U M | U | ≈ 2 | Figure To demonstrate the power of measuring this ratio, consider a muon-coupled HNL with µN U neutrino mode. As easier to measure thatHNLs the are ratio Dirac is fermions,ratio 1, and is as approximately if predicted 3 we byrobustly (see are the excluded the operating Majorana center (if in panel HNL every of neutrino hypothesis. event figure mode, can If then be the properly expected identified as with equal probability.respectively, These and event are rates drawn95%, are from and defined a 99% credible as Poisson regionspseudoexperiments. distribution. for the ratio We then determine the 68.3%, a mass this mass, the branchingof ratio the relevant channels)mixing for five yearsassume of that neutrino the mode HNL operation is as a Majorana a fermion function which of therefore the decays to antineutrino mode predict more in neutrino mode iswhether typically the HNL has Dirac (where the ratioshould be is 1) predicted will by require figure many events. | The vertical line indicates whereof the number data of collection signal in events is neutrino 20. mode. We have included only five years abundance. This explains why, for all couplings, for heavy enough Figure 29 those with lepton number mixing Majorana fermion; if it were a Dirac fermion, the preferred ratio would be approximately 3. Below JHEP02(2020)174 N and M (7.6) (7.4) (7.5) ν,M n ) as . ) 1 events are 7.5 ). We denote − will be nearly ¯ ν,M confidence level . For each final = . 28 n N ( σ ! L ρ ν 2 M assuming HNLs are ∓ ) , L ν µ . ν r ! ! 2 r | log ν ν + − 4 → − N N µN 1 (by identifying the sign (1 + ) N , with U − | = +1 and L

log log ν,M L n 2∆ log − − ( , and − ν L and compare the likelihood at this ν + ν − π ν,M n n ∓ n D e log U , we give the number of expected signal + 2 − log log → ν ν + − ! )) 29 N 2 D N N ) , ˆ U ν + + ( ν r – 49 – , the log-likelihood is r π ν + ν − ν 4 ). We use a likelihood ratio to compare the two ¯ ∓ ν,D n n n µ n D (1 + − − ( U ¯ ν (

→ L , since this is our null hypothesis. For the Dirac hypoth- ) = ¯ ν,D N ν log ν − n 1 events in both running modes (see figure N − , n Since such an analysis would take place only after an initial , we may re-express our test statistic, using eq. ( ν,M ν + = n = )) + log n decays completely visibly, then its mass may be measured from 21 ( ν,D − D L ) and ν ˆ ν,M = 2 U N D /n and predictions L ( n U L ν ( ν,D + (10 MeV) precision, corresponding to nearly perfect knowledge of as a function of the HNL mass and mixing. We perform a frequentist ν,D log . On the top axis of figure N n 2∆ n O 9 , to the Majorana hypothesis value. Our test statistic for distinguishing ν,D ( − ν ≡ n D − , we optimistically assume that, with enough events, ˆ L U ν 10 = +1 and demonstrates the ideal ability of the DUNE MPD to determine whether r N L × 9. , as log 29 2 > αN & U L L ≡ 2 | . For the Dirac hypothesis, there is a (mass-dependent) ratio between the expected ∆ Defining For the Majorana hypothesis, the expected numbers of To study the extent to which the MPD could discriminate between the Dirac and Ma- Figure = 2∆ We also performed a Bayesian analysis and obtained qualitatively similar results. µN − 21 D ¯ ν,M U We consider the Majoranaif fermion hypothesis preferred over Dirac at 3 clearly maximized for esis, we maximize thebest-fit likelihood point, with respectbetween to the Dirac and Majorana fermion hypotheses is hypotheses; in practice, wenumbers consider of events the difference in their log-likelihoods. For observed and similarly for the antineutrino mode. For the Majorana hypothesis, the likelihood is equal in both neutrino andn antineutrino modes; we denotenumbers these of expectations as the numbers ofU events predicted by the Dirac hypothesis, as a function of the mixing perfectly measured. If the invariant mass of the finalthat state it particles. can attain While theas detector far is as not this perfect, analysis we is assume concerned. state, we calculate the expectedMajorana number particles of decays to eachanalysis charge to state address how distinctder the the Majorana-assumed Dirac data hypothesis. discovery are of from data generated un- these final states aevents between finite the fraction samples, of limitingMajorana the the hypotheses. ability time. of the This detector is to tantamount separate to thejorana Dirac redistributing hypotheses and using the these typeswe of separately final study states the (without decays using kinematic information), events for a Majorana HNL given the corresponding valueHNLs of are Dirac orcan Majorana be fermions perfectlyof if, identified the as on charged an having lepton lepton event-by-event basis, in number the the +1 final signal or state). events In the real world, a detector will misidentify | JHEP02(2020)174 ), 7.6 5, in (7.8) (7.7) . 1 should a factor of = 0 = +1 and 2 ≈ | a contours lie L a αN σ U | for an electron- ; and imperfect . ∓ In various colors, , we now assume 29 ! π ) = 0 but ν 24 22 ! e r a ) ) ν a → r ) − a N − 75. That the 3 . + (1 2 a factor of two (or ) , a , 4 ν | = 0 + (1 D 2 r D ) , and compare against the relevant ν, + a a ν, − ν αN a n 1)) ( r n U ) | ) a (1 + a − 1)) ( ν − − 1, where there is no measurable difference r (1 + − ( 30 decays of Dirac HNLs with = 1 corresponds to a perfect detector and ν a → r a is a Majorana fermion. ∼ ( + (1 + (1 ν a ν, D N – 50 – D r . We focus on two cases: perfect identification ν, − ν, + 4 (1 + deviate from 1 — it is easier to rule out the Dirac an an 25

4 (1 + ν r → →

contour from our analysis assuming a perfect efficiency log D and D σ − ν, log ν, + 5. and ν,M n . n 24 n 0 ν r ν,M n → + 2 a = 2 40 events is sufficient; 75). Note that the worst-case scenario is not L . ∼ prior and the efficiency parameter 2∆ = 0 N − a M depicts the results of this analysis for the decay channel. In contrast to what was presented in figure 30 ∓ ) vanishes for π 0; the solid, black curve shows the same for . that corresponds to the fraction of decays that are correctly characterized in terms 7.8 0), corresponding roughly to the toy analysis presented in figure e a . 5 corresponds to pure guessing. For the Majorana hypothesis, and thus the expected . = 1 Clearly, while more than ten events are required to make this distinction at moderate Figure We present our results in terms of contours of the test statistic for a given assumption So far, we have assumed that the charges of the final-state particles are always correctly In practice, this means that we are sensitive to values of → = 1 a = 0 22 2) lower than in the Dirac fermion scenario. a √ be realistic with theelectron DUNE and MPD pion — tracks there in should the HPTPC. be littlesignificance, confusion having between identifying (for consistency with thiswe show analysis) other that existingdashed, constraints black in curve the shows theof same 3 parameter space (discussedrelatively close above). to the The ten-event sensitivity is unsurprising. We note here that identification ( which one is effectively guessingin the lepton eq. number ( for each signal event. Our test statistic coupled HNL. TheN purple curve shows our expected DUNE MPD sensitivity using the regarding the parameter space from figures ( which becomes in the log-likelihood (likewise for antineutrino mode). This substitution modifies eq. ( identified. To take intofactor account that this mayof not be particle the species case, anda we charges. introduce In an efficiency practice, numbers of events, thisexpected has asymmetry. no To effect. account for In this the imperfection, Dirac we interpretation, make this the will replacements wash out any neutrino hypothesis when the expectedleptons ratio is of more positively discrepantAs charged than expected, and what the negatively test charged is statisticbetween expected vanishes the if for two the hypotheses. Majorana neutrino hypothesis. The test statistic grows as JHEP02(2020)174 , 75. 24 . is a , as- ∓ N = 0 π a . The pur- µ ∓ π → e . In contrast to N 2 → . N , Dirac/Majorana dis- 40 HNL decays are N σ 5 ∼ . known 1 known N = 1. The solid black curve N . In contrast with figure ∓ ,M a ,M and efficiency factor BEBC π -produced HNLs, we would 75 0 / . . 1 Majorana Sep ∓ N D e / π = 0 = 1 M ± a a e → DUNE Sensitivity CHARM . Dirac → N contour from our analysis assuming σ 3 Exp N σ

. T2K 0 [GeV] N – 51 – M and the eﬃciency factor N M ]. 5 75 in order to discover the nature of . 2 . 0 NA62 75). Our analysis still indicates that . = 0 a 1). Lastly, it is particularly exciting that the parameter space 1 is signiﬁcantly harder to attain because muon and pion tracks = 0

− PIENU a ≈ 1 can look quite distinct from the Majorana HNL expectation of = contours is as of yet largely unconstrained. Not only would the a − 0 ( 1 . . L 8 6

0 σ = 10

(

− −

− is a Majorana fermion. The dashed black curve is the 3 |

| L 10 10 = 1

/N eN

U N a 2 search, displays the results of this procedure for the final state ∓ π = +1) 31 . Expected Dirac/Majorana separation capability in the final state e , the dashed (solid), black curve shows the 3 ). Other existing constraints in the same parameter space are also included. As in L ( → 25 30 N Dirac/Majorana distinction assuming perfect knowledge of increases towards the kaon-production threshold near 500 MeV, owing to the increased Figure N σ 10 decays with N eter space is ruledrequire out efficiency by, of in at particular,the least T2K. For heavier, look nearly identical in themuon HPTPC. tagger This for result the provides DUNE another MPD reason [ for the need of a modes. The purple curveMajorana is fermion the (again, expected assumedfigure sensitivity for curve consistency, for in thefigure contrast DUNE to MPD the if curvean presented efficiency in of required in order to make a meaningful distinction, but more of the corresponding param- DUNE MPD have sensitivity to HNLsstrong where resolving other experiments power have not, betweenparameter but space. Dirac it could and have Majorana HNLs in thissuming hitherto ten unexplored years of data collection, equal amounts of time in neutrino and antineutrino ∼ 20 for each. WeM note that the separationratio between the black andoccupied purple by curves shrinks these as 3 ple curve is the expected DUNEthis sensitivity assumes using that the channel tinction assuming perfect knowledgeis of 3 Figure 30 JHEP02(2020)174 0 − ∓ ρ π 28 and we νπ = 1. + . The a µ µ N if the 25 ∓ → M -mesons π 31 → B µ N N is a Majorana → and N N 2 30 and . . In figure , ∓ ∓ ρ 5 . π known 1 known µ N e N assuming ,M → ,M ∓ → 75 0 and the efficiency factor . . π 1 ∓ Majorana Sep ). The dashed black curve is the N / π N = 0 = 1 N ± NuTeV µ a a µ 25 M DUNE Sensitivity . → Dirac → σ 3 N Exp N 5 . 0 -coupled HNL would require production of [GeV] τ

N T2K

– 52 – M E949 -coupled HNL does not have a fully visible decay mode 2 . τ 0 Dirac/Majorana distinction assuming perfect knowledge of KEK -coupled case. τ σ , which is not possible with the DUNE beam energy. If τ 1 .

8 9 6 7 0 75.

. − − − −

−

| > m

10 10 10 10

) when one combines the distributions of the charge-conjugated ﬁnal 10 µN

U = 0

N 2 a 1 GeV), meaning many events are required to differentiate between the two M 7.4.1 ≈ ]. This anisotropy leads to different predicted energy spectra for the lab-frame . Expected Dirac/Majorana separation capability in the final state ratio in the Dirac-fermion case is close to 1 (see the middle panel of figure N 148 + M ρ − In principle, one could use additional kinematic information — lab-frame energies, an- Unfortunately, the case of a We have also explored a similar study in the channel Dirac/Majorana distinction assuming perfect knowledge of µ with mass σ number of signal events is already quite large. share many of(see the section samestates features [ regarding anisotropyelectron/muon/pion distributions. as We have the simulatedbe these final small differences and — state found such them information to would only assist in the analyses of figures could be produced inDirac abundance, hypotheses then in it the would be possible to probe thegular Majorana distributions, versus etc. —and to Majorana provide additional hypotheses. discriminating power between Specifically, the the Dirac final states to where hypotheses. available for analysis at DUNE.N Study of the saw that this channel canwe improve find on that existing the limitsalso regions from determine of its CHARM parameter nature and space are BEBC. for already However, excluded. which DUNE This could is mostly discover because an the HNL predicted and purple curve is thefermion expected (in contrast sensitivity to from the3 the Dirac-neutrino assumption search in figure The solid black curveefficiency is factor 3 Figure 31 JHEP02(2020)174 is expected τ ), we find that L 4 ). Light particles − µ 1.1 L – 53 – 500 m) and can reach the MPD. In addition to the ∼ final states, and, for some parts of parameter space, as − γβτ π + , the DUNE MPD will observe at least 10 decays of dark 7 π − 10 , or ). Unlike the case of a kinetically-mixed U(1), a leptophilic gauge − ∼ < 5 µ + µ ∼ < , − 8 e − + e 1 GeV) to be copiously produced in meson decays and sufficiently weakly coupled A related model that also has a sizable decay rate into charged leptons is a leptophilic In the case of kinetic mixing of a dark photon with the SM (section New physics connected with neutrinos or dark matter is typically weakly coupled to ∼ < m boson has additional production throughcomplicated the interplay leptonic between decays which of pair chargedof of mesons. lepton-flavor the There numbers is vector is a gauged whichnear and determines the detector. the mass expected Overto the number probe accessible of a mass observable region decays range, of in parameter only space the the not DUNE gauging presently of probed by terrestrial experiments. For photons to many as 100 suchdetector, decays. coupled with The theneutrino excellent surrounding scattering measurement events ECAL capabilities to and of be magnet, adequately the allow suppressed. gaseous the argon backgroundsgauge from boson (section after ten years of dataregions of taking, parameter the space. DUNE Due MPDto to will different a have target-detector complementary sensitivity separations, to DUNE regionSeaQuest. is presently of sensitive untested parameter For space darkparameter to photon 10 other masses future ranging experiments from like 200 MeV SHiP to or 1 GeV and kinetic mixing charged pions and kaons, andcharged final then states. subsequently In decay each in caserates analyzed, the and we gaseous have determined also detector, estimated regions the oftenlarge expected of into enough background parameter to space be seen where above the backgrounds. new physics signal would be states that can also beMPD long-lived. to In sub-GeV this dark work,where mediators we these have or new investigated states heavy the are neutralrenormalizable sensitivity coupled portals: of leptons. to the the SM We vector, degrees havewith scalar, of focused these or freedom couplings on neutrino through can models one portals be of of produced the eq. in so-called ( the decays of mesons, predominantly neutral and enhanced measurement properties of thesignals MPD, suffer the from reduced fewer target beam-induced density backgrounds means than that in the thethe LArTPC. SM, and isthen long-lived. it must If sit dark in matter a more is complicated GeV-scale dark in sector mass that and contains additional thermally light produced, mediator tainties associated with neutrino oscillationit measurements great but power these in capabilitiesModel. searching also The for lend DUNE new MPD light( is physics ideally suited that to is searchthat weakly for they new coupled have particles to a that the long are Standard light lifetime enough ( It is proposed that the DUNEdetector near consisting detector facility of will a include a high-pressurenetic magnetized gaseous multi-purpose calorimeter. argon TPC withtracking, The a and components surrounding momentum of electromag- resolution,down the and to low MPD the energies. HPTPC allow The enables primary for measurements purpose good of of the particles particle MPD is identification, to control the systematic uncer- 8 Conclusions JHEP02(2020)174 σ ϕ ) through is a Dirac 6 N mixing with SM neutrinos N coupling. The magnetic field µ ) decays, it is possible to achieve 3 and vector mass below 10 MeV, DUNE 4 − e, µ = ` ( and 10 – 54 – , 6 + − π ). The possible search channels for a heavy neutral − 7 ` → N events. Should a leptonic resonance be discovered at DUNE, the and − e − + π e + 400 MeV, DUNE can make considerable improvements over existing ` → ∼ < → V ϕ N M ∼ < with gauge coupling between 10 coupling, and by up to two orders of magnitude for τ L τ All the portal models that we have studied have signals that can be separated from The final portal we considered was heavy neutral leptons The scalar portal coupling between the SM Higgs boson and a SM-singlet scalar − or µ Acknowledgments We thank Gordan Krnjaicsearches contained and in Martin this work. Bauer We for are clarification extremely grateful on to different Laura Fields, new Mary physics Bishai, and between new physics models,for signal-background means separation that and taking modelpotential data discrimination. at here, We multiple have leaving angles notin should it investigated allow this the for DUNE future nearnew work. physics detector models, complex Overall, enhancing will the themeasurements. physics provide inclusion program superb of of DUNE sensitivity a beyond to gaseous neutrino a oscillation detector broad class of model hypotheses, should an excessbe be improved found, if or pions to andthe rule muons inclusion out could of more be parameter effectively awhole space, distinguished. near muon would Thus, detector tagger we system, outsidemade advocate including for of both the the off- MPD, ECAL. and movable, There on-axis. allowing are measurements The proposals to different be to kinematics make of the signal and background events, neutrinos from kinematics alone,will as be more is challenging. necessary for final statesbackgrounds involving by SM taking advantage neutrinos, of amass combination cuts, of pointing final-state and particle particle energies, identification. invariant The ability of DUNE to distinguish between e acting on the MPDnumbers allows of good charge identificationdiscrimination and between we the find Diracdata that, and taken from the Majorana in relative neutrino fermion mode. hypotheses, after We five predict years that of learning the Dirac/Majorana nature of through the neutrino portallepton (section (HNL) include two-fermion and (and three-body thus lepton decays, number andwith is depend couplings conserved) to or on a only whether potential Majorana one to fermion. lepton improve flavor Considering upon at HNLs existing a bounds time, by we up find to that an the order DUNE of MPD magnitude, has in the the case of to the vector models,particle the identification scalar capabilities decays will50 to be MeV the a heaviest greatbounds state by benefit searching available for for and aor model thus, resonance pions. discrimination. in again, the invariant For mass distributions of charged leptons could see 3–10 ability to distinguish electrons from muons/pions will give excellentleads model to discrimination. scalar-Higgs mixing anda allows loop for production decay of of light scalars kaons. (section Although the kinematics of production and decay are similar L JHEP02(2020)174 pp . 5 and 6 6 6 6 pn − − − − 4 10 10 10 10 2.5 2.6 × × × × 0.23 0.16 2.89 0.33 0.19 0.19 7 2 2 7 . . . . , providing more 3 6 1 1 120 GeV . We also compare 3 6 6 6 6 pp − − − − for the production. We 10 10 10 10 2.8 2.2 × × × × 0.24 0.15 2.86 0.32 0.18 0.18 Pythia8 6 7 1 5 . . . . 3 5 1 1 120 GeV Pythia8 6 6 7 7 − − − − pn meson production differs, roughly, by s 10 10 10 10 2.2 2.2 × × × × 0.19 0.12 2.52 0.28 0.16 0.16 4 8 4 7 . . . . D/D 1 2 4 6 80 GeV flag within 6 6 7 7 – 55 – pp − − − − 10 10 10 10 28 . 2.5 1.9 × × × × 0.21 0.12 2.49 0 0.15 0.15 1 3 8 3 . . . . 80 GeV 1 2 2 4 211 321 411 431 ‘‘SoftQCD:all’’ 211 321 411 431 111 221 130 310 − − − − Particle ID we see that light meson production rates are around 10% larger for a 6 0 0 S + L − + + − − 0 s s + − η π π π K K D D D D K K lists the number of mesons produced per proton-on-target under several as- 6 . Average number of mesons produced per proton-on-target assuming 80 or 120 GeV Meson Type results, assuming an isoscalar target. This leads to the results in tables pn From table Table protons or neutrons, howeverexpected the number resulting of output mesons isand per similar proton-on-target, in both for our cases. simulations, To we obtain average an 120 the GeV beam than for an 80 GeV beam, while sumptions, all using the provide the associated Particleeach ID with for 80 clarity. GeV We protonspected perform and to four 120 GeV separate be protons. simulations; graphite, two Because we the perform DUNE-LBNF target simulations is assuming ex- the protons are hitting either A Meson production detailsIn and beam this energy appendix, comparison detail we regarding expand the on meson theresults production for simulations rates an discussed extracted 80 GeV inare from proton under section beam consideration with by the those DUNE for collaboration. a 120 GeV proton beam, both of which Neutrino Physics Center forwork of their AdG hospitality is supported duringBJK, in the part KJK, by completion and DOE of OfficeDE-AC02-07CH11359 JLR of with this are Science the work. award U.S. supported #DE-SC0010143. Dept. by PJF, The of Fermi Energy. Research Alliance, LLC under Contract and the entire DUNE Beammeson Interface distributions Working in Group the for DUNE providingof beamline. files Science regarding The awards charged work DE-SC0018327 of and JMBand DE-SC0020262, is as by supported well by Heising-Simons as DOE NSF Office Foundation Grant Grant PHY-1630782 2017-228. JMB further thanks the Fermilab Table 6 protons striking protons or neutrons. See text for more detail. JHEP02(2020)174 ] . = νV 149 23 (B.1) (B.2) s ` ). V + → 13 s . and the final m , . We refer to ) + + 3 νV P ` , p + ) ( 12 ` 3 s ∗ β ) ) 1 ) to future work. 3 p ) p p 2 ( ( ( → p α 7 ( + ∗ β V ℓ ν P + (vector boson α i m 3 1 P p p i v 1 β p is the relevant quark mixing , respectively. These matrix γ v ` 0 ℓ L qq µ is the new vector boson’s gauge ), and P M M would be unchanged. All results V α α m V ν 6 γ g − and ν 3 / p or the charged lepton , and ν m ) m decay channel). + α by using the identity P + decays — see section ( M ν 1 + / 3 V p / m p 13 (neutrino µ s ν K L 2 + ) ) 1 p 3 p P ) ) – 56 – 2 p ( 2 2 ( µ / p p α p + ( ( ℓ ), V γ ν ν and 2 + → β p ` γ u 2 π h p K 0 u ) h qq 3 is the Fermi constant, 0 ν p V ) · 2 m qq 3 M 1 p V F , and eliminate p · m F 2 ) 2 F GeV G j p 5 F 2 p + 2( current relied on production via charged meson decay, − G √ ) (charged lepton + 2 . Feynman diagrams contributing to the process 2 V β P V 10 + 2( ( i 1 L g + √ M p p 2 V m 2 × ( V − g M α we show the two Feynman diagrams that contribute to this decay, in which − 2 16 ≡ . L is the decay constant of the meson = = 32 ij , many of our results for the sensitivity to the leptophilic vector bosons associ- ` m Figure 32 ν s = 1 F 5 M F M i i G After squaring the total matrix element, we express kinematical factors in terms of In figure Finally, we note that the DUNE collaboration is also exploring a “high-energy” beam is emitted by either the final-state neutrino coupling, matrix element for thisstate decay. momenta We as label the initial meson momentuminvariants as where for a version of this result for the V the matrix elements ofelements may these be two expressed diagrams as as B Derivation of chargedIn meson section decays into leptophilicated with vector the bosons In this appendix, we provide a derivation for the partial width of such a decay (see ref. [ we present regarding new physics particleslived being mesons produced would in be thebeam decay unchanged. operation of with neutral We new or leave physics short- studies particlesheavy coming neutral regarding from leptons the long-lived, coming charged results mesons from (mostly of high-energy that the sensitivity to differentless types of powerful new than physics that with with an a 80 GeV 120 GeV beam beam wouldconfiguration, be but mildly in the differences which will thetrinos. be Standard minor. This Model configuration neutrinobeam is flux energy obtained consists or by of target changing composition, higher the meaning energy focusing that neu- table magnets, not the proton a factor of two. Wesamples also and explored find the energy them distributions to of be outgoing largely mesons similar. in these Combining two these two differences, we expect JHEP02(2020)174 ]. ), is . = ≡ , z π 2 12 νV S S (B.5) (B.6) (B.7) (B.8) (B.3) (B.4) 149 ) s , in the m y ) , + − µ 2 m 23 28 12 − 2 2 , s . s 1) y y → i y, 25 ) xm − − , is helicity- − − d . y. ν 2 12 z 2 y V 2 and ≡ ) s K + 68 MeV, ) + (1 ]. )d xy xy 2 ` . )d ` i + M y 2 2 V + 12 2 wy 2 ) m 64 ) s y w + analytically, giving 2 V M y ) + ) + 12 → − − 2 ` )( s z , ) w w (1 + M − y w, x, y 2 2 = 493 + V 2 m m 2 ` ( ) − w − − ) m + 2 M m w, x, y, z w 2 K V (3) w )(2 ( ( . In this parametrization, x wm − ( 2 m L y m )(1 )(1 − 12 M (4) ) + (1 2 2 y y s ≡ + 2 m ) y + ) + 2 L + w w + + 2 ` x − 2 V 2 + 2 m + (1 √ z p + 2 − x x , the integration region for )( 2 m V w ) z ( ( M − m y x (1 + w 1 4 m . Z x ( M ( ). The relevant constants for this )( + 2 w x 13 MeV, x m − ) . − 2 m 2 2 ` Z 33 ) + 2 w )( + ( − first before y νV log m y (1 2 ` m − √ ( w 12 ( 2 z V ) − 2 s e m − y − xy − ≡ z 12 ) (1 m M w 2 ` + 2 = 127 s x − x z ]. The branching fractions of these decays, 0, the matrix element squared is x 2 m S 2 2 − → m | Z m p 2 can be expressed as y V − ( ) may be integrated over 64 2 y m − 2 ` → − ud

2 V 0 ) M 2 3 (2 V ν − 4 m π (1 + . For a given V – 57 – | ) y x qq νV π M + 2 2 w m π z + x m 1) + ) V h M 2 +

− + F 4 m 16 ` 2 m 2 m w − − ) 2 1 m + 2 − m w y

m y √ w w, x, y, z 0. For scalar emission, that is not the case [ ), Br( F 0 ) → 4 ` 23 ( . Deﬁning (1 + ( 3 2 ` ) s y 2 F z y y − qq − π m 2 23 23 x m → + 3 (4) = 511 keV [ νV 1)(2 V G s s − x − )d

m 2 ` 16 L x e − 2 V

2 − 0 − + + 2 m , are depicted in ﬁgure g µ 12 09 MeV, (2 m y 3 2) + 2( . m s F qq V y 1)( w y − g (1 + ( V 2 F 2 and (1 →

− − x − ) = G 2 ) + ( + m 2 2 V x y ], this process, like the two body decay = 35 + 2 V y w, x, y, z F g ( π νV | w M + 2 F ( + . Taking the limit 149 us ) = . We choose to integrate over (4) ` 2 G + V w w x V 2 m ( L ( | ) = 2 2 V 2 m for small M g → + w K ), Br( − = 105 MeV, z m + ym h z 2 V S F νV + 16 µ R g y 2 ν νV 1 ≡ m ` 2 2 23 m ≡ w, x, y, z ) = m s ( Γ( e 23 ) ], where = → s + = + (4) 2 ` → 2 L z , z m m w, x, y − ( w, x, y z , and We use this result to calculate the branching fractions of interest: Br( The dimensionless function Hence, the partial width of To obtain the partial width for this decay, we must integrate over Γ( 57 MeV, [ ( |M| + . K 2 m (3) is integrated between 2 m ∈ (3) L Br( calculation are 139 which scale as The final width then is L where These ranges are determined by the Dalitz criteria, as described in ref. [ zm y z As observed in ref.suppressed and [ vanishes when kinematically allowed regions. It is convenient to define m JHEP02(2020)174 ]. SPIRE via the decays IN 3 ]. − ][ 1 , talk given at the νV νV νV νV (2018). ]. ± ± ]. ± ± µ e = 10 µ e SPIRE → → (2018). IN → → V ± ± ± ± g ][ K K π π SPIRE SPIRE , December 8–10, Madison Zenodo IN , IN [ (2013) 114015 ][ Zenodo (2018). , 1 arXiv:1205.3499 ]. − [ D 88 10 New electron beam-dump experiments to Zenodo , production for SPIRE IN arXiv:1107.4580 [ V [ [GeV] . V Observing a light dark matter beam with neutrino arXiv:1211.2258 Phys. Rev. e Signatures of sub-GeV dark matter beams at arXiv:0906.5614 , (2012) 035022 , M [ – 58 – = ` Exploring portals to a hidden sector through fixed 2 − D 86 10 (2011) 075020 ]. ), which permits any use, distribution and reproduction in Low mass WIMP searches with a neutrino experiment: a arXiv:1807.10334 (2009) 095024 D 84 , SPIRE The DUNE far detector interim design report. Volume 1: physics, Phys. Rev. , IN D 80 ][ and dashed are for 3 CC-BY 4.0 − µ 5 6 7 8 9 High-pressure gaseous argon in the DUNE near detector 10 11 12 10

− − − − − collaboration,

= − − − This article is distributed under the terms of the Creative Commons Phys. Rev. Near detector needs for long-baseline physics High-pressure gas TPC for DUNE near detector

10 10 10 10 10 →

10 10 10

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