We consider supersymmetric models where the scale of supersymmetry breaking
lies between 5 $\times 10^6$ GeV and 5 $\times 10^8$ GeV. In this class of
theories, which includes models of gauge mediated supersymmetry breaking, the
lightest supersymmetric particle is the gravitino. The next to lightest
supersymmetric particle is typically a long lived charged slepton with a
lifetime between a microsecond and a second, depending on its mass. Collisions
of high energy neutrinos with nucleons in the earth can result in the
production of a pair of these sleptons. Their very high boost means they
typically decay outside the earth. We investigate the production of these
particles by the diffuse flux of high energy neutrinos, and the potential for
their observation in large ice or water Cerenkov detectors. The relatively
small cross-section for the production of supersymmetric particles is partially
compensated for by the very long range of heavy particles. The signal in the
detector consists of two parallel charged tracks emerging from the earth about
100 meters apart, with very little background. A detailed calculation using the
Waxman-Bahcall limit on the neutrino flux and realistic spectra shows that
km$^3$ experiments could see as many as 4 events a year. We conclude that
neutrino telescopes will complement collider searches in the determination of
the supersymmetry breaking scale, and may even give the first evidence for
supersymmetry at the weak scale.Comment: 4 pages, 3 figure

F. Halzen

Gustavo Burdman

I. Albuquerque

Ivone F. M. Albuquerque

J. Ahrens

L. Alvarez-Gaumé

M. Dine

P. J. Fox

P. K. F. Grieder

S. Dimopoulos

T. Kobayashi

Z. Chacko

English

arXiv

Albuquerque, Ivone

Burdman, Gustavo

Chacko, Z.

eScholarship - University of California

Lawrence Berkeley National LaboratoryLawrence Berkeley National LaboratoryTitleNeutrino telescopes as a direct probe of supersymmetry breakingPermalinkhttps://escholarship.org/uc/item/6821528bAuthorsAlbuquerque, IvoneBurdman, GustavoChacko, Z.Publication Date2003-12-15 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaarXiv:hep-ph/0312197 v1   15 Dec 2003Neutrino Telescopes as a Direct Probe of Supersymmetry BreakingIvone Albuquerque,1 Gustavo Burdman,2, 3 and Z. Chacko2, 31Department of Astronomy and Space Sciences Laboratory, University of California, Berkeley, CA 947202Theory Group, Lawrence Berkeley National Laboratory, Berkeley, CA 947203Department of Physics, University of California, Berkeley, CA 94720We consider supersymmetric models where the scale of supersymmetry breaking lies between 5×106 GeV and 5 ×108 GeV. In this class of theories, which includes models of gauge mediatedsupersymmetry breaking, the lightest supersymmetric particle is the gravitino. The next to lightestsupersymmetric particle is typically a long lived charged slepton with a lifetime between a microsec-ond and a second, depending on its mass. Collisions of high energy neutrinos with nucleons in theearth can result in the production of a pair of these sleptons. Their very high boost means theytypically decay outside the earth. We investigate the production of these particles by the diffuseflux of high energy neutrinos, and the potential for their observation in large ice or water Cerenkovdetectors. The relatively small cross-section for the production of supersymmetric particles is par-tially compensated for by the very long range of heavy particles. The signal in the detector consistsof two parallel charged tracks emerging from the earth about 100 meters apart, with very littlebackground. A detailed calculation using the Waxman-Bahcall limit on the neutrino flux and real-istic spectra shows that km3 experiments could see as many as 4 events a year. We conclude thatneutrino telescopes will complement collider searches in the determination of the supersymmetrybreaking scale, and may even give the first evidence for supersymmetry at the weak scale.Introduction — The origin of the radiative stability ofthe weak scale is one of the most important questions inparticle physics today. A natural answer requires newphysics at the TeV scale. Among the candidate theories,weak scale supersymmetry remains the most attractivescenario. Although this is in no small measure due to itstheoretical appeal (it is a simple and natural extensionof the usual space-time symmetries), it is also favoredby data from electroweak observables. These point toa weakly coupled Higgs sector, one without significantdeviations from the standard model in regard to elec-troweak precision observables. However, supersymmetrymust be broken since the superpartners have not yet beenobserved. The supersymmetric spectrum is determinedby the supersymmetry breaking mechanism.Supersymmetric models typically have a symmetry,called R-parity, which ensures that the Lightest Super-symmetric Particle, the ‘LSP’, is stable. Which of thesupersymmetric particles is the LSP? This is determinedby the scale of supersymmetry breaking, which we denoteby√F , and which can lie anywhere between 103 GeVand 1012GeV. If supersymmetry is broken at high scalessuch that√F is larger than 1010GeV the LSP is typicallythe neutralino. If however supersymmetry is broken atlower scales,√F < 1010GeV, the LSP is typically thegravitino. In models where the LSP is the gravitino, theNext to Lightest Supersymmetric Particle (NLSP) tendsto be a charged slepton, typically the right-handed stau.Since the NLSP decays to gravitinos through interactionsthat are suppressed by powers of√F , if the supersymme-try breaking scale is high its lifetime can be quite large.In gauge-mediated SUSY breaking, for instance, we havecτ =( √F107 GeV)4(100 GeVmτ̃R)510 km , (1)where mτ̃R is the stau mass. Thus, for√F ≥ 107GeVif these NLSPs were to be produced by very high energycollisions they could travel very long distances before de-caying. In the last several years many interesting andrealistic scenarios have been proposed in which the scaleof supersymmetry breaking√F is low and could lie be-tween 5× 106GeV and about 5× 108GeV. These includemodels of gauge mediation[1], and gauge and Yukawamediation[2], warped higher dimensional models in whichsupersymmetry is broken on an infrared brane and there-fore the scale√F has been warped down [3], theory spacerealizations of higher dimensional models [4] and modelsof supersoft supersymmetry breaking which are charac-terized by Dirac gauginos[5]. In all these classes of modelsthe NLSP is typically a right handed stau.The existence of diffuse fluxes of high energy neutri-nos, possibly associated with the production of cosmicrays, has been widely discussed in the literature. Col-lisions of these high energy neutrinos with nucleons inthe earth at energies above threshold for supersymmetricproduction frequently result in the production of a pairof supersymmetric particles, which promptly decay intoNLSPs. These typically have a high boost γNLSP ≃ 1000or larger and therefore will not decay inside the earth pro-vided the supersymmetry breaking scale√F > 107GeV.For 5 × 106 <√F < 107GeV a significant fraction ofthe decays will occur inside the earth. Since the NLSPis charged, its upward going tracks could in principle bedetected in large ice or water Cerenkov detectors, suchas ICECUBE [6]. This is in analogy with the standardmodel charged current interaction giving muons, the pri-mary signal in neutrino telescopes.Naively, one would expect that the event rates forNLSPs -which typically have masses in the 100 GeVrange- are negligible when compared to those for muons,2since their production cross section must be considerablysmaller than that of the standard model interactions.The reason is that the SM interactions come primarilyfrom very small values of x, the parton momentum frac-tion, whereas the supersymmetric process is limited tox > m2/2MP Eν , with m given essentially by the sumof the produced supersymmetric particles. This naiveexpectation is however, misleading. The crucial observa-tion is that the range of a slepton is much larger thanthat of a muon, since energy loss due to radiation setsin at much higher energies. In neutrino telescopes, muonevents must be produced either right outside the detectoror in it, since the muon range for the energies of interestis in the few to tens of kilometers. Thus, most of the up-going CC events produced in the earth are lost. On theother hand, the range of NLSPs is typically in the hun-dreds to thousands of kilometers. Then, unlike for themuon [7], a significant fraction of the NLSPs producedwill range into the detector.In what follows we compute the number of NLSPevents. For this purpose we calculate the supersymmetricproduction cross sections and the NLSP range.The SUSY Cross Section— In the scenarios under con-sideration, every νN interaction producing supersym-metric particles will result in a pair of NLSPs, which havea very long lifetime. In what follows, we will assume thislifetime to be large enough so that NLSPs do not decayin the earth. For simplicity, we also neglect mixing withHiggsinos in the gaugino sector. The dominant process isanalogous to the SM CC interactions and corresponds tothe t-channel exchange of charginos producing νN → ℓ̃ q̃,as shown in Figure 1(a) and (b). The neutrino, alwaysproduced left-handed by the weak interactions, can in-teract either with a left-handed down-type quark (a), orwith a right-handed up-type quark (b). This results inthe partonic cross sections:dσ(a)dt=πα2 sin4 θWM2w̃s (t − M2w̃)2(2)dσ(b)dt=πα2 sin4 θW(tu − m2ℓ̃Lm2q̃)s2 (t − M2w̃)2, (3)where s, t and u are the usual Mandelstam variables,and Mw̃, mℓ̃L and mq̃ are the chargino, the left-handedslepton and the squark masses respectively. The left-handed slepton and the squark decay promptly to thelighter “right-handed” slepton plus non-supersymmetricparticles. We also include the subdominant neutralinoexchange, Figure 1 (c)-(d). We take mw̃ = 250 GeV,mℓ̃L = 250 GeV and three values for the squark masses:mq̃ = 300, 600 and 900 GeV. These are very represen-tative values in the scenarios under consideration. Typ-ically, the τ̃R is the NLSP, being heavier only than theultra-light and very weakly coupled gravitino. Charginosand neutralinos tend to be heavier since they also feelthe SU(2)L interactions. Finally, squarks are heavieru~w~+l~−u− d~−w~+l~−dν ν(b)(a)q~ q~ν∼ ν∼w~3 w~3ν νq q(c) (d)FIG. 1: Feynman diagrams for supersymmetric particle pro-duction in νN collisions Charged current (chargino) interac-tions: (a) Left-left interaction requiring the insertion of thegaugino mass in the t-channel line. (b) Left-right interaction.Neutral current: (c), (d). There are analogous diagrams foranti-neutrinos as well as for strange and charm initial quarks.FIG. 2: νN cross sections vs. the energy of the inci-dent neutrino. The curves correspond to mℓ̃L = 250 GeV,mw̃ = 250GeV; and for squark masses mq̃ = 300 GeV (solid), 600 GeV (dashed) and 900 GeV (dot-dashed). The top curvecorresponds to the SM charged current interactions.still since their masses affected by the strong interactions.In Figure 2 we plot the cross sections for supersymmet-ric production in νN interactions as a function of theneutrino energy. Also plotted for comparison is the SMcharged current cross section. As advertised earlier, theSUSY cross sections are still suppressed with respect tothe SM, even when well above threshold.The NLSP Range— Once produced by the νN inter-3actions in the earth, the NLSP pair should range into thedetector, just as the muons produced by CC events [7].Charged particles lose energy due to ionization processesas well as through radiation. The average energy loss isgiven by [8]−dEdx= a(βγ) + c(βγ) βγ , (4)here a and c characterize the ionization and radiationlosses respectively, and are slowly varying functions ofthe energy. The ionization loss can be approximated bya(βγ) ≃ 0.08MeV cm2gr(17 + 2 lnβγ) , (5)nd is rather independent of the particle mass. On theother hand, assuming c(βγ) ≃ const., the radiative en-ergy loss can be written as c βγ = (bm)E. Thusbµmµ = bτ̃Rmτ̃R , and the radiative energy loss for theNLSPs scales inversely with the mass. This results ina much larger range for the NLSP as compared to themuon. Current bounds on mτ̃R are just above 100 GeV.As a reference value we take mτ̃R = 150 GeV. Therefore,NLSPs produced hundreds, even thousands of kilometersaway are within range of the detector. This is to be con-trasted with the fact that muons must be produced atdistances not larger than tens of kilometers from the de-tector in order to be observed. As we will see, this willsomewhat compensate the suppression of the SUSY crosssections observed earlier.Signals in Neutrino Telescopes— In order to computethe event rates in neutrino telescopes, we need to knowthe incoming neutrino flux. The presence of cosmic neu-trinos is expected on the basis of the existence of highenergy cosmic rays. Several estimates of the neutrinoflux are available in the literature. In most cases, it isexpected that km3 neutrino telescopes will measure thisflux. Here, in order to present projections for the numberof observed SUSY events, we make use of the Waxman-Bahcall (WB) limit [9] as an estimate of the cosmic neu-trino flux. We consider an initial flux containing both νµand νe (in a 2 : 1 ratio). Since the initial interactions (seeFigure 1) produce ℓ̃L and these are nearly degenerate inflavor, the flavor of the initial neutrino does not affectour results. For the same reason, the possibility of largemixing in the neutrino flux is also innocuous here. Inorder to correctly take into account the propagation ofneutrinos and the NLSP ℓ̃R through the earth, we makeuse of a model of the earth density profile as detailed inReference [11].In Figure 3 we show the energy distribution for theNLSP pair events for three choices of squark masses:300 GeV, 600 GeV and 900 GeV. Also shown are theneutrino flux at earth in the WB limit, as well as the en-ergy distribution of upgoing µ’s. We see that, even for theheavier squarks, it is possible to obtain observable event10-210-111010 210 310 410 510 610610710810910101011Eν (GeV)Eν dNl/dEν (km-2 year-1 )FIG. 3: Energy distribution of τ̃R pair events per km2, peryear. From top to bottom: mq̃ = 300, 600 and 900 GeV.Here, mτ̃R=150 GeV and mw̃ = 250 GeV. Also shown are theneutrino flux at earth and the µ flux through the detector. Inall cases we make use of the WB limit for the neutrino flux.TABLE I: Number of events per km2 per year for the WBand MPR fluxes. The first column refers to upgoing muons.The last three columns correspond to upgoing NLSP pairevents, for three different choices of squark masses: 300 GeV,600 GeV and 900 GeV. The number of muon events are givenfor energies above threshold for production of a 250 GeV ℓ̃Lplus a 300 GeV squark, ie, 1.6× 105 GeV.µ mq̃ = 300 GeV 600 GeV 900 GeVWB 106 4 1 0.5MPR 1085 10 3 1rates. In Table I we show the event rates for ℓ̃R pair pro-duction per year and per km2. The rates are given for theWB flux as well as for the Mannheim-Protheroe-Rachen(MPR) flux [10], both for optically thin sources. For com-parison, we also show the rates of upgoing muons. Thus,km3 Cerenkov detectors such as ICECUBE, appear tobe sensitive to most of the parameter space of interest inscenarios with a relatively long lived NLSP.Since the NLSPs are produced in pairs very far fromthe detector and with a very large boost, typical signalevents consist of two tracks separated by δR ≃ L θ, withL the distance to the production point (≃ 100−1000 Km)and θ ≃ pCMSUSY/pboost ≃ 10−3 − 10−4. If we consider Lto be of the order of the NLSP range, then in the lin-ear regime δR ≃ constant ≃ 100m. As we have seen inthe discussion following eqn. (5), for very high energies4TABLE II: Number of events for extended ICECUBE [13] peryear assuming ν flux is given by the WB limit. The ℓ̃L andsquark masses and the number of muons are as in Table I.µ mq̃ = 300 GeV 600 GeV 900 GeV1 ring, 300 m 110 5 2 11 ring, 1000 m 110 6 2 14 rings, 300 m 131 9 3 14 rings, 1000 m 140 16 5 2the range grows logarithmically with energy, leading tosomewhat smaller values of δR ≃ (20− 40)m. The trackseparation is then mildly sensitive to the stau injectionenergy [12]. Then, most NLSP events would consist oftwo parallel but well separated tracks, and are thereforeexpected to be very distinctive and different from back-grounds. In addition, we see from Figure 3 that the signalevents have a harder spectrum than the µ background.Conclusions — We have shown for the first time thatneutrino telescopes are potentially sensitive to the rela-tively long-lived charged NLSPs which are present in awide variety of models of supersymmetry breaking. Theevent rates shown in Table I are already encouraging forexperimental facilities that are been built, such as ICE-CUBE. The region of the supersymmetry breaking pa-rameter space that is available to neutrino telescopes isdetermined, on the one hand, by the twin requirementsthat the NLSP lifetime be long enough to give a signal(√F >∼ 5 × 106 GeV), but not be so long as to disturbBig Bang Nucleosynthesis (√F <∼ 5×108 GeV). Thus theobservation of NLSP events at neutrino telescopes willconstitute a direct probe of the scale of supersymmetrybreaking. This is to be compared with the potential ob-servation of these NLSPs at the Large Hadron Collider(LHC), where for this range of√F , the NLSP decaysoutside the detector and is seen through its ionizationtracks. However, the observation at the LHC would notconstrain the NLSP lifetime significantly. Thus, we seethat neutrino telescopes are complementary to collidersearches. For instance, the observation of NLSP eventsat the LHC, coupled to the non-observation in neutrinotelescopes would point to√F < 107 GeV.Future upgrades of ICECUBE, as well as of the waterdetectors ANTARES [14] and NESTOR [15] will resultin even better sensitivity. As an example, in Table II weshow rates for an expanded version of ICECUBE [13].In the present letter we focused on supersymmetry.However, many other theories give rise to relatively longlived charged particles which can be observed by neutrinotelescopes [12].Acknowledgments — We would like to thank AzrielGoldschmidt and Ian Hinchliffe for useful conversations.I. A. is supported by NSF Grant Physics/Polar Programs0071886. G. B. and Z. C. are supported by the Direc-tor, Office of Science, Office of High Energy and Nu-clear Physics, of the U. S. Department of Energy underContract DE-AC03-76SF00098 and by the N.S.F. underPHY-00-98840.[1] M. Dine, W. Fischler, M. Srednicki, Nuc. Phys. B 189,575 (1981); S. Dimopoulos, S. Raby, Nuc. Phys. B 192,353 (1981); L. Alvarez–Gaumé, M. Claudson, M.B. Wise,Nuc. Phys. B 207, 96 (1982); M. Dine, A.E. Nelson,Phys. Rev. D 48, 1277 (1993); M. Dine, A.E. Nelson,Y. Shirman, Phys. Rev. D 51, 1362 (1995); M. Dine,A.E. Nelson, Y. Nir, Y. Shirman, Phys. Rev. D 53,2658 (1996). For a review, see G.F. Giudice, R. Rattazzi,Phys. Rept. 322, 419 (1999).[2] M. Dine, Y. Nir and Y. Shirman, Phys. Rev. D 55, 1501(1997); T. Han and R. J. Zhang, Phys. Lett. B 428,120 (1998); Z. Chacko and E. Ponton, Phys. Rev. D 66,095004 (2002).[3] T. Gherghetta and A. Pomarol, Nucl. Phys. B 586, 141(2000); W. D. Goldberger, Y. Nomura and D. R. Smith,Phys. Rev. D 67, 075021 (2003); Z. Chacko andE. Ponton, JHEP 0311, 024 (2003); Y. Nomura andD. R. Smith, Phys. Rev. D 68, 075003 (2003).[4] C. Csaki, J. Erlich, C. Grojean and G. D. Kribs, Phys.Rev. D 65, 015003 (2002); H. C. Cheng, D. E. Ka-plan, M. Schmaltz and W. Skiba, Phys. Lett. B 515,395 (2001); Z. Chacko, E. Katz and E. Perazzi, Phys.Rev. D 66, 095012 (2002); T. Kobayashi, N. Maru andK. Yoshioka, Eur. Phys. J. C 29, 277 (2003); N. Maruand K. Yoshioka, arXiv:hep-ph/0311337.[5] P. J. Fox, A. E. Nelson and N. Weiner, JHEP 0208, 035(2002).[6] J. Ahrens et al. [The IceCube Collaboration], Nucl. Phys.Proc. Suppl. 118, 388 (2003).[7] For a detailed discussion of neutrino event rates see I. Al-buquerque, J. Lamoureux and G. F. Smoot, Astrophys.J. Suppl. 141, 195 (2002).[8] K. Hagiwara et al. [Particle Data Group Collaboration],Phys. Rev. D 66, 010001 (2002).[9] E. Waxman and J. N. Bahcall, Phys. Rev. D 59, 023002(1999); J. N. Bahcall and E. Waxman, Phys. Rev. D 64,023002 (2001).[10] K. Mannheim, R. J. Protheroe and J. P. Rachen, Phys.Rev. D 63, 023003 (2001)[11] R. Gandhi, C. Quigg, M. H. Reno and I. Sarcevic,Astropart. Phys. 5, 81 (1996); R. Gandhi, C. Quigg,M. H. Reno and I. Sarcevic, Phys. Rev. D 58, 093009(1998).[12] I. Albuquerque, G. Burdman and Z. Chacko, in prepara-tion.[13] F. Halzen and D. Hooper, arXiv:astro-ph/0310152.[14] J. A. Aguilar et al. [The ANTARES Collaboration],arXiv:astro-ph/0310130.[15] P. K. F. Grieder [NESTOR Collaboration], Nuovo Cim.24C (2001) 771.

Neutrino telescopes as a direct probe of supersymmetry breaking

We consider supersymmetric models where the scale of supersymmetry breaking lies between 5 x 10{sup 6} GeV and 5 x 10{sup 8} GeV. In this class of theories, which includes models of gauge mediated supersymmetry breaking, the lightest supersymmetric particle is the gravitino. The next to lightest supersymmetric particle is typically a long lived charged slepton with a lifetime between a microsecond and a second, depending on its mass. Collisions of high energy neutrinos with nucleons in the earth can result in the production of a pair of these sleptons. Their very high boost means they typically decay outside the earth. We investigate the production of these particles by the diffuse flux of high energy neutrinos, and the potential for their observation in large ice or water Cerenkov detectors. The relatively small cross-section for the production of supersymmetric particles is partially compensated for by the very long range of heavy particles. The signal in the detector consists of two parallel charged tracks emerging from the earth about 100 meters apart, with very little background. A detailed calculation using the Waxman-Bahcall limit on the neutrino flux and realistic spectra shows that km{sup 3} experiments could see as many as 4 events a year. We conclude that neutrino telescopes will complement collider searches in the determination of the supersymmetry breaking scale, and may even give the first evidence for supersymmetry at the weak scale

UNT (University of North Texas) Digital Library

arXiv:hep-ph/0312197 v1   15 Dec 2003Neutrino Telescopes as a Direct Probe of Supersymmetry BreakingIvone Albuquerque,1 Gustavo Burdman,2, 3 and Z. Chacko2, 31Department of Astronomy and Space Sciences Laboratory, University of California, Berkeley, CA 947202Theory Group, Lawrence Berkeley National Laboratory, Berkeley, CA 947203Department of Physics, University of California, Berkeley, CA 94720We consider supersymmetric models where the scale of supersymmetry breaking lies between 5×106 GeV and 5 ×108 GeV. In this class of theories, which includes models of gauge mediatedsupersymmetry breaking, the lightest supersymmetric particle is the gravitino. The next to lightestsupersymmetric particle is typically a long lived charged slepton with a lifetime between a microsec-ond and a second, depending on its mass. Collisions of high energy neutrinos with nucleons in theearth can result in the production of a pair of these sleptons. Their very high boost means theytypically decay outside the earth. We investigate the production of these particles by the diffuseflux of high energy neutrinos, and the potential for their observation in large ice or water Cerenkovdetectors. The relatively small cross-section for the production of supersymmetric particles is par-tially compensated for by the very long range of heavy particles. The signal in the detector consistsof two parallel charged tracks emerging from the earth about 100 meters apart, with very littlebackground. A detailed calculation using the Waxman-Bahcall limit on the neutrino flux and real-istic spectra shows that km3 experiments could see as many as 4 events a year. We conclude thatneutrino telescopes will complement collider searches in the determination of the supersymmetrybreaking scale, and may even give the first evidence for supersymmetry at the weak scale.Introduction — The origin of the radiative stability ofthe weak scale is one of the most important questions inparticle physics today. A natural answer requires newphysics at the TeV scale. Among the candidate theories,weak scale supersymmetry remains the most attractivescenario. Although this is in no small measure due to itstheoretical appeal (it is a simple and natural extensionof the usual space-time symmetries), it is also favoredby data from electroweak observables. These point toa weakly coupled Higgs sector, one without significantdeviations from the standard model in regard to elec-troweak precision observables. However, supersymmetrymust be broken since the superpartners have not yet beenobserved. The supersymmetric spectrum is determinedby the supersymmetry breaking mechanism.Supersymmetric models typically have a symmetry,called R-parity, which ensures that the Lightest Super-symmetric Particle, the ‘LSP’, is stable. Which of thesupersymmetric particles is the LSP? This is determinedby the scale of supersymmetry breaking, which we denoteby√F , and which can lie anywhere between 103 GeVand 1012GeV. If supersymmetry is broken at high scalessuch that√F is larger than 1010GeV the LSP is typicallythe neutralino. If however supersymmetry is broken atlower scales,√F < 1010GeV, the LSP is typically thegravitino. In models where the LSP is the gravitino, theNext to Lightest Supersymmetric Particle (NLSP) tendsto be a charged slepton, typically the right-handed stau.Since the NLSP decays to gravitinos through interactionsthat are suppressed by powers of√F , if the supersymme-try breaking scale is high its lifetime can be quite large.In gauge-mediated SUSY breaking, for instance, we havecτ =( √F107 GeV)4(100 GeVmτ̃R)510 km , (1)where mτ̃R is the stau mass. Thus, for√F ≥ 107GeVif these NLSPs were to be produced by very high energycollisions they could travel very long distances before de-caying. In the last several years many interesting andrealistic scenarios have been proposed in which the scaleof supersymmetry breaking√F is low and could lie be-tween 5× 106GeV and about 5× 108GeV. These includemodels of gauge mediation[1], and gauge and Yukawamediation[2], warped higher dimensional models in whichsupersymmetry is broken on an infrared brane and there-fore the scale√F has been warped down [3], theory spacerealizations of higher dimensional models [4] and modelsof supersoft supersymmetry breaking which are charac-terized by Dirac gauginos[5]. In all these classes of modelsthe NLSP is typically a right handed stau.The existence of diffuse fluxes of high energy neutri-nos, possibly associated with the production of cosmicrays, has been widely discussed in the literature. Col-lisions of these high energy neutrinos with nucleons inthe earth at energies above threshold for supersymmetricproduction frequently result in the production of a pairof supersymmetric particles, which promptly decay intoNLSPs. These typically have a high boost γNLSP ≃ 1000or larger and therefore will not decay inside the earth pro-vided the supersymmetry breaking scale√F > 107GeV.For 5 × 106 <√F < 107GeV a significant fraction ofthe decays will occur inside the earth. Since the NLSPis charged, its upward going tracks could in principle bedetected in large ice or water Cerenkov detectors, suchas ICECUBE [6]. This is in analogy with the standardmodel charged current interaction giving muons, the pri-mary signal in neutrino telescopes.Naively, one would expect that the event rates forNLSPs -which typically have masses in the 100 GeVrange- are negligible when compared to those for muons,2since their production cross section must be considerablysmaller than that of the standard model interactions.The reason is that the SM interactions come primarilyfrom very small values of x, the parton momentum frac-tion, whereas the supersymmetric process is limited tox > m2/2MP Eν , with m given essentially by the sumof the produced supersymmetric particles. This naiveexpectation is however, misleading. The crucial observa-tion is that the range of a slepton is much larger thanthat of a muon, since energy loss due to radiation setsin at much higher energies. In neutrino telescopes, muonevents must be produced either right outside the detectoror in it, since the muon range for the energies of interestis in the few to tens of kilometers. Thus, most of the up-going CC events produced in the earth are lost. On theother hand, the range of NLSPs is typically in the hun-dreds to thousands of kilometers. Then, unlike for themuon [7], a significant fraction of the NLSPs producedwill range into the detector.In what follows we compute the number of NLSPevents. For this purpose we calculate the supersymmetricproduction cross sections and the NLSP range.The SUSY Cross Section— In the scenarios under con-sideration, every νN interaction producing supersym-metric particles will result in a pair of NLSPs, which havea very long lifetime. In what follows, we will assume thislifetime to be large enough so that NLSPs do not decayin the earth. For simplicity, we also neglect mixing withHiggsinos in the gaugino sector. The dominant process isanalogous to the SM CC interactions and corresponds tothe t-channel exchange of charginos producing νN → ℓ̃ q̃,as shown in Figure 1(a) and (b). The neutrino, alwaysproduced left-handed by the weak interactions, can in-teract either with a left-handed down-type quark (a), orwith a right-handed up-type quark (b). This results inthe partonic cross sections:dσ(a)dt=πα2 sin4 θWM2w̃s (t − M2w̃)2(2)dσ(b)dt=πα2 sin4 θW(tu − m2ℓ̃Lm2q̃)s2 (t − M2w̃)2, (3)where s, t and u are the usual Mandelstam variables,and Mw̃, mℓ̃L and mq̃ are the chargino, the left-handedslepton and the squark masses respectively. The left-handed slepton and the squark decay promptly to thelighter “right-handed” slepton plus non-supersymmetricparticles. We also include the subdominant neutralinoexchange, Figure 1 (c)-(d). We take mw̃ = 250 GeV,mℓ̃L = 250 GeV and three values for the squark masses:mq̃ = 300, 600 and 900 GeV. These are very represen-tative values in the scenarios under consideration. Typ-ically, the τ̃R is the NLSP, being heavier only than theultra-light and very weakly coupled gravitino. Charginosand neutralinos tend to be heavier since they also feelthe SU(2)L interactions. Finally, squarks are heavieru~w~+l~−u− d~−w~+l~−dν ν(b)(a)q~ q~ν∼ ν∼w~3 w~3ν νq q(c) (d)FIG. 1: Feynman diagrams for supersymmetric particle pro-duction in νN collisions Charged current (chargino) interac-tions: (a) Left-left interaction requiring the insertion of thegaugino mass in the t-channel line. (b) Left-right interaction.Neutral current: (c), (d). There are analogous diagrams foranti-neutrinos as well as for strange and charm initial quarks.FIG. 2: νN cross sections vs. the energy of the inci-dent neutrino. The curves correspond to mℓ̃L = 250 GeV,mw̃ = 250GeV; and for squark masses mq̃ = 300 GeV (solid), 600 GeV (dashed) and 900 GeV (dot-dashed). The top curvecorresponds to the SM charged current interactions.still since their masses affected by the strong interactions.In Figure 2 we plot the cross sections for supersymmet-ric production in νN interactions as a function of theneutrino energy. Also plotted for comparison is the SMcharged current cross section. As advertised earlier, theSUSY cross sections are still suppressed with respect tothe SM, even when well above threshold.The NLSP Range— Once produced by the νN inter-3actions in the earth, the NLSP pair should range into thedetector, just as the muons produced by CC events [7].Charged particles lose energy due to ionization processesas well as through radiation. The average energy loss isgiven by [8]−dEdx= a(βγ) + c(βγ) βγ , (4)here a and c characterize the ionization and radiationlosses respectively, and are slowly varying functions ofthe energy. The ionization loss can be approximated bya(βγ) ≃ 0.08MeV cm2gr(17 + 2 lnβγ) , (5)nd is rather independent of the particle mass. On theother hand, assuming c(βγ) ≃ const., the radiative en-ergy loss can be written as c βγ = (bm)E. Thusbµmµ = bτ̃Rmτ̃R , and the radiative energy loss for theNLSPs scales inversely with the mass. This results ina much larger range for the NLSP as compared to themuon. Current bounds on mτ̃R are just above 100 GeV.As a reference value we take mτ̃R = 150 GeV. Therefore,NLSPs produced hundreds, even thousands of kilometersaway are within range of the detector. This is to be con-trasted with the fact that muons must be produced atdistances not larger than tens of kilometers from the de-tector in order to be observed. As we will see, this willsomewhat compensate the suppression of the SUSY crosssections observed earlier.Signals in Neutrino Telescopes— In order to computethe event rates in neutrino telescopes, we need to knowthe incoming neutrino flux. The presence of cosmic neu-trinos is expected on the basis of the existence of highenergy cosmic rays. Several estimates of the neutrinoflux are available in the literature. In most cases, it isexpected that km3 neutrino telescopes will measure thisflux. Here, in order to present projections for the numberof observed SUSY events, we make use of the Waxman-Bahcall (WB) limit [9] as an estimate of the cosmic neu-trino flux. We consider an initial flux containing both νµand νe (in a 2 : 1 ratio). Since the initial interactions (seeFigure 1) produce ℓ̃L and these are nearly degenerate inflavor, the flavor of the initial neutrino does not affectour results. For the same reason, the possibility of largemixing in the neutrino flux is also innocuous here. Inorder to correctly take into account the propagation ofneutrinos and the NLSP ℓ̃R through the earth, we makeuse of a model of the earth density profile as detailed inReference [11].In Figure 3 we show the energy distribution for theNLSP pair events for three choices of squark masses:300 GeV, 600 GeV and 900 GeV. Also shown are theneutrino flux at earth in the WB limit, as well as the en-ergy distribution of upgoing µ’s. We see that, even for theheavier squarks, it is possible to obtain observable event10-210-111010 210 310 410 510 610610710810910101011Eν (GeV)Eν dNl/dEν (km-2 year-1 )FIG. 3: Energy distribution of τ̃R pair events per km2, peryear. From top to bottom: mq̃ = 300, 600 and 900 GeV.Here, mτ̃R=150 GeV and mw̃ = 250 GeV. Also shown are theneutrino flux at earth and the µ flux through the detector. Inall cases we make use of the WB limit for the neutrino flux.TABLE I: Number of events per km2 per year for the WBand MPR fluxes. The first column refers to upgoing muons.The last three columns correspond to upgoing NLSP pairevents, for three different choices of squark masses: 300 GeV,600 GeV and 900 GeV. The number of muon events are givenfor energies above threshold for production of a 250 GeV ℓ̃Lplus a 300 GeV squark, ie, 1.6× 105 GeV.µ mq̃ = 300 GeV 600 GeV 900 GeVWB 106 4 1 0.5MPR 1085 10 3 1rates. In Table I we show the event rates for ℓ̃R pair pro-duction per year and per km2. The rates are given for theWB flux as well as for the Mannheim-Protheroe-Rachen(MPR) flux [10], both for optically thin sources. For com-parison, we also show the rates of upgoing muons. Thus,km3 Cerenkov detectors such as ICECUBE, appear tobe sensitive to most of the parameter space of interest inscenarios with a relatively long lived NLSP.Since the NLSPs are produced in pairs very far fromthe detector and with a very large boost, typical signalevents consist of two tracks separated by δR ≃ L θ, withL the distance to the production point (≃ 100−1000 Km)and θ ≃ pCMSUSY/pboost ≃ 10−3 − 10−4. If we consider Lto be of the order of the NLSP range, then in the lin-ear regime δR ≃ constant ≃ 100m. As we have seen inthe discussion following eqn. (5), for very high energies4TABLE II: Number of events for extended ICECUBE [13] peryear assuming ν flux is given by the WB limit. The ℓ̃L andsquark masses and the number of muons are as in Table I.µ mq̃ = 300 GeV 600 GeV 900 GeV1 ring, 300 m 110 5 2 11 ring, 1000 m 110 6 2 14 rings, 300 m 131 9 3 14 rings, 1000 m 140 16 5 2the range grows logarithmically with energy, leading tosomewhat smaller values of δR ≃ (20− 40)m. The trackseparation is then mildly sensitive to the stau injectionenergy [12]. Then, most NLSP events would consist oftwo parallel but well separated tracks, and are thereforeexpected to be very distinctive and different from back-grounds. In addition, we see from Figure 3 that the signalevents have a harder spectrum than the µ background.Conclusions — We have shown for the first time thatneutrino telescopes are potentially sensitive to the rela-tively long-lived charged NLSPs which are present in awide variety of models of supersymmetry breaking. Theevent rates shown in Table I are already encouraging forexperimental facilities that are been built, such as ICE-CUBE. The region of the supersymmetry breaking pa-rameter space that is available to neutrino telescopes isdetermined, on the one hand, by the twin requirementsthat the NLSP lifetime be long enough to give a signal(√F >∼ 5 × 106 GeV), but not be so long as to disturbBig Bang Nucleosynthesis (√F <∼ 5×108 GeV). Thus theobservation of NLSP events at neutrino telescopes willconstitute a direct probe of the scale of supersymmetrybreaking. This is to be compared with the potential ob-servation of these NLSPs at the Large Hadron Collider(LHC), where for this range of√F , the NLSP decaysoutside the detector and is seen through its ionizationtracks. However, the observation at the LHC would notconstrain the NLSP lifetime significantly. Thus, we seethat neutrino telescopes are complementary to collidersearches. For instance, the observation of NLSP eventsat the LHC, coupled to the non-observation in neutrinotelescopes would point to√F < 107 GeV.Future upgrades of ICECUBE, as well as of the waterdetectors ANTARES [14] and NESTOR [15] will resultin even better sensitivity. As an example, in Table II weshow rates for an expanded version of ICECUBE [13].In the present letter we focused on supersymmetry.However, many other theories give rise to relatively longlived charged particles which can be observed by neutrinotelescopes [12].Acknowledgments — We would like to thank AzrielGoldschmidt and Ian Hinchliffe for useful conversations.I. A. is supported by NSF Grant Physics/Polar Programs0071886. G. B. and Z. C. are supported by the Direc-tor, Office of Science, Office of High Energy and Nu-clear Physics, of the U. S. Department of Energy underContract DE-AC03-76SF00098 and by the N.S.F. underPHY-00-98840.[1] M. Dine, W. Fischler, M. Srednicki, Nuc. Phys. B 189,575 (1981); S. Dimopoulos, S. Raby, Nuc. Phys. B 192,353 (1981); L. Alvarez–Gaumé, M. Claudson, M.B. Wise,Nuc. Phys. B 207, 96 (1982); M. Dine, A.E. Nelson,Phys. Rev. D 48, 1277 (1993); M. Dine, A.E. Nelson,Y. Shirman, Phys. Rev. D 51, 1362 (1995); M. Dine,A.E. Nelson, Y. Nir, Y. Shirman, Phys. Rev. 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Neutrino telescopes as a direct probe of supersymmetrybreaking

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Neutrino Telescopes as a Direct Probe of Supersymmetry Breaking

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Neutrino Telescopes as a Direct Probe of Supersymmetry Breaking

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