JHEP04(2020)187 Springer April 1, 2020 April 5, 2020 April 28, 2020 : : : December 20, 2019 : Revised Accepted Published c,b Received , Published for SISSA by https://doi.org/10.1007/JHEP04(2020)187 and Aaron C. Vincent c,b [email protected] , Ningqiang Song . 3 a,b 1912.06656 The Authors. c Deep Inelastic Scattering (Phenomenology), Phenomenology of Large extra

In scenarios with large extra dimensions (LEDs), the fundamental Planck scale , [email protected] E-mail: [email protected] Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada Arthur B. McDonald CanadianDepartment Astroparticle of Physics Physics, Research Institute, Engineering99 Physics University and Ave, Astronomy, Queen’s Kingston, University, ON K7L 3N6, Canada North Carolina State University,Raleigh, Department NC of 27695-8202, Physics, U.S.A. b c a Open Access Article funded by SCOAP dimensions ArXiv ePrint: through Cherenkov light echosnext due generation to of delayed neutrino neutronthough telescopes the recombination. can identification probe We of find unique LEDs topologies that with could the a push Planck theirKeywords: scale reach up even further. to 6 TeV, opening the door totime, a we higher identify energy a rangeappear number than of in Earth-based unique the colliders. signatures nextand of generation Here, the microscopic of for Pacific black large-scale the Ocean holes neutrino first energy Neutrino as observatories distributions, Explorer. they such and would as unusual These ratios IceCube-Gen2 signatures of include hadronic-to-electronic energy new deposition, event visible topologies, Abstract: can be low enoughblack that collisions holes. between high-energy High-energy particles cosmic may produce neutrinos microscopic can carry energies much larger than a PeV, Katherine J. Mack, Signatures of microscopic blackdimensions holes at and future extra neutrino telescopes JHEP04(2020)187 32 that can be much ? M 4 29 14 , while allowing gravity to “leak” into one 32 27 – 1 – 18 brane 14 GeV. Such scenarios have been tested extensively in 18 ]. This allows a true Planck scale D 26 6 10 – 24 1 16 ∼ 14 8 P l 21 25 M 22 7 dimensions [ 1 26 21 bulk 3.2.1 Track events 3.2.2 Double bang-like event 7.1 Signatures of7.2 new physics Exclusion and detection prospects 5.1 Showers 5.2 Muon tracks 5.3 Double bang-like events 3.3 New unique topologies 3.1 Flavor composition 3.2 Track and double-bang energy distributions models with Large Extra Dimensionselectroweak (LEDs), scales the can large be hierarchy atgauge between least gravity interactions partly and to the explained a byor confining 3+1-dimensional more the extra Standard Modellower (SM) than the observed 1 Introduction Among the diverse signaturesducing of microscopic new black physics holes above in the particle TeV scale, collisions the remains possibility one of of pro- the most alluring. In B Probability distribution of C Inital energy loss and cross section 7 Conclusions A Expected topology as a function of neutrino flavor 6 Vacuum instability 4 Cherenkov timing and light echos 5 Detection prospects 3 Event topology Contents 1 Introduction 2 Black hole production and decay in neutrino telescopes JHEP04(2020)187 ] tells . This 13 ], and in CM 9 E , 8 = • neutrino-nucleus ] by searching for M to be above about ? 27 – M ]. The reach of collider elastic 14 28 ] proposed the search for 46 between two colliding particles b ] discussed low energy muons with high 45 ] studied the connection between black hole of a black hole with mass 37 – 2 – H ]: even without BH formation, such events can r 47 ], supernova and neutron star cooling [ 7 ] further studied the zenith dependence of the cosmogenic 44 , ]. If only one LED exists, Solar System-scale modifications ], particularly if they are observed with energies above the GZK 43 ] explored the observational consequences of micro black hole 36 11 , 12 – ] prohibit a TeV-scale Planck mass. However, two or more LEDs 1 10 29 ], depending on the number of extra dimensions. 12 ] mainly focused on the expected number of black hole events in IceCube and – , a smoking gun signature of extra dimensions. The hoop conjecture [ 7 ? 42 – M 38 & Many preliminary studies of this prospect were performed in the decade prior to the In this article, we examine in detail the prospects of observing microscopic black holes A vastly-reduced Planck scale also allows for the creation of microscopic black holes CM distinction between gravity-mediated andand Standard a Model full phenomenological interactionstherefore analysis remains to has unclear, construct never a beenof complete performed. detection set in Our of the goal observable next signatures in generation and this of quantify work large-scale the is neutrino prospects observatories. neutrino flux by including blackpropagate hole through production the and Earth. decaymultiplicity In into showers addition, neutrinos ref. as when [ neutrinos arare muon signature tracks with of large blackscattering angular separation. holes was Gravity-mediated also and considered ref.lead in [ to ref. new [ and unique observational signatures. Despite those preliminary studies, the carried out in theproduction intervening years. from cosmogenic Ref.lighted [ neutrino-nucleon two possible scattering solutions and to theRefs. proton proton [ decay lifetime, problem, and which canother high- arise detectors, in while LED refs. models. [ trino telescopes offer a uniqueallows advantage for in a that events far cannatures more be that detailed completely can accounting contained. help of This distinguish deposited ordinary energy electroweak interactions and from uniquedetection BHs. topological of sig- the first high-energy astrophysical neutrinos at IceCube, but few have been creation anywhere in ourwhich can cosmic place volume limits through on its LED models potential with to certainproduced trigger very in high vacuum collisions fundamental decay, of scales. neutrino high-energy observatories neutrinos such with as detector IceCube-Gen2. nucleons Compared in with next-generation cosmic ray detectors, neu- experiments is limited by thean finite alluring CM alternative, collision as energy. high-energyhas Cosmic been cosmic known accelerators rays for thus some can time, provide reach andof extensive much BHs studies in higher have air been momenta. showers performed [ This onlimit. the production A recent study [ (BHs) in the collision betweenE two high-energy particles withus centre that of mass a (CM) blackis energy hole smaller will than form twicehas if the mainly the horizon been impact radius studied parameter the high-multiplicity in signature the from context rapid Hawking of evaporation high-energy [ colliders [ collider experiments [ of Newtonian gravity [ remain allowed by observation.3–25 Current TeV constraints [ limit the scale terms of gravitational force tests [ JHEP04(2020)187 ]) + n 27 = ( ), muon TeV, this H ∼ T • M showers 6-20, depending ∼ -like signature of multiple (or double cascade) signa- (also called kebab cascades double bang -bang signature. If a muon is also produced, n – 3 – 10 PeV, the > For sufficiently distant sources, the mixing of neutrino flavors decaying electronically or hadronically far enough away from  τ a few hundred GeV. The BH will only emit a few ( , and at energies ∼ In addition to changing the ratio of topologies, BH events also yield H is the number of extra dimensions. For a black hole mass of T tracks n , where cascades arrayed on a muon track.multiple If tracks more are than expected one in muon an isenergetic event. produced enough, from Finally, it if BH may one decay, interact ofin the with the decay the products detector. nucleus remains and yield another black hole bang accompanying hadronic shower dueThis to manifests the itself high as multiplicityenergies a between of lower the ratio BH second of and decay first muon-to-showerto products. showers energy, the seen and three in a double-bang topologies events. lower outlinedcan ratio In above, decay addition of at BHs different can times produce yieldingit multiple an will tau be leptons, highly which collimated with the taus, producing a if they are interpreted assumingpresence Standard of Model new processes physics. — indicating the possible Topology. a lower amount of energy deposition into leptonic final states, with respect to the ture produced by a the primary vertex to beto separately all identified. degrees As of BHsthe can freedom Hawking evaporate (as temperature), democratically long we will astopologies, show their which that can masses they look are yield like a lower unitarity very than nonstandard violation the ratio in BH of the mass neutrino and oscillation matrix production scenario, the characteristicsneutrino of the flavor detected inferences events arenucleus from made interaction which is will incoming the beastrophysical principal neutrinos. different. ingredient Possible in topologies The inferring are and topology the tau of flavor a composition neutrino- of Flavor composition. via oscillation should resultdetector. in While an this approximately is even true mix in of both flavors Standard arriving Model at interactions the and the black hole- At these masses, BH evaporation is effectively instantaneous. Particle emission from H 2. 1. /r of microscopic black holes in neutrino telescopes: degree of freedom. Becauseration interactions products are will observed bedifficult, in as highly the electronic “fixed-target” collimated. and frame,longer-lived hadronic evapo- Searches particles events for (muons lead and high-multiplicity tocannot taus) events immediate will be cascades, become lie while detected, on trackshave because top from identified the of several key each momentum signatures other. of that the Missing can momentum indicate incoming the neutrino creation is and subsequent unknown. decay We BH evaporation follows a1) thermal distribution withcorresponds a to Hawking temperature on initial BH mass) particlesevaporation in products its will decay. be Because drawn of from the every Standard high Model Hawking (and temperature, potentially these BSM [ JHEP04(2020)187 , , . 5 7 s. The 3 − ] that the ini- 48 s after the initial 6 briefly discusses the − 6 focuses on the reconstructed GeV from collisions of ultrahigh 3.1 8 by mentioning new morphologi- peak ratio/energy deposition plane we examine the energy distribution 3 10 ∼ ]. Since then, over 100 such events have 3.2 ν 52 E – 49 , the BH formation rates can contribute to a ? – 4 – M , we examine in detail the specific observational signa- Because a majority of events will take the form of cas- 3 focuses on Cherenkov light timing signatures, and in section 4 ], extending from the tens of TeV (where the atmospheric contribution neutrinos is expected around 53 cosmogenic size of the neutronshower peak composition. relative to We theevaporating will total BHs show energy occupy a that can specific be infrom region, standard used the which charged as may current allow a and them neutral proxy to current for be interactions the differentiated on a statistical basis. cades, we will focushadronic on energy deposition a in methodtial shower of Cherenkov events. shower discriminating produced It the by wasevents proportion neutrino-nucleus shown is of deep in followed inelastic electronic ref. by scatteringinteraction, [ to a (DIS) and delayed thereafter muon by a decay third signal peak around due 10 to neutron capture at 10 Cherenkov light timing. The IceCube detector consists of a cubic kilometer of ice below the geographic South We begin our analysis by describing production and evaporation of BHs in LED models While it is unlikely to be a clear diagnostic signature in the near term, an additional 3. processes such as activeflux galactic of nuclei. Anenergy cosmic additional rays contribution with to intergalactic radiation. the extragalactic Pole, instrumented with approximately 5000 digital optical modules (DOMs) designed to contained events seen in the IceCube detectorbeen [ catalogued [ is expected to sharplymuon signatures fall), of up neutrinos to interactingof an several outside isotropic the PeV distribution detector, in of theseenergy, high energy. and energy indicate are neutrinos. consistent the Combined with These an presence with extragalactic appear origin, to throughgoing likely follow from a high-energy astrophysical power law in 2 Black hole productionWith and the decay exception in ofpositive neutrino neutrinos detection produced telescopes of in neutrinos the from core-collapse beyond supernova 1987A, our the Galaxy first came in the form of high-energy flavor signature in the presence ofin LEDs. track In and section double-bangcal events, signatures. and Section wewe end evaluate the section detection prospectsimplications at of micro future black experiments. hole Section creation for vacuum stability. We conclude in section of energy, and reliesthe on interactions a observed. robust It reconstruction maywe therefore of do be the not an incoming propose interesting target particle it for energy as future a based searches, diagnostic but on here. in neutrino telescopes. Intures section of such events in an IceCube-like detector. Section effect is that assignificant CM rise energies in rise the total above rate neutrino-nucleus of cross interaction section. with Thisderived incoming neutrino leads neutrino energy to energy, spectrum an which at increase couldother the in new appear high physics the end. as models, a as However, this well change as is in with highly the a degenerate simple with change in the neutrino flux as a function JHEP04(2020)187 . = us N (2.2) (2.3) (2.1) √ is the = v • ]. We will M 54 for detailed discussion. C , ) , is the momentum exchange of 2) TeV requires neutrino energies u, Q − ( 2) d i Q & ( − f / d ? 1 ( / i  M 1 X 1 2)  is the maximum impact parameter that ? − d/ 2 max us d 2) M Γ( √ − 2 d  / ], and especially in the context of ultra high ( duπb / 1 6) 1 – 5 – 59 − ]. It may increase the energy threshold for BH ? − /s – 4] d 2 ? ( 1 / M 60 M 56 2 π d 3 Z k 1) + 3 spatial dimensions of a BH with mass − d = = n − 2 )  d d = ( s BH r = d → d k [1 + ( νN / σ ) is d k CM E ( ) d ( s . Therefore, probing a Planck mass r ν E = 2 N ]: m ], who argued that the nonlinear effects neglected by prior authors called into 2 max 55 59 b √ ) is the parton distribution function (PDF) of the proton or neutron, where is [ Due to the nonlinearity in the formation of black holes, part of the collisional energy, The black hole production cross section from neutrino collisions with a nucleon The center-of-mass energy of a collision between a neutrino and a nucleon at rest is = v, Q s ( put this number betweenet 10% al. and [ 30%,question but the robustness the of situation theirof was results, reach. and summarized In that by athe the Yoshino full, absence initial rigorous of energy calculation a remained loss self-consistent out to quantum be gravity theory, 0 we and nevertheless keep set in mind that it may affect the BH production momentum and angular momentum mayhole be becomes stationary lost and in starts theboth Hawking evaporation. form analytically of The and energy gravitons loss before numericallyenergy has the in been neutrino-nucleon black studied [ scattering inproduction [ and reduce the productionHowever, cross we section, note see that appendix gravitational energy loss is very model dependent — early estimates f fraction of energy carriedthe by collision. the The individual sum parton, is and over all quark flavors and gluons. is the Schwarzschild radius in The geometric factor where allows BH production and efficiencies but scaling up detector dimensions. n, p of 10 PeV or more.degree, Because the of fact the decliningnot that neutrino large high-energy flux enough at showers to high haveperform energies, yield our a and analyses a to large with signal a future spatialuse with lesser experiments the extent, in sufficient IceCube mind, IceCube numbers configuration such as of as is a IceCube-Gen2 fully template likely [ for contained future events. detectors, keeping We the same detector between neutrinos and nucleirecorded (and acts electrons) as in agered the proxy DOMs ice. for leads to theinformation The a event to number be classification energy, of extracted. in and photoelectrons event the topologies, geometrical√ which distribution in of turn trig- allows for flavor detect the Cherenkov light emitted by charged particles produced in high energy collisions JHEP04(2020)187 ], ] for 66 , . The where 70 ? 65 M min = M min M ] does not include 1 boson exchange) and ], which could carry a Z 62 , but decreases quickly as the 61 ] or explicitly consider both n 68 , ] does; the most stringent existing 6 11 , , 5 10 – 6 – = 10 TeV the black hole production is subdominant ? ] code to accept collisions between high-energy neutrinos , assuming a minimum black hole mass M ? 64 ]. Rotation would also make the emission less isotropic, but M , 67 boson exchange) interactions. We refer the reader to ref. [ 63 ,  the neutrino-nucleon cross section as a function of neutrino energy 55 ]. Some authors have proposed that an evaporating black hole might 1 W 55 , is raised. At 27 ? ]. In terms of the possibility of split branes, we assume for simplicity that M 69 = 10 EeV, even assuming 6 extra dimensions. In the same figure, the black ν E We show in figure We employ a set of numerical tools that we modify to model the production, evapora- In the last stage of the evaporation when the black hole mass drops below Planck scale up to line shows the SM-only expectationcharged including current neutral (CC, current (NC, a complete discussion of how these processes are modeled. Once a spectrum of evaporation limits either restrict theirpossibilities analysis [ to thethe former entire Standard [ Model is confined to the brane andfor only a gravity can range pass of into Planckcross the masses section bulk. increases with the number of extra dimensions this is unlikely to haveing. a significant In impact the due absence tonon-rotating the of black expectation holes greybody of for factors a conservativeconsidered for study. high depends gravitons Whether level on of or for the beam- not rotating extrabrane brane black tension, dimension tension holes, whereas model needs the we to — Randall-Sundrum assume be the model ADD [ model [ of this work, we consideras only this the case case includes without the rotation,servative simplest assumption). splitting, black hole brane production Rotation tension, models or wouldthough (and recoil, likely we is result note in some in that cases a superradiancehighly a rotating higher may con- enhance blackholes evaporation [ the flux emission [ probability of gravitons for modify the BlackMax [ and nuclei at rest in themodel detector the volume. production and BlackMax evolution is of afactors black Monte holes of Carlo at evaporation simulator colliders. designed products, It to includes andbetween relevant fermions, can greybody brane model tension the and effects bulk of recoil BH from rotation, gravition brane emission. splitting For the purpose may produce distinct signatures,evaporation. such as We a leave delayed theassume flash exploration total due of evaporation to this for subsequent the interesting accretion scenarios possibility and that for follow. futuretion, work, and and energy deposition by microscopic black holes in the detector material. We first the semiclassical treatment is nominimum longer number of applicable, particles we which assume conserveof the the the black black energy, hole hole momentum [ and bursts all intonot gauge a fully charges decay butsmall rather electric leave charge. behind This a would alter Planck-mass the relic spectrum [ at the final stages of evaporation, and spectrum, modified by a “greybodyand factor”, the which angular depends momentum onkinematically of the and the particle thermally spin BH. accessible and degrees Becauseemission mass, of evaporated is freedom, particles expected. a are mixthree drawn Hadronic of colors, from leptonic showers and and all will eight hadronic gluon dominate, degrees because of of freedom per the helicity. six quark flavors, rate accordingly. The particles emitted by Hawking radiation follow the a blackbody JHEP04(2020)187 ] 72 ], a multipar- = 6. The total n 75 , 74 = 1 TeV (dash-dotted ? M are produced by muons . We now turn to specific 4 Tracks ]. We employ the CT14NNLO [ 71 – 7 – ]. The latter step gives the list of four-momenta 73 = 6 extra dimensions for the results presented below. n = 1 extra dimensions and the upper bound has n (or cascades) occur when energy is immediately deposited in a roughly spher- . The black hole production cross section from neutrino-nucleon interactions as a function Showers Finally, to account for energy deposition of these interaction products in the detector We will focus on the case of products from neutrino-nucleus interactionswill in evaporate to the a ice. subsetand of thus Because every the SM event microscopic topology degree black — of can holes freedom, be the expected set to ofical be final-state markedly distribution particles different leading from — to the SM a case. large, but contained, signal. 3 Event topology The spatial distributionknown of as deposited the electromagnetic event topology. energy Different in topologies the are detector due volume to the is difference in final-state volume as Cherenkov light, theticle PYTHIA transport results code are fed thatreturn into accounts FLUKA to for [ the interaction details ofsignatures of high-energy of BHs particles our that in FLUKA can matter. be simulations identified We in with section our simulations. PDFs, implemented with LHAPDF6of [ propagating particles originating at the interaction vertex. A smaller number ofcross LEDs section, and has thus the the total straightforwardwhich event rate, effect are but of due will not to lowering change the the the observational high-multiplicity BH signatures, Hawking production evaporation products. band, the lower limit represents Standard Model (SM) neutral current and charged current cross section is shownproducts by has the black been line. produced,heavy we states pass and the hadronization results of to coloured PYTHIA particles 8 [ in order to model decay of Figure 1 of the incoming neutrino energy. Thered), hatched 2 colored TeV bands (dashed correspond to magenta), 3 TeV (solid green) and 10 TeV (dotted blue) respectively. For each JHEP04(2020)187 ]  τ 77 (3.1) charged . These τ , we refine 3. We will ν . . ’s if the double-pulse 0 track τ ν 3.2 3.3 ≤ ]. Following [ A 76 E . ≤ 98 . 0 showers . − 5 2 2 E E − + 1 1 and section E E ’s yield muon tracks, as can µ ≡ ν – 8 – 3.2.2 A ’s which deposit their energy almost immediately. E  e in section . A 4 0, and vice versa.) We require E (or double cascade), is expected if charged tau production and > are, respectively, the energies of the first and second shower. (So A signature is produced when the tau created from a 2 E E , 2 and > E 1 double-bang 1 E E double bang ’s can produce double bangs and τ ν where leptons, or direct production of relax our condition on when current interaction decays electronically orto a hadronically visible inside second the shower.decays detector, to We leading clearly require separate the the tau secondwe shower to from construct travel the the farther primary energy one than [ asymmetry 100 m before it threshold (1 TeV in themuons following can sections), be the eventintermediate produced is tau directly classified leptons. as from Besidesor a the muons, higher) we produced BH also in evaporation, neutrino-nucleon consideras interaction high or which track energy decay events. from outside taus the the (5 detector PeV decay of Events that do not meet criteria 1 or 2 are classified as The If one or more high-energy muon is produced with a total energy above a certain In the following, we will employ a set of criteria to determine the observed topology  3. 2. 1. τ trino. decays leptonically. All flavors canof produce cascades via NC interactions,Every immediate topology decay is associatedthe with nucleus an and subsequent initial hadronic shower shower, due making to misidentification a the constant momentum concern. transferred to our analysis to ask how theby energy black distribution hole in creation. track and We double-bang discuss events new, is non-standard modified 3.1 topologies in section Flavor composition In SM interactions, event topology is directly related to the flavor of the progenitor neu- We begin this sectioncreation by changes first the asking inferred flavor how composition a at modified high distribution energies. of In topologies section from BH events, in which theto double-bang the from use tau of decay timing cannot in be section resolved inof space. each event We that return we simulate. propagate away from thetopology, the interaction vertex, eventuallydecay both escaping occur the within the detector. detector,separate with but a A correlated large enough cascades. third spatialdown separation Timing the to origin information identify of two can each additionally topology. be This has used been to used narrow for example to search for (or, at very high energies, taus, though their energy deposition rate is much lower) as they JHEP04(2020)187 ] 70 (3.2) (3.3) (3.4) is Avo- A N , ) , ν ) E ν ( Ξ E ( can be obtained by → N NC i eff ν σ ) ), only a small region is σ M ν τ ) ν ν ν E ( : ν E 2. ν ( / i dE 6 µ ν dE . The fit agrees well with the ν dφ : 1 = 1 dφ ) is the exposure time, e . ) ν ν ν q T E E ( Att q ( dx cx Att ], where we use a fitting function as in [ Att ) ) 1 + ν 50 )), the probability of a given set of observed ν E τ ice E ( α ρ ( : – 9 – NC eff CC µ , 10 TeV). The results are shown in the left panel i ) = M α ν / eff x ν : ]. As neutrinos propagate over large, uncorrelated ν ( is the attenuation factor due to the absorption and M e E eff 85 ν dE ( α – ( M 10 Att dE }| max ) is the effective mass of the detector, for a given neu- 78 min Ξ E ν , . A reconstructed flavor composition outside of this region E { max E ( Z 70 min ( 4 E = log P E Θ A , Z i x ν eff A TN M and = TN 3 = − indicates different neutrino flavors, NC , 10 EeV where the black hole production cross section can be comparable sh conditional on each possible flavor composition, in order to reconstruct the CC , ], computing ≤ i } N Ξ ν ν Ξ 79 N e, µ, τ 7 kg m { E . and the best-fit parameters are listed in table = 2 ≤ i In the Standard Model, the total number of expected events for a topology Ξ = (sh, We therefore begin by asking: in the presence of BH creation from neutrino-nucleus The flavor composition inferred from a sample of neutrino events is a well-known = 916 ice ρ of figure IceCube effective masses, especiallyeffective mass for up neutrinos to above 10 EeV 1 where PeV. the We detector also sensitivity is extrapolate saturated. the The effective mass to or larger thanassumed to the be Standard 20 PeV. Model Atonly such cross high downgoing sections. energies neutrinos the Earth need The isfitting be the almost minimum IceCube opaque deposited considered, to effective mass neutrinos. energy and shown in Thus is ref. [ gadro’s number, and trino flavor and process.rial times The a latter detectorregeneration can efficiency. of be neutrinos interpreted20 in as PeV the the quantity Earth. of target We focus mate- on ultra high energy neutrinos with for CC events. For NC events, only showers are produced: where tr, db) is generally given by classify the topology ofaccording each to event the into final showersway state (sh), to particles ref. tracks [ from (tr), BH andtopologies evaporation. double bangs We then (db), proceedSM interpretation in of a the similar observed events. of the ternary plottherefore in indicates some figure non-unitarity in theor oscillation matrix, a the misunderstanding presence of of new experimental physics, uncertainties. interactions, what is theassuming Standard reconstructed Model flavor processes composition only? when We the first simulate sample a is number analyzed of BH events, and diagnostic for new physicsdistances to [ Earth, their flavors mixover incoherently, leading all to flavors. a signal that Outallowed has of been after averaged the oscillation. possibleincluded, combinations Once this of experimental leads ( uncertainties to an in allowed the region mixing delimited by parameters the are blue contour in the central area JHEP04(2020)187 ν E CC (red), e ν weighting function Right: = 2. The total all-flavor ]. γ 70 d q ) found in [ 100 IceCube-years. We then classify the ∼ true ) for different types of interactions in IceCube. ) E 3 cylindrical detector with a height of 1.25 km ( 3.4 3 eff (km – 10 – M c = 3 TeV. used in eq. ( ? eff M M = min ], since neutrinos deposit almost all of their energy in the detector. CC 0.071 0.16 4.8 CC 0.18 0.42 4.7 CC 0.59 1.3 5.2 M 70 BH 0.50 1.1 4.6 e τ µ ν ν ν best-fit ]. We model it as a 7.9 km CC (blue), NC (gray) and black hole productions (black), for IceCube. In this effective mass as a function of the incoming neutrino energy for All Flavors NC 0.059 0.13 3.5 τ 86 ν Left: )). The maximum of the distribution is normalized to 1. In producing results in this . 3.6 . Best-fit parameters of , estimated to be between 2 and 3. For better event reconstruction we assume the γ ) which governs the black hole production rate’s dependence on incoming neutrino energy The cosmogenic neutrino spectrum can be approximated as a powerlaw with a spectral We wish to evaluate the detection prospects of a detector the size of the planned ν CC (green), E ( µ sume 10 years of exposure, whichevents is into equivalent three to categories according to their topologies: tracks, showers and double bangs. index optimistic neutrino energy spectrum with the spectral index for black hole production is takenenergy to obtained be from the [ effective mass as a function of the true deposited IceCube-Gen2 [ and a radius of 1.42 km, about 10 times larger than the current IceCube detector. We as- Table 1 f (see eq. ( section, we draw 1000production black of hole non-rotating events black randomlyblack holes according hole on mass to a is tensionless this set brane. distribution. to For We this assume specific the case, the minimum Figure 2 ν section we use the7.9/0.644 to same simulate efficiency the function,from larger the but volume IceCube of rescale collaboration IceCube-Gen2. thefor and black overall The the hole normalization dashed solid productions lines lines by are is show a obtained the taken factor from effective from of the mass the fit. The effective mass JHEP04(2020)187 A is: (3.6) ν E ] to avoid for details. 87 A = 3 TeV and ? ) (3.5) M 1 − s . We refer the reader 2 3 − ). The total cross section cm 1 3.3 − , ) ν E 45. We also assume the neutrino (GeV . ( ) and ( eff 18 3.2 = 6 − M , the production cross section and the ) is obtained assuming ] for a true deposited energy of 10 ν ν . 70 E × astro ( 2 BH ν φ 2 /dE σ − ν BH 6 ν  σ – 11 – dφ ν ν 6 ν ] where dE dφ E 53 100 TeV ) =  ν ). Taus are allowed to randomly travel a certain distance E 1 ( f astro πφ = 4 ν ν 6 dE dφ for more technical details. A . Total neutrino-nucleon interaction cross section with different topologies as a function of The black hole production cross section Black hole production is independent of the incoming neutrino flavor. To obtain the 6 extra dimensions (seebefore figure decay, according to thecriteria probability outlined distribution above of to their select lifetime.for the more We track, implement details). shower the and We double also bang require events (see the appendix muon energy to be higher than 1 TeV [ according to the all-flavorflavor-independent neutrino detector efficiency flux based on [ which is also shown in the right panel of figure to appendix event topology from blackBlackMax. hole decay, We we then simulate passheavy 1000 the particle black evaporation decay. hole products events Black to using hole modified PYTHIA production 8 as for a function hadronization of and neutrino energy is weighted with the same normalizationflux as has in no [ angularin dependence. Standard The Model expected processes are numberfor obtained of different from events neutrino-nucleon eqs. with scattering ( processes different is topologies shown in figure ing the cross sections we require a minimum energy deposition of 20 PeV. Seeastrophysical appendix neutrino flux is therefore given by Figure 3 incoming neutrino energies. Standarddashed Model and showers, dashed-dotted tracks and linestopologies. double respectively, The bangs noting contributions are from that neutrinos shown and black in antineutrinos solid, hole have been events averaged over. will In produce produc- all three JHEP04(2020)187 is a (3.8) (3.7) a N ). ]. assuming , the energy 2 88 3.5 2 , Ξ . The atmospheric , N ) 2 Ξ a f ! ) N Ξ i ν Ξ ν N E N ( i P BH ν ( σ ) a ν ν 6 N i , given in table Ξ ν dE i dφ = 3. We then reconstruct the flavor N ) i ν P db ( E ( N − e BH ν Ξ Y M ν – 12 – is the expected number of events for a topology ) = dE i decreases from 6% to about 0.2% once the energy = 99 and Ξ db ν shower track double bang N sh db max ,N f min N E sh E Z db. , ,N A tr sh , as given by = 50, , N TN | 2 tr a db is the fraction of track, shower and double bang events ob- 1 2 = 3 TeV and 6 extra dimensions in the latter case. Double bangs are , N ? ,N = sh } M , ⊕ Ξ i, BH SM 2.31 8.31 0 SM 5.07 5.39 2.83 CC and black hole events. The neutrino flux is taken from eq. ( SM 28.58 0 0 α N { and Ξ = tr τ e τ µ ( ν ν ν ν L e, µ, τ with Ξ = tr ] by constructing the likelihood All Flavor Total BH 62.96 36.36 0.20 All Flavor Total SM 35.96 13.70 2.83 = Ξ . Expected number of events with different topologies from Standard Model and black hole 79 f i We would like to see how the black hole production in such a future detector would The expected number of events in Standard Model interactions and black hole produc- where from the Standard Model interaction ofneutrino neutrino background flavor is negligible in this energy range (20 PeV to 10 EeV) [ mock data as the(1 : sum 1 of : 1) Standardcomposition favor Model assuming ratio, Standard i.e. and Model-only black interactions.in hole We ref. follow events [ a from similar table procedure as holes. It should alsoasymmetry be condition is noted implemented, that meaning thatcompared the with tau emitted the is particles usually which less energetic initiate the primary shower. affect the reconstruction of the flavor composition at the Earth. To do so we generate and muons and tausblack only hole make mass up increases, a moreprobability small particles of fraction muon can production. of be the emitted, Asdistribution we which emission. of can significantly incoming We see increases neutrinos note from the whichat the that produce 100 right as black panel holes PeV the of features or figure a higher non-negligible energies, tail which explains the larger track-to-shower ratio for black where tained from the black holethan simulations tracks described since above. only Black a holes limited produce number more of showers particles are emitted in black hole evaporation, the low energy muons producedtau in double the bang hadronization are secondaries. seen, If we consider both it muon as tracktion and a is double summarized bang in event. table Table 2 production. We assume only produced in JHEP04(2020)187 ], we (3.9) ]. The . Due 79 4 90 , region and 89 , σ  ) ) db db distribution [ ,N 2 ,N sh χ sh ,N tr ,N tr N | N | max a, max a, regions for Standard Model interactions ,N ,N σ } max ⊕ } i, ⊕ α i, { α ( { L ( – 13 – L  asymptotically approaches a λ 2 ln is also varied to obtain the maximum likelihood for all − } ⊕ i, ) = α } { can have a significant effect on the best fit location. This is in ⊕ i, 4 α |{ db values using Wilks’ theorem. The results are shown in figure ,N − sh p flavor content. In addition, the larger track-to-shower ratio imposes a slight ,N τ tr ν N . Allowed regions for the neutrino flavor composition at the Earth assuming black hole ( λ We end this section by noting that the choice of energy threshold in constructing contrast to an SM-only data sampleIt which is by construction clear should that be a robust significantoscillation to measurement region such of choices. can a provide flavor a compositionTo hint that obtain for is outside the a the new more allowed detailed physics robust processes analysis we of prediction are the of considering track here. the and signatures double-bang distributions. of new physics, we now turn to a preference for muon neutrinosfrom over SM electron interactions neutrinos. andthe oscillations The (1 : only flavor 1 combination is : obtained 1) marginally flavor contained ratio in is the excludedthe at 3 ternary 95% plot CL. in figure where in the denominator possible flavor compositions. Since translate it to to the paucity offrom large double bang events in black hole decay, the preferred region is away we vary to maximizetest the statistic likelihood given a certain flavor composition. We construct the (without BH formation) aftershown neutrino in blue oscillation contours. withfrom any inverted The flavor ordering. solid combination blueblack Neutrino at line star oscillation the in is parameters source the obtained are centre are from taken indicates normal the from (1 ordering NuFIT : and 4.1 1 dashed : [ 1) linenormalization flavor is factor ratio. for the neutrino flux and can be treated as a nuisance parameter which Figure 4 production in neutrino-nucleon interactions in IceCube.show The the solid, dotted 68%, and dashed 95% black and contours 99.7% CL respectively. The 3 JHEP04(2020)187 times is the c sh CC. The ], though E µ CC events. 91 ν 53 PeV). µ . ν due to a lower in ? = 0 sh M CC events on one is the total energy ν E µ E µ 10 ν E ' µ by simulating 1000 black E ), a lepton produced by BH ν 5 3, as described in the beginning /E . . This enables us to distinguish ` ? 0 E M is the total number of evaporation ≤ is the energy of muon produced in ≡ A µ ) N E y E on a statistical basis. We note that the − . The energy of muons can in principle ≤ sh µ CC, the black circles are mostly above the E 98 . /E µ 0 µ =1 TeV, 2 TeV, 3 TeV and 10 TeV the fraction − ν . Here − – 14 – E ? µ µ ν M E is the proton mass. The charged current events that /dE ) p = µ ν m sh E ( E charged current events are drawn randomly according to of the energy, where vividly shows a butterfly shape with dσ µ 5 where ν /N p CC events with 1 m µ 2 ∼ ν / 2 ? M = min line. In the black hole case, only one muon (or, rarely, two) is emitted during E (i.e. distributions are peaked at large (1 sh where we show the distribution of track energy to shower energy ratio: the ratio in ` -nucleon scattering and E 5 µ The left panel of figure We show the shower energy and muon energy in figure ν = µ 3.2.2 Double bang-likeIf event a tau lepton is oneinside of the the detector, evaporation a products black and hole itthe event decays produces tau’s hadronically two decay or cascades time. electronically separated by To a beto distance classified satisfy as the a energy double asymmetry bang condition event, the energy of the cascades has black hole tracks and fraction of track events producedtotal by number BHs of also decreases particles withis emitted. increasing 34%, For 34%, 32%, 28%, respectively. evaporation, or isfraction produced of in the the energyare subsequent of below hadronization that the process. line, incomingfigure as neutrino, It expected. which carries is This onlythe tendency why black a hole is most case clearly of extendstrend seen the to is also small colored independent in values dots of whereas the incoming it right peaks neutrino panel at energy of and we simulate start at a neutrino-proton CM collision energywing of and 1 black TeV hole ( trackmomentum events is on the transferred other. toE Since the almost muon all in of the incoming neutrino’s be reconstructed from thestochastic energy energy of loss the canuniformly track lead in as to log a space, uncertainty function into in order of 10 the to track EeV. reconstruction. illustrate length The ourenergy) minimum [ Samples results is energy are across for the drawn black whole hole energy range, simulation up (to achieve the necessary CM total energy of theof evaporation products the that muons initiate producedthe showers, in and next a subsection. blackthe hole differential The decay. cross We section the address tau production and decay in products. The rest ofshower of the products neutrino that energy do is not invariably escape released very in farhole the from production (mostly) the events hadronic interaction at vertex. differentAs Planck before scales we using BlackMax pass and the 1000 BlackMax simulations to Pythia 8 for hadronization. 3.2.1 Track events If one of thecontrast with evaporation SM products events, in islepton which a most muon, of the a momentumdecay black is will carried hole only away event by carry looks the outgoing like a track. In 3.2 Track and double-bang energy distributions JHEP04(2020)187 A E = 6 ) in (see sh n i L /E h µ = E τ delineates the sh /m 0 E 5 cτ . τ E = 0 µ E = 100 m correspondingly. . It is manifested that L 6 2 where / τ E = distribution of the ratio log( 2 E Right: , and the dotted line ). sh E 6 – 15 – = µ E 1 TeV for an event to be considered a track event, and black = 3 TeV (green histogram) which produce muon tracks dur- ? > µ M E reduces the production cross section but does not affect the distri- n for details. CC events (black circles). Red, magenta, green and blue dots correspond 5 CC events are contained. Each case is based on 1000 simulations, sampled µ =1 TeV, 2 TeV, 3 TeV and 10 TeV, respectively. Simulations assume ν µ CC is characterized by a small cascade, followed by a large shower, . Simulated taus are forced to decay regardless of the distance they spectrum instead and a minimum energy deposition of 20 PeV as described ν ? τ 6 2 ) and the dash-dotted line is obtained with ν M − i E L CC will leave the detector before decay. This is not necessarily the case ). We require h total energy of muons versus total energy of shower particles in black hole simula- ν τ E ν ( CC and black hole events in the same way as in our track analysis, and show . See section for . Here, we instead refer to all two-cascade events — whether or not they satisfy 10 ) with τ Left: 3 A ν sh . 3.1 /E µ Since we focus on high energy incoming neutrinos (PeV or higher), most of the taus E however for black hole decay, wherewhich taus can are only be onethe or less a two energetic. few cascades: of thewhereas The evaporation black products difference hole results yieldsof a in the large different energy shower, asymmetry followed energy by is distributions a shown in in smaller the cascade. right The panel distribution of figure which most of the tausin will between. decay within The 100 solid m. lineappendix Double-bang is like obtained events by will assuming be detectable produced in the asymmetry condition —simulate as “double bang-like” eventsthe (abbreviated results later in as figure dbl).travel and We their energyselected loss and the is total neglected. number ofline events Only is above 1000 hadronic which in each taus and case. are electronic We more also decay draw likely events a to horizontal are solid leave the detector and a dash-dotted line below log( in section of section flatly in log holes not producing muonsfrom are taus not as shown. evaporationthe products We total (See also muon figure neglect energyhistogram) the to and possible total BH additional shower events energying contributions with ratio evaporation across for all log energy flat ranges neutrino for flux. CC events Dashed (black black and blue lines show the distribution of Figure 5 tions (colored dots) and to simulations with extra dimensions. Lowering butions. The dashed lineregion depicts in which where 90% of JHEP04(2020)187 . 3.1 ) due ◦ 001 for details. . 0 5 ∼ =1 TeV, 2 TeV, 3 TeV, CC (shaded black) and ? τ . See section ν (typically M neutrino flux and a minimum ◦ 3.1 in 2 threshold, the solid line shows CC is peaked at the negative 02 − A . τ 2 E E ν E = 1 E . ◦ 1 . – 16 – charged current events (black circles). Red, magenta, green events. For about 12% of black hole events, more than τ 1 TeV to produce a clear second cascade. Tau energy loss is ν ], around 0 > 92 τ E multitrack histogram of the energy asymmetry factor is the result of multiple tau leptons decaying electronically or hadronically the energy of the first cascade versus the energy of the second cascade in black . We require Right: 5 -bang Left: n . that the angular separationto between beaming tracks — is below muchachieved with 0 lower IceCube than [ the angular resolution that can optimisticallyat be different distances from the primary interaction vertex, leading to several cascades one muon or tau track can be produced from BH evaporation. However, we find The High-multiplicity = 3 TeV black hole evaporation (shaded green) for a log flat neutrino spectrum with infinite 2. 1. ? seen in neutrino events, theand high unique multiplicity event of topologies: BH evaporation products can lead to new a BH component, but will require more statistics to3.3 infer the presence New of BHs unique on topologies In its addition own. to a modification of the production rates of events of the topologies usually detector are selected and the detector geometry is described in section is peaked at large positiveend. values for The black distinction hole is eventsBecause consistent and with the the distributions discussion do of overlap, double the bang double events bang in distribution section can be used to exclude appear as “double bang-like.”way In each as case, figure 1000 doublenot bang-like included. events are simulated inM the same detector volume. Dashed lines show theenergy corresponding deposition cases of using 20 PeV. For these, in contrast with the shaded bars, only tau decays inside the Figure 6 hole simulations (colored dots) and and blue dotsand correspond 10 to TeV, simulations respectively.the in The region 6 dashed above extra which lineregion dimensions below most depicts with which of the most the of the taus taus leave are the supposed to detector, decay and within 100 the m. dash-dotted Events line in between shows would the JHEP04(2020)187 - n , wherein a ± τ ± neutrino spectrum between τ 2 − E double black hole bang – 17 – ± ± = 3 TeV in IceCube-Gen2. μ μ ? ± μ ± M degrees. μ 2 , one may even see a ? − . M 7 ±  τ ν E ± τ kebab double black hole bang multitrack n-bang can occur when high-energy muons are produced simultaneously with one ± τ kebab . New event topologies that can arise from neutrino-nucleus interactions that result in the BH-induced shower. the detector. Kebabsassumption. account for Note that about there 3% is of about total 1% BH overlap between events multitrack with and thehigh-energy kebab. evaporation same product flux interacts again in the detector, producing a second bangs account for about 0.2%20 of PeV total and BH 10 events for EeV assuming or more tau leptons.or Tracks can from either tau be decay produced within by the muons detector, from or BH high evaporation energy taus (above 5 PeV) escaping in a row. We require the mutual separation of the bangs to be larger than 100 m. In the event that The Unless one of these smoking-gun signatures is seen, we have shown in this section that 4. 3. These are illustrated in figure event topology allows forproduction a rates limited can be identification different of from BH the events: SM track case, and and double-bang more importantly, the ratio of hadronic or electronic decayssignatures. of energetic Note tau thatboosted, leptons opening these resulting will angles in be are time-delayed well cascade greatly below (“bang”) 10 exaggerated: because the collisions are highly Figure 7 creation of a microscopic blackhole hole. as a See black text circle. forproducts Because technical of most description. weak evaporation decays, Here products there we will willwhich always represent be be the propagate hadronic, a black electronic, large cascade at or distances the low-energy interaction in vertex. the High-energy ice muons are shown as orange arrows. The blue circles represent JHEP04(2020)187 , here y . The shower (where ]: rather than 8 ν 48 hadronic cascade /E e E ) = y − s after the first, and is due to µ ], which models subsequent propagation, 94 , 93 – 18 – interactions produce an electromagnetic cascade, largely e ν parameter commonly used to indicate the fraction of the neutrino energy y s is the largest, and comes from the immediate energy deposition by primary ] found that this leads to a distinctive three-peak signature in the time-evolution 7 − 48 The time evolution curves of the Cherenkov light produced when a single 1 PeV color- As in the previous section, we perform our black hole simulations using our modified Electromagnetic and hadronic showers are not spatially distinguishable. However, In the SM, charged current photons. We note onetreating improvement hadronic with events as respect a towith single hadron, the the we aid analysis will of in include Pythia, the ref. which full [ leads effects to of hadronization slightlyneutral more particle overlap is between injected NC into and the CC ice events. are shown in the left panel of figure few muons (which come fromthird meson peaks decay) and should neutrons, be the much amplitude lower of than the in second hadronic and version showers. of BlackMax, and pass thesedecay. results to This Pythia output 8 is for then hadronizationdecay, fed and and into heavy particle FLUKA interaction [ with the detector material, including the production of Cherenkov around 10 particles. The secondthe peak decay is of low-energy visible muonsbetween between produced 0.1 1 in and and the 1 shower. 10 for ms, The all is third, types due reaching of to its interaction, maximum neutron but capture. because This CC three-peak events signature produce is electrons predicted which lead to very given that their compositionshadronic are showers, quite as copious different, neutrons oneice. and can Ref. muons [ search decay for andof an recombine the with “afterglow” Cherenkov nuclei from light in produced the by a high-energy neutrino. The first peak, which crests transferred to the quark),to as the most electron. ofwhich In can the contrast, lead incoming neutral to neutrino’smuch large current momentum lower numbers events in is of are energy neutrons transferred than seenoutgoing and the via neutrino. pions incoming their in neutrino, as final most state. of These the are energy typically remains with the hadronic shower. resulting in electrons and positrons,Electromagnetic and cascades a very typically few occur hadrons, atis which large cascade the values to Bjorken of low energies. (1 In both SM andfeature of black a hole BH events,drawn event randomly showers is from are the the the rapid SM.of production Including most those all of common polarization a SM topology. states largethat degrees and number shower-type colors, The of events of a caused main freedom high-energy large by particles, number evaporating lie BHs in will be the characterized strong by a (quark high-energy + gluon) sector. This means help distinguish BHs from SMwhich events. represent In the the majority nextunique of section, signature we there predicted turn as observations, to well. and shower-type events, ask whether BHs4 lead to a Cherenkov timing and light echos track-to-shower energy (or second-to-first cascade, in the case of double-bangs) can further JHEP04(2020)187 as a + π (dashed cyan), − will continue to K is shown in red and 3 + π , noting that the second s as the third peak. The µ 8 ]). We therefore use (solid cyan), 48 + are respectively the energy of the K E and p E , we provide coefficients for the peak energy fit – 19 – 3 (dashed red), proton (solid magenta), antiproton(dashed − π we expect that the relation in table GeV, where a s for the first peak, and after 16 1 µ GeV) (solid red), energy of the first peak (line with diamonds) and third peak (line with E/ ( + b π , which grows less efficiently as the particle energy increases. Although = + p Right: π spectrum of Cherenkov light produced as a function of time by propagating a E Left: . The energy of the peak is nearly proportional to the energy of the particle, except for (long-lived eigenstate, dash-dotted cyan), electron (solid blue), positron (dashed blue) and FLUKA is not parallelized, and such a computation requires more than one CPU month. 1 0 L the third peak of we have not simulatedto the computational propagation requirements, of particleshold with up energy to higher at than least 10 10 PeV EeV due in the absence of new interactions. We can also construct a a double-cascade will thus notlinearly overlap with with the the particle third echo. energy.to In a The table peak power law: energies scalepeak almost and the injected particle. and third peak areproxy perfectly for correlated hadrons, (as and alsoseparation, electrons shown we for in will electromagnetic [ focus showers.we on count Because the the of third photons the and beforeprimary larger 1 first peak time peaks. from To the estimate decay the of total any tau peak event energy, that is not long-lived enough to be seen as signatures clearly fall into twopeaks, categories: and hadrons, electrons which and producemuon photons larger and second which neutron and production. lead third to Differentguishable particles electromagnetic from within each showers each other, with category but suppressed are10 the nearly echo times indistin- energy from larger thescales than hadronic shower monotonically, that is as typically from shown about in the the electromagnetic right-hand panel shower. of figure The behavior with energy on the upper one. asterisks) in the Cherenkov lightelectron spectrum is as shown a in function blue.10 of PeV The particle equals peak energy. the energies energy are of normalized the so injected that particle. the energy of the first peak at Figure 8 1 PeV particle in iceare using simulated including FLUKA. The y-axismagenta), is neutron in (solid arbitrary green), units.K antineutron Relatively (dashed long-lived green), particles photon (dotted blue) — these last three overlap on the lower curve, whereas the others overlap JHEP04(2020)187 ) 4.1 CC and neutrino τ 2 ν − E plane. is the energy of the 1 p p E E - 5 3 31 − − , whereas the black hole r CC shower events cluster ν . The result is shown in 10 10 τ ν × × 3.1 65 (4.1) . 45 71 . . 2 GeV, where ydφ/dE a − 1 p E particles, which decay to photons, can GeV) 10 0 E/ π ( b a b = 1.03 4 1.00 1.00 1.02 0.738 p 0.901 1 114 log . – 20 – E 0 − = 31 r CC events after hadronization. Since most of the momen- + − + − 10 e π e π e ν . log is the energy of the injected particle. y , the energy ratio between the third and first peaks. Using the 1 p E . We see that most of the NC events are above the Hadron Line /E 9 3 1st peak 1st peak , we find: 3rd peak 3rd peak p and . This is because the amplitude of each peak scales with the number 3 E 8 ≡ 4.1 , we also show 31 , thus require a higher neutrino energy to produce a shower with the same r y 9 CC, we consider tau decays within 100 m to be showers (rather than double τ CC are much more likely to leave a track or produce two cascades than a single ν . Best-fit parameters of the relation τ being determined by , i.e. the peak ratio decreases with increasing particle energy. We will refer to eq. ( ν + For In figure On the other hand, black holes, which burst into a mixture of hadrons and electromag- However, actual NC events do not produce single mesons. Rather, hadronization will 13 π r bang events) since in such casethe it primary will one. be challenging Note tofrom that distinguish for the such second high cascade from energyshower. neutrinos We (20 nonetheless PeV include ortau higher) them decay tau in with leptons Pythia the 8. analysis. We see As from above, the we figure simulate that the few at higher energies. Thisproduction is cross because section the has NCpeak no rate dependence at goes on low transferred as energy. momentum. This NC is events, strongly which suppressed by the power law flux. lower the peak ratio in individual events. tum goes into the leptonof in such events, they mainly fall below the Hadron Line,netic the particles, value lie right in between. However, when compared to NC events, they cluster spectrum is assumed fromthe left 20 panel PeV of todescribed figure 10 in EeV eq. asof in hadrons section in a jet,the but figure, the though ratio the remains occasional constant. production This of pushes the events to the right of lead to a jet offinal multiple signature mesons to and look baryonsstructures. like as a well To linear as model combination electrons ofwith this and the photons, the correctly, hadronic causing momentum we and the transfer simulate electromagnetic expected NC peak in events an by NC hadronizing event an using up Pythia quark 8. An for as the “Hadron Line”, as it forms a distinctive separation on the Table 3 peak shown in figure new variable parameters in table JHEP04(2020)187 in D (4.2) . For ν ν CC are dφ dE e ) ν ν 1]. E . ( 0 , eff 1 . , events in which M 0 ) ν neutrino spectrum − E 3.1 , muon tracks (total ( 2 distance of events from σ − ν 4 ν E dE . CC (red) and black hole with R CC and black hole production Right: τ ). The number of simulations is 65 ν τ . ν 4.1 + 2 and double-bang events (energy CC, 31 e r ν 10 3.2.1 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0 0.5 0.4 0.3 0.2 0.1 + 1 CC (green), spectrum is simulated assuming (1:1:1) flavor 2 e 2 ν + log − 114 1 E . p 0 – 21 – E √ 10 114 log . ) for NC (blue), 0 . 4.2 ≡ . As expected, NC events are mostly positive while D CC showers can reside above or below the Hadron Line. 3.2.2 9 τ ν CC and black hole events mainly fall into the region [ third peak to first peak energy ratio as a function of the energy of the first peak. τ = 3 TeV and 6 extra dimensions. The solid lines enclose the 90% regions corre- ν ? M Left: . Next, we look at the distribution of events according to their distance from the Hadron = 3 TeV (black). The single Hadron Line is again shown in dashed magenta. is positive above the Hadron Line and negative below. We show the histogram of ? 5.1 Showers We begin withwith shower (1 events. : 1 We(corresponding : to again a 1) assume CM flavor energy antaus of composition 4.5 decay isotropic, TeV). and in Note require that the unlike detector a in after minimum section traveling energy farther deposition than 100 of m 20 are PeV classified as double-bang We now determine the numbertion of observed based events on required to showerstrack ascertain (Cherenkov energy black echo hole to information) produc- showerasymmetry) from energy from section ratio) section from section D the right panel ofnegative, figure and 5 Detection prospects on the decay channel, Line: SM interactions an up quarkcases, is only hadronized shower as events and partthe of tau Hadron the Line decay defined final within in state 100M eq. particles. m ( are In selected. both SM and BH at energies between 20 PeV and 400 PeV, due to the tau decay requirement. Depending Figure 9 Neutrinos from 20 PeV tocomposition. 10 Blue, EeV green, following red the events and with black dots depictspondingly. NC, The dashed magenta lineproportional is to the the Hadron number Line of of eq. events ( predicted in the detector, i.e. JHEP04(2020)187 , 4 ), > 10 sh ? sh BH (5.3) (5.4) (5.1) (5.2) × M N /E ) µ ? , 6 is repre- CC only 3 E ( τ CC shower e 10 ν CC 10 ν τ D,M f × are similar to ν ( , log τ CC BH ν ≡ 79. we then compute CC f . f , ξ τ λ . Events where the sh + ν A = 0 CC and N and E ) CC e , ν D CC τ , NC sh ( ν τ f sh ν N τ CC ) ), and compare the unbinned ν N , ? f D ( ), , and  + ) ) i τ 9 CC ν 3.3 D,M D ) CC f ( , ( max e f sh + ν a, a max N N a, N ) ( CC , ) and ( N SM+BH D e ( sh obs sh ( ν =1 f i Y N 3.2 N e SM a CC ) ν L N f SM+BH D – 22 – ): − selects the events satisfying the minimum energy ( L neutrino spectrum are shown by the dashed lines + e , black holes dominate the events, while for e  4.2 2 CC ν ? BH − NC f ν , f ) = M E a 2 ln sh + N − N ( CL respectively, while the numbers grow to 7 ) NC = 3 TeV at least 2, 16, and 45 events are necessary to claim , L = ) and σ D ? sh ( λ = 10 TeV. . The distribution of the BH events is not very different from 3.7 N M ? are given by eqs. ( 5 NC ) f ). For low and 5 M distribution (Wilks’ theorem). The results are shown as dashed D ( NC σ , 2 B assuming an . For χ sh ) = NC ? , 3 ξ f σ D N M ( . We allow the flux normalization to vary and calculate the test statistic ? . We find the number of observations required to discover BHs increases SM ) = M ? and events for f 10 5 is chosen to maximize the likelihood in each case. From is given by eq. ( from the Hadron Line eq. ( (appendix CC , 10 e D,M D sh sh ν BH 12 ( × max N N a, 6 . shower events from SM+BH distribution N CC events shift to the left, due to the minimum energy cut we impose on the shower sh obs SM+BH -values assuming a µ f We then proceed to addthe information distributions from muon of track events.in Defining the right panel ofthe figure case where they wereν evenly sampled across every decade in energy. However, the SM dramatically with a discovery at the 1 and 1 5.2 Muon tracks and p lines in figure where the likelihood is defined as: in figure 8 TeV, the distributionN is barely distinguishablePoisson from likelihood the when SMwith reconstructing the case. the same events Next using we SM generate and SM+BH distributions of LEDs, the distribution includes both SM and BH interactions: where deposition condition, as in the NC case. We provide a plot of these combined distributions where sented by the green histogram inthe the blue right and panel red of histograms figure regardless of the minimum energy deposition. In the presence tau decays within 100 mtrack. are As still considered mentioned before, as showers, becausemake unless of up the the about decay high 2% results neutrino of inevents energy, total in a showers shower the from muon events Standard in Model SM.distance case, Combining we NC, obtain the following probability distribution for the like events (dubbed “DBL”), regardless of the energy asymmetry JHEP04(2020)187 σ , 3 (5.8) (5.5) (5.6) (5.7) σ , ,   ) i tr BH ξ ( N ) f ? tr p a CL with all shower, muon track effective volume and 10 years of ξ, M N CC 3 ( σ , µ tr ν tr obs =1 BH ). In the SM case we simply have: i Y N N f NC . , and 5   ) + 3.7 + sh ξ σ (   N ) NC CC , i µ , 3 , CC ν µ + σ sh tr D ν f ] with 50 km ( ) and ( N N f CC ) , 96 , ξ sh + e ) = 3.2 – 23 – sh ( ν p ξ 95 ( a N µ CC CC , ν N e SM f sh ν f sh obs =1 N i Y N ) = ?   = a sh N p ξ, M − ( e are given by eqs. ( ) = a SM+BH tr BH N f ( N are the proportion of shower and muon track events. In the SM, L tr p and CC and . Total number of observation required to discriminate black hole production. The , µ tr ν sh CL using only information from showers while the dash-dotted blue lines use both showers p N σ where The likelihood using both shower and muon track events is now energy, making the distributions harderincluding to both distinguish SM from and one BH another. events The reads distribution where and muon tracks.IceCube-Gen2 assuming The SM dashed only green interactionswith and both line solid SM and depicts green BH lineat the interactions. shows the The expected the dashed expected P-ONE total and observations in-ocean solidexposure number orange neutrino in lines of SM telescope show observations the and [ expect SM+BH at observations cases. Figure 10 shaded regions from lightand to double dark bang-like events correspondand included. to 5 The 1 dashed blue lines from bottom to top show the 1 JHEP04(2020)187 ). tr obs 5.5 N (5.9) (5.10) 7 TeV, > and . We find . ? ) by includ- sh obs 10 M   ) N 5.9 i A E ). The results are ( f 5.3 ) and ( dbl p tr 5.8 BH a , up to nearly an order of N N . ? incoming neutrino spectrum + dbl obs M =1 2 10 i Y N − ν CC , . Since more energetic taus are sh BH   µ E tr . Compared with the shower-only ν 77). The number of observations 6 . N   N ) 10 i + ξ + = 4 corresponding to the expected number ( f NC , by extending the horizontal area of the , sh BH 3 10 tr CC sh , p N a τ N dbl ν + N + N . We also include sensitivities for the proposed tr – 24 – obs NC =1 , i Y N CC , sh e 3.1   sh ν N   N ). For SM+BH the distribution is similar to eq. ( ) + A i E rises towards 10 TeV. This is mainly because the shower D ]), located off Vancouver Island. P-ONE has a modular ( CC ( , ? e f 95 τ sh ν CC ν sh M f N p a = N ) = increases in both the SM and BH cases compared to the log flat A sh sh obs p =1 A E i Y N ( E   SM ]. For this projection we take an efficiency similar to that of IceCube- . With BH events, a f N sh 96 p − e − This scenario is depicted as orange lines in figure ) = 2 a = 1 is given by the same relation. We again generate mock data sets with N tr tr ( p p We also draw green and orange lines in figure L This is not quite equivalent to simply scaling the volume, as the likelihood of observing a double-bang 2 instrumented [ Gen2, but increase the effectivedetector. volume to 50 km event before the tau escapes the detector depends on the geometry. and SM+BH (solid) cases. Tothe compute these effective sensitivities mass for IceCube-Gen2 discussed (green),Pacific in we Ocean use section Neutrino Explorer (P-ONE),Absorption the length full-scale follow-up In to Water STRAWapproach, (Strings [ and for by deploying several clusters of strings, up to 50 cubic kilometers could be ing the expected double-bang-likerequired events in ( this casethat are adding shown double with bang the informationdue shaded improves to regions the the (solid sensitivity limited lines) mildly fraction in only of figure at double bang-like eventsof in observed the neutrinos at total future observations. experiments with 10 years of operation in SM only (dashed) In the SM case The frequency of each topology is recalculated in analogy to eqs. ( is shown with dashedprone lines to in escaping the theenergy detector right asymmetry instead panel of of creating figure distribution. a We second then bang, arrive the at probability our of full large likelihood: interaction. 5.3 Double bang-like events Finally we add double-bang informationtion so of the that two-bang all energy topologies asymmetry are in included. the case The of distribu- an shown as dash-dotted lines inanalysis, the this right panel leads of to figure magnitude a improvement slight as increase insignatures sensitivity become at indistinguishable low from onegenerate another, an whereas excess the of BH lower-energy events muons continue with to respect to the total shower energy in each and from the SM+BH distribution and build the test statistic using eq. ( and JHEP04(2020)187 ) σ (5 (5.11) σ (rather than ) and P-ONE σ (2 σ we find, unsurpris- exclude 10 1 TeV (4.3 TeV) at 3 ]. If our Higgs vacuum is (typically estimated to be . 5 I , 105 < –  ? ) 97 M ) max a, max 3 TeV (5.1 TeV) at 3 N a, . ( 4 N ( . To obtain this we follow the above steps, < ? SM ? M L SM+BH M – 25 – L  . If these are observed via their unique signatures as I 2 ln − = 6 extra dimensions. While IceCube-Gen2 is expected to = λ n ] for 68 ), i.e. [ σ 5.3 we show the number of observed events required to ]. However, this decay time can be dramatically reduced in the presence of eV) above which the Higgs quartic coupling term becomes negative. This 11 20 107 10 , 3 TeV at 2 . − 5 106 ], the authors showed that this can be used to place constraints on extra dimensional 19 In figure IceCube-Gen2 allows for the discovery of BHs with with larger detector volume and exposure. > 12 10 ? ? holes are forming from collisionsergies, elsewhere and in that the these, cosmos too, withof are even higher a unable CM to black collision trigger hole en- vacuumimplications evaporation decay. for In signature this the in way, ultimate an athe observation stability next-generation dimensionality of neutrino of our spacetime. telescope cosmos would in have addition to providing clues about ated through the collisioncreate of black holes astrophysical of neutrinos massesdescribed with above in nuclei Λ the could, previous inphysics sections, principle, beyond their presence the also will Standardor constitute Model in indirect (either addition evidence associated to for with it)black new that the holes provides extra are Higgs dimensional potential created theory corrections in that collisions stabilize with the detector vacuum. nucleons, If this will be a sign that black the decay timescale is,verse in [ general, expectedan to evaporating black be hole, much if longerIn the [ initial than mass the of the agetheories black of hole in is the which above Uni- cosmic the instability ray scale. collisions can create black holes. Similarly, black holes cre- Several authors have explored the potentiallyoration catastrophic consequences in of the black hole contextindeed evap- of metastable, Higgs then vacuum∼ there metastability exists [ anopens instability up scale the Λ possibility for stochastic vacuum decay via a tunneling event, for which exclude the Planck scaleM comparable to LHC, P-ONE has the potential to exclude6 higher Vacuum instability probability of SM is small,number of while the SM reverse observations in isGen2 not IceCube-Gen2 allows for true. and the P-ONE We exclusionpushes also with of show horizontal the BH the lines. limit with total IceCube- toM expected 6 TeV (6.9 TeV). This can be compared with the current LHC limit with the same likelihood functionsingly, as that above. more observations Comparing are withconfidence required figure to level, exclude since BHs a than BH discover them may at lead the same to more extreme values of observables where the CL and P-ONE improves the sensitivity limit to 6.9discover) TeV (5.9 black TeV). hole productionbut for certain generate mock observationsthe from inverse SM-only of eq. processes. ( The test statistic is defined as JHEP04(2020)187 ? σ M , 2 σ CL with all showers , muon σ and 3 σ , 2 σ – 26 – We first examined how the flavor composition of high energy = 3 TeV and 6 extra dimensions, we find the purely tau neutrino ? M = 6 extra dimensions is shown in black for comparison. n . Total number of observations required to exclude black hole production as a function of CL using only information from showers while the dash-dotted pink lines use both showers deposition of 20 PeVand and double built bang the events likelihood intau based 10 tracks on and years the double of number bangs IceCube-Gen2reconstruction in of run. the framework shower, We analysis, track at stress aiming ultra that atduction we high a with include complete energies. flavor composition With the assumption of BH pro- Flavor composition. neutrinos detected at theWe Earth focused on could neutrino change energies due between 20 to PeV the and 10 production EeV of with a black minimum holes. energy σ • . The shaded regions from light to dark correspond to 1 ? time, we have investigated the newtelescopes signatures such of as black IceCube-Gen2. hole production and decay in future 7.1 Signatures ofAstrophysical new neutrinos physics can reach energies updimensions, to microscopic tens black of holes EeV. Incenter can the be of presence produced mass of large in energy extra up neutrino-nucleus of scattering a the if myriad collision the of is possibilities above in the the Planck scale next in generation the of bulk. neutrino telescopes. This opens For the first and muon tracks. Dashedat green IceCube-Gen2 and orange and lines P-ONEat depict within 95% the 10 expected CL years for total assuming number SM of only observations interactions. LHC bound7 on Conclusions Figure 11 M tracks and dobule bangand events 3 included. Dashed pink lines from bottom to top show the 1 JHEP04(2020)187 CC. τ ν CC are e ν CC, in cases τ CC, regardless ν µ ν CC and µ ν contrasted with SM A E and, if seen, may be a clear sign -bang, the kebab and the double 1 TeV, IceCube-Gen2 can resolve . n 5 3.3 < 9 TeV. In terms of exclusion, the limits . ? 6 M When this applies to double bang events, based on the BH shower, track, and double < ? ? M M for a summary of our projected limits. We note – 27 – We also show the signatures of tracks and double 4 ]. This is to say, tau track events from the SM are 108 In addition, the time evolution of Cherenkov light en- energy ratio than muon tracks. Therefore, full energy de- sh = 3 TeV as a benchmark throughout the paper to illustrate We also find that BH production may lead to unique topologies /E ? tr M E CL within 10 years. A fully upgraded Pacific ocean detector with a σ , since muons from Hawking radiation carry only a fraction of BH energy. ? M effective volume will be sensitive to 3 Hadron Line. We found thatfound NC below, events while cluster BH above events the lie hadron in line between. and ables us to breaksimulated the the degeneracy propagation of betweention. different SM particles and We in find BH ice that insingle to the Hadron shower obtain neutron Line, events. the echo-to-primary which timing We isphotons. peak informa- have roughly ratio We 10 then of times built a larger a hadron than new falls the variable onto ratio to a of quantify electrons the and distance of peak ratio to the Unique topologies. that do not existblack in hole the bang. SM: These theof are multitrack, new described the physics. in section Cherenkov light timing. of Double bang energy cascadewe find ratios. BH decay suppresses theshower, energy resulting ratio in between a the large second shower energy and asymmetry the factor first the flavor contour wouldratio prefer in mostly that muon scenario is neutrino excluded scenario. atTrack muon-to-shower 95% The ratios. CL. (1:1:1) flavor bangs from BH production.energy-to-shower energy We ratio have in shown the that BH the case tracks compared with feature SM a lower muon case would be strongly disfavored due to the lack of double bangs in BH events and We have been using • • • • pendent analyses of the track-to-showerin energy ratio which combining black hole production is present or not,the are ample signatures desired. brought This about is byever, large left we extra for dimensions note future in that neutrino work. telescopes. all the How- signatures remain valid for higher Planck scale. We also note are 4.3 TeV and 6 TeV instead.that it See could table be challengingogy. to Nonetheless, distinguish muons muon and taus tracks suffer fromthe from tau average different energy tracks energy loss merely loss when from rate propagating,a topol- of where muon a at tau is energies typicallycharacterized above one by 10 a order TeV lower of [ magnitude lower than that of number of observed high energyproduction neutrino as events a required function to ofbang discover the or Planck signatures scale exclude discussed black above. hole BH We production found at for 3 50 km 7.2 Exclusion andTo detection forecast prospects the power of future detectors to test extra dimension models, we computed the JHEP04(2020)187 ] ] 109 110 ], Pierre 112 for exclusion 3) 0) . . 11 ) 4 6 σ < < (3 ] are sensitive to the 1 ( 9 ( σ . . ], HAWC [ -bang search and thus 6 5 114 n (TeV), exclusion < < 111 ? M for discovery limits and 10 3) 9) . . ) 2 4 5 σ < < – 28 – (5 1 ( 9 ( σ . . 3 5 6 (TeV), detection < < ? M ] have already been obtained from proton-proton collisions 68 [ ? M ], the planned EUSO-SPB2 and POEMMA [ 113 ], are able to detect the radio emission from shower originating from 115 P-ONE Experiment IceCube-Gen2 . Projections for the 6-extra-dimension fundamental scale that can be detected or excluded If LEDs exist in nature, the next generation of neutrino telescopes could allow us a We have focused on future “plum-pudding” configuration IceCube-like Cherenkov tele- improve the sensitivity for BH discovery. A detailed analysis isglimpse also beyond left our for four-dimensional furtherena, brane. work. the With observation a of plethora microscopicinteresting of black in new holes itself, and in but unique neutrino-nucleon also phenom- interaction opens is up not the only window to new physics above the Planck scale, Auger Observatory [ Cherenkov emission induced bye.g. air GRAND showers from [ tauEarth-skimming decay, neutrinos and with future unprecedentedtelescopes radio sensitivity. will telescopes, We considerably stress enlarge that the these effective neutrino volume for BH track energy and time evolution ofradio Chenrenkov telescopes light are are still not a powerful availableevents, tool in which to the determine can radio the detector, be shower energy complementaryact ratio to in right double IceCube-Gen2 below bang BH the searches.the horizon Neutrinos or rock may inside and inter- mountain subsequentlyneutrinos. ranges, decay producing Gamma in tau ray the leptons and which air. Cherenkov leave telescopes These like neutrinos MAGIC [ are called Earth-skimming tector exposure, which willsignal likely can occur thus before provide the additional Future motivation Circular and Collider. guidance for Any that positive scopes. project. Other types ofshould experiments have are an also planned. effective volume The 20 IceCube-Gen2 times radio larger array [ than IceCube-Gen2. Although the muon produce black holes indifferent. proton-proton Such collisions models and cantion neutrino-proton only in be collisions colliders directly are and constrainedastrophysical vastly neutrino neutrino by energy telescopes. comparing of tens black of Furthermore,higher hole EeV, considering produc- than we might the 100 eventually TeV expected explore in the highest Planck future scales upgrades of neutrino telescopes, merely by increasing de- at the LHC, whichP-ONE. is Compared with comparable hadron to colliders,as the IceCube a exclusion and study other limit of neutrino of quantumparticle telescopes gravity IceCube-Gen2 can detection in serve but capabilities, neutrino-nucleon inferior scattering, andwhere with to systematics. quarks different microphysics, For and example, leptons in are split-brane confined models to [ different slices of the brane, cross sections to with upcoming experiments. Weand consider P-ONE detectors with with the 10limits proposed years for properties of a of running range IceCube-Gen2 time. of fundamental See scales. figure that stringent limits on Table 4 JHEP04(2020)187 (A.1) (A.2) , ) τ min E − ) where Ξ =tr and ) y , 3.2 ) − min (1 ν E E 174 is the branching ratio of − . y )Θ( ν = 0 E min µ f Θ( E charged current interactions. In the ) , − τ τ , y ν y ν ν ) but the total cross section is instead CC is given by eq. ( E E ( dy µ 3.2 and ν µ CC ν µ ν )) Θ( – 29 – dσ ν E dy ( 1 0 is the probability for the tau to leave the detector. In ) esc Z P , y ) esc ν µ P f E ) = ( ν dy − E τ ( CC ν tr dσ + (1 → N µ dy µ f CC is also given by eq. ( 1 ν ( 0 σ τ Z × CC events can also leave a track. This can be realised either when the ν is the differential cross section in the interaction. The step function Θ is τ ν ) = ν nucleon interaction cross section is given by E /dy = 5 PeV is the minimum energy of the − ( ). µ The tracks can be produced in µ tr ν CC ν ]. The number of track events from τ min → 3.1 dσ E 76 N τ ν Taus from σ where a tau decaying into muons, and section tau decays to atrack muon events or from when it escapes the detector without decaying. The number of where added to satisfy requirementenergy of associated the with the minimum track energy to deposition be (we above require 20 PeV the in cascade our flavor composition analysis in latter case, a tau produced inWe the generally interaction can require either decay the totrack tau muon [ or energy leave the to detector. bethe total higher than 5 PeV to clearly identify the tau A Expected topology asIn a this function section, of we neutrinodifferent present event flavor the topologies. cross sections of Standard ModelTracks. interactions classified by for Innovation. Research at Perimeterthrough Institute is the supported Department by the of GovernmentProvince Innovation, of of Science, Canada Ontario and through Economic the Development, Ministry and of by Research and the Innovation. We thank Shirley Li for help withinto FLUKA, accepting and neutrinos. Shivesh Mandalia We further for helpingWe acknowledge Dejan coax also PYTHIA Stojkovic thank for the insightful anonymous comments. for referees inspiring for discussions insightful about comments. theDonald NS project. Canadian thanks This Astroparticle Francis work Physics Halzen was Research supportedat Institute. by the Computations the Centre were Arthur for performed B. Advanced Mc- Computing, and supported in part by the Canada Foundation mic ray telescopes may shinebeyond light the on scope its of mystery, and our enable world. us to explore the dimensions Acknowledgments including insights into the stability of the Standard Model. Near future neutrino and cos- JHEP04(2020)187 ] τ if ν 77 z ) (A.6) (A.7) (A.8) (A.3) (A.4) (A.5) y are the − 2 ] without , , (1 E ) ) 20 PeV. In ν 70 A E > τ ) min E ( 2 and E = ) ]. Following [ E min 1 H 2 − τ E E min 76  E + ) ) 1 E y − 3. Another criterion . ) E 0 − − min z ) E ≤ − (1 y ν − , ) where A − 2 z E 3 )(1 . E ) y E 0 y (1 ν , ≤ − )Θ( = 967 m is the average distance + − ≤ E CC interactions is . i 1  A 98 min τ L . 0 E  follows the distribution +(1 h ν ( E t 0 E )Θ( +(1 0 t y / γτ tr y − ( ) , t . ≤ − ( γτ 2 ν − min i ν y E E −  E L 98 ν E γc . h  − E 0 is obtained from eq. (22) of ref. [ − Θ( Θ( 1 cylindrical detector with a height of 1.25 km i = exp y with the average tau energy is given by − while the energy of the second shower depends e ) for a hadronic decay and E ν db L 3 had 0 )Θ( db τ h z y P 1 y esc E – 30 – P if otherwise ν γτ = ( − e) − /m ) = exp E Θ( , , τ ν A ¯ → t > t 1 0 (1 = × ) = had) )(1 E E ) E ν dz ( τ τ y 1 ( ) ( ¯ ,y E = → E dz E | ν esc − , y t τ γ dn × ν P E ( ( ) = ( (1 ) f E dy A ν dz ( dn dy τ in the boosted frame and 1 E , y E CC ν ( τ 0 ν CC τ ν dz Z = E dσ H 1 s is the average lifetime of tau at rest. This yields ( 0 dy dσ 2 + Z dy τ E 13 CC ν 1 dy  − 0 1 0 Z × dσ R 10 A “double bang” signature is produced when the tau created from a dy × ) = 1 ν 0 is the energy distribution of the daughter neutrino or electron in the tau R 91 E . 78 GeV is the mass of tau. The lifetime ( . ] and db ) = = 2 ν → = 1 is the lifetime of a 0 ) the cross section of double bang events from 116 dn/dz N E τ t τ ( τ ν τ 3.2 m ¯ σ E decay [ The energy of the primary shower on the decay channel; where is that the minimum depositedeq. energy ( must be at least 20 PeV, i.e. charged current interaction decays electronicallymakes or hadronically a inside visible the detector, secondit which shower. decays to We clearly requirewe separate construct the the the tau second energy shower to asymmetry energy from travel of the farther the primary than first one and 100 [ second m showers. before We require where Double bang. and the dust zone. The boost factor and a radius of 1.42 km, the criterion for a partly contained tau track is roughly where the tau travels before leaving the detector. IceCube-Gen2, which we model as a 7.9 km JHEP04(2020)187 , ) , A ) A (A.9) E ( (A.14) (A.13) (A.11) E ) ( ) H A ) ) A H E ) ( E min ( min , H min E E ) H  ) E ) − − min − ) z min ) z E ) min z E y E − − − − − z − ) (A.12) ) ) , )(1 z z y )(1 ) y y min  − y + (1 − 0 . − E − tr y − ) t )(1 ( γτ − y ν , y − y + (1 E +(1 ν + (1 − ν  + (1 y y E y ( E ( ( ( y ν dy ν )Θ( ( ν +(1 e y Θ( E ν exp E CC interactions where all the neutrino CC E ν ) y E ( e − − Θ( ν dσ ν , y Θ( )Θ( Θ( ν  (1 e) E y 0 ν e dy E sh had sh ( − db 1 E Θ( P dy → t P γτ 0 dz i CC interaction is more tricky. We consider two (1 Z τ e) e) NC − ν ν ( – 31 – τ  E ν had) → dσ → had) dn ) = ) dz dz τ ν τ → dz dy ( ( dz , y → dz E τ 1 ν had) 1 ( 0 ( 0 τ ) and the total cross section reads dn dn E R ( sh Z ( → ) = exp dz dy ) dn dz dz ν → 3.3 dn τ τ 1 1 ( CC N , y 0 ν E dz ) = 0 e ( ν R dz 1 ν ν Z 0 dn dσ ) E 1 σ R E ( 0 had dy ( , + ) , y dz Z dy e db τ ν 1 and the average energy of taus in hadronic and electronic decays CC 1 ν ,y 0  NC P 0 E ν R σ ( Z dy × dσ ) E ( τ /γc dy ,y CC ν dy ν τ ) = 1 CC ν 0 ν dσ E R ( dy E dσ ( dy τ CC Showers are produced in neutral current interactions from all neutrino flavors ν 1 sh dy 0 R 1 = 100 m → 0 ) (A.10) dσ R ν N τ db E dy t ν ) = ( 1 0 ν σ R E had τ ( ¯ = e τ E ¯ E types of shower events.In In the the other one case, case,energy the the asymmetry tau tau condition travels travels farther for lessformer than a than is 100 double 100 given m by m bang and before is decays it not in decays. satisfied. the detector, The but cross the section of the energy is deposited in the detector. The total cross section is The identification of shower events from where the rate is shown in eq. ( regardless of flavor. Showers are also produced in respectively. Showers. and propagates before decay. The probabilityin for the a detector tau is to travel farther than 100 m and decay where reads the tau decays to an electron or positron instead. We neglect the energy loss when the tau JHEP04(2020)187 τ ν , . ) (C.1) ) (A.15) (A.17) min min E ) E ) CC, and − − ) replaced by min increases, the ) min e z A 0 increases the E z ν E ) ? ) reads E y > ( − − M − 2.1 ) − H z z ) )(1 loss y f y − , ) + (1 − − y )(1 ) with ( y u, Q ν ( + (1 + (1 i − E , f y y A.11 ( (  ν i ν )Θ( 0 )–( X + (1 y E E db y t γτ − ( Θ( A.7 . We note that ν 2 max − )Θ( (1 e) y E  ν 13 − E → Θ( duπb dz exp τ e) s (1 ( 2 ν ) − → had) E dn loss dz – 32 – τ f ( → dz dz − 1 ) = 1 τ 0 had) (1 D dn ν ( / R 2 ? E ) 1 → dz dz ) by considering Standard Model NC, dn ( M ). 1 , y τ 0 Z A ( ν R dz 4.2 had ), which permits any use, distribution and reproduction in , E 1 ) = E e 0 sh ( dn ( R dy P , y H ) τ ν dz BH CC ν 1 − E , y 0 → ( ν R dy dσ ) τ E νN CC ν ( dy dy σ CC-BY 4.0 , y 1 ) = 1 0 τ ν dσ CC ν A R E This article is distributed under the terms of the Creative Commons E ( dy dy dσ defined in eq. ( ( 1 0 τ e CC H ν R dy D 1 0 dσ is the initial energy loss in BH formation. The BH production cross section ) (A.16) R ν ) = dy ν E loss 1 ( 0 E f ( R ) where e τ had is great than or equal to 50%. τ A ¯ = E ¯ E E ( loss e f Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. where including the initial energy lossBH is production shown threshold in and figure a significant drop in BH production rate is observed when C Inital energy loss andIn cross case part section of the initial particle energy is lost in BH production, eq. ( Here we show theHadron probability Line distribution ofCC the interactions, distance as of well thecombined as shower SM+BH black events distributions hole from become production. indistinguishable the from As the the SM. Planck scale For the latter case theH cross section is given by eqs. ( B Probability distribution of and and the average tau energy reads where JHEP04(2020)187 = 3 TeV and ? M assuming SM only D = 1 TeV (red), 3 TeV (pink), ? M – 33 – neutrino spectrum is applied with (1:1:1) flavor ratio and a 2 − E . Probability distribution of the distance from the hadron line . The black hole production cross section from neutrino-nucleon interactions as a function = 6 extra dimensions. The solid, dashed, dash-dotted and dotted green lines correspond to 0, of the incoming neutrinon energy by including the10%, initial 50%, energy 90% loss. energythe loss We black assume respectively. line. 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