An efficient method for calculating inclusive conventional and prompt atmospheric leptons fluxes is presented. The coupled cascade equations are solved numerically by formulating them as matrix equation. The presented approach is very flexible and allows the use of different hadronic interaction models, realistic parametrizations of the primary cosmic-ray flux and the Earth's atmosphere, and a detailed treatment of particle interactions and decays. The power of the developed method is illustrated by calculating lepton flux predictions for a number of different scenarios.
Muons and neutrinos from cosmic ray interactions in the atmosphere originate from decays of mesons in air-showers. Sibyll-2.3c aims to give a precise description of hadronic interactions in the relevant phase space for conventional and prompt leptons in light of new accelerator data, including that from the LHC. Sibyll is designed primarily as an event generator for use in simulation of extensive air showers. Because it has been tuned for forward physics as well as the central region, it can also be used to calculate inclusive fluxes. The purpose of this paper is to describe the use of Sibyll-…
We reexamine the charm contribution to atmospheric lepton fluxes in the context of perturbative QCD. We include next-to-leading order corrections and discuss theoretical uncertainties due to the extrapolations of the gluon distributions at small-x. We show that the charm contribution to the atmospheric muon flux becomes dominant over the conventional contribution from pion and kaon decays at energies of about 10^5 GeV. We compare our fluxes with previous calculations.
The observation of astrophysical neutrinos requires a detailed understanding of the atmospheric neutrino background. Since neutrinos are produced in meson decays together with a charged lepton, important constraints on this background can be obtained from the measurement of the atmospheric muon flux. Muons, however, can also be produced as mu+ mu- pairs by purely electromagnetic processes. We use the Z-moment method to study and compare the contributions to the atmospheric muon and neutrino fluxes from different sources (pi/K decay, charmed and unflavored hadron decay, and photon conversion in…
In order to estimate the possibility to observe exotic physics in a neutrino telescope, it is essential to first understand the flux of atmospheric neutrinos, muons and dimuons. We study the production of these leptons by high-energy cosmic rays. We identify three main sources of muons of energy E > 10^6 GeV: the weak decay of charm and bottom mesons and the electromagnetic decay of unflavored mesons. Contrary to the standard assumption, we find that eta mesons, not the prompt decay of charm hadrons, are the dominant source of atmospheric muons at these energies. We show that, as a consequence…
We update predictions for lepton fluxes from the hadroproduction of charm quarks in the scattering of primary cosmic rays with the Earth's atmosphere. The calculation of charm-pair hadroproduction applies the latest results from perturbative QCD through next-to-next-to-leading order and modern parton distributions, together with estimates on various sources of uncertainties. Our predictions for the lepton fluxes turn out to be compatible, within the uncertainty band, with recent results in the literature. However, by taking into account contributions neglected in previous works, our total unce…
The atmospheric muon flux is generated with CORSIKA 6.030 (using QGSJET high-energy interaction model) and fitted with the formula from Gaisser (1990). Spectra and mass distribution of primaries were taken according to the poli-gonato model of Horandel (2003). A convenient parameterization of the cos(th)->cos(th*) correction, originally tabulated in Volkova (1969), is presented. This correction, together with muon energy losses and decay, is shown to significantly improve the fit to the simulated data.
The differential energy distribution for electrons and taus produced from lepton pair production from muons in transit through materials is numerically evaluated. We use the differential cross section to calculate underground lepton fluxes from an incident atmospheric muon flux, considering contributions from both conventional and prompt fluxes. An approximate form for the charged current differential neutrino cross section is provided and used to calculate single lepton production from atmospheric neutrinos. We compare the fluxes of underground leptons produced from incident muons with those …
Prompt neutrino fluxes are basic backgrounds in the search of high-energy neutrinos of astrophysical origin, performed by means of full-size neutrino telescopes located at Earth, under ice or under water. Predictions for these fluxes are provided on the basis of up-to-date theoretical results for charm hadroproduction in perturbative QCD, together with a comprehensive discussion of the various sources of theoretical uncertainty affecting their computation, and a quantitative estimate of each uncertainty contribution.
The flux of high-energy (>GeV) neutrinos consists primarily of those produced by cosmic-ray interactions in the atmosphere. The contribution from extraterrestrial sources is still unknown. Current limits suggest that the observed spectrum is dominated by atmospheric neutrinos up to at least 100 TeV. The contribution of charmed hadrons to the flux of atmospheric neutrinos is important in the context of the search for astrophysical neutrinos because the spectrum of such "prompt" neutrinos is harder than that of "conventional" neutrinos from decay of pions and kaons. The prompt component therefor…
We calculate the prompt neutrino flux from atmospheric charm production by cosmic rays, using the dipole picture in a perturbative QCD framework, which incorporates the parton saturation effects present at high energies. We compare our results with the next-to-leading order perturbative QCD result and find that saturation effects are large for neutrino energies above 10^6 GeV, leading to a substantial suppression of the prompt neutrino flux. We comment on the range of prompt neutrino fluxes due to theoretical uncertainties.
Effects on atmospheric prompt neutrino fluxes of present uncertainties affecting the nucleon composition are studied by using the PROSA fit to parton distribution functions (PDFs). The PROSA fit extends the precision of the PDFs to low x, which is the kinematic region of relevance for high-energy neutrino production, by taking into account LHCb data on charm and bottom hadroproduction. In the range of neutrino energies explored by present Very Large Volume Neutrino Telescopes, it is found that PDF uncertainties are far smaller with respect to those due to renormalization and factorization scal…
We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, $k_T$ factorization including low-$x$ resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for…
We compare the leading and next-to-leading order QCD predictions for the flux of atmospheric muons and neutrinos from decays of charmed particles. We find that the full NLO lepton fluxes can be approximated to within 10% by the Born--level fluxes multiplied by an overall factor of 2.2-2.4, which depends slightly on the PDF. This supports the approach in Thunman, Ingelman, Gondolo (1996). We also find that their very low lepton fluxes are due to the mild slope they used for the gluon distribution function at small momentum fractions, and that substantially larger lepton fluxes result when the s…
We review the calculation of the prompt lepton flux, produced in the atmosphere by the semileptonic decay of charmed particles. We describe side by side the intermediary ingredients used by different authors, which include not only the charm production model, but also other atmospheric particle showering parameters. After evaluating separately the relevance of each single ingredient, we analyze the effect of different combinations over the final result. We highlight the impact of the prompt lepton flux calculation upon high-energy neutrino telescopes.
We present a semi-analytic calculation of the tau-lepton flux emerging from the Earth, induced by the incident high energy neutrinos interacting inside the Earth for $10^{5} \leq E_ν/{\rm GeV} \leq 10^{10}$. We obtain results for the energy dependence of the tau-lepton flux coming from the Earth-skimming neutrinos, because of the neutrino-nucleon charged-current scattering as well as the resonant $\barν_e e^-$ scattering. We illustrate our results for several anticipated high energy astrophysical neutrino sources such as the AGNs, the GRBs, and the GZK neutrino fluxes. The tau lepton fluxes re…
New \textit{ab initio} calculations of the isotopic reactor antineutrino fluxes are provided with exact numerical calculations of the lepton wave functions, assuming all the decay branches are allowed GT transitions. We illustrate that the analytical Fermi function and finite size effect each could have the largest spectral deviation of $\mathcal{O}(10\%)$, whereas the effect of their combination could result in spectral deviations at the level of 5%-10%. Meanwhile, we also find that several forms of the extended charge distributions have negligible effects on the spectral variation. Using the…
We calculate event rate and demonstrate the observational feasibility of very high energy muons (1-1000 TeV) in a large mass underground detector operating as a pair-meter. This energy range corresponds to surface muon energies of $\sim$(5 TeV - 5000 TeV) and primary cosmic ray energies of $\sim$ (50 TeV - 5 $\times 10^4$ TeV). Such measurements would significantly assist in an improved understanding of the prompt contribution to $ν_e, ν_μ$ and $μ$ fluxes in present and future ultra-high energy neutrino detectors. In addition, they would shed light on the origin of the observed 'knee' in the c…
The impact of measurements of heavy-flavour production in deep inelastic $ep$ scattering and in $pp$ collisions on parton distribution functions is studied in a QCD analysis at next-to-leading order. Recent combined results of inclusive and heavy-flavour production cross sections in deep inelastic scattering at HERA are investigated together with heavy-flavour production measurements at the LHC. Differential cross sections of charm- and beauty-hadron production measured by the LHCb collaboration at the centre-of-mass energies of 5, 7 and 13 TeV as well as the recent measurements of the ALICE e…
The phenomenon of fully coherent energy loss (FCEL) in the collisions of protons on light ions affects the physics of cosmic ray air showers. As an illustration, we address two closely related observables: hadron production in forthcoming proton-oxygen collisions at the LHC, and the atmospheric neutrino fluxes induced by the semileptonic decays of hadrons produced in proton-air collisions. In both cases, a significant nuclear suppression due to FCEL is predicted. The conventional and prompt neutrino fluxes are suppressed by $\sim 10...25\%$ in their relevant neutrino energy ranges. Previous es…
We evaluate the prompt atmospheric neutrino flux using the different QCD models for heavy quark production including the $b$ quark contribution. We include the nuclear correction and find it reduces the fluxes by $10 \% - 50\%$ according to the models. Our heavy quark results are compared with experimental data from RHIC, LHC and LHCb.
We discuss the transverse momentum distribution for the production of massive lepton-pairs in hadron reactions at fixed target and collider energies within the context of next-to-leading order perturbative quantum chromodynamics. For values of the transverse momentum $Q_T$ greater than the pair mass $Q$, $Q_T > Q$, we show that the differential cross section is dominated by subprocesses initiated by incident gluons. Massive lepton-pair differential cross sections are an advantageous source of constraints on the gluon density, free from the experimental and theoretical complications of photon i…
We evaluate the prompt atmospheric neutrino flux including nuclear correction and $B$ hadron contribution in the different frameworks: NLO perturbative QCD and dipole models. The nuclear effect is larger in the prompt neutrino flux than in the total charm production cross section, and it reduces the fluxes by $10\% - 30\%$ depending on the model. We also investigate the uncertainty using the QCD scales allowed by the charm cross section data from RHIC and LHC experiments.
We compute the next-to-leading order QCD predictions for the vertical flux of atmospheric muons and neutrinos from decays of charmed particles, for different PDF's (MRS-R1, MRS-R2, CTEQ-4M and MRST) and different extrapolations of these at small partonic momentum fraction x. We find that the predicted fluxes vary up to almost two orders of magnitude at the largest energies studied, depending on the chosen extrapolation of the PDF's. We show that the spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon distribution function at very small x. This suggests …
The hadroproduction of lepton pairs with mass $Q$ and transverse momentum $Q_T$ can be described in perturbative QCD by the same partonic subprocesses as prompt photon production. We demonstrate that, like prompt photon production, lepton pair production is dominated by quark-gluon scattering in the region $Q_T>Q/2$. This leads to sensitivity to the gluon density in kinematical regimes that are accessible both at collider and fixed target experiments while eliminating the theoretical and experimental uncertainties present in prompt photon production.
We discuss the possible existence of an observational window, in the TeV-PeV energy range, for the detection of prompt neutrinos from the decay of charmed particles produced in cosmic ray interactions with the atmosphere. We calculate the event rates for muon and tau neutrinos of heavy quark, mostly charm, origin. We argue that their prompt fluxes are observable in a kilometer-scale neutrino telescope, even though the calculations are subjected to large uncertainties, which we quantify. We raise the possibility that a small component of prompt neutrinos may already be present in the observed s…
The FLUKA calculation of the atmospheric neutrino fluxes have been cross-checked by comparing predictions on lepton fluxes in atmosphere to experimental data. The dependence of predicted neutrino fluxes on the shape and normalization of primary spectrum is also investigated
Leptonic originated High energy neutrinos from astrophysical objects
High Energy & Cosmic Ray Research Centre, University of North Bengal（北孟加拉大学高能与宇宙射线研究中心）；High Energy & Cosmic Ray Research Center, University of North Bengal（北孟加拉大学高能与宇宙射线研究中心）
The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater is calculated taking into consideration predictions of recent charm production models in which the small-x behaviour of the gluon distribution is probed. We discuss the possibility of distinguishing the PQCD models of the charm production differing in the small-x exponent of the gluon distribution, in measurements of the muon flux at energies …
The event generator Sibyll can be used for the simulation of hadronic multiparticle production up to the highest cosmic ray energies. It is optimized for providing an economic description of those aspects of the expected hadronic final states that are needed for the calculation of air showers and atmospheric lepton fluxes. New measurements from fixed target and collider experiments, in particular those at LHC, allow us to test the predictive power of the model version 2.1, which was released more than 10 years ago, and also to identify shortcomings. Based on a detailed comparison of the model …
Leptogenesis is studied within the seesaw neutrino mass model in a regime where all sterile neutrinos have prompt rather than delayed decays. It is shown that during neutrino thermal production lepton asymmetries are generated in both active lepton and sterile neutrino sectors. The large B-L asymmetry is slowly pumped into the chemically decoupled right-handed quarks and leptons and baryon number sector which later protect B-L from fast L violating processes. The dependence of the final baryon asymmetry on couplings and masses is totally different from the decay scenario. B does not vanish in …
The hadroproduction of lepton pairs with mass Q and finite transverse momentum Q_T is described in perturbative QCD by the same partonic subprocesses as prompt photon production. We demonstrate that, like prompt photon production, lepton pair production is dominated by quark-gluon scattering in the region Q_T>Q/2. This feature leads to sensitivity to the gluon density in kinematical regimes accessible in collider and fixed target experiments, and it provides a new independent method for constraining the gluon density.
It is widely believed that charm meson production and decay may play an important role in high energy astrophysical sources of neutrinos, especially those that are baryon-rich, providing an environment conducive to pp interactions. Using slow-jet supernovae (SJS) as an example of such a source, we study the detectability of high-energy neutrinos, paying particular attention to those produced from charmed-mesons. We highlight important distinguishing features in the ultra-high energy neutrino flux which would act as markers for the role of charm in the source. In particular, charm leads to sign…
A Monte Carlo Calculation of Atmospheric Muon and Neutrino Fluxes
用基于Lund Monte Carlo方法的级联模拟程序研究了宇宙线与大气相互作用中μ子和中微子的产生。由此产生的“常规”μ子和中微子通量（来自$π,K$衰变）与早期的计算吻合良好，而本研究中使用的改进的魅粒子处理给出了显着较低的“提示”通量相比，早期的估计。这意味着从宇宙源探测非常高能量中微子的前景更好。
We present a three-dimensional calculation of atmospheric neutrino fluxes using accurate models of the geomagnetic field, hadronic interactions, tracking and decays. Results are presented for the Super-Kamiokande (SK) and Sudbury Neutrino Observatory (SNO) sites using the GEANT-FLUKA hadronic code. We make a comparison with previous one-dimensional calculations and other three-dimensional results. The recently reported geometrical enhancement of low energy, horizontal neutrinos is confirmed. The effect on observed leptons is however, restricted to a small overall increase in flux. We report ea…
We compute deep-sea energy spectra and zenith-angle distributions of the atmospheric muons, both conventional and prompt. The prompt muon contribution to the muon flux underwater is calculated taking into consideration predictions of recent charm production models in which probed is the small-x behavior of the gluon distribution inside of a nucleon. We argue for a possibility to discriminate the PQCD models of the charm production differing in the slope of the gluon distribution, in measurements with neutrino telescopes of the muon flux at energies 10-100 TeV.
The charm contribution to the atmospheric fluxes of muons and muon neutrinos may be enhanced by as much as a factor of 10 when one includes the contributions of D->pi,K->leptons and folds in uncertainties in the charm cross section and energy distribution. In the energy range considered here, from 100 GeV to 10 TeV, the charm contribution is small compared to the conventional flux of muons and muon neutrinos.
In the TeV energy region and above, the uncertainty in the level of prompt atmospheric neutrinos would limit the search for diffuse astrophysical neutrinos. We suggest that neutrino telescopes may provide an empirical determination of the flux of prompt atmospheric electron and muon neutrinos by measuring the flux of prompt down-going muons. Our suggestion is based on the consideration that prompt neutrino and prompt muon fluxes at sea level are almost identical.
We evaluate the flux of tau neutrinos produced from the decay of pair produced taus from incident muons using a cascade equation analysis. To solve the cascade equations, our numerical result for the tau production $Z$ moment is given. Our results for the flux of tau neutrinos produced from incident muons are compared to the flux of tau neutrinos produced via oscillations and the direct prompt atmospheric tau neutrino flux. Results are given for both downward and upward going neutrinos fluxes and higher zenith angles are discussed. We conclude that the direct prompt atmospheric tau neutrino fl…
If neutrino masses and mixings are suitable to explain the atmospheric and solar neutrino fluxes, this amounts to contributions to FCNC processes, in particular $μ\to e, γ$. If the theory is supersymmetric and the origin of the masses is a see-saw mechanism, we show that the prediction for BR($μ\to e, γ$) is in general larger than the experimental upper bound, especially if the solar data are explained by a large angle MSW effect, which recent analyses suggest as the preferred scenario.
We study charged lepton flavor violation associated with a light leptophilic axion-like particle (ALP), $X$, at the $B$-factory experiment Belle II. We focus on production of the ALP in the tau decays $τ\to X l$ with $l=e,μ$, followed by its decay via $X\to l^- l^+$. The ALP can be either promptly decaying or long-lived. We perform Monte-Carlo simulations, recasting a prompt search at Belle for lepton-flavor-violating $τ$ decays, and propose a displaced-vertex (DV) search. For both types of searches, we derive the Belle~II sensitivity reaches in both the product of branching fractions and the …
We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the h…
High-energy neutrinos from decays of mesons, produced in collisions of cosmic ray particles with air nuclei, form unavoidable background for detection of astrophysical neutrinos. More precise calculations of the high-energy neutrino spectrum are required since measurements in the IceCube experiment reach the intriguing energy region where a contribution of the prompt neutrinos and/or astrophysical ones should be discovered. Basing on the referent hadronic models QGSJET II-03, SIBYLL 2.1, we calculate high-energy spectra, both of the muon and electron atmospheric neutrinos, averaged over zenith…
Prompt neutrino fluxes due to the interactions of high-energy cosmic rays with the Earth's atmosphere are backgrounds in the search for high-energy neutrinos of galactic or extra-galactic origin performed by Very Large Volume Neutrino Telescopes. We summarize our predictions for prompt neutrinos, showing their basic features as emerging from the calculation in a QCD framework capable of describing recent charm data from the Large Hadron Collider.
We propose new searches that exploit the unique signatures of decaying sterile neutrinos with masses below $M_W$ at the LHC, where they can be produced in rare decays of Standard Model gauge bosons. We show that for few-GeV-scale sterile neutrinos, the LHC experiments can probe mixing angles at the level of $10^{-4}-10^{-3}$ through powerful searches that look for prompt leptons in association with displaced lepton jets. For higher-mass sterile neutrinos, ${\it i.e.}$, $M_N \gtrsim 15$ GeV, Run II can explore similarly small mixing angles in prompt multilepton final states. This represents an …
During the stalled-shock phase of our 3D hydrodynamical core-collapse simulations with energy-dependent, 3-flavor neutrino transport, the lepton-number flux (nue minus antinue) emerges predominantly in one hemisphere. This novel, spherical-symmetry breaking neutrino-hydrodynamical instability is termed LESA for "Lepton-number Emission Self-sustained Asymmetry." While the individual nue and antinue fluxes show a pronounced dipole pattern, the heavy-flavor neutrino fluxes and the overall luminosity are almost spherically symmetric. Initially, LESA seems to develop stochastically from convective …
The convergence of the iterative solutions of the transport equations of cosmic muon and tau neutrinos propagating through Earth is studied and analyzed. For achieving a fast convergence of the iterative solutions of the coupled transport equations of nu_tau, nubar_tau and the associated tau^{\pm} fluxes, a new semi-analytic input algorithm is presented where the peculiar tau-decay contributions are implemented already in the initial zeroth order input. Furthermore, the common single transport equation for muon neutrinos is generalized by taking into account the contributions of secondary nu_m…
Neutrino fluxes at high rapidity and at high energy are sensitive to QCD dynamics of heavy-flavor production in kinematic regions where measurements have not yet been made. The FASER$ν$ and SND@LHC experiments scheduled for Run 3 at the LHC and the proposed Forward Physics Facility with a suite of experiments during the High-Luminosity LHC phase will probe neutrinos at high pseudorapidity. This short paper reports on recent evaluations of the prompt $ν_τ+\barν_τ$ and $ν_e+\barν_e$ double-differential cross sections in $pp$ collisions at the Large Hadron Collider from the production and decays …
We explore the possibility of utilizing the prompt muon fluxes at very high energies in order to discriminate various models/parametrizations of low-x QCD behaviour of hadronic cross-sections relevant at such energies. We find that the pair meter technique for measuring high energy prompt muons can be very efficient in such an endeavor. As a by product, it allows to cleanly probe the change in composition of the primary cosmic rays expected at high energies.
Astrophysical sources of ultrahigh energy neutrinos yield tau neutrino fluxes due to neutrino oscillations. We study in detail the contribution of tau neutrinos with energies above PeV relative to the contribution of the other flavors. We consider several different initial neutrino fluxes and include tau neutrino regeneration in transit through the Earth and energy loss of charged leptons. We discuss signals of tau neutrinos in detectors such as IceCube, RICE and ANITA.
We present a calculation of the fluxes of muons and muon neutrinos from the decays of pions and kaons that are themselves the decay products of charmed particles produced in the atmosphere by cosmic ray-air collisions. Using the perturbative cross section for charm production, these lepton fluxes are two to three orders of magnitude smaller than the fluxes from the decays of pions and kaons directly produced in cosmic ray-air collisions. Intrinsic charm models do not significantly alter our conclusions, nor do models with a charm cross section enhanced in the region above an incident cosmic ra…
Astrophysical sources of ultrahigh energy neutrinos yield tau neutrino fluxes due to neutrino oscillations. We study in detail the contribution of tau neutrinos with energies above $10^6$ GeV relative to the contribution of the other flavors. We consider several different initial neutrino fluxes and include tau neutrino regeneration in transit through the Earth and energy loss of charged leptons. We discuss signals of tau neutrinos in detectors such as IceCube, RICE and ANITA.
An accurate modeling of neutrino flux attenuation and the distribution of leptons they produce in transit through the Earth is an essential component to determine neutrino flux sensitivities of underground, sub-orbital and space-based detectors. Through neutrino oscillations over cosmic distances, astrophysical neutrino sources are expected to produce nearly equal fluxes of electron, muon and tau neutrinos. Of particular interest are tau neutrinos that interact in the Earth at modest slant depths to produce $τ$-leptons. Some $τ$-leptons emerge from the Earth and decay in the atmosphere to prod…
We investigate the scenario where the dark matter only interacts with the charged leptons in the standard model via a neutral vector mediator $Z'$. Such a scenario with a 430 GeV dark matter can fit the recent positron fluxes observed by the AMS-02 Collaborations, with the reasonable boost factors. We study the possibility of searching such leptophilic $Z'$ via its lepton final states and invisible decay modes at the future electron-positron colliders, such as the International Linear Collider (ILC) and the Compact Linear Collider (CLIC). We find that for the benchmark models with $Z'$ mass fr…
