CONNECTING NEUTRON-ANTINEUTRON OSCILLATION TO BARYOGENESIS

2019 International Workshop on Baryon and Lepton Number Violation (BLV2019)

BIBHUSHAN SHAKYA

based on hep-ph 1806.00011 (PRL) with Christophe Grojean, James D. Wells, Zhengkang Zhang hep-ph 1901.05493 (JHEP) with Aaron Pierce

1 PHYSICALPHYSICAL REVIEW REVIEW LETTERS LETTERS121,121,171801171801 (2018) (2018)

nf realizedrealized in a in similar a similar manner manner in more in more complex complex and andrealistic realisticHere αð Þ isnf the effective strong coupling with n light Heres αsð Þ is the effective strong coupling withf nf light theoriestheories—that—that are compatible are compatible with with an n- ann¯ oscillationn-n¯ oscillation signal signal quarkquark flavors, flavors, whose whose value value is obtained is obtained with with the R theUN RDUNECDEC withinwithin experimental experimental reach reach (for (for discussions discussions of some of some other otherpackage [58]. Corrections from two-loop running as well as baryogenesis scenarios that can also involve n-n¯ oscillation package [58]. Corrections from two-loop running as well as baryogenesis scenarios that can also involve n-n¯ oscillationone-loopone-loop matching matching onto onto lattice lattice QCD QCD operators operators were were signals, see, e.g., [25–43]). signals, see, e.g., [25–43]). recentlyrecently computed computed[56][56]andand are small, are small, and and they they will will be be ImprovedImprovedNEUTRON-ANTINEUTRONn-n¯ noscillation-n¯ oscillation searches searches and and sensitivity sensitivity OSCILLATION: to the to theneglected in our calculations. No additional operators rel- — neglected in our calculations. No additional operators rel- scalescale of new of new physics. physics.Neutron-antineutron—Neutron-antineutron oscillation oscillation has hasevant for n-n¯ oscillation are generated from RG evolution. been searchedEXPERIMENTAL for in the past with both STATUS free neutrons evant for n-n¯ oscillation are generated from RG evolution. been searched for in the past with both free neutrons The Then →nn¯→transitionn¯ transition rate rate is determined is determined by the by matrix the matrix [6,44,45][6,44,45]andand neutrons neutrons bound bound inside inside nuclei nuclei[7,46[also [7,46see–50] Yuri–. 50]Kamyshkov’s.element talk of (Monday)] the low-energy effective Hamiltonian between the Among free neutron oscillation searches, the Institut element of the low-energy effective Hamiltonian between the Among• freewith neutron free neutrons: oscillation Institut searches, Laue-Langevin the Institutneutron (ILL) and antineutron states. Thus, once n¯ O μ n are Laue-Langevin experiment [6] sets the best limit to date neutron and antineutron states. Thus, once nn¯n¯ O0nn¯ μ0 n are Laue-Langevin experiment [6] sets the best limit to date −h1 j h1 jð Þjð i Þj i 8 known, we can relate τnn¯ n¯ Heff¯ n to− the six-quark on the oscillation time, τ > 0.86 × 10 s at8 90% C.L. known, we can relate¼τnnjh¯ j n jHijeff n to the six-quark on the oscillation time,nn¯ τnn¯ > 0.86 × 10 s at 90% C.L.operator coefficients. Recent progress¼ jh j in latticej ij calculations Among intranuclear searches, Super-Kamiokande (Super-K) operator coefficients. Recent progress in lattice calculations Among intranuclear searches, Super-Kamiokande (Super-K)[59–61] has greatly improved the accuracy on n¯ O μ n [7] provides• the best limit,intranuclear which, after correcting searches: for Super-K nuclear [59–61] has greatly improved the accuracyh onj nn¯n¯ ðO0nÞn¯j μi0 n [7] provides the best limit, which, after correcting for nuclearcomparedcompared to previous to previous bag model bag model calculations calculations[53,54]h[53,54]j oftenð oftenÞj i effects, corresponds to τ > 2.7 × 108 s at8 90% C.L. for the effects, correspondsn ton¯ τnn¯ > 2.7 × 10 s at 90% C.L. for theused in the literature. Using the central values presented in free neutron oscillation time. Improved n-n¯ oscillation used in the literature. Using the central values presented in free neutron oscillation time. Improved n-n¯ oscillation[61],[61] and, and assuming assuming that that the operator the operator in Eq. in(1) Eq. gives(1) gives the the searchessearches with with both both free free and and bound bound neutrons neutrons are areunder underdominant contribution to n-n¯ oscillation, we can translate the 9–10 dominant contribution to n-n¯ oscillation, we can translate the consideration, with sensitivities up to 10 9s–10 envisioned 1 consideration, with sensitivities up to 10 s envisioned 1 5 5 Upcoming experiments will improve on sensitivitySuper-KSuper-K by limit limit into intoΛðnn¯Þ ð 3Þ.8 ×3.108 × GeV10 GeV (for a (for representa- a representa- at theat ESS the ESS and andDUNE DUNE[8–12][8. 12]. Λ≳nn¯ up to –three orders of magnitude tive RG rescaling factor of 0.7).≳ An improvement on τnn¯ up We now elucidate the connection between τnn¯ and the tive RG rescaling factor of 0.7). An improvement on τnn¯ up We now elucidate the connection between τnn¯ and the 9 10 11 1 to 10 109 ; 1010 s11 will correspond to probing ð Þ ∼ 1 newnew physics physics• scale scale in theEuropean in EFT the EFT context. Spallation context. The The lowest Source lowest dimen- dimen- (ESS) to 10 10 ; 10 s will correspond to probingΛnn¯ Λðnn¯Þ ∼ ð ð Þ5 Þ sionsion effective effective operators operators contributing contributing to n to-n¯ noscillation-n¯ oscillation at at4.9 74..89; 127.8.4; 12×.410× GeV.105 GeV. These These numbers numbers are representative are representative • ð ð Þ Þ tree level areDeep dimension-9 Underground operators Neutrino of the form ExperimentOnn¯ ∼ of(DUNE) theof whole the whole set of setn of− nn¯ oscillationn¯ oscillation operators operators and doand not do not tree level are dimension-9 operators of the[see form GeorgiaOn Karagiorgi’sn¯ ∼ talk (Monday)] − uudddd . The classification of these operators dates back varyvary significantly significantly with with the starting the starting point point of RG of evolution RG evolutionM M ð uuddddÞ . The classification of these operators dates back to thetoð 1980sthe 1980sÞ[51–[5155] 55]andand was was refined refined recently2 recently in [56] in ,[56],(see(see the Supplemental the Supplemental Material Material[57][57]for details).for details). – — whichwhich established established an alternative an alternative basis basis that that is more is more con- con- A minimalA minimal EFT EFT for n for-n¯ oscillationn-n¯ oscillation and and baryogenesis. baryogenesis.— venientvenient for renormalization for renormalization group group (RG) (RG) running. running. A concise A conciseOneOne of the of simplest the simplest possibilities possibilities for generating for generating the operator the operator in Eq. (1) at tree level is with a Majorana fermion X of mass reviewreview of the of full the set full of set tree-level of tree-leveln-n¯ oscillationn-n¯ oscillation operators operators in Eq. (1) at tree level is with a Majorana fermion X of mass is given in the Supplemental Material [57]. In what follows, M thatM couplesthat couples to the to SM the via SM a via dimension-6 a dimension-6 operator operator of the of the is given in the Supplemental Material [57]. In what follows, 2 we focuswe focus on one on one of these of these operators operators for illustration, for illustration, formform1=Λ1=XuddΛ2 Xudd, which, which originates originates at an at even an even higher higher scale scale ð ð Þ Þ Λ ≫ΛM≫viaM somevia some UV completionUV completion that thatwe remain we remain agnostic agnostic 1 about. A familiar scenario that realizes this EFT setup is 1 c c ¯ c about. A familiar scenario that realizes this EFT setup is L ⊃ c1 ϵijkϵi j k u¯ i PRdcj u¯ PRdcj d PR¯dck L ⊃ c1 ϵ0ijk0 0ϵi j k u¯ i PRdij0 u¯ P0 Rdjk d P0 Rdk supersymmetry (SUSY) with R-parity violation (RPV), 2 2 ð 0 0 0 ð Þð Þð i0 Þð 0 Þð k Þ 0 Þ supersymmetry (SUSY) with R-parity violation (RPV), where the bino plays the role of X and the dimension-6 H:c:;H:c:; where the bino plays the role of X and the dimension-6 þ þ operatoroperator is obtained is obtained by integrating by integrating out squarks out squarks at a heavier at a heavier 1 −51 with c1 Λðnn¯Þ : −5 1 scale. However, this simple EFT with a single BSM state with ≡cð1 ÞΛðnn¯Þ : ð Þ 1 scale. However, this simple EFT with a single BSM state ≡ ð Þ ð Þdoesdoes not allow not allow for sufficient for sufficient baryogenesis baryogenesis due todue unitarity to unitarity HereHereu, duare, d SMare SM up and up and down down quark quark fields, fields, respectively, respectively,relations:relations: in the in absence the absence of B-conserving of B-conserving decay decay channels, channels,X X c c decay cannot generate a baryon asymmetry at leading order and uand, ducare, dc theirare their charge charge conjugates. conjugates.ið0Þ, jið0Þ,, kjð0Þ,arek colorare color decay cannot generate a baryon asymmetry at leading order ð0Þ ð0Þ ð0Þ in the B-violating coupling, a result known as the indices,indices, and and“H.c.“”H.c.denotes” denotes Hermitian Hermitian conjugate. conjugate. The The in the B-violating coupling, a result known as the 1 1 Nanopoulos-Weinberg theorem [62] (see [63] for a recent operator suppression scale Λðnn¯Þ is generally a weighted Nanopoulos-Weinberg theorem [62] (see [63] for a recent operator suppression scale Λð ¯Þ is generally a weighted ¯ ¯ (geometric) average of new particlenn masses, modulo discussion);discussion); meanwhile, meanwhile,2 →22→processes2 processesuX →uXd→d andd¯ d¯ and (geometric) average of new particle masses, modulouX¯ → dd are forced to have the same rate and thus do not appropriateappropriate powers powers of couplings of couplings and and loop loop factors. factors. uX¯ → dd are forced to have the same rate and thus do not If the operator is generated by integrating out new violateviolateCP. CP. If the operator is generated by integrating out new A minimal extension that can accommodate both n-n¯ particles at a high scale M, computing τnn¯ requires RG A minimal extension that can accommodate both n-n¯ particles at a high scale M, computing τnn¯ requires RGoscillation and the observed baryon asymmetry involves evolving the EFT down to a low scale μ0 (usually chosen to oscillation and the observed baryon asymmetry involves evolving the EFT down to a low scale μ0 (usually chosen to two Majorana fermions X1, X2 (with MX gluino in addition to the bino, which is known to allow for ð Þð Þ ð s Þ 0  ð s Þ b  ð s Þ t  gluino in addition to the bino, which is known to allow for ð Þ ð Þ ð Þ sufficient baryogenesis [63–65]. 0.7260.;7260.684; 0.;6840.651; 0.;6510.624; 0.624 sufficient baryogenesis [63–65]. ¼ f g Guided by minimality, we assume that X1;2 are both ¼ 3f 4 5 6 g Guided by minimality, we assume that X1;2 are both for Mfor M 10 ;10103;;10104;;10105; 10GeV6 GeV: : 2 2 SM singlets and consider just one of the many possible ¼ f ¼ f g g ð Þ ð Þ SM singlets and consider just one of the many possible

171801-2171801-2 PHYSICAL REVIEW LETTERS 121, 171801 (2018)

Implications of an Improved Neutron-Antineutron Oscillation Search for Baryogenesis: A Minimal Effective Theory Analysis

Christophe Grojean,1,2 Bibhushan Shakya,3,4 James D. Wells,4 and Zhengkang Zhang4 1Deutsches Elektronen-Synchrotron (DESY), 22607 Hamburg, Germany 2Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany 3Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA 4Leinweber Center for Theoretical Physics (LCTP), University of Michigan, Ann Arbor, Michigan 48109, USA (Received 19 July 2018; revised manuscript received 26 September 2018; published 23 October 2018)

Future neutron-antineutron (n-n¯) oscillation experiments, such as at the European Spallation Source and the Deep Underground Neutrino Experiment, aim to find first evidence of baryon number violation. We investigate implications of an improved n-n¯ oscillation search for baryogenesis via interactions of n-n¯ mediators, parametrized by an effective field theory (EFT). We find that even in a minimal EFT setup there is overlap between the parameter space probed by n-n¯ oscillation and the region that can realize the observed baryon asymmetry of the Universe. The mass scales of exotic new particles are in the tera- electron-volt–peta-electron-volt regime, inaccessible at the LHC or its envisioned upgrades. Given the innumerable high energy theories that can match, or resemble, the minimal EFT that we discuss, future n-n¯ oscillation experiments could probe many viable theories of baryogenesis beyond the reach of other experiments.

DOI: 10.1103/PhysRevLett.121.171801

NEUTRON-ANTINEUTRON OSCILLATION: Introduction.—The search for physics beyond the stan-THEORETICALin an effective MOTIVATION field theory (EFT), where B-violating, dard model (BSM) requires effort at both high energy and L-conserving interactions can appear first at the intensity frontiers. In this regard, a particularly powerful• dimension-9a test of level baryon[3] ,number in the violation form of ΔB 2, ΔL 0 probe is offered by rare processes that violate (approxi- operators. In this case, neutron-antineutronj (nj -¼n¯) oscillation¼ mate) symmetries of the SM, such as baryon and lepton• complementary(see Ref. [4] tofor proton a recent decay: review) probes is wellbaryon placed number to search for numbers (B and L), which can be inaccessible to high B-violatingviolation without phenomena lepton and number shed light violation on baryogenesis [5]. energy colliders but within reach of low-energy experi- Current measurements constrain the free neutron oscil- • n − n¯ effective operator is dimension8 9: probes new physics ments. A well-known example is proton decay, whose lation time to be τnn¯ 10 s [6,7]. Upcoming experiments, at a relatively low scale that≳ could give companion signals nonobservation leads to strong constraints on ΔB ΔL in particularat at other the European experiments Spallation Source (ESS) and 1 new physics even at the scale of grand unified¼ theories¼ also potentially the Deep Underground Neutrino Æ • (GUTs), ∼1016 GeV [1,2]. baryonExperiment number violation (DUNE), intricately are poised tied to to improvean important the reach up 9–10 Baryon and lepton number violation are intricately tied to 10 earlys [8 Universe–12]. As phenomenon: we will see in detail below, to one of the outstanding puzzles in fundamental physics, such numbers baryogenesis translate into new physics scales of roughly 6 1=5 5–6 the origin of the baryon asymmetry in the Universe. If τnn¯ Λ ∼ O 10 GeV , well above the energies ð QCDÞ ð Þ baryogenesis occurs at temperatures above the weak scale, directly accessible at existing or proposed colliders. B-L violation is required to avoid washout by electroweak Discussions of the physics implications of a potential sphalerons. In this regard, constraints from proton decay n-n¯ oscillation discovery,3 in particular for baryogenesis, (which conserves B − L) are not applicable. Here we are therefore both important and timely. consider instead B-violating, L-conserving new physics The purpose of this Letter is to explore the connection at an intermediate (sub-GUT) scale so that baryogenesis between n-n¯ oscillation and baryogenesis in the context of may proceed both above and below weak scale temper- a minimal EFT extension of the SM that realizes direct low atures. From the low-energy point of view, effects of heavy scale baryogenesis from B-violating decays of new par- new particles are encoded in higher dimensional operators ticles mediating n-n¯ oscillation. While there exist numerous baryogenesis frameworks, such as electroweak baryogen- esis [13], Affleck-Dine baryogenesis [14], and leptogenesis [15] (see, e.g., [16–24] for reviews), the choice of our Published by the American Physical Society under the terms of minimal EFT is motivated from the bottom up by imminent the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to improvements in n-n¯ oscillation searches. Despite being the author(s) and the published article’s title, journal citation, simplistic, this minimal setup provides a useful template and DOI. Funded by SCOAP3. to identify viable baryogenesis scenarios—which may be

0031-9007=18=121(17)=171801(7) 171801-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 121, 171801 (2018)

Implications of an Improved Neutron-Antineutron Oscillation Search for Baryogenesis: A Minimal Effective Theory Analysis

Christophe Grojean,1,2 Bibhushan Shakya,3,4 James D. Wells,4 and Zhengkang Zhang4 1Deutsches Elektronen-Synchrotron (DESY), 22607 Hamburg, Germany 2Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany 3Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA 4Leinweber Center for Theoretical Physics (LCTP), University of Michigan, Ann Arbor, Michigan 48109, USA (Received 19 July 2018; revised manuscript received 26 September 2018; published 23 October 2018)

Future neutron-antineutron (n-n¯) oscillation experiments, such as at the European Spallation Source and the Deep Underground Neutrino Experiment, aim to find first evidence of baryon number violation. We investigate implications of an improved n-n¯ oscillation search for baryogenesis via interactions of n-n¯ mediators, parametrized by an effective field theory (EFT). We find that even in a minimal EFT setup there is overlap between the parameter space probed by n-n¯ oscillation and the region that can realize the observed baryon asymmetry of the Universe. The mass scales of exotic new particles are in the tera- electron-volt–peta-electron-volt regime, inaccessible at the LHC or its envisioned upgrades. Given the innumerable high energy theories that can match, or resemble, the minimal EFT that we discuss, future n-n¯ oscillation experiments could probe many viable theories of baryogenesis beyond the reach of other experiments.

DOI: 10.1103/PhysRevLett.121.171801

NEUTRON-ANTINEUTRON OSCILLATION: Introduction.—The search for physics beyond the stan-THEORETICALin an effective MOTIVATION field theory (EFT), where B-violating, dard model (BSM) requires effort at both high energy and L-conserving interactions can appear first at the intensity frontiers. In this regard, a particularly powerful• dimension-9a test of level baryon[3] ,number in the violation form of ΔB 2, ΔL 0 probe is offered by rare processes that violate (approxi- operators. In this case, neutron-antineutronj (nj -¼n¯) oscillation¼ mate) symmetries of the SM, such as baryon and lepton• complementary(see Ref. [4] tofor proton a recent decay: review) probes is wellbaryon placed number to search for numbers (B and L), which can be inaccessible to high B-violatingviolation without phenomena lepton and number shed light violation on baryogenesis [5]. energy colliders but within reach of low-energy experi- Current measurements constrain the free neutron oscil- • n − n¯ effective operator is dimension8 9: probes new physics ments. A well-known example is proton decay, whose lation time to be τnn¯ 10 s [6,7]. Upcoming experiments, at a relatively low scale thatTHIS≳ could give TALK companion signals nonobservation leads to strong constraints on ΔB ΔL in particularCanat at upcomingother the European experiments Spallation searches Source shed (ESS) and ¼ ¼ n − n¯ 1 new physics even at the scale of grand unified theories also potentiallylight on the viable Deep baryogenesis Underground Neutrino Æ 16 • baryonExperiment number violation (DUNE), intricately are poised tied to to improvean important the reach up (GUTs), ∼10 GeV [1,2]. mechanisms? Can the new physics to 109–10earlys [8 Universe–12]. As phenomenon: we will see in detail below, Baryon and lepton number violation are intricately tied that gives rise to n − n¯ also be to one of the outstanding puzzles in fundamental physics, such numbers baryogenesis translate into new physics scales of roughly 6 1=responsbile5 5–6 for baryogenesis? the origin of the baryon asymmetry in the Universe. If τnn¯ Λ ∼ O 10 GeV , well above the energies ð QCDÞ ð Þ baryogenesis occurs at temperatures above the weak scale, directly accessible at existing or proposed colliders. B-L violation is required to avoid washout by electroweak Discussions of the physics implications of a potential sphalerons. In this regard, constraints from proton decay n-n¯ oscillation discovery,4 in particular for baryogenesis, (which conserves B − L) are not applicable. Here we are therefore both important and timely. consider instead B-violating, L-conserving new physics The purpose of this Letter is to explore the connection at an intermediate (sub-GUT) scale so that baryogenesis between n-n¯ oscillation and baryogenesis in the context of may proceed both above and below weak scale temper- a minimal EFT extension of the SM that realizes direct low atures. From the low-energy point of view, effects of heavy scale baryogenesis from B-violating decays of new par- new particles are encoded in higher dimensional operators ticles mediating n-n¯ oscillation. While there exist numerous baryogenesis frameworks, such as electroweak baryogen- esis [13], Affleck-Dine baryogenesis [14], and leptogenesis [15] (see, e.g., [16–24] for reviews), the choice of our Published by the American Physical Society under the terms of minimal EFT is motivated from the bottom up by imminent the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to improvements in n-n¯ oscillation searches. Despite being the author(s) and the published article’s title, journal citation, simplistic, this minimal setup provides a useful template and DOI. Funded by SCOAP3. to identify viable baryogenesis scenarios—which may be

0031-9007=18=121(17)=171801(7) 171801-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 121, 171801 (2018) realized in a similar manner in more complex and realistic nf Here αsð Þ is the effective strong coupling with nf light theories—that are compatible with an n-n¯ oscillation signal quark flavors, whose value is obtained with the RUNDEC within experimental reach (for discussions of some other packagePHYSICAL[58]. Corrections REVIEW LETTERS from two-loop121, 171801 running (2018)PHYSICAL as well as REVIEW LETTERS 121, 171801 (2018) baryogenesis scenarios that can also involve n-n¯ oscillation one-loop matching onto lattice QCD operators were nf realized in a similar manner in more complex and realistic Here αð Þ is the effective strong coupling with n light signals, see, e.g., [25–43]). realized in a similar manner in more complex and realistic nf s f recently computed [56]theoriesand—that areHere are small,α compatiblesð Þ is and the with they effective an willn-n¯ oscillation strong be coupling signal with nf light Improved n-n¯ oscillation searches andtheories sensitivity—that are to compatible the with an n-n¯ oscillation signal quark flavors, whose value is obtained with the RUNDEC neglected in our calculations.within experimental Noquark additional flavors, reach (for whose operators discussions value rel- is of obtained some other with thepackage RUND[58]EC. Corrections from two-loop running as well as — within experimental reach (for discussions of somebaryogenesis other scenarios that can also involve n-n¯ oscillation scale of new physics. Neutron-antineutron oscillation has evant for n-n¯ oscillation are generatedpackage [58] from. Corrections RG evolution. from two-loop runningone-loop as well as matching onto lattice QCD operators were baryogenesis scenarios that can also involve n-n¯ oscillationsignals, see, e.g., [25–43]). been searched for in the past with both free neutrons The n → n¯ transition rate isone-loop determined matching by the onto matrix lattice QCD operatorsrecently were computed [56] and are small, and they will be signals, see, e.g., [25–43]). Improvedrecentlyn-n¯ oscillation computed searches[56] andand sensitivity are small, to the and theyneglected will be in our calculations. No additional operators rel- [6,44,45] and neutrons bound inside nuclei [7,46–50]. scale of new physics.—Neutron-antineutron oscillation has Improved n-n¯ oscillationelement searches of and the sensitivity low-energy to the effectiveneglected Hamiltonian in our calculations. between the No additional operatorsevant for rel-n-n¯ oscillation are generated from RG evolution. Among free neutron oscillation searches, the Institut— been searched for in the past with both free neutrons scale of new physics. Neutron-antineutronneutron and antineutron oscillation states. has Thus,evant once for n-n¯n¯oscillationOnn¯ μ0 aren are generated from RG evolution.The n → n¯ transition rate is determined by the matrix Laue-Langevin experiment [6] sets thebeen best searched limit to for date in the past with both free neutrons[6,44,45] and neutrons−h1 boundj ð insideÞj nucleii [7,46–50]. element of the low-energy effective Hamiltonian between the 8 known, we can relateAmongτnn¯ freen¯ HThe neutroneff nn → oscillationn¯totransition the six-quark searches, rate is the determined Institut by the matrix on the oscillation time, τnn¯ > 0.86 × [6,44,45]10 s atand 90% neutrons C.L. bound inside nuclei [7,46–50]¼. jh j j ij neutron and antineutron states. Thus, once n¯ Onn¯ μ0 n are operator coefficients. RecentLaue-Langevin progresselement experiment in of the lattice low-energy[6] calculationssets the effective best limit Hamiltonian to date between the Among free neutron oscillation searches, the Institut known, we can relate τ n¯ H n −h1 toj theð six-quarkÞj i Among intranuclear searches, Super-Kamiokande (Super-K) on the oscillationneutron time, and antineutronτ > 0.86 × states.108 s Thus, at 90% once C.L.n¯ O μ n are nn¯ eff Laue-Langevin experiment[59[6]–sets61] thehas best greatly limit improved to date the accuracy onnn¯ n¯ Onn¯ μ0 n nnoperator¯ 0 coefficients. Recent¼ jh progressj j inij lattice calculations [7] provides the best limit, which, after correcting for nuclear Among intranuclear searches,h Super-Kamiokandej ð Þj i (Super-K)−h1 j ð Þj i compared to8 previous bag modelknown, calculations we can relate[53,54]τnn¯ oftenn¯ Heff n to the[59 six-quark61] has greatly improved the accuracy on n¯ O μ n 8 on the oscillation time, τnn¯ > 0.86 × 10 s at 90% C.L. ¼ jh j j ij – nn¯ 0 effects, corresponds to τnn¯ > 2.7 × 10 s at 90% C.L. for the [7] providesoperator the best limit, coefficients. which, after Recent correcting progress for nuclear in lattice calculations h j ð Þj i Among intranuclear searches,used Super-Kamiokande in the literature. (Super-K) Using the central values presented8 in compared to previous bag model calculations [53,54] often free neutron oscillation time. Improved n-n¯ oscillation effects, corresponds[59–61] tohasτnn¯ greatly> 2.7 × improved10 s at 90% the accuracy C.L. for the on n¯ usedOnn¯ inμ0 then literature. Using the central values presented in [7] provides the best limit, which,[61], after and correcting assuming for that nuclearfree the neutron operatorcompared oscillation in to Eq. previoustime.(1) Improvedgives bag model then-n¯ calculationsoscillation h[53,54]j ð oftenÞj i searches with both free and bound neutrons are under 8 [61], and assuming that the operator in Eq. (1) gives the effects, corresponds to τnn¯ >dominant2.7 × 10 contributions at 90% C.L.searches for to n the-n¯ oscillation, with both free we and can bound translate neutrons the are under 9–10 used in the literature. Using the central values presenteddominant contribution in to n-n¯ oscillation, we can translate the consideration, with sensitivities up to free10 neutrons envisioned oscillation time. Improved n-n¯ oscillation1 9–10 consideration,[61] with5, and sensitivities assuming up that to 10 the operators envisioned in Eq. (1) gives the 1 5 Super-K limit into Λðnn¯Þ 3.8 × 10 GeV (for a representa- Super-K limit into Λðnn¯Þ 3.8 × 10 GeV (for a representa- at the ESS and DUNE [8–12]. searches with both free and bound neutrons areat under≳ the ESS anddominant DUNE contribution[8–12]. to n-n¯ oscillation, we can translate the ≳ tive RG rescaling9–10 factor of 0.7). An improvement on τ up tive RG rescaling factor of 0.7). An improvement on τnn¯ up We now elucidate the connection betweennn¯ τnn¯ and the We now elucidate the connection betweenconsideration,τnn¯ and with the sensitivities up to 10 s envisioned 1 5 9 10 11 1 9 10 11 new physicsSuper-K scale in limit the EFT into context.Λðnn¯Þ The3.18 × lowest10 GeV dimen- (for ato representa-10 10 ; 10 s will correspond to probing Λðnn¯Þ ∼ new physics scale in the EFT context.at The the lowest ESS and dimen- DUNE [8–12]to. 10 10 ; 10 s will correspond to probing≳Λðnn¯Þ ∼ ð Þ5 sion effectivetive operators RG rescaling contributing factor of to 0.7).n-n¯ oscillation An improvement at 4.9 on7.τ8n;n¯12up.4 × 10 GeV. These numbers are representative We now elucidate the connectionð between τnnÞ¯5 and the ð Þ sion effective operators contributing to n-n¯ oscillation at 4.9 7.8; 12.4 × 10 GeV.tree level These are numbers dimension-99 10 are operators representative11 of the form O of the whole1 set of n − n¯ oscillation operators and do not new physics scale in the EFT context. The lowest dimen- to 10 10 ; 10 s will correspondnn¯ to∼ probing Λðnn¯Þ ∼ ð Þ ¯ ð Þ vary significantly with the starting point of RG evolution M tree level are dimension-9 operators of the form Onn¯ ∼ of the whole set of n −uuddddn oscillation. The4.9 classification7.8; operators12.4 × of105 these andGeV. do operators These not numbers dates back are representative sion effective operators contributing to n-n¯ oscillationð at Þ (see the Supplemental Material [57] for details). uudddd . The classification of these operators dates back vary significantly withto the the starting 1980sof[51 theð point–55] whole ofandÞ RG set was of evolution refinedn n¯ oscillation recentlyM in operators[56], and do not tree level are dimension-9 operators of the form whichOnn¯ ∼ established an alternative basis− that is more con- A minimal EFT for n-n¯ oscillation and baryogenesis.— ð Þ (see the Supplemental Materialvary[57] significantlyfor details). with the starting point of RG evolution M to the 1980s [51–55] and was refineduudddd recently. The in classification[56], of these operators datesvenient back for renormalization group (RG) running. A concise One of the simplest possibilities for generating the operator which established an alternative basistoð that the is 1980sÞ more[51 con-55] and wasA minimal refined recently EFT for in n[56]-n¯ ,oscillation(see the and Supplemental baryogenesis. Material—[57] for details). – FROM n − n¯ TO BARYOGENESIS:review of the full set of tree-level n-n¯ oscillation operators in Eq. (1) at tree level is with a Majorana fermion X of mass venient for renormalization group (RG)which running. established A concise an alternativeOne of basis the simplest that is more possibilitiesis given con- in the for SupplementalA minimal generating EFT Material the for operatorn[57]-n¯ oscillation. In what follows, and baryogenesis.M that couples— to the SM via a dimension-6 operator of the venient for renormalizationA SIMPLISTIC group (RG) running. APPROACH A concisewe focus onOne one of of the these simplest operators possibilities for illustration, for generating theform operator1=Λ2 Xudd, which originates at an even higher scale review of the full set of tree-level n-n¯ oscillation operators in Eq. (1) at tree level is with a Majorana fermion X of mass ð Þ review of theConsider full set a four-fermion of tree-levelM that BNVn- couplesn¯ operatoroscillation toinvolving the operators SM a SM via singlet ain dimension-6 Eq.fermion(1) atX tree operator level is with of the a Majorana fermionΛX≫ofM massvia some UV completion that we remain agnostic is given in the Supplemental Material [57]. In what follows, 1 about. A familiar scenario that realizes this EFT setup is is given in the Supplemental Material [57]2 . In what follows, M that couples toc the SMc via a dimension-6¯ c operator of the L ⊃ c1 ϵijkϵi j k u¯ PRdj u¯ PRdj d PRdk we focus on one of these operators for illustration, form 1=Λ Xudd, which originates at an20 even0 0 i higheri0 scale0 k 0 we focus on one of these operatorsð for illustration,Þ form 21=Λ Xuddð , whichÞð originatesÞð at anÞ even highersupersymmetry scale (SUSY) with R-parity violation (RPV), Λ ≫ M via some UV completion thatðM via weÞ some remain UV agnostic completion that we remainwhere agnostic the bino plays the role of X and the dimension-6 Integrating X out gives the n − n¯ operator Λ ≫H:c:; 1 1 about. A familiar scenario thatabout. realizesþ A familiar this EFT scenario setup that is realizes this EFToperator setup is is obtained by integrating out squarks at a heavier c c ¯ c c c ¯ c 1 −5 L ⊃ c1 ϵijkϵi j k u¯ PRdj u¯ PRdj dL ⊃PRcd1 k ϵijkϵi j k u¯ PRdj u¯ PRdj d PRdkwith c1 Λðnn¯Þ : 1 scale. However, this simple EFT with a single BSM state 0 0 0 i i0 0 k 0 0 0 0 supersymmetryi i0 0 (SUSY)k 0 with supersymmetryR-parity violation (SUSY) (RPV), with R-parity violation (RPV), 2 ð Þð Þð 2 Þ ð Þð Þð Þ ≡ ð Þ ð Þ does not allow for sufficient baryogenesis due to unitarity where the bino plays the role of X and the dimension-6 H:c:; where the bino playsHere theu role, d are of SMX upand and the down dimension-6 quark fields, respectively, relations: in the absence of B-conserving decay channels, X H:c:; Can X also be responsible for baryogenesis? þ þ operator is obtained by integratingc c operator out is squarks obtained at by a heavier integrating out squarksdecay at a heavier cannot generate a baryon asymmetry at leading order 1 −5 and u , d are their charge conjugates. ið0Þ, jð0Þ, kð0Þ are color 1 −5 with c1 Λðnn¯Þ : 1 scale. However, this simple EFT with a singlein BSM the stateB-violating coupling, a result known as the with c1 Λðnn¯Þ : ≡ ð Þ1 scale. However, this simpleindices,ð Þ EFT and “ withH.c.” adenotes single Hermitian BSM state conjugate. The ð Þ ð Þ does not allow for1 sufficient baryogenesis dueNanopoulos-Weinberg to unitarity theorem [62] (see [63] for a recent ≡ operator suppression scale ð Þ is generally a weighted Here u, d are SM up and downdoes quark not allow fields, for respectively, sufficient baryogenesisrelations: in the dueΛ absencenn¯ to unitarity of B-conserving decay channels, X ¯ ¯ (geometric) average of new particle masses, modulo discussion); meanwhile, 2 → 2 processes uX → d d and Here u, d are SM up and down quark fields,c respectively,c relations: in the absence of B-conserving decay channels, X and u , d are their charge conjugates. ið0Þ, jð0Þ, kð0Þ are color decay cannot generate a baryon asymmetry at leadinguX¯ → dd orderare forced to have the same rate and thus do not c c appropriate powers of couplings and loop factors. and u , d are their charge conjugates. iðindices,0Þ, jð0Þ, k andð0Þ are“H.c. color” denotesdecay Hermitian cannot conjugate. generate aIf The baryon the operatorin asymmetry the isB generated-violating at leading by coupling, integrating order a out result new knownviolate asCP the. “ ” in1 the B-violatingparticles coupling, atNanopoulos-Weinberg a a high result scale M known, computing theorem asτ therequires[62] (see RG[63] forA a minimal recent extension that can accommodate both n-n¯ indices, and H.c. denotes Hermitianoperator conjugate. suppression The scale Λðnn¯Þ is generally a weighted nn¯ 1 Nanopoulos-Weinbergevolving theorem thediscussion); EFT[62] down(see to[63] meanwhile, a lowfor scale aμ recent2(usually→ 2 processes chosen to uXoscillation→ d¯ d¯ and and the observed baryon asymmetry involves operator suppression scale ð Þ is generally(geometric) a weighted average of new particle masses, modulo 0 two Majorana fermions X , X (with M

171801-2 PHYSICAL REVIEW LETTERS 121, 171801 (2018) realized in a similar manner in more complex and realistic nf Here αsð Þ is the effective strong coupling with nf light theories—that are compatible with an n-n¯ oscillation signal quark flavors, whose value is obtained with the RUNDEC within experimental reach (for discussions of some other packagePHYSICAL[58]. Corrections REVIEW LETTERS from two-loop121, 171801 running (2018)PHYSICAL as well as REVIEW LETTERS 121, 171801 (2018) baryogenesis scenarios that can also involve n-n¯ oscillation one-loop matching onto lattice QCD operators were nf realized in a similar manner in more complex and realistic Here αð Þ is the effective strong coupling with n light signals, see, e.g., [25–43]). realized in a similar manner in more complex and realistic nf s f recently computed [56]theoriesand—that areHere are small,α compatiblesð Þ is and the with they effective an willn-n¯ oscillation strong be coupling signal with nf light Improved n-n¯ oscillation searches andtheories sensitivity—that are to compatible the with an n-n¯ oscillation signal quark flavors, whose value is obtained with the RUNDEC neglected in our calculations.within experimental Noquark additional flavors, reach (for whose operators discussions value rel- is of obtained some other with thepackage RUND[58]EC. Corrections from two-loop running as well as — within experimental reach (for discussions of somebaryogenesis other scenarios that can also involve n-n¯ oscillation scale of new physics. Neutron-antineutron oscillation has evant for n-n¯ oscillation are generatedpackage [58] from. Corrections RG evolution. from two-loop runningone-loop as well as matching onto lattice QCD operators were baryogenesis scenarios that can also involve n-n¯ oscillationsignals, see, e.g., [25–43]). been searched for in the past with both free neutrons The n → n¯ transition rate isone-loop determined matching by the onto matrix lattice QCD operatorsrecently were computed [56] and are small, and they will be signals, see, e.g., [25–43]). Improvedrecentlyn-n¯ oscillation computed searches[56] andand sensitivity are small, to the and theyneglected will be in our calculations. No additional operators rel- [6,44,45] and neutrons bound inside nuclei [7,46–50]. scale of new physics.—Neutron-antineutron oscillation has Improved n-n¯ oscillationelement searches of and the sensitivity low-energy to the effectiveneglected Hamiltonian in our calculations. between the No additional operatorsevant for rel-n-n¯ oscillation are generated from RG evolution. Among free neutron oscillation searches, the Institut— been searched for in the past with both free neutrons scale of new physics. Neutron-antineutronneutron and antineutron oscillation states. has Thus,evant once for n-n¯n¯oscillationOnn¯ μ0 aren are generated from RG evolution.The n → n¯ transition rate is determined by the matrix Laue-Langevin experiment [6] sets thebeen best searched limit to for date in the past with both free neutrons[6,44,45] and neutrons−h1 boundj ð insideÞj nucleii [7,46–50]. element of the low-energy effective Hamiltonian between the 8 known, we can relateAmongτnn¯ freen¯ HThe neutroneff nn → oscillationn¯totransition the six-quark searches, rate is the determined Institut by the matrix on the oscillation time, τnn¯ > 0.86 × [6,44,45]10 s atand 90% neutrons C.L. bound inside nuclei [7,46–50]¼. jh j j ij neutron and antineutron states. Thus, once n¯ Onn¯ μ0 n are operator coefficients. RecentLaue-Langevin progresselement experiment in of the lattice low-energy[6] calculationssets the effective best limit Hamiltonian to date between the Among free neutron oscillation searches, the Institut known, we can relate τ n¯ H n −h1 toj theð six-quarkÞj i Among intranuclear searches, Super-Kamiokande (Super-K) on the oscillationneutron time, and antineutronτ > 0.86 × states.108 s Thus, at 90% once C.L.n¯ O μ n are nn¯ eff Laue-Langevin experiment[59[6]–sets61] thehas best greatly limit improved to date the accuracy onnn¯ n¯ Onn¯ μ0 n nnoperator¯ 0 coefficients. Recent¼ jh progressj j inij lattice calculations [7] provides the best limit, which, after correcting for nuclear Among intranuclear searches,h Super-Kamiokandej ð Þj i (Super-K)−h1 j ð Þj i compared to8 previous bag modelknown, calculations we can relate[53,54]τnn¯ oftenn¯ Heff n to the[59 six-quark61] has greatly improved the accuracy on n¯ O μ n 8 on the oscillation time, τnn¯ > 0.86 × 10 s at 90% C.L. ¼ jh j j ij – nn¯ 0 effects, corresponds to τnn¯ > 2.7 × 10 s at 90% C.L. for the [7] providesoperator the best limit, coefficients. which, after Recent correcting progress for nuclear in lattice calculations h j ð Þj i Among intranuclear searches,used Super-Kamiokande in the literature. (Super-K) Using the central values presented8 in compared to previous bag model calculations [53,54] often free neutron oscillation time. Improved n-n¯ oscillation effects, corresponds[59–61] tohasτnn¯ greatly> 2.7 × improved10 s at 90% the accuracy C.L. for the on n¯ usedOnn¯ inμ0 then literature. Using the central values presented in [7] provides the best limit, which,[61], after and correcting assuming for that nuclearfree the neutron operatorcompared oscillation in to Eq. previoustime.(1) Improvedgives bag model then-n¯ calculationsoscillation h[53,54]j ð oftenÞj i searches with both free and bound neutrons are under 8 [61], and assuming that the operator in Eq. (1) gives the effects, corresponds to τnn¯ >dominant2.7 × 10 contributions at 90% C.L.searches for to n the-n¯ oscillation, with both free we and can bound translate neutrons the are under 9–10 used in the literature. Using the central values presenteddominant contribution in to n-n¯ oscillation, we can translate the consideration, with sensitivities up to free10 neutrons envisioned oscillation time. Improved n-n¯ oscillation1 9–10 consideration,[61] with5, and sensitivities assuming up that to 10 the operators envisioned in Eq. (1) gives the 1 5 Super-K limit into Λðnn¯Þ 3.8 × 10 GeV (for a representa- Super-K limit into Λðnn¯Þ 3.8 × 10 GeV (for a representa- at the ESS and DUNE [8–12]. searches with both free and bound neutrons areat under≳ the ESS anddominant DUNE contribution[8–12]. to n-n¯ oscillation, we can translate the ≳ tive RG rescaling9–10 factor of 0.7). An improvement on τ up tive RG rescaling factor of 0.7). An improvement on τnn¯ up We now elucidate the connection betweennn¯ τnn¯ and the We now elucidate the connection betweenconsideration,τnn¯ and with the sensitivities up to 10 s envisioned 1 5 9 10 11 1 9 10 11 new physicsSuper-K scale in limit the EFT into context.Λðnn¯Þ The3.18 × lowest10 GeV dimen- (for ato representa-10 10 ; 10 s will correspond to probing Λðnn¯Þ ∼ new physics scale in the EFT context.at The the lowest ESS and dimen- DUNE [8–12]to. 10 10 ; 10 s will correspond to probing≳Λðnn¯Þ ∼ ð Þ5 sion effectivetive operators RG rescaling contributing factor of to 0.7).n-n¯ oscillation An improvement at 4.9 on7.τ8n;n¯12up.4 × 10 GeV. These numbers are representative We now elucidate the connectionð between τnnÞ¯5 and the ð Þ sion effective operators contributing to n-n¯ oscillation at 4.9 7.8; 12.4 × 10 GeV.tree level These are numbers dimension-99 10 are operators representative11 of the form O of the whole1 set of n − n¯ oscillation operators and do not new physics scale in the EFT context. The lowest dimen- to 10 10 ; 10 s will correspondnn¯ to∼ probing Λðnn¯Þ ∼ ð Þ ¯ ð Þ vary significantly with the starting point of RG evolution M tree level are dimension-9 operators of the form Onn¯ ∼ of the whole set of n −uuddddn oscillation. The4.9 classification7.8; operators12.4 × of105 these andGeV. do operators These not numbers dates back are representative sion effective operators contributing to n-n¯ oscillationð at Þ (see the Supplemental Material [57] for details). uudddd . The classification of these operators dates back vary significantly withto the the starting 1980sof[51 theð point–55] whole ofandÞ RG set was of evolution refinedn n¯ oscillation recentlyM in operators[56], and do not tree level are dimension-9 operators of the form whichOnn¯ ∼ established an alternative basis− that is more con- A minimal EFT for n-n¯ oscillation and baryogenesis.— ð Þ (see the Supplemental Materialvary[57] significantlyfor details). with the starting point of RG evolution M to the 1980s [51–55] and was refineduudddd recently. The in classification[56], of these operators datesvenient back for renormalization group (RG) running. A concise One of the simplest possibilities for generating the operator which established an alternative basistoð that the is 1980sÞ more[51 con-55] and wasA minimal refined recently EFT for in n[56]-n¯ ,oscillation(see the and Supplemental baryogenesis. Material—[57] for details). – FROM n − n¯ TO BARYOGENESIS:review of the full set of tree-level n-n¯ oscillation operators in Eq. (1) at tree level is with a Majorana fermion X of mass venient for renormalization group (RG)which running. established A concise an alternativeOne of basis the simplest that is more possibilitiesis given con- in the for SupplementalA minimal generating EFT Material the for operatorn[57]-n¯ oscillation. In what follows, and baryogenesis.M that couples— to the SM via a dimension-6 operator of the venient for renormalizationA SIMPLISTIC group (RG) running. APPROACH A concisewe focus onOne one of of the these simplest operators possibilities for illustration, for generating theform operator1=Λ2 Xudd, which originates at an even higher scale review of the full set of tree-level n-n¯ oscillation operators in Eq. (1) at tree level is with a Majorana fermion X of mass ð Þ review of theConsider full set a four-fermion of tree-levelM that BNVn- couplesn¯ operatoroscillation toinvolving the operators SM a SM via singlet ain dimension-6 Eq.fermion(1) atX tree operator level is with of the a Majorana fermionΛX≫ofM massvia some UV completion that we remain agnostic is given in the Supplemental Material [57]. In what follows, 1 about. A familiar scenario that realizes this EFT setup is is given in the Supplemental Material [57]2 . In what follows, M that couples toc the SMc via a dimension-6¯ c operator of the L ⊃ c1 ϵijkϵi j k u¯ PRdj u¯ PRdj d PRdk we focus on one of these operators for illustration, form 1=Λ Xudd, which originates at an20 even0 0 i higheri0 scale0 k 0 we focus on one of these operatorsð for illustration,Þ form 21=Λ Xuddð , whichÞð originatesÞð at anÞ even highersupersymmetry scale (SUSY) with R-parity violation (RPV), Λ ≫ M via some UV completion thatðM via weÞ some remain UV agnostic completion that we remainwhere agnostic the bino plays the role of X and the dimension-6 Integrating X out gives the n − n¯ operator Λ ≫H:c:; 1 1 about. A familiar scenario thatabout. realizesþ A familiar this EFT scenario setup that is realizes this EFToperator setup is is obtained by integrating out squarks at a heavier c c ¯ c c c ¯ c 1 −5 L ⊃ c1 ϵijkϵi j k u¯ PRdj u¯ PRdj dL ⊃PRcd1 k ϵijkϵi j k u¯ PRdj u¯ PRdj d PRdkwith c1 Λðnn¯Þ : 1 scale. However, this simple EFT with a single BSM state 0 0 0 i i0 0 k 0 0 0 0 supersymmetryi i0 0 (SUSY)k 0 with supersymmetryR-parity violation (SUSY) (RPV), with R-parity violation (RPV), 2 ð Þð Þð 2 Þ ð Þð Þð Þ ≡ ð Þ ð Þ does not allow for sufficient baryogenesis due to unitarity where the bino plays the role of X and the dimension-6 H:c:; where the bino playsHere theu role, d are of SMX upand and the down dimension-6 quark fields, respectively, relations: in the absence of B-conserving decay channels, X H:c:; Can X also be responsible for baryogenesis? þ þ operator is obtained by integratingc c operator out is squarks obtained at by a heavier integrating out squarksdecay at a heavier cannot generate a baryon asymmetry at leading order 1 −5 and u , d are their charge conjugates. ið0Þ, jð0Þ, kð0Þ are color 1 −5 with c1 Λðnn¯Þ : 1 scale. However, this simple EFT with a singlein BSM the stateB-violating coupling, a result known as the with c1 Λðnn¯Þ : ≡Sakharovð Þ1 conditions:scale. However, this simpleindices,ð Þ EFT and “ withH.c.” adenotes single Hermitian BSM state conjugate. The ≡ ð Þ ð Þ does not allow for1 sufficient baryogenesis dueNanopoulos-Weinberg to unitarity theorem [62] (see [63] for a recent does not allow(above for sufficient operator violates suppression baryogenesis B) scale dueΛðnn¯Þ tois unitarity generally a weighted Here u, d• areBaryon SM up number and down violation quark fields, respectively, relations: in the absence of B-conserving decay channels, X ¯ ¯ (geometric) average of new particle masses, modulo discussion); meanwhile, 2 → 2 processes uX → d d and Here u, d are SM up and down quark fields,c respectively,c relations: in the absence of B-conserving decay channels, X and u , d are their charge conjugates. ið0Þ, jð0Þ, kð0Þ are color decay cannot generate a baryon asymmetry at leadinguX¯ → dd orderare forced to have the same rate and thus do not c c • Out of equilibrium condition ( X → udd decaysappropriate are out powers of eq. processes) of couplings and loop factors. and u , d are their charge conjugates. iðindices,0Þ, jð0Þ, k andð0Þ are“H.c. color” denotesdecay Hermitian cannot conjugate. generate aIf The baryon the operatorin asymmetry the isB generated-violating at leading by coupling, integrating order a out result new knownviolate asCP the. (no CP asymmetry in the tree level indices, and “H.c.” denotes Hermitian conjugate.• C,CP The violationin1 the B-violatingparticles coupling, atNanopoulos-Weinberg a a high result scale M known, computing theorem asτ therequires[62] (see RG[63] forA a minimal recent extension that can accommodate both n-n¯ operator suppression scale Λðnn¯Þ is generally a weighteddecay process) nn¯ 1 Nanopoulos-Weinbergevolving theorem thediscussion); EFT[62] down(see to[63] meanwhile, a lowfor scale aμ recent2(usually→ 2 processes chosen to uXoscillation→ d¯ d¯ and and the observed baryon asymmetry involves operator suppression scale ð Þ is generally(geometric) a weighted average of new particle masses, modulo 0 two Majorana fermions X , X (with M

171801-2 2

C.L. Among intranuclear searches, Super-Kamiokande often used in the literature. Using the results in [62], (Super-K) [10] provides the best limit, which, after cor- and assuming the operator in Eq. (1) gives the domi- 8 recting for nuclear e↵ects, corresponds to ⌧nn¯ > 2.7 10 s nant contribution to n-¯n oscillation, we can translate the ⇥ (1) > 5 at 90% C.L. for the free neutron oscillation time. Im- Super-K limit into ⇤nn¯ 4 10 GeV (for a represen- proved n-¯n oscillation searches with both free and bound tative RG rescaling factor⇠ of⇥ 0.7). An improvement on 9 10 11 neutrons are under consideration, with sensitivities up to ⌧nn¯ up to 10 (10 , 10 ) s will correspond to probing 9-10 10 s envisioned at the ESS and DUNE [11–15]. ⇤(1) 5(8, 13) 105 GeV. These numbers are represen- nn¯ ⇠ ⇥ We now elucidate the connection between ⌧nn¯ and the tative of the whole set of n-¯n oscillation operators,PHYSICAL and REVIEW LETTERS 121, 171801 (2018) new physics scale in the EFT context. The lowest dimen- do not vary significantly with the starting point of RG sion e↵ective operators contributing to n-¯n oscillation evolution MB-conserving(see Appendix operators for details). in addition to the two B-violating If all three operator coefficients have similar sizes, at tree level are dimension-nine operators of the form ones. Our minimal EFT thus consists of the following ΛX1 ∼ ΛX2 ∼ Λc, it is difficult to obtain the observed baryon (uudddd). The classification of these operators AminimalEFTforn-n¯ oscillation and baryogenesis Onn¯ ⇠ — One of thedimension-6 simplest possibilities operators that for generating couple X1; the2 to op- the SM [66]: asymmetry in the region of parameter space probed by n-n¯ dates back to the 1980s [54–58] and was refined recently 4 ’ erator in Eq. (1) at tree level is with a Majorana fermion oscillation. For MX1;2 10 GeV, the Λ s that can be in [59], which established an alternative basis more conve- L η ϵijk u¯ cP d d¯ cP X ≳ X of mass M that couples⊃ X1 to thei SMR viaj ak dimension-R 1 probed are sufficiently low for X1;2 to remain close to nient for renormalization group (RG) running. A concise 1 ð Þð Þ six operator of the form 2 Xuddijk , whichc originates¯ c at equilibrium until their abundances become negligible, review of the full set of tree-level n-¯n oscillation opera- ⇤ηX ϵ u¯ i PRdj dkPRX2 an even higher scale ⇤ þ M 2 viað some UVÞð completionÞ while efficient washout suppresses B L generation. tors is provided in the Appendix. In what follows, we i − that we remain agnostic about.ηc u¯ APL familiarX1 X¯ 2P scenarioRui thatH:c:; ð Þ focus on one of these operators for illustration, þ ð Þð Þþ For lower masses and higher Λ’s, on the other hand, X2 realizes this EFT setup is supersymmetry−2 (SUSY)−2 with −2 with ηX Λ ; ηX Λ ; ηc Λc : may freeze out with a significant abundance, and decay out 1 R-parity violation (RPV),1 whereX1 the bino2 playsX2 the role c ✏ ✏ (¯ucP d )(¯uc P d )(d¯c P d )+h.c., j j ≡ j j ≡ j j ≡ of equilibrium at later times when washout has become 1 ijk i0j0k0 i R j i0 R j0 k R k0 L 2 of X and the dimension-six operator is obtained by in- 3 inefficient, so that both limitations from the higher mass (1) 5 ð Þ with c ⇤ . (1) tegrating out squarks at a heavier scale. However, this 1 ⌘ nn¯ regime are overcome. However, its CP-violating branching simple EFTBoth withX1 aand singleX2 BSMmediate staten-n does¯ oscillation not allow—integrating for them 2 2 fraction ϵCP ∼ M =Λ is too small to generate the desired Here u, d are SM up and down quark fields, respec- sucient baryogenesisout at tree level due togives unitarity relations: in the X2 tively, and uc,dc are their charge conjugates. i( ),j( ),k( ) absence of B-conserving decay channels, X decay can- YB. We find that for ΛX ΛX Λc, the maximum YB 0 0 0 1 ¼ 2 ¼ are color indices, and “h.c.” denotes hermitian conju- not generate a baryon asymmetry1 at leading1 order in1 the possible in the ESS-DUNE sensitivity region is O 10−13 , (1) B-violating coupling,c a1 result known as the Nanopoulos- : 4 ð Þ gate. The operator suppression scale ⇤nn¯ is generally ¼ 1 5 ¼ M 4 þ M 4 ð Þ well below the observed value. Λð Þ X1 ΛX1 X2 ΛX2 a weighted (geometric) average of new particle masses, Weinberg theorem [63] (seeð [64]nn¯ Þ for a recent discussion); Achieving the desired baryon asymmetry in the ESS- modulo appropriate powers of couplings and loop factors. meanwhile, 2 2 processes uX d¯d¯ anduX ¯ dd are This! setup contains! all of the necessary! ingredients for DUNE reach region therefore requires hierarchical Λ’s; If the operator is generated by integrating out new forced to have the same rate and thus do not violate CP. baryogenesis [67]: the Lagrangian in Eq. (3) violates B and such scenarios can arise if new particles in the UV theory particles at a high scale M, computing ⌧ requires RG A minimal extension that can accommodate both n n¯ nn¯ P, while nonzero phases of η , η , and ηcan lead to CP that mediate the corresponding operators have hierarchical oscillation and the observed baryon asymmetryX1 X2 involvesc evolving the EFT down to a low scale µ0 (usually chosen masses and/or couplings, or if the EFT operators are two Majoranaviolation; fermions departureX ,X from(with equilibriumM Eq.140 (3)GeV, to capture resulting the generic in Y qualitative28 Y features). Our possi- aim is to the two scenarios considered in this Letter (arbitrary normaliza- ble in a two n-¯n mediators setup,B ¼ which79 B− canL be realized tion). In the late decay scenario, the n-n¯ mediator is long-lived findin more regions complicated of parameter and realistic space frameworks. that can achieve the and decays out of equilibrium to generate a baryon asymmetry. In −11 FIG. 1. Sketches of the evolution of the heavier n-¯n mediator observedCalculationYB of8. the6 × baryon10 asymmetry[68,69], with— The suitable relevant choiceabundancethe earlyYX , decaywashout scenario, rate wo departureand baryon from asymmetry equilibriumYB (thin dotted ¼ 2 of processesCP phases. for baryogenesis Technical details include of this calculation can bein thecurve) two scenarios is small, considered but suppressed in this letter washout (arbitrary enables nor- efficient baryo- found in the Supplemental Material [57]. malization).genesis. In See the late the textdecay for scenario, details. the n-¯n mediator is B violating processes: single annihilation uX1,2 long-lived and decays out of equilibrium to generate a baryon • ! asymmetry. In the early decay scenario, departure from equi- d¯d¯, dX1,2 u¯d¯,decayX1,2 udd, and o↵- resonance scattering! udd u¯d¯d¯;! librium (thin dotted curve) is small, but suppressed washout ! 171801-3enables ecient baryogenesis. See text for details. B conserving processes: scattering uX uX , co- • 1 ! 2 annihilation X1X2 uu¯ , and decay X2 X1uu¯ ; ! ! higher mass regime are overcome. However, its CP vio- as well as their inverse and CP conjugate processes. CP 2 2 lating branching fraction ✏CP MX /⇤ is too small to violation arises from interference between tree and one- ⇠ 2 generate the desired YB. We find that for ⇤X1 = ⇤X2 = loop diagrams in uX d¯d¯, uX uX and X 1,2 $ 1 $ 2 2 $ ⇤c, the maximum YB possible in the ESS/DUNE sensi- uud, and additionally from udd u¯d¯d¯ (in a way that 13 tivity region is (10 ), well below the observed value. $ O is related to X2 uud by unitarity). In each case, CP Achieving the desired baryon asymmetry in the violation is proportional$ to Im(⌘ ⌘ ⌘ ) ⇤ 6.We X⇤ 1 X2 c ⇠ 4 ESS/DUNE reach region therefore requires hierarchical work at leading order in the EFT expansion, i.e. (⇤ ) O ⇤’s; such scenarios can arise if new particles in the UV for the rates of CP-conserving processes and the CP- theory that mediate the corresponding operators have hi- symmetric components of CP-violating processes, and 6 erarchical masses and/or couplings, or if the EFT opera- (⇤ ) for the CP-violating rates. We choose a mass tors are generated at di↵erent loop orders. We find com- ratioO M /M = 4, which maximizes (X udd) X2 X1 2 ! patible regions of parameter space in two distinct scenar- (X2 u¯d¯d¯) for fixed MX (see Eq. (A.33)). ! 2 ios, one with late decays of X2 and the other with earlier We calculate the baryon asymmetry by numerically decays. These are schematically illustrated in Fig. 1, and solving a set of coupled Boltzmann equations to track discussed in turn below (a detailed analysis with bench- the abundances of X1,2 and B L (B) above (below) mark numerical solutions is presented in the Appendix). T = 140 GeV (we assume sphalerons are active when 28 T>140 GeV, resulting in YB = YB L). Our aim is Late decay scenario — For ⇤X2 ⇤c ⇤X1 , n- 79 ⇠ to find regions of parameter space that can achieve the n¯ oscillation is dominated by X1 exchange and probes 11 observed Y =8.6 10 [70, 71], with suitable choice the MX1 -⇤X1 parameter space (see Fig. 2). This hierar- B ⇥ of CP phases. Technical details of this calculation can chy leads to weaker interactions for X2 compared to the be found in the Appendix. degenerate case, causing it to freeze out with a higher abundance Y fo . Also, X becomes long-lived and decays If all three operator coecients have similar sizes, X2 2 after washout processes have become ine↵ective, thereby ⇤X1 ⇤X2 ⇤c,itisdicult to obtain the observed baryon⇠ asymmetry⇠ in the region of parameter space creating substantial baryon asymmetry (see Fig. 1). In > 4 this case, its CP-violating branching fraction scales as probed by n-¯n oscillation. For MX1,2 10 GeV, the 2 2 2 2 2 ⇤’s that can be probed are suciently low⇠ for X to re- ✏CP M ⌘X1 ⌘X2 ⌘c/ max(⌘ , ⌘ ) M /⇤ and 1,2 ⇠ X2 X2 c ⇠ X2 X1 main close to equilibrium until their abundances become does not decouple as ⇤X2 and ⇤c are both increased, fo negligible, while ecient washout suppresses B( L) gen- enabling YB Y ✏CP to reach the observed value. ⇠ X2 eration. For lower masses and higher ⇤’s, on the other Numerically, we find that this baryogenesis scenario is > hand, X2 may freeze out with a significant abundance, viable with ⇤X2 , ⇤c 20 ⇤X1 in the parameter space and decay out of equilibrium at later times when washout probed by n-¯n oscillation.⇠ In Fig. 2, we show regions in

has become inecient, so that both limitations from the the MX1 -⇤X1 plane that can accommodate the observed BARYOGENESIS: AN OUTLINE

Produce (thermalize) X 2 (X1) in the early Universe

X 2 decays populate baryon asymmetry

baryon + asymmetry

from hep-ph 1410.0108 Baldes et.al. (also get contributions from scattering processes, which are subdominant in the parameter space relevant for n − n¯)

washout: baryon asymmetry is washed out by BNV inverse annihilations and decays; are efficient at high temperatures, weaken at low temperatures

8 TWO SCENARIOS FOR BARYOGENESIS

produce3 asymmetry after washout processes have gone out of equilibrium Both X1 and X2 mediate n-¯n oscillation — integrating Late decay them out at tree level gives YX2 Early decay 1 1 1 suppress washout processes early on c1 = (1) 5 = 4 + 4 . (4) MX ⇤ MX ⇤ ⇤nn¯ 1 X1 2 X2 Γwo YB This setup contains all the necessary ingredients for baryogenesis [69]: the Lagrangian in Eq. (3) violates B and P , while nonzero phases of ⌘X1 , ⌘X2 , and ⌘c can lead to CP violation; departure from equilibrium can occur in multiple ways, as we discuss below. Although a clear simplification, we expect the minimal set of operators in Eq. (3) to capture the generic qualitative features possi- T~MX T~MX H~ΓX (late decay) ble in a two n-¯n mediators setup, which can be realized 2 1 2 in more complicated and realistic frameworks. FIG. 1. Sketches of the evolution of the heavier n-¯n mediator

Calculation of the baryon asymmetry — The relevant abundance YX2 , washout rate wo and baryon asymmetry YB processes for baryogenesis include in the two scenarios considered in this letter (arbitrary nor- malization). In the late decay scenario, the n-¯n mediator is B violating processes: single annihilation uX1,2 long-lived and decays out of equilibrium to generate9 a baryon • ! asymmetry. In the early decay scenario, departure from equi- d¯d¯, dX1,2 u¯d¯,decayX1,2 udd, and o↵- resonance scattering! udd u¯d¯d¯;! librium (thin dotted curve) is small, but suppressed washout ! enables ecient baryogenesis. See text for details. B conserving processes: scattering uX uX , co- • 1 ! 2 annihilation X1X2 uu¯ , and decay X2 X1uu¯ ; ! ! higher mass regime are overcome. However, its CP vio- as well as their inverse and CP conjugate processes. CP 2 2 lating branching fraction ✏CP MX /⇤ is too small to violation arises from interference between tree and one- ⇠ 2 generate the desired YB. We find that for ⇤X1 = ⇤X2 = loop diagrams in uX d¯d¯, uX uX and X 1,2 $ 1 $ 2 2 $ ⇤c, the maximum YB possible in the ESS/DUNE sensi- uud, and additionally from udd u¯d¯d¯ (in a way that 13 tivity region is (10 ), well below the observed value. $ O is related to X2 uud by unitarity). In each case, CP Achieving the desired baryon asymmetry in the violation is proportional$ to Im(⌘ ⌘ ⌘ ) ⇤ 6.We X⇤ 1 X2 c ⇠ 4 ESS/DUNE reach region therefore requires hierarchical work at leading order in the EFT expansion, i.e. (⇤ ) O ⇤’s; such scenarios can arise if new particles in the UV for the rates of CP-conserving processes and the CP- theory that mediate the corresponding operators have hi- symmetric components of CP-violating processes, and 6 erarchical masses and/or couplings, or if the EFT opera- (⇤ ) for the CP-violating rates. We choose a mass tors are generated at di↵erent loop orders. We find com- ratioO M /M = 4, which maximizes (X udd) X2 X1 2 ! patible regions of parameter space in two distinct scenar- (X2 u¯d¯d¯) for fixed MX (see Eq. (A.33)). ! 2 ios, one with late decays of X2 and the other with earlier We calculate the baryon asymmetry by numerically decays. These are schematically illustrated in Fig. 1, and solving a set of coupled Boltzmann equations to track discussed in turn below (a detailed analysis with bench- the abundances of X1,2 and B L (B) above (below) mark numerical solutions is presented in the Appendix). T = 140 GeV (we assume sphalerons are active when 28 T>140 GeV, resulting in YB = YB L). Our aim is Late decay scenario — For ⇤X2 ⇤c ⇤X1 , n- 79 ⇠ to find regions of parameter space that can achieve the n¯ oscillation is dominated by X1 exchange and probes 11 observed Y =8.6 10 [70, 71], with suitable choice the MX1 -⇤X1 parameter space (see Fig. 2). This hierar- B ⇥ of CP phases. Technical details of this calculation can chy leads to weaker interactions for X2 compared to the be found in the Appendix. degenerate case, causing it to freeze out with a higher abundance Y fo . Also, X becomes long-lived and decays If all three operator coecients have similar sizes, X2 2 after washout processes have become ine↵ective, thereby ⇤X1 ⇤X2 ⇤c,itisdicult to obtain the observed baryon⇠ asymmetry⇠ in the region of parameter space creating substantial baryon asymmetry (see Fig. 1). In > 4 this case, its CP-violating branching fraction scales as probed by n-¯n oscillation. For MX1,2 10 GeV, the 2 2 2 2 2 ⇤’s that can be probed are suciently low⇠ for X to re- ✏CP M ⌘X1 ⌘X2 ⌘c/ max(⌘ , ⌘ ) M /⇤ and 1,2 ⇠ X2 X2 c ⇠ X2 X1 main close to equilibrium until their abundances become does not decouple as ⇤X2 and ⇤c are both increased, fo negligible, while ecient washout suppresses B( L) gen- enabling YB Y ✏CP to reach the observed value. ⇠ X2 eration. For lower masses and higher ⇤’s, on the other Numerically, we find that this baryogenesis scenario is > hand, X2 may freeze out with a significant abundance, viable with ⇤X2 , ⇤c 20 ⇤X1 in the parameter space and decay out of equilibrium at later times when washout probed by n-¯n oscillation.⇠ In Fig. 2, we show regions in has become inecient, so that both limitations from the the MX1 -⇤X1 plane that can accommodate the observed LATE DECAY SCENARIO

3

Both X1 and X2 mediate n-¯n oscillation — integrating Late decay them out at tree level gives YX2 Early decay 1 1 1 c1 = (1) 5 = 4 + 4 . (4) long MlifetimeX ⇤ MforX ⇤X : ⇤nn¯ 1 X1 2 X22 Γwo YB This setupsuppress contains all all the couplings necessary ingredients of X 2 : for baryogenesis [69]: the Lagrangian in Eq. (3) violates B and P , while nonzero phases of ⌘ , ⌘ , and ⌘ can lead η , η small (ΛX1 ,X2Λ large)c to CP violation;X2 departurec from equilibriumX2 c can occur in multiple ways, as we discuss below. Although a clear simplification,n − n¯ signal we expect dominantly the minimal set mediated of operators in by X1 Eq. (3) to capture the generic qualitative features possi- T~MX T~MX H~ΓX (late decay) ble in a two n-¯n mediators setup, which can be realized 2 1 2 in more complicated and realistic frameworks. FIG. 1. Sketches of the evolution of the heavier n-¯n mediator

Calculation of the baryon asymmetry — The relevant abundance YX2 , washout rate wo and baryon asymmetry YB processes for baryogenesis include in the two scenarios considered in this letter (arbitrary nor- malization). In the late decay scenario, the n-¯n mediator is B violating processes: single annihilation uX1,2 long-lived and decays out of equilibrium to generate a baryon • ! asymmetry. In the early decay scenario, departure from equi- d¯d¯, dX1,2 u¯d¯,decayX1,2 udd, and o↵- resonance scattering! udd u¯d¯d¯;! librium (thin dotted curve) is small, but suppressed washout ! enables ecient baryogenesis. See text for details. B conserving processes: scattering uX uX , co- • 1 ! 2 annihilation X1X2 uu¯ , and decay X2 X1uu¯ ; ! ! higher mass regime are overcome. However, its CP vio- as well as their inverse and CP conjugate processes. CP 2 2 lating branching fraction ✏CP MX /⇤ is too small to violation arises from interference between tree and one-10 ⇠ 2 generate the desired YB. We find that for ⇤X1 = ⇤X2 = loop diagrams in uX d¯d¯, uX uX and X 1,2 $ 1 $ 2 2 $ ⇤c, the maximum YB possible in the ESS/DUNE sensi- uud, and additionally from udd u¯d¯d¯ (in a way that 13 tivity region is (10 ), well below the observed value. $ O is related to X2 uud by unitarity). In each case, CP Achieving the desired baryon asymmetry in the violation is proportional$ to Im(⌘ ⌘ ⌘ ) ⇤ 6.We X⇤ 1 X2 c ⇠ 4 ESS/DUNE reach region therefore requires hierarchical work at leading order in the EFT expansion, i.e. (⇤ ) O ⇤’s; such scenarios can arise if new particles in the UV for the rates of CP-conserving processes and the CP- theory that mediate the corresponding operators have hi- symmetric components of CP-violating processes, and 6 erarchical masses and/or couplings, or if the EFT opera- (⇤ ) for the CP-violating rates. We choose a mass tors are generated at di↵erent loop orders. We find com- ratioO M /M = 4, which maximizes (X udd) X2 X1 2 ! patible regions of parameter space in two distinct scenar- (X2 u¯d¯d¯) for fixed MX (see Eq. (A.33)). ! 2 ios, one with late decays of X2 and the other with earlier We calculate the baryon asymmetry by numerically decays. These are schematically illustrated in Fig. 1, and solving a set of coupled Boltzmann equations to track discussed in turn below (a detailed analysis with bench- the abundances of X1,2 and B L (B) above (below) mark numerical solutions is presented in the Appendix). T = 140 GeV (we assume sphalerons are active when 28 T>140 GeV, resulting in YB = YB L). Our aim is Late decay scenario — For ⇤X2 ⇤c ⇤X1 , n- 79 ⇠ to find regions of parameter space that can achieve the n¯ oscillation is dominated by X1 exchange and probes 11 observed Y =8.6 10 [70, 71], with suitable choice the MX1 -⇤X1 parameter space (see Fig. 2). This hierar- B ⇥ of CP phases. Technical details of this calculation can chy leads to weaker interactions for X2 compared to the be found in the Appendix. degenerate case, causing it to freeze out with a higher abundance Y fo . Also, X becomes long-lived and decays If all three operator coecients have similar sizes, X2 2 after washout processes have become ine↵ective, thereby ⇤X1 ⇤X2 ⇤c,itisdicult to obtain the observed baryon⇠ asymmetry⇠ in the region of parameter space creating substantial baryon asymmetry (see Fig. 1). In > 4 this case, its CP-violating branching fraction scales as probed by n-¯n oscillation. For MX1,2 10 GeV, the 2 2 2 2 2 ⇤’s that can be probed are suciently low⇠ for X to re- ✏CP M ⌘X1 ⌘X2 ⌘c/ max(⌘ , ⌘ ) M /⇤ and 1,2 ⇠ X2 X2 c ⇠ X2 X1 main close to equilibrium until their abundances become does not decouple as ⇤X2 and ⇤c are both increased, fo negligible, while ecient washout suppresses B( L) gen- enabling YB Y ✏CP to reach the observed value. ⇠ X2 eration. For lower masses and higher ⇤’s, on the other Numerically, we find that this baryogenesis scenario is > hand, X2 may freeze out with a significant abundance, viable with ⇤X2 , ⇤c 20 ⇤X1 in the parameter space and decay out of equilibrium at later times when washout probed by n-¯n oscillation.⇠ In Fig. 2, we show regions in has become inecient, so that both limitations from the the MX1 -⇤X1 plane that can accommodate the observed 4

Late decay scenario

7 10 1 X 1 τ Λ X 1 X n Λ Λ n = 25 50 10 11 = 100 c = = s Λ c Λ c = Λ = = 10 10 2 X 2 Λ X 2 s Λ X Λ 6 11 3×10 - 10 9 10 s ×

GeV 8.6

/ = B 1 Y X Λ 106

Super

- 2 K X limit M <

1 5 X 3×10 Λ 103 104 105 106

MX1 / GeV

FIG. 2. Parameter space of the11 minimal EFT probed by FIG. 3. Parameter space of the minimal EFT probed by n-¯n oscillation for the late decay scenario, assuming MX2 = n-¯n oscillation for the early decay scenario, assuming MX2 = 11 4 MX1 .For⇤X2 = ⇤c =50⇤X1 , the green shaded region can 4 MX1 . Points represent solutions with YB =8.6 10 11 ⇥ accommodate YB =8.6 10 .For⇤X = ⇤c =25⇤X found in a scan over ⇤X < ⇤X < 100 ⇤X , MX < ⇤c < ⇥ 2 1 2 1 2 2 (100 ⇤X ), viable region is between dashed red (dot-dashed ⇤X .Forallthesepoints,⇤X 10 ⇤X is needed to suppress 1 2 1 ⇠ 2 blue) lines. The gray shaded region marks ⇤X1

baryon asymmetry for various choices of ⇤X /⇤X = 2 1 would be ecient until T MX1 ,i.e.untiln1 starts ⇤c/⇤X . In each case, the lower boundary of the viable ⇠ 1 to fall exponentially. In contrast, by increasing ⇤X1 ,we region is e↵ectively determined by the requirement that enter a regime where washout is dominated by X2 pro- X2 freezes out with sucient abundance. As we move up- cesses at high temperatures and becomes inecient as ward from this lower boundary, increasing all three ⇤’s soon as the temperature falls below MX2 (washout due while keeping their ratios fixed, at some point we enter a to udd u¯d¯d¯, whose rate T 11/M 2⇤8 falls steeply with $ ⇠ regime where X2 decouples from the SM bath while rel- T , is also irrelevant at this point), resulting in a short fo eq 1 T 3 ativistic, and Y saturates at Y (T MX )= 2 , period of baryon asymmetry generation from X decays X2 X2 2 ⇡ s 2 so that further increasing the ⇤’s only reduces ✏CP and (see Fig. 1). Note that increasing ⇤X1 with respect to hence the final YB. Furthermore, for suciently high ⇤X2 also helps to increase departures from equilibrium

⇤X2 and ⇤c, X2 dominates the energy density of the uni- compared to the degenerate case. verse before it decays (this does not happen for X1 in the Fig. 3 shows points in the MX -⇤X plane that can parameter space we consider), so that its decay injects 2 2 realize the observed YB through this early decay pro- significant entropy into the plasma, diluting the baryon cess, based on a numerical scan over the region ⇤X < asymmetry. Both of these e↵ects – saturation and dilu- 2 ⇤X < 100 ⇤X , MX < ⇤c < ⇤X . For the ma- tion – determine the upper boundary of the viable region. 1 2 2 2 jority of these points, ⇤X1 is within a factor of two < Early decay scenario — For the opposite hierarchy from 10 ⇤X2 ,while⇤c 3 MX2 . The results can be understood from the⇠ competing e↵ects of baryon ⇤X1 ⇤X2 , n-¯n oscillation is dominated by X2 exchange asymmetry generation and washout, / and probes the MX2 -⇤X2 parameter space (see Fig. 3). B=0 wo 2 2 2 2 1 4 4 6 2 2 ⇠ M n (⇤ ⇤ ⇤ ) /(n ⇤ + n ⇤ ) (M /⇤ ) In this case, X2 is short-lived, and its abundance closely 2 X1 X2 c 1 X1 2 X2 c 2 2 2 2 (M M )/T ⇠ · follows the equilibrium curve. However, small departures min ⇤ /⇤ , ⇤ /⇤ e X2 X1 ,wherethe X2 X1 X1 X2 from equilibrium, always present in an expanding uni- rate of baryon asymmetry generation B=0 is calcu- 6 verse because interaction rates are finite, can be sucient lated from CP-violating X2 decays. First of all, a lower for baryogenesis if washout can be suppressed. The rates ratio ⇤c/MX2 is always preferable (within the range of for washout processes involving X1 and X2 are propor- EFT validity), while the ratio ⇤X2 /⇤X1 has an opti- 4 4 tional to n ⇤ and n ⇤ ,respectively,wheren are mal value of 1/10 as a result of balancing between 1 X1 2 X2 1,2 the number densities of X .If⇤ ⇤ , washout faster baryon⇠ asymmetry generation at higher tempera- 1,2 X1 ⇠ X2 PHYSICAL REVIEW LETTERS 121, 171801 (2018)

FIG. 3. Parameter space of the minimal EFT probed by n n¯ FIG. 2. Parameter space of the minimal EFT probed by n-n¯ − oscillation for the early decay scenario, assuming that oscillation for the late decay scenario, assuming that MX 4MX . The thicker (solid and dashed) black lines are MX 4MX . The thicker (solid and dashed) black lines are 2 ¼ 1 2 1 obtained using central values of nuclear matrix elements from obtained¼ using central values of nuclear matrix elements from Ref. [61], while the thinner dotted lines show the effect of current [61], while the thinner dotted lines show the effect of current lattice calculation uncertainty on the Super-K limit. Points lattice calculation uncertainty on the Super-K limit. For −11 represent solutions with YB 8.6 × 10 found for several ΛX Λc 50ΛX , the green shaded region can accommodate 2 1 fixed = ratios while¼ scanning over M ; . ¼ ¼ −11 ΛX1 ΛX2 Λc ∈ X2 ΛX2 YB 8.6 × 10 . For ΛX2 Λc 25ΛX1 (100ΛX1 ), the viable ð Þ ¼ ¼ ¼ The gray shaded region marks ΛX 140 GeV, resulting in YB = YB L). Our aim is Late decay scenario — For ⇤X2 ⇤c ⇤X1 , n- 79 ⇠ to find regions of parameter space that can achieve the n¯ oscillation is dominated by X1 exchange and probes 11 observed Y =8.6 10 [70, 71], with suitable choice the MX1 -⇤X1 parameter space (see Fig. 2). This hierar- B ⇥ of CP phases. Technical details of this calculation can chy leads to weaker interactions for X2 compared to the be found in the Appendix. degenerate case, causing it to freeze out with a higher abundance Y fo . Also, X becomes long-lived and decays If all three operator coecients have similar sizes, X2 2 after washout processes have become ine↵ective, thereby ⇤X1 ⇤X2 ⇤c,itisdicult to obtain the observed baryon⇠ asymmetry⇠ in the region of parameter space creating substantial baryon asymmetry (see Fig. 1). In > 4 this case, its CP-violating branching fraction scales as probed by n-¯n oscillation. For MX1,2 10 GeV, the 2 2 2 2 2 ⇤’s that can be probed are suciently low⇠ for X to re- ✏CP M ⌘X1 ⌘X2 ⌘c/ max(⌘ , ⌘ ) M /⇤ and 1,2 ⇠ X2 X2 c ⇠ X2 X1 main close to equilibrium until their abundances become does not decouple as ⇤X2 and ⇤c are both increased, fo negligible, while ecient washout suppresses B( L) gen- enabling YB Y ✏CP to reach the observed value. ⇠ X2 eration. For lower masses and higher ⇤’s, on the other Numerically, we find that this baryogenesis scenario is > hand, X2 may freeze out with a significant abundance, viable with ⇤X2 , ⇤c 20 ⇤X1 in the parameter space and decay out of equilibrium at later times when washout probed by n-¯n oscillation.⇠ In Fig. 2, we show regions in

has become inecient, so that both limitations from the the MX1 -⇤X1 plane that can accommodate the observed PHYSICAL REVIEW LETTERS 121, 171801 (2018)

FIG. 3. Parameter space of the minimal EFT probed by n −n¯ FIG. 2. Parameter space of the minimal EFT probed by n-n¯ 13 oscillation for the early decay scenario, assuming that oscillation for the late decay scenario, assuming that MX 4MX . The thicker (solid and dashed) black lines are MX 4MX . The thicker (solid and dashed) black lines are 2 ¼ 1 2 1 obtained using central values of nuclear matrix elements from obtained¼ using central values of nuclear matrix elements from Ref. [61], while the thinner dotted lines show the effect of current [61], while the thinner dotted lines show the effect of current lattice calculation uncertainty on the Super-K limit. Points lattice calculation uncertainty on the Super-K limit. For −11 represent solutions with YB 8.6 × 10 found for several ΛX Λc 50ΛX , the green shaded region can accommodate 2 1 fixed = ratios while¼ scanning over M ; . ¼ ¼ −11 ΛX1 ΛX2 Λc ∈ X2 ΛX2 YB 8.6 × 10 . For ΛX2 Λc 25ΛX1 (100ΛX1 ), the viable ð Þ ¼ ¼ ¼ The gray shaded region marks ΛX

Furthermore, for sufficiently high ΛX2 and Λc, X2 domi- generation from X2 decays (see Fig. 1). Note that increasing nates the energy density of the Universe before it decays ΛX1 with respect to ΛX2 also helps to increase departures (this does not happen for X1 in the parameter space we from equilibrium compared to the degenerate case.

171801-4 to address the above problems, enabling low scale baryogenesis with rich phenomenology. Furthermore, while R-parity violating supersymmetry has an unstable lightest supersym- metric particle (LSP) and therefore no dark matter candidate 1 (except possibly a long-lived gravitino, see, e.g., [11]), the hidden/dark sector can contain additional particles that account for the dark matter. In this paper, we will study both a minimal hidden sector (where the only hidden sector particle relevant for baryogenesis is the hidden sector gaugino) and an ex- tended hidden sector containing a WIMP dark matter particle, which also impacts the process of baryogenesis. sector U(1)0 is spontaneously broken by a hidden Higgs vacuum expectation value (vev), one analogously also has mixing of the hidden sector gaugino with the hidden sector Higgsinos (for simplicity, we assume two HiggsinosII. FRAMEWORK for the sake of anomaly cancellation, as in the MSSM), A SPECIFIC EXAMPLE: which can also be suppressed by raising the hidden Higgsino mass term µ0. In this paper, for GAUGINOOur framework PORTAL consists of BARYOGENESIS the MSSM extended by two key ingredients: baryon number simplicity, we assume µ0 M and µ M . This decouples the remaining neutralinos, Z0 Z A. Pierce, B. Shakya, hep-ph 1901.05493 violation via an RPV coupling, and a kinetic˜ mixing portal to a U(1)0 symmetry residing in a and the only relevant gauginosconsider for our a supersymmetric purposes are theframework MSSM with bino a Bhiddenand sector the hidden sector ˜ connectedhidden sector. to us via kinetic mixing portal (+ gaugino portal) gaugino B0. For baryonX number2 : (mostly) violation, hidden sector we add gaugino to the MSSM superpotential the following RPV term From now on, we will use the notation B˜0, B˜ to denote the mass eigenstates, which contain X 1 : (mostly) MSSM bino ✏ admixtures of the gauge eigenstate of the opposite sector. Crucially, we alsoc assumec c that the baryon number violation from RPV coupling WRP V = ijk00 Ui Dj Dk. (1) two mass terms carryCP a relative violation phase: from Im(m ˜ m⇤ ) =0.ThiswillbethesourceofCPviolation B0 B˜ 6 necessary for baryogenesis.integratingWe Finally, set out other(heavy) we assume RPV squarks terms,that giveB˜ which isthe the four-fermion breakLSP, so lepton it couplings, can number only decaywith and Λ via can∼ m the0 induce proton decay, to zero. 2 RPV coupling. The above RPV coupling ijk00 is constrained by various measurements , depending on the flavor

In addition to the hiddenindices gaugino (i,B˜ j,0, k the). In hidden this paper, sector for contains, simplicity at minimum, we work with Higgs a bosons single ijk00 without specifying the h0, Higgsinos H˜ 0, and the darkflavor gauge indices. boson Z0. These particles decay much faster than the

B˜0: For the mass hierarchy mRegarding˜ >m >m the field˜ , the content dark Higgsino of the hidden decays sector, as H˜ 0 twoh variations0B˜0,the are worth studying. One H0 h0 B0 baryon asymmetry populated via late decays of hidden sector gaugino! ˜ dark Higgs boson decaysFIG. as 1.canh0 Tree consider andB˜0 loopB˜0 via level a minimal decays small of but the setup hidden non-vanishing gaugino whereB0 allthat ofB interfere˜0 theH˜ torelevant0 producemixing, a hidden baryon while sector the gaugino phenomenology ! asymmetry. The crosses in the second diagram represent14 mass insertions, necessary to introduce the Z0 boson undergoes 2-bodyarises decays from into the the portal SM via coupling a kinetic to mixing the visible term. sector. The B˜ Alternatively,0 interactions additional particles in the phases on the two gaugino masses that give rise to the CP asymmetry in the interference term. with both the Z0 and the h0hiddenvanish sector as the Higgsinosmay endowH˜ 0 theare hidden decoupled. gaugino Therefore, with additional the presence interactions, which can a↵ect ˜ ˜ (where B˜ is the total decay width of the B0)representsthefractionofB0 decays that produce a of these additional particlesbaryogenesis. in0 the hidden We sector now is outline cosmologically these two irrelevant, possibilities and in all turn, relevant before returning to discuss their baryon asymmetry. WI incorporates the washout or dilution of the asymmetry from subsequent processes. Note that, due to the long lifetime of the B˜ , its production/freeze-out and decays interactions of the B˜0 arise viaphenomenology. its ✏ mixing with the visible sector0 bino B˜. occur at di↵erent epochs, and the related quantities, Y ˜ and ✏ respectively, can be calculated B0 CP independently.1 If R-parity In the remainder is unbroken, of this section,the presence we discuss of the the calculation gaugino of portal each of nevertheless the above carries interesting cosmological im- B. Extended Hiddencontributions. Sector with WIMP Dark Matter plications for dark matter, see [15–17]. 2 A. CalculationFor a somewhat of ✏ old but comprehensive discussion of RPV supersymmetry and constraints, see [12]. The presence of additional particles inCP the hidden sector is an attractive possibility from the Since the decay processes shown in Fig.1 depend on ✏ as well as , the decay can have a point of view of dark matter, since the traditional dark matter candidate,00 4 the visible sector long lifetime, easily satisfying the out of equilibrium condition. 4 LSP, is unstable in the absenceHere, it is important of R-parity to note. that While there exists hidden another sectors decay channel allow in addition for a wide to those variety of possibilities in termsshown of additional in Fig.1. As a field consequence content, of the Nanopoulos-Weinbergthere are two important theorem [24], considerationsin order for the to ˜ generated CP asymmetry to be first order in the RPV coupling, the B0 must˜ have an additional keep in mind: (1) additionaldecay channel field when content the RPV coupling should is not set to introduce zero (See [8] for new a detailedB0 discussion.).decay channels This is into 5 realized for m ˜

implementation as well as the least constrained experimentally. 6 8 A SPECIFIC EXAMPLE: GAUGINO PORTAL BARYOGENESIS A. Pierce, B. Shakya, hep-ph 1901.05493

dark green: partial washout

washout freezeout

rel. freezeout / eq. abundance from decay freeze-in

decay insufficient after BBN asymmetry FIG. 3. Regions of parameter space where the desired amount of baryon asymmetry can be produced

FIG. 3. Regions of parameter space where the desired amount of baryon asymmetry can be produced from cosmological histories where the B˜0 freezes out (green, yellow) or freezes in (blue), for m0 = max(1 from cosmological histories where the B˜0 freezes out (green, yellow) or freezes in (blue), for m0 = max(1 TeV, 10 m ˜ ),m˜ =0.3 m ˜ , and 00 =0.1. In the green region, the B˜0 thermalizes and freezes out B0 B B0 FIG. 3. Regions of parameter space where the desired amount of baryon asymmetry can be produced˜ TeV, 10 m ˜ ),m˜ =0.3 m ˜ , and 00 =0.1. In the green region, the B˜0 thermalizes and freezes out via scattering processes (Fig. 2), whereas in the yellow region the B0 reaches equilibrium abundance by B0 B B0 ˜ ˜ 15 ˜ via scattering processes (Fig. 2), whereas in the yellow region the B˜ reachesfrom cosmological equilibrium histories abundance where by virtue the B0 offreezes the decay out (green, process yellow)f B0 orf. freezes Dark green in (blue), and black for m points0 = max(1 denote regions where the washout 0 ! ˜ virtue of the decay process f˜ B˜ f. Dark green and black points denoteTeV, 10 regionsmB˜ ),m whereB˜ =0 the.3 washoutmB˜ , andprocesses00 =0. (baryon1. In the number green violatingregion, the inverseB0 thermalizes decay and/or and annihilation) freezes out are faster than Hubble at the ! 0 0 0 ˜ ˜ processes (baryon number violating inverse decay and/or annihilation)via are scattering faster than processes Hubble (Fig. at 2), the whereastime of B in0 decay; the yellow in the region dark the greenB0 regions,reaches a equilibrium sucient amount abundance of baryon by asymmetry survives despite

˜ virtue of the decay process f˜ Bpartial˜0f. Dark washout, green while and black in the points black region denote the regions observed where baryon the washout asymmetry in the Universe cannot be time of B0 decay; in the dark green regions, a sucient amount of baryon asymmetry survives despite! ˜ partial washout, while in the black region the observed baryon asymmetryprocesses in the (baryon Universe number cannot violating be matched. inverse Red decay region and/or denotes annihilation) parameter are space faster where than the HubbleB0 decay at occurs the after BBN (T = 1 MeV). time of B˜ decay; in the dark green regions, a sucient amount of baryon asymmetry survives despite matched. Red region denotes parameter space where the B˜0 decay occurs after0 BBN (T = 1 MeV). Next, we perform an extensive scan over parameter space covering the following ranges: partial washout, while in the black region the observed baryon asymmetry in the Universe cannot be

Next, we perform an extensive scan over parameter space coveringmatched. the Red following region ranges: denotes parameter space where the B˜ 8 decay occurs after BBN (T = 1 MeV). 10 GeV

8 10 GeV

2 1 TeV. Log (m /m ˜ ) between 0.5 and 5. Since there are LHC limits on sub-TeV squarks even 10 0 B0 2 1 TeV. 10 < ✏ < 10 . • Log10(m0/m ˜ ) between 0.5 and 5. Since there are LHC limits on sub-TeV squarks even • B0 10 3 4 10 < ✏ < 10 . 10 < 00 < 0.5. • for RPV supersymmetry [33–35],• we additionally also enforce m0 > 1 TeV. 14 4 10 3 10 < 00 < 0.5. 10 < ✏ < 10 . • • 14 4 10 < 00 < 0.5. • 14 A SPECIFIC EXAMPLE: GAUGINO PORTAL BARYOGENESIS A. Pierce, B. Shakya, hep-ph 1901.05493

dark green: partial washout 4

Late decay scenario

7 10 1 X 1 washout τ Λ X 1 X n n Λ Λ freezeout = 25 50 10 11 = 100 c = = s Λ c Λ c = Λ = = 10 10 2 X 2 Λ X 2 s Λ X Λ 6 11 3×10 - 10 9 10 s ×

GeV 8.6

rel. freezeout / / = B 1 Y X

eq. abundance from decay Λ 6 freeze-in 10 Super

- 2 K X limit M < decay insufficient 1 5 X 3×10 Λ after BBN asymmetry 103 104 105 106 M / GeV FIG. 3. Regions of parameter space where the desired amount ofX1 baryon asymmetry can be produced FIG. 2. Parameter space of the minimal EFT probed by FIG. 3. Parameter space of the minimal EFT probed by

n-¯n oscillation for the late decay scenario, assuming MX2 = n-¯n oscillation for the early decay scenario, assuming MX2 = ˜ 11 FIG. 3. Regions of parameter space where the desired amount of baryon asymmetry can be produced from cosmological histories where the B0 freezes4 outMX1 .For (green,⇤X2 = ⇤c yellow)=50⇤X1 , the or green freezes shaded region in can (blue),4 MX1 for. Pointsm0 represent= max(1 solutions with YB =8.6 10 11 ⇥ accommodate YB =8.6 10 .For⇤X = ⇤c =25⇤X found in a scan over ⇤X < ⇤X < 100 ⇤X , MX < ⇤c < ⇥ 2 1 2 1 2 2 (100 ⇤X1 ), viable region is between dashed red (dot-dashed ⇤X2 .Forallthesepoints,⇤X1 10 ⇤X2 is needed to suppress ˜ blue) lines. The gray shaded region marks ⇤ ˜

for washout processes involving X1 and X2 are propor- EFT validity), while the ratio ⇤X2 /⇤X1 has an opti- 4 4 8 tional to n ⇤ and n ⇤ ,respectively,wheren are mal value of 1/10 as a result of balancing between 1 X1 2 X2 1,2 10 GeV

2 1 TeV. Log (m /m ˜ ) between 0.5 and 5. Since there are LHC limits on sub-TeV squarks even 10 0 B0 2 1 TeV. 10 < ✏ < 10 . • Log10(m0/m ˜ ) between 0.5 and 5. Since there are LHC limits on sub-TeV squarks even • B0 10 3 4 10 < ✏ < 10 . 10 < 00 < 0.5. • for RPV supersymmetry [33–35],• we additionally also enforce m0 > 1 TeV. 14 4 10 3 10 < 00 < 0.5. 10 < ✏ < 10 . • • 14 4 10 < 00 < 0.5. • 14 vious section, the desired amount of baryon asymmetry can be produced over a large range of mass scales. While experimental evidence will prove dicult for heavy scales, additional phenomenology is possible on several fronts if the superpartners are light, as we now describe.

Collider and Direct Signatures: There are stringent constraints on squarks from the LHC even with RPV [33–37], where to address the above problems, enabling low scaleresonant baryogenesis production provides with rich additional phenomenology. search modes [38]. Under various assumptions, such constraints currently lie at the (100) GeV - 1 TeV scale. In our studies in Sec.IV, we restricted Furthermore, while R-parity violating supersymmetry has an unstableO lightest supersym- m to lie above 1 TeV in light of such constraints, but baryogenesis can be realized with lower metric particle (LSP) and therefore no dark matter0 candidate 1 (except possibly a long-lived masses. In our framework, TeV scale squarks (assuming a large enough Higgs boson mass can gravitino, see, e.g., [11]), the hidden/dark sectorbe generated) can contain can therefore additional be accessible particles to collider that account searches, e.g. forq ˜ q q(qqq). This ! 0 ! for the dark matter. In this paper, we will studyis in contrast both with a minimal the MSSM hidden implementation sector of (where baryogenesis the in [10, 11], where the sfermions only hidden sector particle relevant for baryogenesisare required is the to be hidden several orders sector of magnitude gaugino) heavier and an in order ex- to satisfy the out of equilibrium condition and are therefore beyond the reach of colliders. tended hidden sector containing a WIMP dark matter particle, which also impacts the process Likewise, direct searches also constrain the existence of a kinetically mixed light Z0. Recall of baryogenesis. that the gauge boson kinetic mixing angle ⌘ is in principle di↵erent from the gaugino mixing angle ✏, but one generally expects ⌘ ✏. Current limits (see Fig.6 in [39]) are at the level ⇠ 3 2 of ⌘ 10 for GeV scale Z0 (deteriorating to ⌘ 10 above 100 GeV), but much stronger II. FRAMEWORK ⇠ ⇠ below the GeV scale due to beam dump and SN1987A limits. In our framework, such probes 3 are therefore relevant only if the Z0 is extremely light (below GeV scale), or if ✏ 10 . Our framework consists of the MSSM extended by two key ingredients: baryon number ⇠ Low Energy Signatures: violation via an RPV coupling, and a kinetic mixingThe presence portal of to light a U superpartners(1)0 symmetry with RPV residing couplings in a can give rise to several low energy hidden sector. signatures. These depend on the flavor structure of the RPV coupling ijk, i.e., which quarks are n − n¯ REVISITED For baryon number violation, we add to theinvolved MSSM in superpotential the RPV interactions. the We following briefly discuss RPV the term most interesting signatures relevant to if RPV coupling involves ourfirst framework generation here, quarks, and refer can the get interested bino-mediated reader to [12] n for− an¯ more comprehensive discussion

of variousc c lowc energy constraints on RPV supersymmetry. However, W RP V = ijk00 U i D j D k . is antisymmetric; vanishes if j=k=1.(1) If the coupling involves first generation quarks, a particularly strong test of baryon number at least one flavor off-diagonal mixing needed in the squark sector to get n − n¯ violation comes from searches for neutron-antineutron oscillations n n¯. 7 In our scenario, since We set other RPV terms, which break lepton number and can induce proton decay, to zero. the coupling of the B˜0 to SM is suppressed by ✏, the n n¯ oscillation is primarily mediated by squark. Note that the RPV coupling 00 2= 0, hence generating this e↵ective vertex requires a The above RPV coupling ijk00 is constrained bythe various MSSM measurements bino B˜,viae↵111ective, dependingBudd˜ four-fermion on the couplings flavor obtained by integrating out the indices (i, j, k). In this paper,flavor for simplicity o↵-diagonal we7 mixingFor work studies with term discussing a in single then n¯ squarksignals00 inwithout sector, the context leading specifying of baryogenesis to a the suppression scenarios, see [40–42]. of the signal [12]. ijk flavor indices. Current n n¯ constraints [43, 44] can be translated to the following bound on this o↵-diagonal 18 Regarding the field contentmixing of the angle: hidden sector, two variations are worth studying. One m 2 m ˜ 0.5 0.01 current bounds roughly 0 B0 ✓˜1j < . (19) can consider a minimal setup wheretranslate all of the to relevant hidden⇠ 100 sector TeV gauginoTeV phenomenology00 ⇣ ⌘ ⇣ ⌘ ✓ ◆ Upcoming experiments [45, 46] will improve on this sensitivity by more than an order of mag- arises from the portal coupling• other to processes the visible (e.g. sector. dinucleon Alternatively, decays) do not additional involve this particles unknown in mixing the hidden sector may endow thenitude hidden and gaugino couldangle, probe with but our additionalsuffer framework from large interactions, in uncertainties the presence which of suchcan a flavor↵ect o↵-diagonal mixing. baryogenesis. We now outline• EDMs: these Theresuppressed two are possibilities other by multiple processes in powers turn, that of do before tiny not portal su returning↵er coupling from to this discuss(CP unknown phase their resides mixing suppression, such as double nucleon decays (suchin the as hiddenpp sector)K+K+ or nn K0 K0). Such processes most strongly phenomenology. ! ! < 4 171 constrain 11200 , 11300 ( 10 , 10 respectively for TeV scale superpartners), but involve large ⇠ 1 If R-parity is unbroken, the presenceuncertainties of the gaugino from portal hadronic nevertheless and nuclear carries matrix interesting elements, cosmological see [12, im- 47] for details. plications for dark matter, see [15–17].EDM measurements are a powerful probe of CP violation and are known to constrain even 2 For a somewhat old but comprehensivePeV scale discussion sfermions of RPV [13, supersymmetry 14]. In our framework, and constraints, the EDM see contribution[12]. arises through a gaugino- sfermion loop diagram. However, since the CP phase relevant to baryogenesis resides in the 4 combination of the two gaugino masses, Arg(m ˜ m⇤ ), both gaugino mass insertions are required B0 B˜ on the gaugino propagator in the loop to generate the EDMs. This suppresses the amplitude by ✏2, greatly suppressing the EDMs, which can be estimated (for down-type fermions) as:

2 6 2 df mf ✏ TeV m ˜ m ˜ µ Im[e2i✓] B0 B tan . (20) 10 29 e cm ⇡ MeV 10 3 m TeV TeV 100 TeV ✓ 0 ◆ ⇣ ⌘⇣ ⌘ ⇣ ⌘ 29⇣ ⌘⇣ ⌘ Future experimental limits are expected to reach d 10 ecm[48],withelectron,proton, e,p,n ⇠ and neutron EDMs expected to provide comparable reach if all sfermions are at the same scale. We see that the ✏2 contribution can suppress the EDMs below observable limits even for TeV scale sfermions and gauginos 8, making them likely unobservable even with improved future 3 measurements unless ✏ 10 . ⇠ Dark Matter Signatures: If the hidden sector also contains a WIMP dark matter particle, as in the extended hidden sector scenario we considered, additional signatures are possible at both direct and indirect detection experiments.

8 In the presence of o↵-diagonal flavor mixing in the sfermion sector, the EDMs can get enhanced by various

fermion mass ratios [13].

19 SUMMARY

• n − n¯ an important test of baryon number violation • sensitivity will increase by several orders of magnitude with upcoming experiments, (ESS) • could shed light on an important BNV process in the early Universe: baryogenesis

• within a simplified framework involving SM singlet fermions: could probe parameter space that produces the desired baryon asymmetry via late or early decays

• n − n¯ can probe parameter space far beyond the reach of other traditional searches (colliders, EDMs etc)

• an explicit model: baryogenesis via a gaugino portal • current n − n¯ bounds already placing meaningful constraints on flavor off-diagonal mixing angles in the squark sector

18