Direct Detection of Kaluza-Klein Particles in Neutrino Telescopes
Ivone F. M. Albuquerque, Gustavo Burdman, Christopher A. Krenke, Baran Nosratpour
aa r X i v : . [ h e p - ph ] M a r Direct Detection of Kaluza-Klein Particles in Neutrino Telescopes
Ivone F. M. Albuquerque, Gustavo Burdman, Christopher A. Krenke,
2, 3 and Baran Nosratpour Instituto de F´ısica, Universidade de S˜ao Paulo, S˜ao Paulo, Brazil Department of Physics, University of Arizona, Tucson, AZ 85721, USA Department of Physics, University of Maryland, College Park, MD 20742, USA
In theories with universal extra dimensions (UEDs), all standard model fields propagate in thebulk and the lightest state of the first Kaluza-Klein (KK) level can be made stable by imposing a Z parity. We consider a framework where the lightest KK particle (LKP) is a neutral, extremelyweakly interacting particle such as the first KK excitation of the graviton, while the next-to-lightestKK particle (NLKP) is the first KK mode of a charged right-handed lepton. In such a scenario,due to its very small couplings to the LKP, the NLKP is long-lived. We investigate the productionof these particles from the interaction of high energy neutrinos with nucleons in the Earth, anddetermine the rate of NLKP events in neutrino telescopes. Using the Waxman-Bahcall limit for theneutrino flux, we find that the rate can be as large as a few hundreds events a year for realisticvalues of the NLKP mass. PACS numbers: 11.30.pb, 13.15+g, 12.60.jv, 95.30.Cq
I. INTRODUCTION
Although the standard model (SM) is a successful de-scription of the energy scales experimentally probed sofar, it is expected that new physics will appear at theTeV scale. This is precisely the energy regime soon to bestudied at the Large Hadron Collider (LHC). It is also thenatural scale for the dynamical origin of electroweak sym-metry breaking, as well as for the solution of the hierar-chy problem. Typical solutions of these problems involveeither symmetries (e.g. supersymmetry), some dynam-ical mechanism of electroweak symmetry breaking (e.g.technicolor), or a combination of symmetry and dynamics(e.g. little Higgs). In a somewhat different class are ex-tensions of the SM involving compact extra dimensions.In Large Extra Dimensions [1] only gravity propagatesin the extra dimensional bulk, and the true fundamentalscale of gravitation is O (1) TeV. On the other hand, intheories with one curved extra dimension [3], gravity isweak at the TeV scale due to the warping produced bythe bulk metric.Here we consider a more generic brand of extra di-mensional theories, universal extra dimensions (UEDs),where all fields propagate in the extra dimensionalbulk [2]. Its main motivation is phenomenological: ifcompact extra dimensions exist and all fields propagatein them, the inverse compactification radius could bejust above the weak scale, setting the stage for a lot ofnew physics possibilities at the TeV scale. Furthermore,adding a mild assumption, the presence of a reflectionsymmetry leading to a Z -parity, UED theories are en-dowed with a candidate for dark matter: the lightest KKparticle or LKP.Although at leading order the spectrum of each KKlevel is degenerate, it splits under radiative corrections,as well as when generic higher dimensional operators aretaken into account [4]. In theories with one extra di- mension, if only the loop contributions coming from thephysics below the cutoff are considered, one obtains thespectrum of the minimal UED standard model (mUED)of Ref. [4]. In this case, the LKP is most likely to bethe first KK mode of the photon γ (1) . Other possibili-ties for the LKP include the first KK mode of the gravi-ton G (1) [5], and (in theories where neutrino masses areDirac) the first KK excitation of the right-handed neu-trino ˜ N (1) [6]. Other light particles include the KK ex-citation of a right-handed charged lepton, ℓ (1) , and thecharged Higgs KK mode [7]. The splitting between theLKP and ℓ (1) is typically only a few GeV, depending onthe choice of parameters [26].The mUED spectrum is merely illustrative, and ul-traviolet physics contributions to boundary terms couldsignificantly alter it, making for instance, ℓ (1) the NLKP,while either G (1) or ˜ N (1) remains the LKP. In such ascenario, the decay of the NLKP to the LKP would behighly suppressed, making the NLKP lifetime very large.We will consider this possibility in this paper. This sit-uation is analogous to what happens in some supersym-metric scenarios (e.g. gauge mediation) where the grav-itino is the lightest supersymmetric particle and a righthanded charged slepton is the next to lightest one. Thephenomenology associated to a long-lived ℓ (1) includeshighly ionizing tracks at colliders. It also implies that ℓ (1) can be produced by the interactions of high energyneutrinos with the earth and propagate through it untilreaching a detector, in very close analogy to the case ofNLSP sleptons studied in Refs. [9, 10, 11, 12, 13].We will show that interactions of high energy neutri-nos (E ν > GeV) with nucleons in the Earth will pro-duce pairs of NLKPs. The rate of events will allow thediscovery of the latter in km neutrino telescopes. Thisanalysis follows the same steps as for NLSP detection[9, 12]. The crucial observation is the same as for theNLSP, the small NLKP production cross section is com-pensated by its large range. The NLKP loses much lessenergy while traveling through the Earth when comparedto SM leptons. This allows the detection of NLKPs thatare produced far away from the detector.As the NLKPs are produced in pairs, the main back-ground consists of di-muon events. We will show thatthere are at least two ways to separate these from thesignal. For lower mass NLKPs, the measured energyspectrum will have a bump in the region from 10 to10 GeV due to the fact that the energy loss in the de-tector will resemble the one from lower energy muons. Inaddition, for both low or high mass NLKPs, the separa-tion between the pair that crosses the detector will belarger than the one for the di-muon pair, and will allowto distinguish the signal from the background.This paper is organized as follows: we first determinethe NLKP production cross section; in Section III we de-scribe the NLKP energy loss while traveling through theEarth; the analysis of the signal and comparison with thebackground are discussed in Section IV and the conclu-sions follow in the last section.
II. NLKP PRODUCTION
In this section, we compute the production cross sec-tion for the NLKP pair. Due to the presence of the Z -parity, all KK modes produced will eventually cascadedown to a NLKP. Since KK modes are produced in pairs,KK production initiated by νN scattering will result in apair of NLKPs. The dominant process for ν − N -initiatedKK production involves the t-channel production of a lefthanded lepton KK mode L (1) i (with generation index i )and a quark KK mode ( Q (1) ) via a gauge boson KK mode( W (1) ). This process is analogous to the charged current(CC) in the SM. We also include the subdominant pro-cess which is analogous to the neutral current process inthe SM. This involves the exchange of a neutral gaugeboson KK mode ( Z (1) ). These processes are shown inFigure 1.The neutrino, which is always left-handed, can inter-act with a left handed down-type quark (a) or with aright-handed up-type antiquark (b). This results in thepartonic cross sections: dσ (a) dt = 8 πα sin θ W ( s − m L (1) i − m Q (1) ) s ( t − M W (1) ) (2.1) dσ (b) dt = 8 πα sin θ W × (2.2) (cid:20) m L (1) i m Q (1) + u − u ( m L (1) i + m Q (1) ) (cid:21) s ( t − M W (1) ) (2.3)where s, t and u are the usual Mandelstam variables,and m L (1) i , m Q (1) and M W (1) are the L (1) i , Q (1) and W (1) N ( 1 ) Z (1) W ( 1 ) N ( 1 ) W ( 1 ) Z (1) Q ( 1 ) Q ( 1 ) Q ( 1 ) Q ( 1 ) L ( 1 ) L ( 1 ) (a)(c) (b)(d) ν νν ν dd uu FIG. 1: Feynman diagrams for KK mode production in νN collisions. Charged current (charged gauge boson KK mode)interactions: (a) Left-left interaction requiring the insertion ofthe gauge KK mode mass in the t-channel line. (b) Left-rightinteraction. Neutral current: (c), (d). There are analogousdiagrams for anti-neutrinos as well as for strange and charminitial quarks. masses, repectively. The subdominant neutral gauge bo-son KK mode ( Z (1) ) exchange is shown in Figure 1 (c)-(d). Each of these processes will produce a L (1) i and a Q (1) and both of these particles will promptly produce adecay chain ending with a ℓ (1) i .Bounds from direct searches from the Tevatron, aswell as from electroweak precision constrains [2], result in R − >
300 GeV for 5D, while for 6D is R − >
500 GeV.We will assume three illustrative values for the NLKPmass: 300, 600 and 900 GeV. Finally, we need to specifythe cutoff of the theory. Using naive dimensional analy-sis, we find for the 5D case, that Λ R ∼ π/g , where g is the strong coupling constant. We then take Λ R ≃ /R . In order to evaluate the uncer-tainty introduced by this procedure in the cross sectioncalculation, we scanned values of Λ R up to 30, with nosignificant effects in the results.The NLKP production cross section is shown in Fig-ure 2 as a function of the neutrino energy. For com-parison, the SM charged current (top gray curve) andthe di-muon (solid red curve) background cross sectionsare also shown. As expected, the NLKP production crosssections ( σ NLKP ) are significantly lower than the SM one.However, depending on the neutrino energy and the L (1) i mass, it can be larger than the di-muon background. Inthe next section we will show that the the fact that σ NLKP is rather suppressed (as compared to the SM one) will becompensated by the sizable NLKP range resulting fromthe combination of its long lifetime and small energy loss.It is also interesting to compare the σ NLKP to the NLSPproduction as obtained in Ref. [9]. The NLKP produc-tion is significantly larger than the one for NLSPs, which -36 -35 -34 -33 -32 E ν (GeV) σ ( c m ) FIG. 2: νN cross sections vs. the energy of the incident neu-trino. The violet dashed, blue circled and black crossed linescorrespond respectively to 300, 600 and 900 GeV NLKPs.The top gray curve corresponds to the SM charged currentinteractions and the full red one to the di-muon background. translates into a larger number of events at the detector,as we will see below. III. NLKP ENERGY LOSS
After production, the NLKPs lose energy due to ion-ization and radiation processes. The average energy lossis given by [14]: − dEdx = a ( E ) + b ( E ) E , (3.4)where a ( E ) represents the ionization losses, and b ( E ) thecontributions from different radiation processes. The lat-ter includes bremsstrahlung, pair production and photo-nuclear interactions. There is also energy loss due toweak interactions, but this will only be of importanceat very high energy [18], and we will neglect it for theremaining of this work.At the high energies where NLKPs can be produced,radiation losses dominate over ionization. Among radia-tion processes, both pair production and bremsstrahlungbecome less important for heavy particles. Althoughphotonuclear processes dominate tau lepton propagationlosses [15, 16], a mass suppression will occur for leptonsof much heavier masses [12, 17]. In order to determine the NLKP energy losses, we fol-low closely the calculations done for NLSP propagationin Refs. [12] and [17]. Radiation losses dominate abovea propagating energy of 1 TeV. Among them, pair pro-duction and bremsstrahlung are less important for theNLKP when compared to photo-nuclear interactions, ascan be seen in Figure 3. Even so, the energy loss dueto photo-nuclear interactions is suppressed by the NLKPmass. As mentioned in Ref. [9] and shown explicitely inRefs. [12] and [17], the important energy region for thisprocess is the one at low photon virtuality Q . The rea-son is that the structure function involved in the processis determined by a cross section which is dominated byphysics at low Q ≃ . However, due to the largeNLKP mass, the minimum value for the photon virtualitywill be larger, therefore avoiding the effects of resonancesand other nonperturbative processes which occur at lower Q . This is in contrast to the case of the τ lepton, wherethe resonant region still dominates and results in a muchlarger photo-nuclear energy loss.Figure 3 shows the radiation loss term of eq. (3.4) ver-sus neutrino energy for muons, taus and the 300 GeVNLKP. As expected, the photo-nuclear process domi-nates the NLKP radiation loss. However, it is still quitesuppressed due to the NLKP heavy mass and the totalenergy loss is still considerably below the one for SM lep-tons. Energy suppression will be enhanced for heavierNLKP mass.We then conclude that the NLKP energy loss is quitesuppressed in comparison with SM leptons. As we willsee below, this means that its range through the Earthis much larger, allowing for the detection of NLKPs thathave been produced hundreds or even thousands of kilo-meters from the detector. IV. NLKP SIGNALS AND RATE IN NEUTRINOTELESCOPESA. Neutrino Flux
The NLKP event rate in neutrino telescopes dependson the incoming neutrino flux. This is largely determinedby the high energy cosmic ray spectrum [19]. There areother potentially relevant sources of the neutrino flux,such as atmospheric charm production [20]. For the pur-pose of this work we will neglect these other contribu-tions, only considering the flux of cosmic neutrinos, forwhich we use two alternative estimates: the work of Wax-man and Bahcall (WB) [21] and the one of Manheim,Proterhoe and Rachen (MPR) [22]. The integrated num-ber of events resulting from the MPR limit is consider-ably larger than the WB. We find our NLKP rates assum-ing each of these limits as our incoming neutrino flux. Allplots are produced assuming the WB limit as our neu-trino flux.Waxman and Bahcall fix the cosmic ray spectrum toa power law curve with spectral index −
2. The neutrino -10 -9 -8 -7 -6 b ( c m / g ) -13 -12 -11 -10 -9 -8 -7 -6 -10 -9 -8 -7 -6 E (GeV) b ( c m / g ) -9 -8 -7 -6 -5 E (GeV)
FIG. 3: Radiation energy loss b(E) parameter due to pairproduction, bremsstrahlung and photonuclear processes formuon, tau and a 300 GeV NLKP. The plot labeled “Tot”is the sum of all contributions. The muon, tau and NLKPcurves are as labeled in the first plot. Heavier NLKPs willhave lower b(E) parameters. upper limit is deduced assuming that each nucleon willinteract with photons and produce a pion. The chargedpions will then decay producing neutrinos. Their argu-ment requires that the sources are optically thin, whichmeans that most of the protons escape the source with-out interacting. As a result, the neutrino upper limit isgiven by (cid:18) dφ ν dE (cid:19) WB = (1 − × − E GeV cm − s − sr − , (4.5)where the range in the coefficient depends on the cosmo-logical evolution of the sources. The evolution accountsfor the source activity and redshift energy loss due to thecosmological expansion. We take the upper end as theneutrino flux incoming through the Earth.On the other hand, instead of taking a fixed power lawbehaviour for all cosmic ray spectrum, Manheim, Proter-hoe and Rachen determine the spectrum at each energydirectly from data. Here we consider the limit MPR ob-tain assuming optically thin sources, although they alsodetermine a limit for optically thick sources (See com-ments about optically thick sources in [19]). Figure 4shows both WB and MPR limits for the muon plus anti-muon neutrino flux.As seen in Section II, the NLKP production is inde- -18 -17 -16 -15 -14 -13 E ν (GeV) E d Φ ν / d E ( c m - s - s r - ) WB limitMPR limit (transparent sources)MPR limit (opaque sources)
FIG. 4: Upper bound on differential neutrino flux as calcu-lated by WB [21] (shaded area) and MPR [22] (red lines). TheWB limit ranges from the limit with no cosmological evolution(upper edge) and with cosmological evolution (lower edge).The MPR limit is shown for optically thin sources (red dot-ted line) as used in this paper and for optically thick sources(red dot-dashed line). pendent of the initial neutrino flavor. For this reason weconsider both electron and muon neutrinos, and neutrinomixing does not affect our results.
B. NLKP Signals
We now have all the ingredients to determine theNLKP rate at neutrino telescopes. In order to under-stand the signal in detail, we performed a Monte Carlosimulation generating approximately 30,000 events foreach NLKP mass (300, 600 and 900 GeV).Once the incoming neutrino flux is determined, an in-teraction point is randomly chosen based on the NLKPproduction probability. This results from a convolutionof the neutrino survival probability with the probabilityof interacting and producing a NLKP. The neutrino sur-vival probability P S is given by exp( R ndl ), where n is theEarth number density and l is the distance the neutrinotravels. We use the Earth density profile as described in[23, 24].The primary particles ( L (1) i and Q (1) produced in theneutrino interaction) angular distribution at the CM israndomly determined based on the differential produc- -2 -1 E ν (GeV) E ν d N l / d E ν ( k m - y e a r - ) E ν (GeV) E ν d N l / d E ν ( k m - y e a r - ) FIG. 5: NLKP pair event energy distribution per km , peryear, at the detector. Plus violet line corresponds to 300GeV; blue circled line to 600 GeV and crossed black line to900 GeV NLKP. For reference the neutrino flux at earth (fullblack line); and the µ (dotted green line) and the di-muon(squared red line) flux through the detector are also shown.In all cases we make use of the WB limit for the neutrino flux. tion cross section. The center of mass (CM) angular dis-tribution of the two NLKPs produced is assumed to bethe same as the one between the two primary particles.This is a good approximation [12] for events with energywell above the production threshold where most of theevent rate comes from. The events close to the produc-tion threshold have a broader angular distribution. Thesewould enhance the separation differences between signaland background and therefore make our results conser-vative. The CM angular distribution is then boosted tothe laboratory frame.Once the NLKPs are produced their propagationthrough the Earth is simulated. Their energy loss – whichis mass dependent – is taken into account. The NLKPenergy distribution as a function of neutrino energy isshown in Figure 5. As can be seen, the 300 and 600 GeVNLKP event rate is much larger than the muon’s for en-ergies above NLKP production threshold. The 900 GeVNLKP rate will be comparable with that for muons, butstill larger than the di-muon background rate.Although these are rather large rates, they do not di-rectly translate into observed NLKPs due to the fact thatNLKPs are hard to identify. Neutrino telescopes measuretheir energy in two ways[19, 25]: low energy events (be- TABLE I: Number of events per km per year for differentNLKP masses and neutrino fluxes at the Earth. The NLKPmasses are 300, 600 and 900 GeV. The number of NLKPevents are given for energies above threshold for productionof a L (1) ℓ and a Q (1) while the muon rate for energies above1000 GeV. The column µ + µ − corresponds to the di-muonbackground. No cuts were applied at this stage. µ µ + µ − L (1) R L (1) R (300) (600) (900)WB 552 30 489 21 3MPR 39654 1914 1476 47 5 low ∼
100 GeV) have their energy reconstructed fromthe track length, whereas for the more energetic onesthe energy is reconstructed from the amount of Cerenkovlight deposited in the photomultiplier tubes. Taking theCerenkov radiation as proportional to the amount of de-posited energy in the detector is a good approximationfor SM leptons. But the NLKPs lose a lot less energythan SM leptons. Thus, if a NLKP track is assumed tobe a SM lepton such as a muon, it will be assigned amuch lower energy as such. For this reason and in orderto compare event rates, the muon rate must be integratedfrom energies lower than the KK production threshold.Table I shows the event rate per year per km both forthe WB flux, as well as for the MPR optically thin flux.The numbers are clearly encouraging for km neutrinotelescopes. Two features will be important to distiguishthe signal from the background : the separation betweenthe pair of particles inside the detector; and – for lowermass NLKPs – a bump in the energy spectrum will ap-pear. These features will be discussed at the end of thissection.
1. Di-muon Background
Due to their large boost most NLKP pairs go throughthe detector in two well separated and approximatelyparallel tracks. Events well separated are produced farfrom the detector and as the production angle betweenthem is small the tracks will be almost parallel. There-fore, single muons can be eliminated by a two trackrequirement. The main remaining background are di-muons. These are produced from charmed hadrons fromthe following chain : νN → µ − H c → µ − µ + H x ν , where H c is a charm hadron produced from a muon neu-trino CC interaction and H x can be either a strange ornon-strange hadron.The cross section for charm production from a neu-trino interaction was calculated in Ref. [12], as well asthe di-muon energy loss, propagation and separation atthe detector. In what follows we reproduce these results,and compare with the NLKP signal.
2. NLKPs Separation
The separation between the NLKPs will be given bythe distance traveled times the angle ( θ ) between the pairin the laboratory frame. As the boost from CM to labis large, θ is very small. However, this is compensatedby the production being far away from the detector. Theproduction point being typically a few 1000 km from thedetector and θ ∼ − − − the separation between thetwo NLKPs will be a few tens to a few hundred meters.On the other hand, di-muon events have to be pro-duced close to the detector, otherwise they lose all theirenergy before arriving at it. For this reason their sepa-ration is typically smaller than the one for most of thesignal events.The separation distribution for each NLKP mass atthe detector is shown in Figure 6. The simulated detec-tor is placed at the same depth as the IceCube telescope[25]. We also show the di-muon background separationfor comparison. While the dimuon separation is at most ∼
100 m, the pair of NLKP can be more than 100 me-ters apart. For instance, for a 300 GeV NLKP, 52% ofthe events are more than 50 m apart and 28% are morethan 100 m apart. The di-muon background has only 8%with more than 50 m and 1.3% with more than 100 mseparation. The 600 and 900 GeV NLKPs have botharound 60% of events with more than 50 m separationand around 42% with more than 100 m separation.In order to estimate the statistical significance of theseparation cut, we determine the S/ √ B ratio, where S and B are respectively the number of signal and back-ground events. We find that for the 300 GeV NLKP, arequirement that the pair of NLKPs are at least 10 me-ters apart will yield a significance of 85, ie, 436 of the 489NLKPs will be more than 10 meters apart, while only 25di-muons will have more than 10 meters separation. Forthe 600 GeV NLKP, a requirement of 86 m separationwill allow a 5 σ significance in one year, with 9 signalevents and 3 di-muons. For the 900 GeV, the separationis harder, a 2 σ significance can be achieved in a year witha separation cut of 150 m, while a 5 σ significance needs5 years to be achieved.
3. The NLKP Bump
Another feature of the NLKP signal comes from thefact that these particles lose less energy than a SM lep-ton. This implies that NLKPs will have their energyreconstructed as if they where lower energy leptons. Fig-ure 7 shows both NLKP and di-muon simulated energydistribution as they arrive at the detector. Althoughthe NLKPs are more energetic than the di-muons, the d i s t r i bu t i o n NLKP(300)NLKP(600)NLKP(900) d i s t r i bu t i o n µ + µ - FIG. 6: Track separation distribution between NLKP pair(top) and for the di-muon background (bottom). energy deposited in the PMTs will resemble lower en-ergy muons and therefore they have to be compared withthem. However this will generate a sizeable excess in thereconstructed energy spectrum, at least if the number ofNLKP events is large enough. In order to understandhow this feature will change the reconstructed energyspectrum, we simulate the reconstructed energy by tak-ing all NLKPs as muons. This was done by determiningthe deposited energy in the detector and reconstructingthis energy as if deposited by a muon. These events werethen added to the SM muon energy spectrum. The con-sequence is that the high energy NLKPs will be recon-structed as lower energy events that will end up as abump around energies of TeVs.Figure 8 shows the energy distribution of the muon fluxthrough the detector (top plot, blue circles) and the samedistribution with the addition of 300 GeV NLKPs recon-structed as muons. A visible “crown” with few events ineach energy bin in the 1 to 100 TeV region will clearlyindicate the presence of KK particles. This feature willbe enhanced when the NLKPs are included in the di-muon energy spectrum (bottom plot). When the signalis reconstructed as di-muons, a pronounced crown showsup in the reconstructed energy spectrum. This feature isobservable for NLKPs in the lower mass range, since therate of higher mass NLKPs would not be large enoughto observably enhance the spectrum in the lower energyregion. We expect this feature to be observable up toNLKP masses of about ∼
600 GeV. Thus, for these lowermass NLKPs there will be two distinct ways to separate E at detector (GeV) d i s t r i bu t i o n NLKP(300)NLKP(600)NLKP(900)dimu
FIG. 7: Arrival energy distribution of the NLKP at the de-tector for m L (1) R = 300 ,
600 and 900 GeV. Also shown is thearrival distribution for the di-muon background. the signal from the main background.
V. CONCLUSIONS
We have shown that in a UED scenario where theNLKP is a the first KK mode of a right handed chargedlepton, neutrino telescopes such as IceCube will be ableto directly observe these ℓ (1) i ’s up to masses of severalhundred GeV, perhaps even 1 TeV. This complementshadron collider searches, where signals for this UED sce-nario would consist of large missing energy, and per-haps one or two highly-ionizing tracks. The similarityof the UED signals with the analogous supersymmetricscenario, for instance with gravitino dark matter and aslepton NLSP, can make the identification of the under-lying theory difficult. On the other hand, the event rateat neutrino telescopes coming from this UED scenariois considerably higher than the one resulting from thesupersymmetric case and studied in Refs. [9, 12]. We have made a detailed study of the background andthe signal, and shown that the track separation of NLKPsis a good discriminant with respect to the di-muon back-ground. In addition, for the case of smaller NLKPsmasses, we have shown that the NLKP signal results ina bump in the detected di-muon spectrum, since NLKPslose energy similarly to lower energy muons. Combiningthis feature with the characteristic track separation of thesignal tracks should enhance the statistical significance ofa potential signal. -2 -1 -2 -1 E ν (GeV) E ν d N l / d E ν ( k m - y e a r - ) FIG. 8: Top: Energy distribution of the muon flux throughthe detector (blue circles) and the same flux plus the 300 GeVNLKP spectrum reconstructed as muons (violet plus line).Bottom: Same as above but now using the di-muon fluxthrough the detector.
Acknowledgments —