Neutrino Signals in IceCube from Weak Production of Top and Charm Quarks Vernon Barger1, Edward Basso1, Yu Gao2;3, and Wai-Yee Keung4 1Department of Physics, University of Wisconsin, Madison, WI 53706, USA 2Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA 3Department of Physics and Astronomy, Wayne State University, Detroit, MI, 48201 USA 4Physics Department, University of Illinois at Chicago, IL 60607 Deep inelastic scattering of very high-energy neutrinos can potentially be enhanced by the pro- duction of a single top quark or charm quark via the interaction of a virtual W -boson exchange with a b-quark or s-quark parton in the nucleon. The single top contribution shows a sharp rise at neutrino energies above 0.5 PeV and gives a cross-section contribution of order 5 percent at 10 PeV, while single charm has a low energy threshold and contributes about 25 percent. Semileptonic decays of top and charm give dimuon events whose kinematic characteristics are shown. The angular separation of the dimuons from heavy quark production in the IceCube detector can reach up to one degree. Top quark production has a unique, but rare, three muon signal. I. INTRODUCTION and hadrons contribute to the observed Cherenkov light. The IceTop array of ice tanks on the surface is used to The ultra-high energy cross-section for neutrino deep detect and reconstruct air showers; it thereby vetoes the inelastic scattering (DIS) has long been of theoretical in- large cosmic muon backgrounds. terest. See, e.g.[1]. The DIS cross-section contributions There are two classes of events: due to the b-quark to t-quark transition and the s-quark 1)\Track-like" events are those with a highly energetic to c-quark transition, mediated by W -boson exchange[2], muon produced in the interaction of a νµ within the de- may be observable in the IceCube experiment. With the tector or in the surrounding ice or rock. In addition to recently improved determinations of the b-quark and the rejection of cosmic muon backgrounds by IceTop, the s-quark parton distributions function (PDFs), single top- Earth also serves as a filter to eliminate cosmic muon quark and single charm-quark production by neutrinos backgrounds. Muons with arrival directions above 85 de- can be calculated with a high degree of confidence and grees in zenith angle must originate from neutrino in- this is one objective of our study. teractions, even if the muon track originates outside the The IceCube experiment has recently reported results detector volume. from 7 years of data[3]. Neutrino events with energies in 2) \Shower-like" events are those with an electromag- the range 240 TeV to 10 PeV are found at a level that sig- netic shower that is contained in the detector but without nificantly exceeds the atmospheric neutrino background a muon track. These events are due to νe or ντ charged- which is steeply falling with increasing energy. These current events , as well as neutral current events. observations have sparked interest in possible origins of The Class 1 track events are up-going in the detector. the high energy events [4], including astrophysics sources, They are essentially free of the atmospheric background, such as AGN and star-burst galaxies [5], or new physics, but they provide only partial sky coverage. There is a such as leptoquarks [6{8] and the decays of very-long- significant loss of the very high energy neutrino flux in arXiv:1611.00773v3 [hep-ph] 10 May 2017 lived neutral particles associated with quasi-stable dark the propagation of the neutrinos through the Earth. matter[9{12]. The Class 2 shower events are required to have the The Standard Model contributions from the produc- visible electromagnetic energy confined within the detec- tion of a single top-quark and a single charm-quark will tor volume. The cosmic muon background is rejected by enhance the DIS neutrino cross at PeV-energies and IceTop. The Class 2 events have full sky coverage. thus these contributions are relevant to IceCube observa- The contributions to the atmospheric neutrino flux tions. We evaluate their DIS contributions and consider from pair-production of charm particles by the strong in- the characteristics of dimuon events associated with the teraction have been considered [13{16], with the conclu- semileptonic decays of the t-quark and c-quark. sion that this source cannot explain the excess of events We begin with a brief overview of the IceCube experi- observed by IceCube above 30 TeV[14]. ment and datasets. IceCube is a 1 km3 photomultiplier- In the Class 1 track events, the most probable neutrino instrumented detector located in the South Pole ice sheet. energy cannot be precisely determined because the high- The detector measures the total Cherenkov light emission energy muon often passes through and exits the detector. in a high-energy neutrino event. The produced leptons However, the neutrino direction of the track events is well 2 determined to less than 0.5 degree. In the Class 2 shower events, the energy of the inci- ν l− dent neutrino is reasonably well determined, while the neutrino direction has large uncertainty (with a median b uncertainty of 10 degrees). W + Thus, the two Classes of events are complementary in ¯ their physics information. The neutrino flux is steeply f ′ t falling up to 100 TeV, as expected for neutrinos of at- mospheric origin. Above 240 TeV, the neutrino flux has b f −2 a flatter energy spectrum that is consistent with a Eν power law, typical of an astrophysics Fermi acceleration FIG. 1: Leading order Feynman diagram for neutrino pro- mechanism of cosmic rays [17]. Whether there is a maxi- duction of the t-quark from the b-quark parton in the nu- mum energy cut-off of the neutrino flux remains an open cleon, νb ! `t. The W-boson decays to a fermion and an question. anti-fermion The three most energetic shower events have energies of 1.041 PeV, 1.141 PeV and 2.0 PeV, with 15% energy interaction is shown in Fig. 1, along with the top-quark resolution. A track event was found with an exceptionally decay to a b-quark and a real W-boson. high-energy muon and 2:6 0:3 PeV deposited energy. νb `t ± The charged current subprocess gives the deep These are the highest energy neutrinos ever recorded inelastic t-quark production cross-section.! In the excel- by any experiment. The high-energy neutrino flux in- lent approximation that the quark mixing matrix element ferred by IceCube depends on the effective area of the Vtb = 1, the differential DIS cross section is given by detector, under the assumption that the neutrino inclu- 2 2 4 sive cross-section can be accurately modeled by charged- dσ GF (^s mt )mW 0 2 = 2− 2 2 b(x ; µ ) ; (1) current and neutral-current DIS on light-quark flavors. dxdy π(Q + mW ) Our study evaluates the impact of the b-quark to t-quark q p p and the s-quark to c-quark transitions, treating the b- where the momentum transfer = ν ` sets the scale Q2 = q2 > 0. The Bjorken scaling− variables are quark as a massless parton in the proton [18, 19] in the 5- 2 − 2 x = Q =2p q and y = pN q=mN , with Q = sxy; flavor formalism. In addition, we simulate the muon dis- · · y = (Eν E`)=Eν = Eh=Eν is the fraction of the neu- tributions in dimuon events for a further probe of heavy − quark contributions. Our focus is on events in which the trino energy that is transferred to hadrons. The CM en- ergy squared of νN scattering is s = 2mN Eν , neglecting deep inelastic interaction on a proton target of a νµ gives 2 the small mN contribution. From kinematics, the frac- a fast primary muon. 0 2 tional momentum of the b-parton is x = x+mt =ys. The 2 0 subprocess CM energy squared iss ^ = (pν + pb) = x s. The domains of the x; y variables are II. SLOW SCALING IN TOP-QUARK PRODUCTION m2 m2=s < y < 1 and 0 < x < 1 t : (2) t − sy In a 4-flavor parton scheme (4FS), the leading-order Note that b(x0; µ2) is evaluated at the slow scaling vari- (LO) partonic process for the QCD production of a b- able, i.e. x0. quark is gluon to b¯b and the top-quark is produced from After variable substitutions, we also obtain the formula the b-quark in an overall 2 to 3 particle process. In the 4FS, the integration over the final-state bottom-quark 2 2 2 4 dσ G (2mN Eν x + m =y m )m m2 momenta leads to logarithmic dependence on m . In a = F t − t W b(x + t ; µ2) ; b dxdy π m2 m E xy 2 sy 5-flavor scheme (5FS), these logarithms are re-summed ( W + 2 N ν ) to all orders in the strong coupling into a b-quark parton (3) y x > m2=s distribution function (PDF). with (1 ) t . Note that the numerator factor (xs + m2=y− m2) xs whens ^ m2, and thus xb(x) In the 5FS, the b-quark mass is set to zero, and all t t t is obtained− in Eq.−! (3) well above threshold. A similar collinear divergences are absorbed into the PDF through formula applies to the anti-neutrino case. In our calcula- mass factorization. The dependence on the b-quark mass tions we take m for both factorization and renormaliza- is encoded as a boundary condition on the Renormaliza- t tion scales, as found in other applications to reproduce tion Group Equations.