Radiative corrections to anti-neutrino proton scattering at low energies
U. Raha, F. Myhrer, K. Kubodera
备注：
Text, especially regrading the 1/m_N corrections, has been augmented following comments by the referee. 14 pages, 1 figure. To be published in Phys. Rev C
For the low-energy anti-neutrino reaction, $\barν_e + p \to e^+ + n$, which is of great current interest in connection with on-going high-precision neutrino-oscillation experiments, we calculate the differential cross section in a model-independent effective field theory (EFT), taking into account radiative corrections of order $α$. In EFT, the short-distance radiative corrections are subsumed into well-defined low-energy constants the values of which can in principle be determined from the available neutron beta-decay data. In our low-energy EFT, the order-$α$ radiative corrections are considered to be of the same order as the nucleon recoil corrections, which include the "weak magnetism" contribution. These recoil corrections have been evaluated as well. We emphasize that EFT allows for a systematic evaluation of higher order corrections, providing estimates of theoretical uncertainties in our results.
We discuss QED radiative corrections at first and second order for the parity violating asymmetry $A_\text{PV}$ in elastic electron proton scattering. A measurement of $A_\text{PV}$ is planned at low energies and with high precision by the forthcoming P2 experiment at the new MESA facility in Mainz. Bremsstrahlung leads to a shift of the momentum transfer $Q^2$ which affects the determination of the weak charge of the proton.
The structure function approach and the parton picture, developed for the theoretical description of the deep inelastic electron-proton scattering, also proved to be very effective for calculation of radiative corrections in Quantum Electrodynamics. We use them to calculate radiative corrections to the cross section of electron-proton scattering due to electron-photon interaction, in the experimental setup with the recoil proton detection, proposed by A.A. Vorobev to measure the proton radius. In the one-loop approximation, explicit expressions for these corrections are obtained for arbitrary …
The interpretation of high-precision lepton-nucleon scattering experiments requires the knowledge of higher-order radiative corrections. We present a calculation of the cross section for unpolarized lepton-proton scattering including leptonic radiative corrections up to second order, including one- and two-loop corrections, radiation of one and two photons and one-loop corrections for one-photon radiation. Numerical results are given for the planned P2 experiment at the MESA facility in Mainz, and some results are also discussed for Qweak and the suggested MUSE experiment.
Here we consider a contribution of Delta(1232) resonance to real photon radiative corrections for elastic $ep$-scattering. The effect is found to be small for past experiments to study unpolarized cross section as well as for the recent VEPP-3 experiment to investigate two-photon exchange effects by precision measurement of $e^\pm p$-scattering cross sections ratio.
We have evaluated the amplitude for muon capture by a proton, mu + p --> n + nu, to O(p^3) within the context of heavy baryon chiral perturbation theory (HBChPT) using the new O(p^3) Lagrangian of Ecker and Mojzis (E&M). We obtain expressions for the standard muon capture form factors and determine three of the coefficients of the E&M Lagrangian, namely, b_7, b_{19}, and b_{23}. We describe progress on the next step, a calculation of the radiative muon capture process, mu + p --> n + nu + gamma.
The differential cross section for elastic scattering of protons on electrons at rest is calculated taking into account the QED radiative corrections to the leptonic part of interaction. These model-independent radiative corrections arise due to emission of the virtual and real soft and hard photons as well as to vacuum polarization. We analyze an experimental setup when both the final particles are recorded in coincidence and their energies are determined within some uncertainties. The kinematics, the cross section, and the radiative corrections are calculated and numerical results are presen…
A unified treatment of both chiral and radiative corrections to the low-energy elastic lepton-proton scattering processes is presented in Heavy Baryon Chiral Perturbations Theory. The proton hadronic chiral corrections include the next-to-next-to leading order corrections whereas the radiative corrections include the next-to-leading order terms in our novel power counting scheme. We find that the net fractional well-defined chiral corrections with respect to the leading order Born cross section can be as large as $10\%$ ($20\%$) for electron (muon) scattering process for MUon proton Scattering…
We study the radiative energy loss contribution to proton stopping in $AA$ collisions. The analyses is performed within the light-cone path integral approach to induced gluon emission. We have found that the radiative correction can fill in partly the midrapidity dip in the net proton rapidity distribution in $AA$ collisions at $\sqrt{s}\sim 10$ GeV. We argue that at $\sqrt{s}\sim 10$ GeV the net proton fluctuations at midrapidity may be dominated by the initial fluctuations of the proton flow, which, to a good accuracy, should be binomial.
The largest radiative corrections to the cross section of electron-proton scattering at high energies are associated with emission of photons, real and virtual, by electron. They contain large logarithms coming from soft and collinear photons. Cancellation of the contributions of the soft photons to virtual and real corrections is well known. Less known is the fact that the contributions of the photons collinear to scattered electrons are also cancelled for the most of experiments. On the contrary, contributions of the photons collinear to initial electrons as a rule are not cancelled. It is s…
We estimate the radiative corrections of order $α/π$ to the magnetic moments of the proton and the neutron. The photon-loop diagram of the vertex-correction type is evaluated with phenomenological nucleon vector form factors. Infrared-finiteness and gauge-invariance require the inclusion of the wave-function renormalization factor from the self-energy diagram. Using recent empirical form factor parametrizations the corrections amount to $δκ_p= -3.42 \cdot 10^{-3}$ and $δκ_n= 1.34 \cdot 10^{-3}$. We study also the effects from photon-loops with internal $Δ(1232)$-isobars. For two customary vers…
Radiative corrections to the annihilation of proton--antiproton into electron--positron are revisited, including virtual and real (soft and hard) photon emission. This issue is relevant for the time-like form factors measurements planned at the PANDA experiment at the FAIR facility, in next future. The relevant formulas are given. A stand-alone Monte-Carlo integrator is developed on the basis of the calculated radiative cross section and its application to the PANDA experiment is illustrated.
We analyse the proton recoil energy and angular distribution of the radiative beta-decay of the neutron to leading order in the large baryon mass expansion by taking into account the contributions of the proton-photon correlations. We show that the account for the proton-photon correlations does not contradict the description of the radiative corrections to the lifetime of the neutron and the proton recoil energy spectrum of the neutron beta-decay in terms of the functions (α/π) g_n(E_e) and (α/π) f_n(E_e), where E_e is the electron energy. In addition we find that the contributions of the pro…
The near-threshold behavior of the ppbar invariant mass spectrum from the psi(3686) -> gamma ppbar decay reported recently by the BESIII Collaboration is analyzed. The enhancement in the ppbar invariant mass spectrum near threshold is nicely reproduced by the ppbar final-state interaction based on the isospin averaged 1S0 partial-wave amplitude as predicted by the Julich nucleon--antinucleon model. Contributions from the f_2(1910) or f_2(1950) mesons, as promoted in earlier works, are not needed.
Model independent radiative correction to the recoil proton polarization for the elastic electron-proton scattering is calculated within method of electron structure functions. The explicit expressions for the recoil proton polarization are represented as a contraction of the electron structure and the hard part of the polarization dependent contribution into cross-section. The calculation of the hard part with first order radiative correction is performed. The obtained representation includes the leading radiative corrections in all orders of perturbation theory and the main part of the secon…
Radiative effects in the electroproduction of photons in polarized ep-scattering are calculated in the leading log approximation and analyzed numerically for kinematical conditions of current measurement at Jefferson Lab. Radiative corrections to the cross sections, their azimuthal distributions and Fourier coefficients are in particular focus. Kinematical regions where the radiative corrections are considerable are identified.
We evaluate the leading-order QED radiative corrections to the timelike Compton scattering (TCS) process $γp \to l^- l^+ p$. We study these corrections in two energy regimes using different models for the TCS amplitude. In the low-energy regime we calculate the contribution due to the proton and its lowest-energy excitation, the $Δ(1232)$ resonance. In the high-energy near-forward kinematical regime we calculate the TCS amplitude in a handbag approach in terms of Generalized Parton Distributions (GPDs). On the level of cross sections we find the QED radiative corrections to be in the $5 -10\%$…
We calculate the cross-section for the thermal $n+p\rightarrow d+γ$ process in chiral perturbation theory to next-to-next-to-leading order using heavy-fermion formalism. The exchange current correction is found to be $(4.5\pm 0.3)~\%$ in amplitude and the chiral perturbation at one-loop order gives the cross section $σ_{th}^{np}=(334\pm 2)\ {\mbox mb}$ which is in agreement with the experimental value $(334.2\pm 0.5)\ {\mbox mb}$. Together with the axial charge transitions, this provides a strong support for the power of chiral Lagrangians for nuclear physics.
QED radiative corrections to elastic electron-proton scattering at low energies are discussed. Corrections to the electron line and effects due to vacuum polarization are computed. Higher order effects are estimated for the conditions of the experiment on the electric and magnetic proton form factors by A1 Collaboration. Calculations are performed within the next-to-leading approximation. Inclusion of the higher order effects can affect the value of the proton charge radius extracted from the experimental data.
We investigate the effect of high order radiative corrections in unpolarized electron proton elastic scattering and compare with the calculations at lowest order, which are usually applied to experimental data. We show that higher order terms play a role, starting from values of the momentum transfer squared, $Q^2$, larger than the electron mass. Particular attention is devoted to the $ε$ dependence of radiative corrections.
The annihilation of proton and antiproton to electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.
The inverse $β$-decay reaction, $ \barν_e p \to e^+ n$, for low-energy anti-neutrinos coming from nuclear reactors is of great current interest in connection with high-precision measurements of the neutrino mixing angle $θ_{13}$. We have derived analytic expressions, up to next-to-leading order in heavy-baryon chiral perturbation theory, for the radiative corrections (RCs) and the nucleon-recoil corrections both for this reaction and for the related neutron $β$-decay process. We show that the recoil corrections, which include the "weak magnetism" contribution, are small for neutron $β$-decay, …
Manifestly Lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at chiral next-to-leading order $(\mathcal{O}(p^2))$ with a nonzero lepton mass, which are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model calculation, but they are somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry.
A short review of simulation results of anti-proton-proton and anti-proton-nucleus interactions within the framework of Geant4 FTF (Fritiof) model is presented. The model uses the main assumptions of the Quark-Gluon-String Model or Dual Parton Model. The model assumes production and fragmentation of quark-anti-quark and diquark-anti-diquark strings in the mentioned interactions. Key ingredients of the model are cross sections of string creation processes and an usage of the LUND string fragmentation algorithm. They allow one to satisfactory describe a large set of experimental data, especially…
The scotogenic mechanism for radiative neutrino mass is generalized to include neutron-antineutron oscillation as well as proton decay. Dark matter is stabilized by extending the notion of lepton parity to matter parity. Leptogenesis is also a possible byproduct. This framework unifies the description of all these important, but seemingly unrelated, topics in physics beyond the standard model of particle interactions.
Radiative corrections are calculated for antineutrino proton quasielastic scattering, neutrino deuteron scattering, and the asymmetry of polarised neutron beta decay from which $G_{A}/G_{V}$ is determined. A particular emphasis is given to the constant parts that are usually absorbed into the coupling constants, and thereby those that appear in the processes that concern us are unambiguously tied among each other.
We discuss the theoretical approach and practical algorithms for simulation of radiative events in elastic ep-scattering. A new Monte Carlo generator for real photon emission events in the process of elastic electron-proton scattering is presented. We perform a few consistency checks and present numerical results.
We investigate the effect of high order radiative corrections in unpolarized electron proton elastic scattering and compare with the calculations at lowest order, which are usually applied to experimental data. Particular attention is devoted to the $ε$ dependence of radiative corrections, which is directly related to the electric proton form factor. We consider in particular the effects of the interference terms for soft and hard photon emission. Both quadratic amplitude describing the collinear emission along the scattered electron as well as the interference with the amplitudes of emission …
We systematically calculate the radiative corrections of order $α/π$ to elastic muon-proton scattering at low momentum transfers. These include vacuum polarization, photon-loop form factors of the muon and the proton, two-photon exchange corrections and soft photon radiation. In particular, we discuss these corrections for the kinematics of the upcomimg AMBER experiment with a $100\,$GeV muon beam energy. It is found that for the ratio to the Born cross section, only the minor terms from the photon-loop form factors of the proton and two-photon exchange depend on the proton structure predeterm…
We investigate whether the apparent discrepancy between proton electric form factor from measurements using the Rosenbluth separation technique and polarization transfer method is due to the standard approximations employed in radiative correction procedures. Inaccuracies due to both the peaking approximation and the soft-photon approximation have been removed in our simulation approach. In contrast to results from (e,e'p) experiments, we find them in this case to be too small to explain the discrepancy.
A statistical analysis of the elastic unpolarized electron proton scattering data shows that, at large momentum transfer, the size and the $ε$ dependence of the radiative corrections, as traditionally calculated and applied, may induce large correlations of the parameters of the Rosenbluth fit, which prevent a correct extraction of the electric proton form factor. Using the electron QED structure (radiation) function approach the cross section of elastic electron-proton scattering in leading and next-to leading approximations is calculated and expressed as a correction to the Born cross sectio…
QED radiative corrections have been calculated for leptonic and hadronic variables in parity-violating elastic ep scattering. For the first time, the calculation of the asymmetry in the elastic radiative tail is performed without the peaking-approximation assumption in hadronic variables configuration. A comparison with the PV-A4 data validates our approach. This method has been also used to evaluate the radiative corrections to the parity-violating asymmetry measured in the G0 experiment. The results obtained are here presented.
One of the striking features of particle production at high beam energies is the near equal abundance of matter and antimatter in the central rapidity region. In this paper we study how this symmetry is reached as the beam energy is increased. In particular, we quantify explicitly the energy dependence of the approach to matter/antimatter symmetry in proton-proton and in heavy-ion collisions. Expectations are presented also for the production of more complex forms of antimatter like antihypernuclei.
A new version of Monte Carlo generator ELRADGEN for simulation of real photon emission in elastic electron-proton scattering is presented. The extensions in the new version include opportunity to deal with polarized particles: longitudinally polarized electron and arbitrary polarized proton. Simulation strategy, specifications of used kinematics, structure of the contributions to the observed cross section, cross-checks, and numerical results for BLAST experimental setup are presented and briefly discussed.
The first measurement of the radiative muon capture (RMC) rate on a proton was recently carried out at TRIUMF. The TRIUMF group analyzed the RMC rate in terms of the theoretical formula of Beder and Fearing, and found the surprising result that the pseudoscalar coupling g_P is 1.5 times the value expected from PCAC. To assess the reliability of the theoretical framework used by the TRIUMF group to relate the RMC rate to the pseudoscalar form factor, we calculate the RMC rate in chiral perturbation theory, which provides a systematic framework to describe all the vertices involved in RMC, fulfi…
Radiative corrections to elastic electron-proton scattering are analyzed in effective field theory. A new factorization formula identifies all sources of large logarithms in the limit of large momentum transfer, $Q^2\gg m_e^2$. Explicit matching calculations are performed through two-loop order. A renormalization analysis in soft-collinear effective theory is performed to systematically compute and resum large logarithms. Implications for the extraction of charge radii and other observables from scattering data are discussed. The formalism may be applied to other lepton-nucleon scattering and …
We calculate ordinary and radiative muon capture on the proton in an effective field theory of pions, nucleons and delta isobars, working to third and second order in the small scale expansion respectively. Preceding calculations in chiral effective field theories only employed pion and nucleon degrees of freedom and were not able to reproduce the photon spectrum in the pioneering experiment of radiative muon capture on the proton from TRIUMF. For the past few years it has been speculated that the discrepancy between theory and experiment might be due to Delta(1232) related effects, which are …
We consider radiative corrections to polarization observables in elastic electron-proton scattering, in particular, for the polarization transfer measurements of the proton form factor ratio $μG_E/G_M$. The corrections are of two types: two-photon exchange (TPE) and bremsstrahlung (BS); in the present work we pay special attention to the latter. Assuming small missing energy or missing mass cut-off, the correction can be represented in a model-independent form, with both electron and proton radiation taken into account. Numerical calculations show that the contribution of the proton radiation …
Radiative effects in the electroproduction of photons in polarized $ep$-scattering are calculated with the next-to-leading (NLO) accuracy. The contributions of loops and two photon emission were presented in analytical form. The covariant approach of Bardin and Shumeiko was used to extract the infrared divergence. All contributions to the radiative correction were presented in the form of the correction to the leptonic tensor thus allowing for further applications in other experiments, e.g., deep inelastic scattering. The radiative corrections (RC) to the cross sections and polarization asymme…
We present a simple explanation for the recently observed near-threshold proton-antiproton enhancement. It is described by a set of low-energy parameters deduced from the analysis of NantiN experiments at LEAR. We predict a related effect in photoproduction reaction under study by CLAS collaboration.
Collective flow as a consequence of hydrodynamical evolution in heavy ion collisions is intensively studied by theorists and experimentalists to understand the behavior of hot quark matter. Due to their large mass, heavy ions suffer collective effects even at low (SPS) or intermediate energies (RHIC). In case of light systems such as (anti)proton-proton interactions, collective effects was not expected. Within a global model such as EPOS, where light and heavy systems are treated using the same physics, it appears that Tevatron data are better described if a flow is introduced. Then the extrap…
A numerical study of QED radiative corrections for the SMC experiment at SPS is been performed. The semi-analytical program POLRAD is been used to get the size of the radiative corrections for the proton to get the size of the radiative corrections for the measurements of the proton spin dependent structure functions $g_1^p(x)$ and $g_2^p(x)$. A brief description of the program POLRAD is given.
The processes proton + antiproton -> gamma + heavy-flavour jet(s) + X and proton + proton -> gamma + heavy-flavour jet(s) + X are studied in the framework of a special two-Higgs-doublet model, the MCPM. As distinguishing feature of this model we find that radiative Higgs-boson production and decay lead to heavy flavour c jets but no b jets in the above processes. Thus, the prediction is that b jets should be given by the normal QCD processes whereas for c jets an excess over the QCD expectation should occur. We present results both for Tevatron and LHC energies.
The total cross section for radiative neutron capture on a proton, $np \to d γ$, is evaluated at big bang nucleosynthesis (BBN) energies. The electromagnetic transition amplitudes are calculated up to next-to leading order within the framework of pionless effective field theory with dibaryon fields. We also calculate the $dγ\to np$ cross section and the photon analyzing power for the $d\vecγ\to np$ process from the amplitudes. The values of low energy constants that appear in the amplitudes are estimated by a Markov Chain Monte Carlo analysis using the relevant low energy experimental data. Ou…
In the Standard Model of electroweak interactions and in the tree--approximation we calculate the rate and branching ratio of the neutron radiative beta decay with one-real photon emission by taking into account the contributions of the weak magnetism and proton recoil to order 1/m_p of the large proton mass m_p expansion. We find that the obtained contributions of the weak magnetism and proton recoil increase the rate and branching ratio of the neutron radiative beta decay by about 0.70%. This is large compared with the contribution of the weak magnetism and proton recoil of about 0.16% to th…
Secondary charged hadrons multiplicity distributions in proton-proton and proton-antiproton collisions differ on principle. There are three types of inelastic processes in proton-antiproton scattering. The first type is production of secondary hadrons shower at gluon string decay. The second type is shower produced from two quark strings decay, the third type is shower produced from three quark strings decay. At the same time there are only two types of inelastic processes for proton-proton scattering - gluon string shower and two quark strings shower. Theoretical description of multiplicity d…
Minimal $SU(5)$ Grand Unified models predict massless neutrinos and struggle to achieve gauge coupling unification compatible with the observed lower limit on the proton lifetime. Both of these issues can be resolved by embedding minimal radiative neutrino mass models into $SU(5)$. We systematically analyze the possible ways to realize radiative neutrino mass generation in $SU(5)$ and provide a list of the minimal models. We find various models that have not been considered in the literature and demonstrate the compatibility of radiative neutrino masses with gauge coupling unification and prot…
Radiative corrections to the subprocess of annihilation of quark-antiquark pair of prompt photon production in proton-proton collisions at NICA energies $\sqrt{\mathbf{s}}$= 10 GeV
Baku State University（巴库国立大学）；Institute of Physical Problems, Baku State University（巴库国立大学物理问题研究所）
We investigate the dispersive contribution by radiative processes such as (pi- proton to neutron gamma) and (pi- proton to Delta gamma) to the pion-nucleon scattering lengths of charged pions in the heavy baryon limit. They give a large isospin violating contribution in the corresponding isoscalar scattering length, but only a small violation in the isovector one. These terms contribute 6.3(3)% to the 1s level shift of pionic hydrogen and give a chiral constant F_pi^2f_1=-25.8(8) MeV.
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at low momentum transfer values. Energy dependence of the elastic diffraction slopes is approximated by various analytic functions. The expanded "standard" logarithmic approximations allow to describe experimental slopes in all available energy range reasonably. Various approximations differ from each other both in the low energy and very high energy domains. Predictions for diffraction slope parameter are obtained for elastic proton-proton sca…
I study hard collisions between unpolarized protons and antiprotons where a lepton-antilepton pair is detected in coincidence with a final proton-antiproton pair, and no more particles are produced, in the regime 10 GeV^2 << s << 1000 GeV^2, M > 4 GeV, q_T < 3 GeV/c. The present work is centered on azimuthal asymmetries. Because of momentum conservation, a Boer-Mulders term in the momentum distribution of a quark implies a balancing effect in the momentum distribution of some spectators. This produces azimuthal asymmetries of the final hadrons. To analyze this, I have organized a parton-level …
The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on the all available experimental data at intermediate square of momentum transfer in the main. Energy dependence of the elastic diffraction slope is approximated by various analytic functions in a model-independent fashion. The expanded standard logarithmic approximations allow to describe experimental slopes in all available energy range at qualitative level reasonably. Various fitting functions differ from each other both in low energy and very high energy domains. Predictions fo…
We report a serious kinematics problem in the bremsstrahlung photon part of the order-$α$ outer (model independent) radiative correction calculations for those neutron (and nuclear beta) decay observables (like electron-neutrino correlation parameter measurement) where the proton (recoil particle) is detected. The so-called neutrino-type radiative correction calculations, which fix the neutrino direction in the bremsstrahlung photon integrals, use 3-body decay kinematics to connect the unobserved neutrino direction with the observed electron and proton (recoil particle) momenta. But the presen…
The differential cross-sections are calculated for proton-proton and proton-antiproton elastic scattering using the phenomenological model based on the analytic parameterizations for global scattering parameters (total cross-section and $ρ$ - parameter), crossing symmetry and derivative relations. We confront our model predictions with experimental data in wide range of energy and momentum transfer. The suggested method may be useful for PAX Program (GSI) as well as for high-energy experiments at RHIC and LHC.
