Weak interactions in two-nucleon system at low energies are explored in the framework of effective field theory. We review our recent calculations of parity-violating observables in radiative neutron capture on a proton at threshold where both pionful and pionless theories are employed.
Even though the total hadronic nucleus-nucleus cross section is among the most fundamental observables, it has only recently been measured precisely for lead-lead collisions at the LHC. This measurement implies the nucleon width should be below 0.7 fm, which is in contradiction with all known state-of-the-art Bayesian estimates. We study the implications of the smaller nucleon width on quark-gluon plasma properties such as the bulk viscosity. The smaller nucleon width dramatically improves the description of several triple-differential observables.
We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for the nucleon-nucleon potentials.
We calculate elementary proton-proton and neutron-proton bremsstrahlung and their contribution to the $e^+e^-$ invariant mass distribution. At 4.9 GeV, the proton-proton contribution is larger than neutron-proton, but it is small compared to recent data. We then make a first calculation of bremsstrahlung in nucleon-nucleon reactions with multi-hadron final states. Again at 4.9 GeV, the many-body bremsstrahlung is larger than simple nucleon-nucleon bremsstrahlung by more than an order of magnitude in the low-mass region. When the bremsstrahlung contributions are summed with Dalitz decay of the …
We report an attempt to calculate the deep inelastic scattering structure functions from the hadronic tensor calculated on the lattice. We used the Backus-Gilbert reconstruction method to address the inverse Laplace transformation for the analytic continuation from the Euclidean to the Minkowski space.
An effective field theory program to analyze and interpret hadronic parity violation in two-, three-, and few-nucleon systems is described. Observables can be parameterized in terms of five low-energy constants, which have to be determined from experimental input. Results for parity-violating observables in the two- and three-nucleon sectors are presented, including a discussion of the relevance of parity-violating three-nucleon interactions.
We present a nucleon resonance analysis by simultaneously considering all pion- and photon-induced experimental data on the final states gamma N, pi N, 2 pi N, eta N, K Lambda, K Sigma, and omega N for energies from the nucleon mass up to sqrt(s) = 2 GeV. In this analysis we find strong evidence for the resonances P_{31}(1750), P_{13}(1900), P_{33}(1920), and D_{13}(1950). The omega N production mechanism is dominated by large P_{11}(1710) and P_{13}(1900) contributions. In this first part, we present the results of the pion-induced reactions and the extracted resonance and background properti…
This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. In this paper we focus on the importance of diquark correlations, which we describe by a quasi-local four-fermion effective 't Hooft interaction induced by instantons. The same interaction is also shown to generate extra quark-antiquark pair of the "sea". Its higher order iteration can be included via "pion-mediation": both taken together yield a quantitative description of the observed flavor asymmetry of antiquar…
The pi+ d scattering and the d(p,n) charge exchange reaction are used to study the Delta-Nucleon interaction in the Delta resonance energy region. Various observables, such as inclusive and exclusive cross sections, angular distributions, and analyzing powers, are calculated in a coupled channel approach and shown to be influenced by the Delta-Nucleon potential.
Electromagnetic current-current correlators in pionic and nucleonic medium have been evaluated in the static limit to obtain electrical conductivities for pion and nucleon components respectively, where former decreases and latter one increases with the variation of temperature $T$ and baryon chemical potential $μ_N$. Therefore, total electrical conductivity of pion and nucleon system exhibits a valley structure in the $T$-$μ_N$ plane. To get non-divergent and finite values of correlators, finite thermal widths of medium constituents, pion and nucleon have been considered, where these thermal …
We study one-particle spectra and a two-particle correlation function in the 130 GeV/nucleon Au+Au collisions at RHIC by making use of a hydrodynamical model. We calculate the one-particle hadronic spectra and present the first analysis of Bose-Einstein correlation functions based on the numerical solution of the hydrodynamical equations which takes both longitudinal and transverse expansion into account appropriately. The hydrodynamical model provides excellent agreement with the experimental data in the pseudorapidity and the transverse momentum spectra of charged hadrons, the rapidity depen…
I review the novel results and developments presented at the Third Workshop on Physics and Detectors for DA$Φ$NE that deal with hadronic physics. Topics discussed include: the scalar quark condensate, kaon decays, the sector of scalar and vector mesons, kaon-nucleon scattering, pion- and kaon-nucleon sigma terms, and strange nuclear physics.
We investigate the hadron-hadron total cross sections at high energies in the framework of holographic QCD. In our model setup, the involved strong interaction is described by the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel, and the two form factors are obtained from the bottom-up AdS/QCD models. We show that the resulting nucleon-nucleon total cross section is consistent with the experimental data recently measured by the TOTEM collaboration at the LHC. As examples to see the general versatility of the model, we also present our analysis on the pion-nucleon and pion-pion cases, wh…
We present results for two-body observables that are sensitive to the parity-violating component of nucleon-nucleon interactions. These interactions are studied using an effective field theory in which the only dynamic degrees of freedom are nucleon fields. The observables we study are cross-section asymmetries in nucleon-nucleon scattering and asymmetries and induced polarizations in the process np \to dγ.
We study the total cross section for photo production of open charm hadrons near threshold using a hadronic Lagrangian. Both two-body final states involving $Λ_c$ and a charmed meson as well as three-body final states involving nucleon and a charm-anticharm meson pair are included. With appropriate cut-off parameters in the form factors at interaction vertices, the model gives a total cross section that is consistent with the measured data at center-of-mass energy of 6 GeV. The result is compared with the prediction from the leading-order perturbative QCD.
We motivate lattice QCD studies of the parity-violating pion-nucleon coupling constant and extend flavor-conserving hadronic parity-violation from QCD to partially-quenched QCD. The parity-violating pion-nucleon coupling and the anapole form factor (and moment) of the proton are computed to one-loop order in the partially-quenched chiral expansion. For the parity-violating pion-nucleon interaction, we include the contributions from total derivative operators necessary to match the kinematics that will be used in lattice simulations.
We review the uncertainties in the spin-independent and -dependent elastic scattering cross sections of supersymmetric dark matter particles on protons and neutrons. We propagate the uncertainties in quark masses and hadronic matrix elements that are related to the $π$-nucleon $σ$ term and the spin content of the nucleon. By far the largest single uncertainty is that in spin-independent scattering induced by our ignorance of the $<N | {\bar q} q | N>$ matrix elements linked to the $π$-nucleon $σ$ term, which affects the ratio of cross sections on proton and neutron targets as well as their abs…
We perform a systematical investigation of the possible deuteron-like bound states with configuration $Ξ_{cc}N (\bar{N})$, where $N(\bar{N})$ denotes the nucleon (anti-nucleon), in the framework of the one-boson-exchange-potential model. In the spin-triplet sector we take into account both the ${}^3S_1$ and ${}^3D_1$ channels due to non-vanishing tensor force. There exist several candidates of the loosely bound molecular states for the $Ξ_{cc}N$ and $Ξ_{cc}\bar{N}$ systems, which lie below the threshold of $Λ_cΛ_c$ or $Λ_c{\barΛ}_c$. We also investigate the possible loosely bound states with c…
We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft SU(3) flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of WIMPs. Based on SU(2) Chiral Perturbation Theory, we provide expressions for the proton and neutron scalar couplings $f_u^{p,n}$ and $f_d^{p,n}$ with the pion-nucleon sigma-term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-i…
Hadronic transport models may be utilized to extract bulk nuclear properties. Deduction of in-medium nucleon-nucleon cross sections and of nuclear viscosity is discussed, as well as the extraction of momentum dependence of nucleonic mean field. Moreover, determination of the nuclear incompressibility and of constraints on the nuclear pressure at supranormal densities is described.
Parity violation in elastic electron-nucleon scattering is studied with the basic goal of improving the understanding of electroweak hadronic structure with special emphasis on the strangeness content in the nucleon. Models for the parity-violating (PV) asymmetry are provided and compared with the world data measured at very different kinematics. The effects introduced in the PV asymmetry due to alternative descriptions of the hadronic structure are analyzed in detail. In particular, a wide selection of prescriptions for dealing with the electromagnetic and neutral current weak interaction nuc…
We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) momentum-space Faddeev calculations of elastic proton-deuteron (pd) scattering and breakup to the case when also a three-nucleon force (3NF) is acting. In addition we formulate that approach in the application to electron- and gamma-induced reactions on 3He. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of a 3-dimensional Lippmann-Schwinger equation (LSE). The resulting equations have the same structure as the Faddeev equations which …
The spectral function of rho meson in hot/dense hadronic matter is studied by taking into account the nucleon-loop on quantum hadrondynamics model level. Different from the hot pion gas effect which changes the spectral function slightly, the nucleon-antinucleon polarization (Dirac sea) makes the spectral function very sharp and shifted towards the low invariant mass region significantly due to the decreasing effective nucleon mass.
The parity-violating nucleon-nucleon (NN) potential is considered up to next-to-next-to leading order in heavy-baryon chiral perturbation theory. We include one-pion exchange at leading order and the two-pion exchange and two-nucleon contact terms at next-to-next-to-leading order. The effects of intermediate (two-pion exchange) and short-range (two-nucleon contact) terms are probed by calculating the photon asymmetry $A_γ$ in $\vec{n} p \to d γ$ employing Siegert's theorem and an accurate phenomenological potential for the parity-conserving NN interaction. We explore in detail the uncertaintie…
The application of effective field theories to hadronic parity violation in two- and three-nucleon systems is described. These methods provide several important advantages over the traditionally used meson-exchange models, e.g., model independence and the possibility to reliably estimate theoretical errors. We focus on the so-called "pionless" theory and describe calculations of various two- and three-nucleon observables. The role of parity-violating three-nucleon interactions is also discussed.
The analysis on the hadron-hadron scattering at high energies in the framework of holographic QCD is presented. Combining the Pomeron exchange kernel and the hadron-Pomeron couplings which are obtained from the bottom-up AdS/QCD models, we calculate the total cross sections. Our calculation for the nucleon-nucleon scattering is consistent with the experimental data including the recent ones measured by the TOTEM collaboration at the LHC. Within the framework, one can consider other processes involving other hadrons. As examples to show this feature of the model, the resulting total cross secti…
Modifications of Delta(1232) and nucleon spectral functions at finite temperature and baryon density are evaluated in terms of resonant scattering off thermal pions, as well as a renormalization of the vacuum Delta-width including vertex corrections. The interactions are based on effective Lagrangians of pions and baryon resonances, with underlying parameters (coupling constants and form factors) determined by the elastic pi N scattering phase shift in the isobar channel, and by empirical decay branchings of excited resonances. Pion modifications are included via interactions in a pion gas, as…
Electromagnetic emission rates from a thermalized hadronic gas are important for the interpretation of dilepton signals from heavy-ion collisions. Although there is a consensus in the literature about rates for a pure meson gas, qualitative differences appear with a finite baryon density. We show this to be essentially due to the way in which the pi-N background is treated in regards to the nucleon resonances. Using a background constrained by unitarity and broken chiral symmetry, it is emphasized that the thermalized hadronic gas can be considered dilute.
A simple model of a composite nucleon is developed in which a fermion and a boson, representing quark and diquark constituents of the nucleon, form a bound state owing to a contact interaction. Photon and pion couplings to the quark provide vertex functions for the photon and pion interactions with the composite nucleon. By a suitable choice of cutoff parameters of the model, realistic electromagnetic form factors are obtained. When a pseudoscalar pion-quark coupling is used, the pion-nucleon coupling is predominantly pseudovector. A virtual photopion amplitude is considered in which there are…
The parity-violating nucleon-nucleon interaction is the key to understanding the strangeness-conserving hadronic weak interaction at low energies. In this brief talk, I review the past accomplishments in and current status of this subject, and outline a new joint effort between experiment and theory that tries to address the potential problems in the past by focusing on parity violation in few-nucleon systems and using the language of effective field theory.
We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LEC's) entering the potential is carried out. We find that it depends on six LEC's: the pion-nucleon PV coupling constant $h^1_π$ and five parameters mul…
We present our analysis on high energy hadron-hadron scattering in the framework of the holographic QCD. Combining the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel and gravitational form factors of the involved hadrons which are obtained by using the bottom-up AdS/QCD models in the five-dimensional AdS space, we calculate the total cross sections at high energies. We show that our calculations for the nucleon-nucleon scattering agree with the experimental data including the recent ones taken by the TOTEM collaboration at the LHC. The present framework is applicable to any high energ…
New observables with which we can study the two-nucleon weak interactions at low energies are considered. In the breakup of the deuteron by photons, polarization of outgoing neutrons can depend on the parity-violating component of two-nucleon interactions. We express the parity-violating polarization in general forms, and perform numerical calculations with a pionless effective field theory. The theory has unknown parity-violating low energy constants, and the results are expressed in linear combination of them. We discuss the results and their implication to the understanding of the hadronic …
Parity-violating elastic electron-nucleon scattering at low momentum transfer allows one to access the nucleon's weak charge, the vector coupling of the $Z$-boson to the nucleon. In the Standard Model and at tree level, the weak charge of the proton is related to the weak mixing angle and accidentally suppressed, $Q_W^{p,\,{\rm tree}}=1-4\sin^2θ_W\approx0.07$. Modern experiments aim at extracting $Q_W^p$ at $\sim1\%$ accuracy. Similarly, parity non-conservation in atoms allows to access the weak charge of atomic nuclei. We consider a novel class of radiative corrections, an exchange of two pho…
Identical boson Hanbury-Brown-Twiss interferometry as applied to relativistic heavy-ion collisions is reviewed. Emphasis is placed on the use of hadronic scattering models to interpret the physical significance of experimental results. Interferometric studies with center-of-mass energies from < 1 GeV/nucleon up to 5500 GeV/nucleon are considered.
The nucleon sigma term of the isoscalar and isovector quark chromo-magnetic dipole moments are essential inputs for the determination of the CP-odd pion-nucleon couplings induced by quark chromo-electric dipole moments. We demonstrate that the former can be mapped to the third moment of the nucleon twist-three chiral-odd distribution functions $e^q(x)$ which are in principle measurable in semi-inclusive deep inelastic scattering processes. We perform a survey on existing model calculations as well as experimental data on $e^u(x)+e^d(x)$ and derive a predicted range for the isoscalar chromo-mag…
We study a thermodynamically consistent implementation of the nucleon volume in the mean field theory, and find that this volume has large consequences on the properties of hadronic matter under extreme conditions such as in astrophysical objects and high energy heavy-ion collisions. It is shown that we can reproduce the critical temperature $T_{c}\simeq 200$ MeV predicted by lattice QCD calculations for the phase transition from hadronic matter to quark-gluon plasma, by using parameters which are adjusted to fit all empirical data for normal nuclear matter.
We consider a novel class of hard branching hadronic processes a+b->c+d+e, where hadrons c and d have large and nearly opposite transverse momenta and large invariant energy which is a finite fraction of the total invariant energy. We use color transparency logic to argue that these processes can be used to study quark generalized parton distributions (GPDs) for baryons and mesons in hadron collisions hence complementing and adding to the studies of GPDs in the exclusive DIS (deep inelastic scattering) processes. We propose that a number of GPDs can be investigated in hadron facilities such as…
We investigate meson and nucleon dynamics at finite baryon density and temperature by coupling the nucleon field and the omega meson to the three-flavor linear sigma model and calculate hadronic properties around the nuclear liquid-gas transition. We apply the functional renormalization group method, and find that mesonic fluctuations increase the strength of the coefficient of the $U_A(1)$ breaking determinant operator as a function of the chiral condensate. As a consequence, we find that the actual value of the anomaly increases discontinuously at the first order nuclear liquid-gas transitio…
Finite energy QCD sum rules involving nucleon current correlators are used to determine several QCD and hadronic parameters in the presence of an external, uniform, large magnetic field. The continuum hadronic threshold $s_0$, nucleon mass $m_N$, current-nucleon coupling $λ_N$, transverse velocity $v_\perp$, the spin polarization condensate $\langle\bar qσ_{12} q\rangle$, and the magnetic susceptibility of the quark condensate $χ_q$, are obtained for the case of protons and neutrons. Due to the magnetic field, and charge asymmetry of light quarks up and down, all the obtained quantities evolve…
The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calc…
Experiments searching for the electric dipole moment (EDM) of the electron $d_e$ utilise atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to $d_e$. If the source of $CP$ violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce $CP$-odd semileptonic interactions, parametrised by the Wilson coefficient $C_{SP}$, and provide the dominant source of EDMs in paramagnetic systems instead of $d_e$. We evaluate the $C_{SP}$ coefficients …
I discuss the current status of efforts to constrain the strangeness-conserving weak hadronic interaction, which can be isolated in nuclear systems because of the associated parity violation.
The recently developed Nambu-Jona-Lasinio (NJL) - Jet model is used as an effective chiral quark theory to calculate the quark fragmentation functions to pions, kaons, nucleons, and antinucleons. The effects of the vector mesons rho, K* and phi on the production of secondary pions and kaons are included. The fragmentation processes to nucleons and antinucleons are described by using the quark-diquark picture, which has been shown to give a reasonable description of quark distribution functions. We incorporate effects of next-to-leading order (NLO) in the Q^2 evolution, and compare our results …
A survey is given on selected topics of physics in the non-perturbative, hadronic sector of the QCD phase diagramme. Following a brief QCD primer, some highlights of Lattice QCD are summarised. Chiral effective field theory as the low-energy realisation of QCD is reviewed, with applications in pion-pion scattering, the scalar form factor of the nucleon and the interpolation of nucleon properties between lattice QCD results and actual observables. Chiral SU(3) dynamics, incorporating the strange quark, is developed with examples relating to low-energy kaon-nucleon interactions. The quest for qu…
Chiral effective field theories have a long history studying the process of Compton scattering on the nucleon. In this contribution I want to focus on the new developments that have occured since the last Chiral Dynamics conference in Mainz 1997. I will focus exclusively on the spin-dependent sector, where most of the recent work has been done.
The equation of state of symmetric nuclear matter with the inclusion of non-strange dibaryons is studied. We pay special attention to the existence of a dibaryon condensate at zero temperature. These calculations have been performed in an extended quark-meson coupling model with density-dependent parameters, which takes into account the finite size of nucleons and dibaryons. A first-order phase-transition to pure dibaryon matter has been found. The corresponding critical density is strongly dependent on the value of the dibaryon mass. The density behavior of the nucleon and dibaryon effective …
The associate $KΛ(1520)$ photon and hadronic production in the $γp \to K^+Λ(1520)$, $p p \to p K^+ Λ(1520)$ and $π^- p \to K^0 Λ(1520)$ reactions are investigated within the effective Lagrangian approach and the isobar model. We are interested in the contribution from the $N^*(2120)$ (previously called $N^*(2080)$) resonance, which has a significant coupling to the $KΛ(1520)$ channel. The theoretical results show that the current experimental data for the $γp \to K^+Λ(1520)$ reaction favor the existence of the $N^*(2120)$ resonance, and that these measurements can be used to further constrain …
Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics --- the medium --- which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and $N\toΔ$ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter…
In specific kinematics, hard exclusive amplitudes may be factorized into a short distance dominated part computable in a perturbative way on the one hand, and universal, confinement related hadronic matrix elements on the other hand. The extension of this description to processes such as backward meson electroproduction and forward meson production in antiproton-nucleon scattering leads to define new hadronic matrix elements of three quark operators on the light cone, the nucleon-to-meson transition distribution amplitudes, which shed a new light on the nucleon structure.
Experiments with paramagnetic ground or metastable excited states of molecules (ThO, HfF$^+$, YbF, YbOH, BaF, PbO, etc.) provide strong constraints on electron electric dipole moment (EDM) and coupling constant $C_{SP}$ of contact semileptonic interaction. We compute new contributions to $C_{SP}$ arising from the nucleon EDMs due to combined electric and magnetic electron-nucleon interaction. This allows us to improve limits from the experiments with paramagnetic molecules on the $CP$-violating parameters, such as the proton EDM, $|d_p|< 1.1\times 10^{-23} e\cdot $cm, the QCD vacuum angle, $|\…
Nonperturbative effects in $D$-meson production in pion-nucleon and proton-nucleon collisions are investigated within the recombination model. The coalescence of perturbatively created charm quarks with sea- and valence-quarks from projectile and target fragments is shown to be competitive in magnitude with standard fragmentation calculations at both central (small $x_F$) and forward rapidities. Corresponding flavor asymmetries for inclusive $D$-meson production are thus mostly generated on the (light-) parton distribution level, and turn out to be in reasonable overall agreement with availabl…
We explore the possibility of formation of $Δ$ baryons (1232 MeV) in neutron star matter in an effective chiral model within the relativistic mean-field framework. With variation in delta-meson couplings, consistent with the constraints imposed on them, the resulting equation of state is obtained and the neutron star properties are calculated for static and spherical configuration. Within the framework of our model the critical densities of formation of $Δ$s and the properties of neutron stars are found to be very sensitive to the iso-vector coupling compared to the scalar or vector couplings.…
We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD theta term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion-nucleon TV inte…
We examine how the binding of light ($A\leq 8$) nuclei depends on possible variations of hadronic masses, including meson, nucleon, and nucleon-resonance masses. Small variations in hadronic masses may have occurred over time; the present results can help evaluate the consequences for big bang nucleosynthesis. Larger variations may be relevant to current attempts to extrapolate properties of nucleon-nucleon interactions from lattice QCD calculations. Results are presented as derivatives of the energy with respect to the different masses so they can be combined with different predictions of the…
We study the cooling of isolated neutron stars. The main cooling regulators are introduced: EoS, thermal transport, heat capacity, neutrino and photon emissivity, superfluid nucleon gaps. Neutrino emissivity includes main processes. A strong impact of medium effects on the cooling rates is demonstrated. With taking into account of medium effects in reaction rates and in nucleon superfluid gaps modern experimental data can be well explained.
Weak interactions between quarks give rise to hadronic parity violation which can be observed in nuclear and few-nucleon systems. We study the QCD renormalization of the isotensor component of parity violation at next-to-leading order accuracy. The renormalization group is employed to evolve the interaction down to hadronic scales. As the results are renormalization scheme dependent, we compare various schemes, including 't Hooft-Veltman dimensional regularization, and several regularization independent-momentum subtraction schemes.
We derive the relativistic quantum transport equation for the pion distribution function based on an effective Lagrangian of the QHD-II model. The closed time-path Green's function technique, the semi-classical, quasi-particle and Born approximation are employed in the derivation. Both the mean field and collision term are derived from the same Lagrangian and presented analytically. The dynamical equation for the pions is consistent with that for the nucleons and deltas which we developed before. Thus, we obtain a relativistic transport model which describes the hadronic matter with $N$, $Δ$ a…