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W-Boson and Trident Production in Tev--Pev Neutrino Observatories

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W-Boson and Trident Production in Tev--Pev Neutrino Observatories W -boson and trident production in TeV{PeV neutrino observatories Bei Zhou1, 2, ∗ and John F. Beacom1, 2, 3, y 1Center for Cosmology and AstroParticle Physics (CCAPP), Ohio State University, Columbus, OH 43210 2Department of Physics, Ohio State University, Columbus, OH 43210 3Department of Astronomy, Ohio State University, Columbus, OH 43210 (Dated: February 18, 2020) Detecting TeV{PeV cosmic neutrinos provides crucial tests of neutrino physics and astrophysics. The statistics of IceCube and the larger proposed IceCube-Gen2 demand calculations of neutrino- nucleus interactions subdominant to deep-inelastic scattering, which is mediated by weak-boson couplings to nuclei. The largest such interactions are W -boson and trident production, which are mediated instead through photon couplings to nuclei. In a companion paper [1], we make the most comprehensive and precise calculations of those interactions at high energies. In this paper, we study their phenomenological consequences. We find that: (1) These interactions are dominated by the production of on-shell W -bosons, which carry most of the neutrino energy, (2) The cross section on water/iron can be as large as 7.5%/14% that of charged-current deep-inelastic scattering, much larger than the quoted uncertainty on the latter, (3) Attenuation in Earth is increased by as much as 15%, (4) W -boson production on nuclei exceeds that through the Glashow resonance on electrons by a factor of ' 20 for the best-fit IceCube spectrum, (5) The primary signals are showers that will significantly affect the detection rate in IceCube-Gen2; a small fraction of events give unique signatures that may be detected sooner. I. INTRODUCTION interactions. We focus on those in which the coupling to the nucleus and its constituents is through a virtual ∗ The recent detections of TeV{PeV neutrinos by Ice- photon, γ , instead of a weak boson [50{66]. The most Cube [2{7] are a breakthrough in neutrino astrophysics. important processes are on-shell W -boson production, in ∗ Though the sources of the diffuse flux have not been which the underlying interaction is ν` + γ ! ` + W , and ∗ − + identified, important constraints on their properties have trident production, in which it is ν + γ ! ν + `1 + `2 . been determined [8{22]. In addition, there is a candidate In a companion paper [1], we make the most compre- source detection in association with a blazar flare [23, 24]. hensive and precise calculations of these cross sections The IceCube detections are also a breakthrough in neu- at high energies. The cross section of W -boson produc- trino physics. By comparing the observed spectra of tion can be as large as 7.5% of the DIS cross section events that have traveled through Earth or not, the cross for water/ice targets (and as large as 14% for iron tar- section can be measured at energies far above the reach gets, relevant for neutrino propagation through Earth's of laboratory experiments [25{30]. And many models of core) [1]. For trident production, the most important new physics have been powerfully limited by the IceCube channels are a subset of W -boson production followed by data [31{44]. leptonic decays [1]. To set a scale, IceCube has identified With new detectors | KM3NeT [45], Baikal- 60 events above 60 TeV in 7.5 years of operation [5,6], GVD [46], and especially the proposed IceCube-Gen2 so taking these subdominant processes into account will (about 10 times bigger than IceCube) [47] | the dis- be essential for IceCube-Gen2. Moreover, the W -boson covery prospects will be greatly increased, due to im- and trident events have complex final states, which may provements in statistics, energy range, and flavor infor- allow their detection even sooner, in IceCube. mation. At high energies, neutrino-nucleus interactions In this paper, we detail the phenomenological conse- are dominated by deep inelastic scattering (DIS) me- quences of these processes. In Sec. II, we focus on their arXiv:1910.10720v2 [hep-ph] 19 Feb 2020 diated by weak-boson couplings to nuclei [48, 49]. For cross sections. In Sec. III, we focus on their detectability. charged-current (CC) interactions, νe leads to a shower, We conclude in Sec.IV. νµ leads to a shower and a long muon track, and ντ leads to two showers that begin to separate spatially at ∼ 100 TeV [7]. For neutral-current (NC) interactions II. W -BOSON PRODUCTION CROSS of all flavors, showers are produced. Cherenkov light is SECTIONS AND IMPLICATIONS produced by muon tracks and through the production of numerous low-energy electrons and positrons in showers. In this section, we briefly review the total cross sec- With these coming improved detection prospects, new tion for W -boson production (Sec.IIA; details are given questions can be asked, including the role of subdominant in our companion paper [1]), and present new calcula- tions of the differential cross sections (Sec. IIB). Then we talk about the implications, including the cross sec- ∗ [email protected]; orcid.org/0000-0003-1600-8835 tion uncertainties (Sec. IIC) and the effects on neutrino y [email protected]; orcid.org/0000-0002-0005-2631 attenuation in Earth (Sec. IID). 2 we point out that there are two subprocesses: photon- initiated and quark-initiated. For the former, we use 30 10 Glashow the up-to-date inelastic photon PDF of proton and neu- resonance tron [70, 71] and dynamical factorization and renormal- ( e) 31 ization scales. For the latter, we do the first calculation 10 and find that this sub-process can be neglected below ' 108 GeV. A key result is that our W -boson production ] 2 32 cross section is smaller than that of previous work [58{ m 10 c CCDIS 60]. [ NCDIS Figure1 shows our W -boson production cross sections 16 33 on O for different neutrino flavors, along with other . 10 prod relevant processes. The width of the Glashow resonance son ) -bo , / is due to the intrinsic decay width of the W boson. W , / 34 ( e/ e 10 B. New results for the differential cross sections 35 10 4 5 6 7 8 10 10 10 10 10 For the differential cross sections, the most relevant E [ GeV ] results to detection are the energy distributions of the FIG. 1. Cross sections between neutrinos and 16O for W - charged lepton (E`) and the W boson (EW ). The en- boson production [1], compared to those for CCDIS [67], ergy that goes to the hadronic part is negligible (see next − − NCDIS [67], and the Glashow resonance (¯νee ! W , taking paragraph). As above, the differential cross sections are into account eight electrons) [68]. calculated separately for the three regimes and summed. For the coherent and diffractive regimes, the phase-space variables we chose to calculate the total cross section in A. Review of the total cross sections Ref. [1] are not directly related to the energies of the final states, so some transformations are needed; see Ap- The nuclear production processes for on-shell W pendixA. For the inelastic regime, following Ref. [1], we bosons are use MadGraph (v2.6.4) [72] and analyze the event dis- tributions in terms of the relevant quantities. − + 0 ν` + A ! ` + W + A ; (1a) The energy that goes to the hadronic part, ∆Eh = 2 + − 0 Q =2mh (AppendixA), is negligible compared to the ν¯` + A ! ` + W + A ; (1b) detection threshold, which is ∼ 100 GeV for showers where A and A0 are the initial and final-state nuclei and in IceCube. Here Q2 ≡ −q2 is the photon virtuality; ` is a charged lepton. The neutrino- and antineutrino- the hadronic mass, mh, is the nuclear mass in the co- induced processes have the same total and differential herent regime and the nucleon mass in the diffractive cross sections, but there is flavor dependence. The cou- and inelastic regimes. For the coherent and diffractive pling to the nucleus and its constituents is through a regimes, the corresponding nuclear and nucleon form fac- virtual photon, γ∗ (contributions from virtual W and Z tors are highly suppressed above Q ∼ 0:1 GeV and Q ∼ 8 2 bosons are only important for Eν > 10 GeV [1]). The 1 GeV, respectively, which leads to ∆Eh . (0:1) =2=16 ' 3 2 process has a high threshold, Eν ' 5 × 10 GeV, due to 0:0003 GeV and ∆Eh . (1) =2=1 ' 0:5 GeV. For the in- the large mass of the W boson, though much lower than elastic regime, although Q2 could be much larger, the the threshold for the Glashow resonance, which peaks at cross section is still dominated by the low-Q2 region 2 2 ' 6:3 PeV. Above threshold, the leptonic decays of the (Q . 10 GeV , i.e., ∆Eh . 10=2=1 ' 5 GeV) be- W boson (branching ratio ' 11% to each flavor) lead to cause the nonperturbative part of the inelastic photon the dominant contributions to trident production. PDF [70, 73] dominates the cross section (see Sec. V.B The interactions happen in three different scattering of Ref. [1]). Above is very different the DIS, in which regimes | coherent, diffractive, and inelastic | in which the energy transferred to the nucleus is 25%Eν on aver- the virtual photon couples to the whole nucleus, a nu- age [27, 48, 49, 67]. cleon, and a quark, respectively. The corresponding Therefore, Eν ' E` + EW is an excellent approxima- cross sections are calculated separately and added to give tion for the coherent and diffractive regimes and a good the total cross section. For the coherent and diffrac- approximation for the inelastic regime. We checked this tive regimes, we deal with the hadronic part in a com- through the distribution of the sum of EW and E` , find- plete way, which takes into account the photon virtual- ing that this is nearly a delta function at Eν .
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