Nuclear form factor, validity of the equivalent photon approximation and Coulomb corrections to muon pair production in photon-nucleus and nucleus-nucleus collisions
We study in detail the influence of the nuclear form factor both on the Born cross section and on the Coulomb corrections to the photo-production of muon pairs off heavy nuclei (gamma Z -> mu+ mu- Z$) and in heavy-ion collisions (ZZ -> ZZ mu+ mu-). Our findings indicate a number of issues which have not been sufficiently described as yet in the literature: (i) the use of a realistic form factor, based on the Fermi charge distribution for the nucleus, is absolutely indispensable for reliable theoretical predictions; (ii) we checked quantitatively that the equivalent photon approximation has a very good accuracy for the discussed processes; and (iii) we present a leading logarithmic calculation of the Coulomb corrections which correspond to multi-photon exchange of the produced mu+/- with the nuclei. These corrections are found to be small (on the percent level). Our result justifies using the Born approximation for numerical simulations of the discussed process at the RHIC and LHC colliders. Finally, we calculate the total cross section for muon pair production at RHIC and LHC.
The cross sections for exclusive muon pair production in nucleus - nucleus collisions are calculated and several differential distributions are shown. Realistic (Fourier transform of charge density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor often used in the literature and discussed recently in the context of higher-order QED corrections. Absorption effects are discussed and quantified. The cross sections obtained with realistic form factors are significantly smaller than those obtained with th…
Coherent production of lepton pair in muon scattering by nucleus is considered. With the help of different approaches (equivalent photon approximation, direct numerical and analytical calculations) we obtain total cross section of this reaction and distributions over invariant masses of final leptons. Special attention is paid to influence of final lepton identity on total and differential cross sections. We also study the role of coherence condition. Total cross sections of charmonia production in muon interaction with electromagnetic field of nucleus are also presented.
The spectrum of electrons from muons decaying in an atomic bound state is significantly modified by their interaction with the nucleus. Somewhat unexpectedly, its first measurement, at the Canadian laboratory TRIUMF, differed from basic theory. We show, using a combination of techniques developed in atomic, nuclear, and high-energy physics, that radiative corrections eliminate the discrepancy. In addition to solving that outstanding problem, our more precise predictions are potentially useful for interpreting future high-statistics muon experiments that aim to search for exotic interactions at…
The hyperfine effect in muon capture rate is analyzed with taking into account of the second-order terms in 1/M in the non-relativistic Hamiltonian. It is shown that in the situation of the dominance of the squared first-order terms the interference of zero-order and second-order terms has no significant influence. General expression for neutrino (recoil nucleus) angular distribution in muon capture by nucleus with non-zero spin is proposed. High sensitivity to $g_P$ of the term related with alignment of the initial mesic atom is discussed in the approximation of dominating Gamow--Teller matri…
We suggest that $e\to μ$ conversion in low-energy electron-nucleus scattering is a new and potentially observable indirect signal of supersymmetry and should be searched for in experiment. We estimate the rate for this process in a straightforward calculation taking into account the existing constraint from non-observation of the $μ\to eγ$ decay and find the cross-section to be $σ< 10^{-8} $fb.
Recently, muon production in electron-proton scattering has been suggested as a possible candidate reaction for the identification of lepton-flavor violation due to physics beyond the Standard Model. Here we point out that the Standard-Model processes $e^- p \to μ^- p \barν_μν_e$ and $e^- p \to e^- n μ^+ ν_μ$ can cloud potential beyond-the-Standard-Model signals in electron-proton collisions. We find that Standard-Model $e p \to μX$ cross sections exceed those from lepton-flavor-violating operators by several orders of magnitude. We also discuss the possibility of using a nuclear target to enh…
The calculation of hadronic polarizability contribution of the nucleus to hyperfine structure of muonic hydrogen and helium is carried out within the unitary isobar model and experimental data on the polarized structure functions of deep inelastic lepton-proton and lepton-deuteron scattering. The calculation of virtual absorption cross sections of transversely and longitudinally polarized photons by nucleons in the resonance region is performed in the framework of the program MAID.
We present an estimate of the electron to muon conversion cross section in fixed-target elastic electron scattering. The matrix element $<μ| j_\mathrm{em}^μ(0) | e>$ is calculated analytically in two scenarios introducing suitable approximations. We consider on the one hand side the case of three light Dirac neutrinos with CKM-type leptonic mixing and on the other hand a typical see-saw scenario. We evaluate the coulombic contribution to the scattering cross section in the limit of vanishing energy transfer to the nucleus and, thus, obtain a realistic estimate for the total conversion cross se…
The coherent contribution of all neutrons in neutrino nucleus scattering due to the neutral current is examined considering the Spallation Neutron Source (SNS) as a source of neutrinos. SNS is a prolific pulsed source of electron and muon neutrinos as well as muon antineutrinos.
The generation of muon-antimuon pairs is calculated in the collision of an ultrarelativistic bare ion with an intense x-ray laser beam. The reaction proceeds nonlinearly via absorption of two laser photons. By systematic study throughout the nuclear chart we show that the interplay between the nuclear charge and size, along with the possibility of nuclear excitation leads to saturation of the total production rates for high-Z ions, in contrast to the usual Z^2 scaling for pointlike projectiles. The process is experimentally accessible by combining present-day ion accelerators with near-future …
We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering $μ^- γ\to μ^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. We find that the anomalous magnetic moment $α/2π$ provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon-nucleus bremsstrahlung process (or …
We have studied a method to extract neutrino flux from the data of neutrino-nucleus reaction by using maximum entropy method. We demonstrate a promising example to extract neutrino flux from the inclusive cross section of muon production without selecting a particular reaction process such as quasi-elastic nucleon knockout.
We study the high-scale validity of a Type-X two Higgs doublet scenario which provides an explanation of the observed value of muon $(g-2)$. This region admits of a pseudoscalar physical state, which is well below the observed 125-GeV scalar in mass. A second neutral scalar particle can be both above and below 125 GeV in such a scenario. Admissible regions in the parameter space are obtained by using the most recent data on muon $(g-2)$, theoretical constraints such as low-scale perturbativity and vacuum stability, and also all experimental constraints, including the available LHC results. Amo…
The Quasi-Elastic (QE) contribution of the nuclear inclusive electron scattering model developed in Nucl. Phys. A627 (1997) 543 is extended to the study of electroweak Charged Current (CC) induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for, among other nuclear effects, long range nuclear (RPA) correlations, Final State Interaction (FSI) and Coulomb corrections. Predictions for the inclusive muon capture in $^{12}$C and the reaction $^{12}$C $(ν_μ,μ^-)X$ near threshold are also given. RPA correlations are shown to …
The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons ($μ^-\rightarrow e^+$) as a signal of lepton number violation. A key background for this search is radiative muon capture where either: 1) a real photon converts to an $e^+ e^-$ pair "externally" in surrounding material, or 2) a virtual photon mediates the production of an $e^+e^-$ pair "internally". If the $e^+$ has an energy approaching the signal region then it can serve as an irreducible background. In this work we describe how the near end-point internal positron spectrum can be related to the…
Bound muons (also pions, kaons, etc) increase the fission barrier and produce some stabilizing effects for highly charged nuclei. If the binding energy of the muon exceeds $mc^2$, it becomes stable. The $1s$ state of a muon inside an exotic nucleus with atomic number $A= 5Z/2$ and such large charge $Z$ that the $1s$ energy $E$ is in the range $0\le E<-mc^2$ is considered.
Nuclear reactions induced by muon neutrino with energies in the range from 0.2 to 1.5 GeV in Monte Carlo calculations framework in the intra-nuclear cascade model are studied. This study was done by comparison between the available experimental data and theoretical values of total cross section, and the energy distribution of emitted lepton energy in the reaction muon neutrino-nucleus, using the targets: $^{12}$C, $^{16}$O, $^{27}$Al, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb. A phenomenological toy model of primary neutrino-nucleon interaction gives a good agreement of our theoretical inclusive neu…
According to the usual application of the sequential-suppression picture to the dynamics of heavy quarkonia in the hot medium formed in ultrarelativistic nuclear collisions, quark-antiquark pairs created in a given bound or unbound state remain in that same state as the medium evolves. We argue that this scenario implicitly assumes an adiabatic evolution of the quarkonia, and we show that the validity of the adiabaticity assumption is questionable.
We analyze the lepton flavor violating process $μ-e$ conversion in the framework of the minimal R-symmetric supersymmetric standard model. The theoretical predictions are determined by considering the experimental constraint on parameter $δ^{12}$ from the lepton flavor violating decay $μ\rightarrow e γ$. The numerical results show that $γ$ penguins and Z penguins dominate the predictions on CR($μ-e$,Nucleus), and the contributions from Higgs penguins and box diagrams are insignificant. The theoretical predictions on conversion rate CR($μ-e$,Nucleus) in a Al or Ti target can be enhanced close t…
The lepton-flavor-violating conversion of a muon into an electron in the field of a nucleus is one of the most sensitive probes of physics beyond the Standard Model and the experiments Mu2e, COMET, and DeeMe will explore uncharted terrain in the near future. An observation of this $μ^-\to e^-$ conversion process opens up the possibility to distinguish the underlying operator or new-physics model by exploiting the target-nucleus dependence of the conversion rate. To facilitate the choice of optimal targets we provide $μ^-\to e^-$ conversion rates for all stable isotopes and estimate nuclear-str…
We present a complete comparison of semi-inclusive $ν_μ$-$^{12}$C cross-section measurements by T2K and MINER$ν$A collaborations with the predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event generator GENIE and an unfactorized approach based on the relativistic distorted wave impulse approximation (RDWIA). Results, that include cross sections as function of the final muon and proton kinematics and correlations between both, show that the agreement with data obtained by the RDWIA approach, that accounts for final-state interactions, matches or improves GENIE-SuSAv2 pr…
The composite model is constructed to describe inelastic high-energy scattering of muons and taus in standard rock. It involves photonuclear interactions at low $Q^2$ as well as moderate $Q^2$ processes and the deep inelastic scattering (DIS). In the DIS region the neutral current contribution is taken into consideration. Approximation formulas both for the muons and tau energy loss in standard rock are presented for wide energy range.
Quasielastic double differential neutrino cross sections can be obtained in a phenomenological model based on the superscaling behavior of electron scattering data. In this talk the superscaling approach (SuSA) is reviewed and its validity is tested in a relativistic shell model. Results including meson exchange currents for the kinematics of the MiniBoone experiment are presented.
Recent developments in the physical model of 1 MeV to 100 TeV hadron and lepton interactions with nuclei and atoms are described. These include a new nuclear cross section library, a model for soft pion production, the cascade-exciton model, the dual parton model, deuteron-nucleus and neutrino-nucleus interaction models, detailed description of muon, pion, and antiproton absorption and a unified treatment of muon and charged hadron electromagnetic interactions with matter. New algorithms are implemented into the MARS13(98)} Monte Carlo code and benchmarked against experimental data. The code c…
The quasielastic scattering of muon neutrinos on oxygen 16 is studied for neutrino energies between 200 MeV and 1 GeV using a relativistic shell model. Final state interactions are included within the distorted wave impulse approximation, by means of a relativistic optical potential, with and without imaginary part, and of a relativistic mean field potential. For comparison with experimental data the inclusive charged--current quasielastic cross section for $ν_μ$--$^{12}C$ scattering in the kinematical conditions of the LSND experiment at Los Alamos is also presented and briefly discussed.
Probing hidden sectors with a muon beam: implication of spin-0 dark matter mediators for muon $(g-2)$ anomaly and validity of the Weiszäcker-Williams approach
The energy reconstruction of high-energy muons depends on the energy loss characteristics. Accurate knowledge of the cross sections of the energy loss processes is necessary for precise measurements of the energy spectrum of muons and muon-induced neutrinos. The cross sections of the two most dominant processes, electron pair production and bremsstrahlung are calculated exact in the coupling parameter $Zα$ to the electromagnetic field of a nucleus for realistic extended screened nuclei. An analytical parametrization of the mass and nuclear-charge dependence of the cross section is given.
We reevaluate electron-positron pair production from electromagnetic interactions of muons in transit through materials. Our approach, through the use of structure functions for inelastic and elastic scattering and including hadronic recoil, make the formalism useful for tau pair production at high energies. Our results for electron-positron pair production agree well with prior evaluations. Tau pair production, has a significant contribution from inelastic scattering in addition to the usual coherent scattering with the nucleus and scattering with atomic electrons.
It is shown that the combination of the structure functions $F_2$ predicted by the CKMT model at low and moderate values of $Q^2$ and MRS99 parton distribution functions at high $Q^2$ gives a good description of the data over complete measured region of $x$ and $Q^2$. Using these structure functions the main characteristics of the muon-nucleus inelastic scattering are calculated. Nuclear effects and contributions of the neutral current and $γ- Z$ interference are taken into account.
We study lepton number violating (LNV) process of muon-positron conversion in nuclei mediated by the exchange of light and heavy Majorana neutrinos. Nuclear structure calculations have been carried out for the case of experimentally interesting nucleus 48Ti in the framework of renormalized proton-neutron Quasiparticle Random Phase Approximation. We demonstrate that the imaginary part of the amplitude of light Majorana neutrino exchange mechanism gives an appreciable contribution to the muon-positron conversion rate. This specific feature is absent in the allied case of neutrinoless double beta…
[Background] Long-Baseline experiments such as T2K, NOvA or the planned Deep Underground Neutrino Experiment (DUNE) require theoretical descriptions of the complete event in a neutrino-nucleus reaction. Since nuclear targets are used this requires a good understanding of neutrino-nucleus interactions. [Purpose] One of the dominant reaction channels in neutrino-nucleus interactions is pion production. This paper aims for a coherent view on all charged current charged pion production data that are avaible from the experiments MiniBooNE, the near detector experiment at T2K and MINERvA. [Methods] …
The quasi-elastic contribution of the nuclear inclusive electron scattering model developed in A. Gil, J. Nieves, and E. Oset: Nucl. Phys. A 627 (1997) 543; is extended to the study of electroweak Charged Current (CC) induced nuclear reactions at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for long range nuclear (RPA) correlations, Final State Interaction and Coulomb corrections. RPA correlations are shown to play a crucial role in the whole range of neutrino energies, up to 500 MeV, studied in this work. Predictions for inclusive muon capt…
We argue that the measurement of open charm gives a unique opportunity to test the validity of pQCD-based and statistical models of nucleus-nucleus collisions at high energies. We show that various approaches used to estimate D-meson multiplicity in central Pb+Pb collisions at 158 A GeV give predictions which differ by more than a factor of 100. Finally we demonstrate that decisive experimental results concerning the open charm yield in A+A collisions can be obtained using data of the NA49 experiment at the CERN SPS.
The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.
[Background] Meticulous modeling of neutrino-nucleus interactions is essential to achieve the unprecedented precision goals of present and future accelerator-based neutrino-oscillation experiments. [Purpose] Confront our calculations of charged-current quasielastic cross section with the measurements of MiniBooNE and T2K, and to quantitatively investigate the role of nuclear-structure effects, in particular, low-energy nuclear excitations in forward muon scattering. [Method] The model takes the mean-field (MF) approach as the starting point, and solves Hartree-Fock (HF) equations using a Skyrm…
We implemented a model of muon pair production through a real photon in PHITS and compared our calculations with data of the muon shielding experiment conducted at SLAC to verify the validity of the implemented model. Our predictions of the muon fluence induced by electrons are in good agreement with the experimental data. To understand the known differences between the calculations of the muon fluence, which have been determined using other Monte-Carlo codes, we quantitatively evaluate the fluctuations in the Monte-Carlo results due to systematic errors in multiple Coulomb scattering, differe…
ALICE (A Large Ion Collider Experiment) is a detector designed to exploit the physics potential of nucleus-nucleus interactions at the LHC. Being a general purpose experiment, it will allow a comprehensive study of hadrons, electrons, muons and photons, produced in the collision of heavy nuclei, up to the highest particle multiplicities anticipated (dNch/dy=8000). In addition to heavy systems (Pb-Pb), we will study collisions at smaller energy densities by using lower-mass ions (e.g. A~40). Reference data will be obtained from pp and p-nucleus collisions. The central part of ALICE covers $|η| …
We use our model for neutrino pion production on the nucleon to study pion production on a nucleus. The model is conveniently modified to include in-medium corrections and its validity is extended up to 2 GeV neutrino energies by the inclusion of new resonant contributions in the production process. Our results are compared with recent MiniBooNE data measured in mineral oil. Our total cross sections are below data for neutrino energies above 1 GeV. As with other theoretical calculations, the agreement with data improves if we neglect pion final state interaction. This is also the case for diff…
The one-loop nuclear structure corrections of order (Z alpha)^5 to the Lamb shift and hyperfine splitting of the deuterium are calculated. The contribution of the deuteron structure effects to the isotope shift (ep)-(ed), (mu p)-(mu d) in the interval (1S - 2S) is obtained on the basis of modern experimental data on the deuteron electromagnetic form factors. The comparison with the similar contributions to the Lamb shift for electronic and muonic hydrogen shows, that the relative contribution due to the nucleus structure increases when passing from the hydrogen to the deuterium.
A quantitative understanding of the weak nuclear response is a prerequisite for the analyses of neutrino experiments such as K2K and MiniBOONE, which measure energy and angle of the muons produced in neutrino-nucleus interactions in the energy range $0.5-3$ GeV and reconstruct the incident neutrino energy to determine neutrino oscillations. In this paper we discuss theoretical calculations of electron- and neutrino-nucleus scattering, carried out within the impulse approximation scheme using realistic nuclear spectral functions.Comparison between electron scattering data and the calculated inc…
We calculate the classical gluon field of a fast projectile passing through a dense medium. We show that this allows us to calculate both the initial state gluon production in proton-nucleus collisions and the final state gluon radiation off a hard parton produced in nucleus-nucleus collisions. This unified description of these two phenomena makes the relation between the saturation scale $Q_s$ and the transport coefficient $\hat q$ more transparent. Also, we discuss the validity of the eikonal approximation for gluon propagation inside the nucleus in proton-nucleus collisions at RHIC energy.
Comparison of structure functions measured in neutrino and charged lepton deep inelastic scattering can be used to test basic properties of parton distribution functions such as the validity of charge symmetry. Recent experiments indicate a substantial discrepancy between $F_2^ν$ and $F_2^μ$ in the region of small Bjorken-x. We discuss nuclear corrections and strange and anti strange quark effects and show that none of them can account for the observed discrepancy. These results suggest surprisingly large CSV effects in nucleon sea distributions.
In the framework of the quasipotential method in quantum electrodynamics we calculate corrections to the nuclear structure proportional to $r_N^2$ from two-photon exchange amplitudes in the fine and hyperfine structure of P-states in muonic hydrogen, as well as the photon-photon interaction amplitudes, leading to the exchange of the axial vector meson. In constructing the quasipotential of the muon-nucleus interaction, we use the method of projection operators on states of two particles with a definite spin and total angular momentum. Analytical calculation of the matrix elements is performed …
We show that the form factor of an electron or a muon is unity for the modulus of the momentum transfer away from the Hagedorn temperatures $T^{e}_0\sim m_e$ and $T^μ_0\sim m_μ$ and lower than the hadronic Hagedorn temperature $T^{\tiny{QCD}}_0\sim m_π$. The structure of the electron or the muon is resolved for momemtum transfers comparable to $T^{e,μ}_0$. This is seen in scattering experiments performed in the 1950s, 1960s, and early 1970s to test the validity of QED. We interprete center-vortex loops with no self-intersection, occurring in the confining phases of each SU(2) gauge-theory fact…
We have investigated the gauge field of a fast moving projectile passing through a dense medium. We provide a simple and unified derivation, in light cone gauge, of the gluon production cross-section in proton-nucleus (initial state interactions), and the radiative gluon spectrum of a hard parton produced in a nucleus-nucleus collision (final state interactions). Finally, we discuss the validity of the eikonal approximation in proton-nucleus collisions at RHIC energies.
The monoenergetic 236 MeV muon neutrino from charged kaon decay-at-rest ($K^+ \rightarrow μ^+ ν_μ$) can be used to produce a novel set of cross section measurements. Applicable for short- and long-baseline accelerator-based neutrino oscillation experiments, among others, such measurements would provide a "standard candle" for the energy reconstruction and interaction kinematics relevant for charged current neutrino events near this energy. This neutrino can also be exercised as a unique known-energy, purely weak interacting probe of the nucleus. A number of experiments are set to come online i…
Cosmic-rays with energies up to $3\times10^{20}$ eV have been observed. The nuclear composition of these cosmic rays is unknown but if the incident nuclei are protons then the corresponding center of mass energy is $\sqrt{s_{nn}} = 700$ TeV. High energy muons can be used to probe the composition of these incident nuclei. The energy spectra of high-energy ($>$ 1 TeV) cosmic ray induced muons have been measured with deep underground or under-ice detectors. These muons come from pion and kaon decays and from charm production in the atmosphere. Terrestrial experiments are most sensitive to far-for…
