We discuss information on thermal modifications of hadron properties which can be extracted from the structure of Euclidean correlation functions of hadronic currents as well as more direct information obtained through the reconstruction of the spectral functions based on the Maximum Entropy Method.
We extend our recent analysis of the dilepton and photon emission rates to the case of finite temperature and baryon density, within the context of a density expansion. To leading order, the effects of the baryon density are assessed using data (photon emission) or constraints from broken chiral symmetry (dilepton emission). Next to leading order effects are worked out, and their contribution qualitatively assessed. The opening of the $πN$ cut causes the photon rate to saturate the empirical photon yield of WA80, but may not be enough to fully account for the excess low mass dileptons seen at …
We extend our early analyses of the dilepton and photon emission rates from a hadronic gas to account for strange mesons using a density expansion. The emission rates are reduced to vacuum correlation functions using three-flavor chiral reduction formulas, and the latters are assessed in terms of empirical data. Using a fire-ball, we compare our results to the low and intermediate mass dilepton data available from CERN. Our results suggest that a baryon free hadronic gas does not account for the excess of low mass dielectrons observed at CERES but do well in accounting for the intermediate dim…
Recent progress of lattice investigations in thermal physics is summarized in this contribution. Hadronic spectral functions can be reconstructed from correlation functions in Euclidean time based on the Maximum Entropy Method without a priori assumptions on the spectral shape. The thermal modifications of hadron properties are investigated in the scalar, pseudo-scalar, vector and axial-vector channels near and above the deconfinement transition temperature for charmonium systems as well as for light quarks. Moreover, the reconstructed vector meson spectral function allows to extract the therm…
We use a simple QCD-based model to study particle production in S+Au collisions at 200 GeV/n. A requisite consistency is met for the hadronic observables (pi0 and pi- spectra) while pursuing estimates for e+e- production. Since radiative decays of initially produced hadrons has accounted for only a portion of the observed dileptons at the CERN SPS, we search for additional mechanisms. By including contributions from prompt secondary hadronic scatterings, pi rho -> pi e+e-, and adding to pi+ pi- annihilation and hadronic decays, the ``excess'' dilepton signal can possibly be interpreted.
Using a Hagedorn resonance gas picture and quark-hadron duality we estimate the dilepton emission rate in the vicinity of the QCD deconfinement phase transition. The result is then used to calculate a dilepton spectrum in ultrarelativistic heavy ion collisions. We show that multibody contributions taken into account in the Hagedorn resonance gas approach provide an enhancement of the production rate of massive dileptons as compared to the previously considered sources.
The vacuum polarisation effects from the nucleon sector lead to large medium modifications of the vector meson masses in the Walecka model. With a quantum hadrodynamic framework including the quantum effects, and using a quasiparticle description for quark gluon plasma(QGP), the dilepton emission rate from the hot and dense matter resulting from relativistic nuclear collisions is calculated. Using a model for the fireball evolution which has been shown to reproduce other observables such as charmonium suppression, photon emission and the abundance of hadronic species, we compare with the dilep…
In this paper we present a comprehensive formalism for dilepton production from the collision of two polarized spin-$\tfrac{1}{2}$ hadrons by identifying the general angular distribution of the cross section in combination with a complete set of structure functions. The various structure functions are computed in the parton model approximation where we mainly consider the case when the transverse momentum of the dilepton pair is much smaller than its invariant mass. In this kinematical region dilepton production can be described in terms of transverse momentum dependent parton distributions.
We discuss low mass dilepton rates ($\le 1$ GeV) from the deconfined phase of QCD using both perturbative and non-perturbative models and compare with those from lattice gauge theory and in-medium hadron gas. Our analysis suggests that the rate at very low invariant mass ($ M\le 200$ MeV) using the nonperturbative gluon condensate in a semiempirical way within the Green function dominates over the Born-rate and independent of any uncertainty associated with the choice of the strong coupling in perturbation theory. On the other hand the rate from $ρ-q$ interaction in the deconfined phase is imp…
We review the production of high-mass lepton pairs in fixed-target experiments, including both Drell-Yan (DY) and heavy quarkonium (J/Psi and Upsilons) production.
Dilepton production in In+In collisions at 158 AGeV is studied within the microscopic parton-hadron-string dynamics (PHSD) transport approach that incorporates explicit partonic degrees-of-freedom, dynamical hadronization as well as the more familiar hadronic dynamics in the final reaction stages. A comparison to the data of the NA60 Collaboration shows that the measured dilepton yield is well described by including the collisional broadening of vector mesons, while simultaneously accounting for the electromagnetic radiation of the strongly coupled quark-gluon plasma (sQGP) via off-shell quark…
We discuss the possibility of same-sign dileptons as a signature for Majorana neutrinos. The production mechanism is given by a single heavy neutrino production and decay proton-proton -> l^{\pm} N X -> l^{\pm} l^{\pm} X'. Cross section and distributions are presented for the LHC energies.
We analyze the dilepton and photon emission rates from a hadronic gas using chiral reduction formulas and a virial expansion. The emission rates are reduced to pertinent vacuum correlation functions, most of which can be assessed from experiment. Our results indicate that in the low mass region, the dilepton and photon rates are enhanced compared to most of the calculations using chiral Lagrangians. The enhancement is further increased through a finite pion chemical potential. An estimate of the emission rates is also made using Haag's expansion for the electromagnetic current. The relevance o…
We address dilepton production in Au+Au collisions at sqrt(s_NN)=200 GeV by employing the parton-hadron-string dynamics (PHSD) off-shell transport approach. Within the PHSD one goes beyond the quasiparticle approximation by solving generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for the Green's functions in the phase-space representation. The approach consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the quark-gluon p…
The rate of dilepton emission from a magnetized hot hadronic medium is calculated in the framework of real time formalism of finite temperature field theory. We evaluate the one loop self-energy of neutral rho-meson containing thermo-magnetic propagators for the charged pions in the loop. The in-medium thermo-magnetic spectral function of rho obtained by solving the Dyson-Schwinger equation is shown to be proportional to the dilepton production rate. The study of the analytic structure of the neutral rho-meson spectral function in such a medium shows that in addition to the usual contribution …
We reinterpret the dilepton emission rate from a hadronic gas expected to be produced in heavy ion collisions in terms of the spectral functions available from the $e^+e^-$ annihilation and the $τ$ lepton decays experiments. We take into account all possible hadronic state especially the multi-pion contributions to the dilepton emission and the parity mixing phenomenon due to the soft final-state corrections. A new compilation of the experimental data for the spectral functions is presented.
We consider the $a_{1} (1260)$ contribution to photon and dilepton productions from hot hadronic matter. The effective lagrangian with $π, ρ$ and $a_{1}$ discussed by Ko and Rudaz is employed, which successfully reproduces the $Γ(a_{1} \rightarrow πγ) = 670$ keV. Our results for the photon production rate are comparable to those obtained by Xiong {\it et al.}, while the dilepton production rates come out smaller than those obtained by Gale {\it et al.} by an order of magnitude.
An introduction to physics of in-medium hadrons with special emphasis towards modification of vector meson properties in dense nuclear matter is given. We start from remarkable analogy between the in-medium behavior of atoms in gases and hadrons in nuclear matter. Modifications of vector meson widths and masses can be registered experimentally in heavy-ion collisions by detecting dilepton spectra from decays of nucleon resonances and light unflavored mesons including $ρ$- and $ω$-mesons. Theoretical schemes for description of the in-medium hadrons are reviewed and recent experimental results o…
We consider the dilepton emission from a dense and hot hadron gas near a critical point. The hadron gas is described as a resonance one. The dilepton spectrum generated by vector resonances is shown to be equivalent to the one generated by quarks.
Temporal meson correlators and their spectral functions are calculated in the deconfined phase using the hard thermal loop resummation technique. The spectral functions exhibit strong medium effects coming from the hard thermal loop approximation for the quark propagator. The correlators, on the other hand, do not differ significantly from free correlators, for which bare quark propagators are used. This is in contrast to lattice calculations showing a clear deviation from the free correlations functions.
A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. We assume a transition from hadronic matter to a quark-gluon plasma at a critical temperature T_C between 130-170 MeV. We include thermal corrections to the hadronic spectra below T_C and use perturbation theory above T_C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated.
The dilepton emission in heavy-ion reactions at low beam energies is examined within a hadronic transport approach. In this article the production of electron-positron pairs from a new approach named SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced. The dilepton emission is consistently taken into account below the hadronic threshold. The calculations are systematically confronted with HADES data in the kinetic energy range of $1 - 3.5A$ GeV for elementary, proton-nucleus and nucleus-nucleus reactions. The present approach employing a resonance treatment based on …
We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cut-off effects on light quark meson correlators at $T\simeq 1.45 T_c$ using clover improved Wilson fermions. We discuss resulting constraints on the electrical conductivity and the thermal dilepton rate in a quark gluon plasma. In addition new results at 1.2 and 3.0 $T_c$ will be presented.
A model of statistical quark-gluon plasma formation is considered.We look the dilepton production at critical temperature $T_{c}\sim170 Mev $ and completely free out temperature $T=150 MeV$ with the initial temperature as $T_{0}=570,400 (250) MeV$. Now we consider that quark mass is depending on the coupling value through parameterisation factor of the fireball formation and temperature. The rate of production is shown for invariant mass $M$ at the particular value of $ E=2.0,3.0 GeV$.It shows the significant production of leptons in this process for small value of invariant mass. However, the…
We calculate the vector current correlation function for light valence quarks in the deconfined phase of QCD. The calculations have been performed in quenched lattice QCD at T=1.45 Tc for four values of the lattice cut-off on lattices up to size 128^3x48. This allows to perform a continuum extrapolation of the correlation function in the Euclidean time interval tau*T -in [0.2, 0.5], which extends to the largest temporal separations possible at finite temperature, to better than 1% accuracy. In this interval, at the value of the temperature investigated, we find that the vector correlation func…
We summarize our current theoretical understanding of in-medium properties of the electromagnetic current correlator in view of recent dimuon data from the NA60 experiment in In(158 AGeV)-In collisions at the CERN-SPS. We discuss the sensitivity of the results to space-time evolution models for the hot and dense partonic and hadronic medium created in relativistic heavy-ion collisions and the contributions from different sources to the dilepton-excess spectra.
The elliptic flows of thermal di-electrons are investigated within a (2+1)-dimension event-by-event hydrodynamic model for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The fluctuating initial conditions are given by the Monte Carlo Glauber model. We find in our event-by-event calculation rather weak correlation between the dilepton emission angles and the event plane angles of charged hadrons. We observe strong fluctuation effects in dilepton elliptic flows when using the event plane angles of dileptons at specific invariant mass $M$. The correlation between the dilepton event plane angle and …
It is investigated under which conditions an adiabatic adaption of the dynamic and spectral information of vector mesons to the changing medium in heavy ion collisions, as assumed in schematic model calculations and microscopic transport simulations, is a valid assumption. Therefore time dependent medium modifications of low mass vector mesons are studied within a non-equilibrium quantum field theoretical description. Timescales for the adaption of the spectral properties are given and non-equilibrium dilepton yields are calculated, leading to the result that memory effects are not negligible …
We predict dilepton invariant-mass spectra for central 5.5 ATeV Pb-Pb collisions at LHC. Hadronic emission in the low-mass region is calculated using in-medium spectral functions of light vector mesons within hadronic many-body theory. In the intermediate-mass region thermal radiation from the Quark-Gluon Plasma, evaluated perturbatively with hard-thermal loop corrections, takes over. An important source over the entire mass range are decays of correlated open-charm hadrons, rendering the nuclear modification of charm and bottom spectra a critical ingredient.
The vector channel spectral function and the dilepton production rate from a QCD plasma at a temperature above a few hundred MeV are evaluated up to next-to-leading order (NLO) including their dependence on a non-zero momentum with respect to the heat bath. The invariant mass of the virtual photon is taken to be in the range K^2 ~ (pi T)^2 ~ (1 GeV)^2, generalizing previous NLO results valid for K^2 >> (pi T)^2. In the opposite regime 0 < K^2 << (pi T)^2 the loop expansion breaks down, but agrees nevertheless in order of magnitude with a previous result obtained through resummations. Ways to t…
The production of large $p_{T}$ dileptons and photons originating from photoproduction processes in p-p collisions at Large Hadron Collider energies is calculated. The comparisons between the exact treatment results and the ones of the equivalent photon approximation approach are expressed as the $Q^{2}$ (the virtuality of photon) and $p_{T}$ distributions. The method developed by Martin and Ryskin is used for avoiding double counting when the coherent and incoherent contributions are considered simultaneously. The numerical results indicate that, the equivalent photon approximation is only ef…
The QGP that might be created in ultrarelativistic heavy-ion collisions is expected to radiate thermal dilepton radiation. However, this thermal dilepton radiation interferes with dileptons originating from hadron decays. In the invariant mass region between the $ϕ$ and $J/Ψ$ peak ($1\,$GeV$\lesssim M_{\ell^+ \ell^-} \lesssim 3 \,$GeV) the most substantial background of hadron decays originates from correlated D$\bar{\mathrm{D}}$-meson decays. We evaluate this background using a Langevin simulation for charm quarks. As background medium we utilize the well-tested UrQMD-hybrid model. The requir…
Dilepton production in heavy-ion collisions at various energies is studied using coarse-grained transport simulations. Microscopic output from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is hereby put on a grid of space-time cells which allows to extract the local temperature and chemical potential in each cell via an equation of state. The dilepton emission is then calculated applying in-medium spectral functions from hadronic many-body theory and partonic production rates based on lattice calculations. The comparison of the resulting spectra with experimental data shows t…
The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalarvector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vect…
Theories of quantum gravity suggest the existence of a minimal length scale. It is interesting to speculate what the consequences of the existence of such a length scale would be for models of large extra dimensions, in particular, the ADD model. When ADD model is conflated with the minimal length scale scenario, processes involving virtual exhange of gravitons cease to be ulraviolent divergent. We study the production of dileptons at hadron colliders as an example of a process mediated by virtual gravitons. We find that the bounds we derive on the effective string scale are significantly diff…
We present cross-correlators of QCD conserved charges at $μ_B=0$ from lattice simulations and perform a Hadron Resonance Gas (HRG) model analysis to break down the hadronic contributions to these correlators. We construct a suitable hadronic proxy for the ratio $-χ_{11}^{BS}/χ_2^S$ and discuss the dependence on the chemical potential and experimental cuts. We then perform a comparison to preliminary STAR results and comment on a possible direct comparison of lattice and experiment.
We show that the dilepton spectra measured by the CERES collaboration in Pb + Au interactions for various charge multiplicities can be reproduced by a hadronic initial state with reduction in the masses of the vector mesons in the thermal bath. Though such an effect may also be achieved by a large broadening of the spectral function we show that the photon spectra is insensitive to this. It is found that for higher multiplicities a good description of the data can also be obtained with quark gluon plasma initial state if the reduction of the vector meson masses in the mixed and hadronic phases…
In the present work, $k_T$-factorization formalism is applied to compute the exclusive dilepton production by timelike Compton scattering (TCS) in $eA$, $pA$ and $AA$ collisions. The nuclear effects are investigated considering heavy and light ions. The production cross section in terms of invariant mass and rapidity distribution of the lepton pair is shown. The analysis is done for electron-ion collisions at the Large Hadron-Electron Collider (LHeC), its high-energy upgrade (HE-LHeC) and at the Future Circular Collider (FCC) in lepton-hadron mode. Additionally, ultraperipheral heavy ion colli…
We calculate electromagnetic production from highly excited hadronic matter created in heavy ion collisions. The rates include the usual lowest order processes in quark-gluon plasma plus the usual reactions in the hadronic phase, related with rho,a_1 mesons. The space-time integration is done using a hydrodynamical model. We have found that dilepton mass spectrum agrees with results of other previous works, but *disagrees* with the CERES dilepton data. In order to explain these data, some "unconventional" production mechanism need to be incorporated: we discuss especially the notion of modifie…
We give a brief survey of theoretical evaluations of light vector mesons in hadronic matter, focusing on results from hadronic many-body theory. We emphasize the importance of imposing model constraints in obtaining reliable results for the in-medium spectral densities. The latter are subsequently applied to the calculation of dilepton spectra in high-energy heavy-ion collisions, with comparisons to recent NA60 data at the CERN-SPS. We discuss aspects of space-time evolution models and the decomposition of the excess spectra into different emission sources.
Pseudo-scalar and vector meson correlation functions were calculated at temperatures below and above the deconfinement transition using ${\cal O}(a)$ improved Wilson fermions in quenched lattice QCD. The spectral functions were reconstructed from the correlator given only at discrete points in Euclidean time by means of the Maximum Entropy Method without a priori assumptions on the spectral shape. The deviation of the spectral functions from the one of a freely propagating quark anti-quark pair is examined above the critical temperature. At 1.5 and 3 $T_c$ the vector spectral function yields a…
The scale invariant unparticle physics recently proposed by Georgi could manifest at low energies as non integral number d_U of invisible particles. Unparticles if existing, could couple to the Standard Model fields and consequently affect the collider phenomenology. We consider the DY process to explore effects of the peculiar propagator of the scalar and tensor unparticle operators. To probe these effects at hadron collider one needs to go beyond LO in QCD and hence the quantitative impact of QCD corrections for unparticle physics at LHC is investigated. We present the K-factors at LHC. Incl…
We study the lightlike and timelike R-current correlators in the AdS-Vaidya spacetime, which are associated with the production of prompt photons and dileptons from a nonequilibrium, rapidly thermalizing, and strongly coupled plasma in the AdS/CFT correspondence. In particular, we focus on the photon production. We find that the amplitude of the photon-emission spectrum increases during the thermalization of the medium. Also, the time-dependent emission rate for hard photons has an oscillatory pattern and thermalizes faster than soft photons.
We study the variation of elliptic flow of thermal dileptons with transverse momentum and invariant mass of the pairs for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The dilepton productions from quark gluon plasma (QGP) and hot hadrons have been considered including the spectral change of light vector mesons in the thermal bath. The space time evolution has been carried out within the frame work of 2+1 dimensional ideal hydrodynamics with lattice+hadron resonance gas equation of state. We find that a judicious selection of invariant mass(M) and transverse momentum (p_T) windows can be use…
We analyse the extraction of the bound-state form factor from vacuum-to-hadron correlator, which is the basic object for the calculation of hadron form factors in the method of light-cone sum rules in QCD. We study this correlator in quantum mechanics, calculate it exactly, and derive the corresponding OPE. We then apply the standard procedures of QCD sum rules to isolate the ground-state form factor from this correlator. We demonstrate that fixing the effective continuum threshold, one of the key ingredients of the sum-rule calculation of bound-state parameters, poses a serious problem for su…
The D0 collaboration has recently introduced new variables, a_T and phi* to more accurately probe the low Q_T domain of Z boson production at hadron colliders than had been previously possible through a direct study of the Q_T distribution. The comparison of such accurate data to precise theoretical predictions from QCD perturbation theory will yield important information on the ability of resummed QCD predictions as well as parton shower models to describe the low Q_T domain and should enable more stringent constraints on non-perturbative effects. In the present paper we provide analytical pr…
Electromagnetic radiation from the quark-gluon plasma (QGP) is an important observable to be considered in heavy ion collision experiments. I will provide an update on recent advancements from perturbation theory and quenched lattice simulations. The resummed next-to-leading order (NLO) emission rate has recently been decomposed into transverse and longitudinal components, and extended to non-zero baryon chemical potential. The associated spectral function has also been tested against the Euclidean correlator, for continuum-extrapolated lattice data (at $μ_{\rm B}=0$).
The collective behavior of hadrons and of electromagnetic radiation in heavy-ion collisions has been widely used to study the properties of the the Quark-Gluon Plasma (QGP). Indeed this collectivity, as measured by anisotropic flow coefficients, can be used to constrain the transport properties of QGP. The goal of this contribution is to investigate the influence of the specific bulk viscosity ($ζ/s$) on dilepton production, both at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. We explore the sensitivity of dileptons to dynamical features that bulk viscosity …
We show that new physics can show up in dileptonic events through its radiative contributions to the dilepton invariant mass, leading to unique "monocline" features in $m_{\ell\ell}$, as well as the angular distribution of the leptons. We focus in particular on the case of dark matter with scalar messengers coupling it to the quarks and leptons. Consistent thermal models require the dark matter to have masses of 100's GeV and have $\gsim 1$ couplings to the Standard Model (SM), implying that radiative corrections to the SM Drell-Yan rate can be sizeable. We consider the case of Majorana, Dirac…
We show how universal, Froissart-like hadronic total cross sections can be obtained in QCD in the functional-integral approach to soft high-energy scattering, and we discuss indications of this behaviour obtained from lattice simulations.
In the Standard Model (SM), dilepton production in hadron--hadron collisions proceeds through the conventional Drell--Yan mechanism $q \bar{q} \rightarrow l^+ l^-$ with the exchange of a gauge boson. Some extensions of the SM contain a quark--lepton contact interaction {\it via} a $q l ϕ$ Yukawa coupling, where $ϕ$ is a scalar. Theories with scalar leptoquarks and $R$--parity violating SUSY models are the most important examples of such extensions. These Yukawa couplings induce a different dynamical configuration compared to the SM ($t$-channel vs. $s$-channel) in the $q\bar{q} \rightarrow l^+…
Recent developments in the evaluation of vector-meson spectral functions in hot and dense matter are discussed with emphasis on connections to the chiral phase transition in QCD. Model independent approaches including chiral low-density expansions, lattice QCD, chiral and QCD sum rules are put into context with model predictions for in-medium vector-spectral function utilizing effective Lagrangians. Hadronic many-body calculations predict a strong broadening (and little mass shift) of the $ρ$ spectral function which rapidly increases close to the expected phase boundary of hadronic and quark-g…
We study the manifestations of chiral symmetry restoration which have a significance for the parity mixing. Restricting to pions and nucleons we establish a formalism for the expression of the vector correlator, which displays the mixing of the axial correlator into the vector one and unifies the cases of the heat bath and the dense medium. We give examples of mixing cross-sections. We also establish a link between the energy integrated mixing cross-sections and the pion scalar density which governs the quenching factors of coupling constants, such as the pion decay one, as well as the quark c…
The first calculation of the next-to-leading-order electroweak corrections to Z-boson + jet hadroproduction including leptonic Z-boson decays is presented, i.e. to the production of a charged lepton--anti-lepton final state in association with one hard jet at the LHC and the Tevatron. The Z-boson resonance is treated consistently using the complex-mass scheme, and all off-shell effects as well as the contributions of the intermediate photon are taken into account. The corresponding next-to-leading-order QCD corrections have also been recalculated. The full calculation is implemented in a flexi…
The notion of "hadronic freedom" is introduced based on the vector manifestation of hidden local symmetry and is used to suggest that the dileptons measured in relativistic heavy-ion collisions do not provide {\em direct} information on the spontaneous breaking of chiral symmetry and hence on the mechanism for mass generation of light-quark hadrons. We give arguments how the dileptons emitted from those vector mesons whose masses are shifted à la Brown-Rho (BR) scaling by the vacuum change in temperature -- as in heavy-ion collisions -- and/or density -- as in cold compressed matter -- could b…
We analyze the dilepton emission rates from the hot pion gas confined to a finite space-time volume. Two models of pion(+) pion(-) annihilation to dileptons are under consideration. The first model mimics an extreme influence of the dense hadron environment on the rho-meson mean free path and mean life time. The second model deals with the standard concept of vector meson dominance when the hadron medium is not accounted. Our results indicate that the dilepton rates are finite in the low invariant mass region M<2m_π. It is found that the rates experience an enhancement in the electron-positron…