Leonard S. Kisslinger, Dara J. Krute
We estimate the relative branching ratio of $σ$ to 2$π$ for the decay of the $Ψ'(2S)$, which we have found to be a mixed charm and hybrid charmonium meson. The external field method and correlators from a previous calculation are used to estimate these decays. We find the $σ$ to 2$π$ branching ratio for $Ψ'(2S)$ to the $J/Ψ(1S)$ decay to be 0.98, in agreement with an experiment at IHEP-BES.
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We study how we can understand the change of the spectral function and the pole location of the correlation function for sigma at finite temperature, which were previously obtained in the linear sigma model with a resummation technique called optimized perturbation theory. There are two relevant poles in the sigma channel. One pole is the original sigma pole which shows up as a broad peak at zero temperature and becomes lighter as the temperature increases. The behavior is understood from the decreasing of the sigma condensate, which is consistent with the Brown-Rho scaling. The other pole cha…
A dependence of the value of the pion-nucleon sigma term on higher partial waves is discussed. Two recent predictions of a high value of sigma term are scrutinezed. It has been concluded that the main reason for obtaining high values of the sigma term are input D waves that are not consistent with analyticity.
Gribov's theory of confinement offers a simple explanaton of the value of the pion nucleon sigma term. There is no need to invoke a large strange quark component in the nucleon.
A brief review of the pion-nucleon sigma-term is given. Aspects of both chiral perturbation theory and phenomenology are discussed.
We evaluate the pion-nucleon and the pion-Delta sigma terms by employing the method of quantum chromodynamics (QCD) sum rules. The obtained value of the pion-nucleon sigma term is compatible with the larger values already anticipated by the recent calculations. It is also found that the pion-Delta sigma term is as large as the pion-nucleon sigma term.
We enforce chiral Ward identities on the vertices of the linear sigma model to take into account the width of the scalar sigma, considered as a true physical resonance. We consider pion scattering at very low energies and, from a fit to the measured phase shifts in the various angular momentum and isospin channels, conclude a mass for the sigma of 600+200-100 MeV. Its width turns out to be of the same size.
A dispersion framework, appropriate for discussing the low-energy pion-nucleon interaction, is reviewed. Sensitivity of the isoscalar D-amplitude at the unphysical Cheng-Dashen point to input from different phase shift analyses and low-energy experiments is discussed.
We calculate the pion decay constant near the critical temperature of the $O(N)$ nonlinear sigma model in the large $N$ limit. Making use of the known low temperature behavior, we construct a Padé approximant to obtain the behavior of $f_π(T)$ at all temperatures.
We study the pion-nucleon sigma term in vacuum and in nuclear matter in the framework of global color model of QCD. With the effective gluon propagator being taken as the $δ$-function in momentum space of Munczek-Nomirovsky model, we estimate that the sigma term at chiral limit in the vacuum is 9/2 times the current quark mass and it decreases with the nuclear matter density. With the presently obtained in-medium pion-nucleon sigma term, we study the in-medium chiral quark condensate and obtain a reasonable variation behavior against the nuclear matter density.
A new result for the pion nucleon Sigma term from a George Washington University/TRIUMF group analysis of pion nucleon data is presented. The value Sigma=79$\pm$7 MeV was obtained, compared to the canonical value 64$\pm$8 MeV found by Koch. The difference is explained simply by the PSI pionic hydrogen value for a(pi -p), the latest results for the $πNN$ coupling onstant, and a narrower Delta resonance. Many systematic effects have been investigated, including Coulomb corrections, and database changes, and our results are found to be robust. In the standard interpretation, our value of Sigma im…
We calculate low-energy meson decay processes and pion-pion scattering lengths in a two-flavour linear sigma model with global chiral symmetry, exploring the scenario in which the scalar mesons $f_0$(600) and $a_0$(980) are assumed to be $\bar q q$ states.
We report the results of the working group on ``Pion (Kaon) and Sigma Polarizabilities''. Interesting possibilities to measure these polarizabilities include the radiative pion photoproduction in the MAMI experiment at Mainz, as well as at the GRAAL facility (actually the latter is being considered for an experimental determination of the pion polarizabilities here for the first time), the experimental plans on Primakoff effect at FNAL, and the measurements at the Frascati $Φ$-factory DA$Φ$NE.
A variety of strong and electroweak interaction properties of the pion and the light scalar sigma meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the sigma meson mass is determined as M_sigma=385.4 MeV. We discuss in detail the gauging of the non-local meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the pi(0) -> gamma gamma and sigma -> gamma gamma processes. We obtain explicit expressions for the relevant form factors and evaluate…
The pion nucleon sigma-term is extracted on the basis of the soliton picture of the nucleon from the mass spectrum of usual and the recently observed exotic baryons, assuming that they have positive parity. The value found is consistent with that inferred by means of conventional methods from pion nucleon scattering data. The study can also be considered as a phenomenological consistency check of the soliton picture of baryons.
Multiple soft pion production in the baryon scattering reactions is considered in the framework of chiral nonlinear sigma model neglecting the pion mass. Treating baryons in the eikonal approximation as classical sources, a set of analytical solutions for the pion field is found. A tree S-matrix is constructed on the basis of these solutions describing the emission (or absorption) of any number of soft pions. Then the contribution of soft virtual pions is taken into account in a closed form. It is shown that the loop corrections strongly suppress the pion radiation, and for the two limiting ca…
We construct effective one-loop vertices and propagators in the linear sigma model at finite temperature, satisfying the chiral Ward identities and thus respecting chiral symmetry, treating the pion momentum, pion mass and temperature as small compared to the sigma mass. We use these objects to compute the two-loop pion self-energy. We find that the perturbative behavior of physical quantities, such as the temperature dependence of the pion mass, is well defined in this kinematical regime in terms of the parameter m_pi^2/4pi^2f_pi^2 and show that an expansion in terms of this reproduces the di…
We discuss the mixing between the sigma meson sigma and the "pure" glueball field H and study the decays of the scalar glueball candidates f_0(1370), f_0(1500) and f_0(1710) (a linear combination of sigma and H) into two pions in an effective linear sigma model.
Chiral Ward identities lead to consistent accounting for the sigma's width in the linear sigma model's Feynman rules. Reanalysis of pion scattering data at threshold imply a mass for the sigma of 600+ 200 - 100 MeV.
We calculate the "pi Sigma Lambda" and "pi Sigma Sigma" coupling constants in light cone QCD sum rules for the structure "sigma_{alpha beta} gamma_5 p^alpha q^beta". A comparison of our results on these coupling constants with prediction of the SU(3) symmetry is presented.
We use a configuration space chiral model in order to evaluate nucleon and delta sigma-terms. Analytic expressions are consistent with chiral counting rules and give rise to expected non-analytic terms in the chiral limit. We obtain the results $σ_N=46$ MeV and $σ_Δ=32$ MeV, which are very close to values extracted from experiment and produced by other groups.
A simple gauged linear sigma model with several parameters to take the symmetry breaking and the mass differences between the vector meson and the axial vector meson into account is considered here as a possibly useful template for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. An analytic procedure is first developed for relating the Lagrangian parameters to four well established (in the QCD application) experimental inputs. One simple equation distinguishes three different cases:1. QCD w…
We evaluate the pi-N-N, pi-Sigma-Sigma and pi-Sigma-Lambda coupling constants using QCD sum rules based on pion-to-vacuum matrix elements of correlators of two interpolating baryon fields. The parts of the correlators with Dirac structure k-slash gamma_5 are used, keeping all terms up to dimension 5 in the OPE and including continuum contributions on the phenomenological side. The ratios of these sum rules to baryon mass sum rules yield stable results with values for the couplings of g_{pi NN}=12+/-5, g_{pi Sigma Sigma}=7+/-4 and g_{pi Sigma Lambda}=6+/-3. The sources of uncertainty are discus…
We have used the Cornwall--Jackiw--Tomboulis method of composite operators and its formulation at finite temperature by Amelino-Camelia and Pi, in order to calculate the effective potential of the O(4) linear sigma model beyond the Hartree approximation. We have obtained a system of gap equations for the effective mass of sigma and the pions as well as for the condensate, the order parameter of the chiral phase transition. We find that the thermal effective mass of the pions at low temperatures remains lower than in the Hartree case, nevertheless deviates from the chiral limit. Our observation…
We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic anti-catalysis in the Bose-Einstein condensation for lower values of the external magnetic field, and catalysis for higher values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.
We study the effect of thermal width of $π$ on the spectral function of $σ$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to take into account finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without pion thermal width, the peak…
We calculate the one-loop contributions to the difference Δ_{πK} between the isoscalar on-shell pion-kaon scattering amplitude at the Cheng-Dashen point and the scalar form factor Γ_K (2M_π^2) in the framework of three flavor chiral perturbation theory. These corrections turn out to be small. This is further sharpened by treating the kaons as heavy fields (two flavor chiral perturbation theory). We also analyze the two-loop corrections to the kaon scalar form factor based on a dispersive technique. We find that these corrections are smaller than in the comparable case of the scalar form factor…
From recent analysis of the $ππ$ scattering amplitude, it has been claimed that there exists a broad and light $σ$ meson. However, if this meson really exists, it must also appear in other observables such as the pion scalar form factor. With the use of unitarity and dispersion relations together with chiral perturbation theory, this form factor is analyzed in the complex energy plane. The result agrees well with the empirical information in the elastic region and reveals a resonance pole at $\sqrt{s}=445-i235$ MeV. This gives further strong evidence for the existence of the $σ$ meson.
We investigate the twist-3 pion and kaon distribution amplitudes of the pseudoscalar (phi^p_{pi,K}) and pseudotensor (phi^{sigma}_{pi,K}) types, based on the effective chiral action from the instanton vacuum. Effects of flavor SU(3) symmetry breaking are explicitly taken into account. The Gegenbauer moments and the moments of the distribution amplitudes (<xi^m>) are also computed. Our results are summarized as follows: a^p_{2,pi} ~ 0.4, a^p_{1,K} ~ 0.02 and a^p_{2,K} ~ 0.14, and a^{sigma}_{2,pi} ~ 0.02 and a^{sigma}_{1,K} ~ a^{sigma}_{2,K} ~ 0; <xi^2>^p_π ~ <xi^2>^p_K ~ 0.37 and <xi>^p_K ~ 0, …
We study the effect of the thermal width of $π$ on the spectral function of $σ$. In order to take into account a finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of the complex pole found in a previous paper. The obtained spectral function for $T\aplg 100 {\rm MeV}$ turns out to possess two broad peaks. Although a sharp peak at $σ\toππ$ threshold was observed in the one-loop calculation without the pion thermal width, the peak is shown to be smeared out. We also search for the poles of the $σ$ propagator and analyze the behavior of the spectral…
We apply the perturbative chiral quark model (PCQM) at one loop to analyse meson-baryon sigma-terms. Analytic expressions for these quantities are obtained in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). Our result for the piN sigma term of about 45 MeV is in good agreement with the value deduced by Gasser, Leutwyler and Sainio using dispersion-relation techniques and exploiting the chiral symmetry constraints.
Working within the linear sigma model at finite temperature, we construct effective one-loop vertices and propagators satisfying the chiral Ward identities, for small pion momentum and mass compared to the sigma mass. We obtain an expansion for the pion dispersion relation up to second order in the parameter m_pi^2/4pi^2f_pi^2. At leading order, this expansion reproduces the dispersion curve obtained in chiral perturbation theory. We also study pion damping and compute the mean free path for pions traveling in the medium before forming a sigma resonance. These results are also in good agreemen…
We investigate the problem of quantum back reactions due to particle production by the parametric resonance mechanism in an environment of nonequilibrium chiral phase transition. We work with the linear sigma model and employ Boyanovsky et al.'s formalism to take account of back reactions under the Hartree-Fock approximation. We calculate the single pion momentum distributions and two pion correlations under the initial condition of thermal equilibrium and small amplitude sigma oscillations around a potential minimum. We observe that the resonance peak survives under the back reaction which is…
We calculate the neutral pion mass in the presence of an external magnetic field of arbitrary strength in the framework of the linear sigma model coupled to quarks at zero temperature. We find nonmonotonic behavior of the pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak-field approximation.
The pion-nucleon sigma term is shown to be equal to the Goldberger-Treiman discrepancy at tree level. Its value estimated this way is very sensitive to the pion-nucleon coupling constant g_{pi NN}. This relation, when combined with the pion-nucleon S-wave scattering lengths, yields a new determination of g_{pi NN} at tree level. The results of a one-loop analysis are also summarized determining an allowed range for the induced pseudoscalar coupling constant g_P.
We examine the mixing between the sigma meson $σ$ and the "pure" glueball field $H$ and study the decays of the scalar glueball candidate $f_0(1500)$ (a linear combination of $σ$ and $H$) into two and four pions in effective linear sigma model. From recent experimental data on $f_0(1500)$ decay to pions we point out that the mixing angle is of order of 0.1.
The quark-level linear sigma model is revisited, in particular concerning the identification of the f_0(400-1200) (or σ(600)) scalar meson as the chiral partner of the pion. We demonstrate the predictive power of the linear sigma model through the pi-pi and pi-N s-wave scattering lengths, as well as several electromagnetic, weak, and strong decays of pseudoscalar and vector mesons. The ease with which the data for these observables are reproduced in the linear sigma model lends credit to the necessity to include the sigma as a fundamental q\bar{q} degree of freedom, to be contrasted with appro…
We study the dynamical consequences imposed on effective chiral field theories such as the quark-level SU(2) linear $σ$ model (L$σ$M) due to the fundamental constraints of massless Goldstone pions, the normalization of the pion decay constant and form factor, and the pion charge radius. We discuss quark-level double counting L$σ$M ambiguities in the context of the Salam-Weinberg $Z = 0$ compositeness condition. Then SU(3) extensions to the kaon are briefly considered.
The latest measurements of the atomic level width in Sigma-hyperonic Pb atom offer the most accurate datum in the region of low-energy Sigma-hyperon physics. Atomic widths are due to the conversion of Sigma-nucleon into Lambda-nucleon. In high angular momentum states this conversion is dominated by the one-pion exchange. A joint analysis of the data of the scattering of negative-Sigma on proton converting into a Lambda and a neutron and of the atomic widths allows to extract a pseudovector pion-hyperon-Sigma coupling constant of 0.048 with a statistical error of +-0.005 and a systematic one of…
The quark-level linear sigma model is employed to compute a variety of electromagnetic and weak observables of light mesons, including pion and kaon form factors and charge radii, charged-pion polarizabilities, semileptonic weak $K_{\ell3}$ decay, semileptonic weak radiative pion and kaon form factors, radiative decays of vector mesons, and nonleptonic weak $K_{2π}$ decay. The agreement of all these predicted observables with experiment is striking. In passing, the tight link between the linear sigma model and vector-meson dominance is shown. Some conclusions are drawn on the linear sigma mode…
We review our recent study of the pion mass dependence of the rho and sigma resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho-pi-pi coupling constant is almost pion mass independent a…
We discuss the implications of a new determination of the pion-nucleon sigma term for the evaluation of the neutralino-nucleon cross-section, and, in turn, for detection rates for relic neutralinos in WIMP direct experiments and in some of the indirect searches. It is shown that the new range for the pion-nucleon sigma term, taken at its face value, favours values of the neutralino-nucleon cross-sections which are sizeably larger than some of the current estimates. Implications for neutralino cosmological properties are derived.
We develop one-loop effective vertices and propagators in the linear sigma model at finite temperature satisfying the chiral Ward identities. We use these in turn to compute the pion dispersion relation in a pion medium for small momentum and temperatures on the order of the pion mass at next to leading order in the parameter m_pi^2/4pi^2f_pi^2 and to zeroth order in the parameter (m_pi/m_sigma)^2. We show that this expansion reproduces the result obtained from chiral perturbation theory at leading order. The main effect is a perturbative, temperature-dependent increase of the pion mass. We fi…
Using the linear sigma model to describe quark--pion interactions, we compute polarization asymmetries in quark fragmentation. We show that the effects of transverse quark polarizations appear in the correlation between the two leading pions in a jet produced by the fragmentation of a quark. Such asymmetries provide a window to the nature of chiral symmetry breaking in QCD.
A model is developed for electromagnetic form factor of the pion. One-loop corrections are included in the linear sigma-model. The rho-meson contribution is added in an extended VMD model. The form factor, calculated without fitting parameters, is in a good agreement with experiment for space-like and time-like photon momenta. Loop corrections to the two-pion hadronic contribution a^{(had, π)}_μto the muon anomalous magnetic moment are calculated. The optimal value of the sigma-meson mass appears to be close to the rho-meson mass.
We estimate the couplings in the Heavy Hadron Chiral Theory (HHCT) lagrangian from the QCD sum rules in an external axial field. We take into account the perturbative correction to the meson correlator in the infinite mass limit. With the perturbative correction and three successive power corrections, the meson correlator in an axial field becomes one of the best known correlators. In spite of this, the corresponding sum rule is not very stable. It yields the result g_1 F^2/(380MeV)^3 = 0.1 - 0.2, where F^2 = f_M^2 m/4 = (380MeV)^3 is the central value of the heavy meson decay constant with th…
An earlier calculation in a generalized linear sigma model showed that the well-known current algebra formula for low energy pion pion scattering held even though the massless Nambu Goldstone pion contained a small admixture of a two-quark two-antiquark field. Here we turn on the pion mass and note that the current algebra formula no longer holds exactly. We discuss this small deviation and also study the effects of an SU(3) symmetric quark mass type term on the masses and mixings of the eight SU(3) multiplets in the model. We calculate the s wave scattering lengths, including the beyond curre…
We use the linear sigma model with quarks to find the magnetic field-induced modifications to the neutral pion mass at one-loop level. The magnetic field effects are introduced by using charged particle propagators in the presence of a magnetic background in the strong field regime. We show that when accounting for the effects of the magnetic field on the model couplings, the vacuum sigma field and the neutral pion self-energy, the neutral pion mass decreases monotonically as a function of the field strength. We find an excellent qualitative and quantitative agreement with recent lattice QCD c…
We calculate the physical mass and the width of the sigma meson by considering that it couples in vacuum to two virtual pions. The mass is calculated by using the spectral function, and we find that it is about 600MeV. In addition, we obtained the value of 250MeV for the width of its spectral function. The value obtained for the mass, is in an excellent agreement with that reported in the Particle data Book for the sigma meson, which is also named f0(600). This result also shows that the sigma meson can be considered as a two pion resonance.
Magnetic field modifications to the pion-quark vertex in the Linear Sigma Model with quarks
研究采用带夸克的线性σ模型，计算恒定均匀磁场下夸克-中性π介子顶点的树图及单圈修正，结果在Ritus形式论与施温格固有时间方法下一致，适用于夸克占据任意朗道能级的情况。
We calculate the variation of the chiral condensate in medium with respect to the quark chemical potential and evaluate the pion-nucleon sigma term via the Hellmann-Feynman theorem. The variation of chiral condensate in medium are obtained by solving the truncated Dyson-Schwinger equation for quark propagator at finite chemical potential, with different models for the quark-gluon vertex and gluon propagator. We obtain the value of the sigma term $σ_{πN}$ = 62(1)(2) MeV, where the first represents the systematic error due to our different model for the quark-gluon vertex and gluon propagator an…
Fermilab E781 plans measurements of gamma-Sigma and $γ$-pion interactions using a 600 GeV beam of Sigmas and pions, and a virtual photon target. Pion polarizabilities and radiative transitions will be measured in this experiment. The former can test a precise prediction of chiral symmetry; the latter for a_1(1260) ----> pi + gamma is important for understanding the polarizability. The experiment also measures polarizabilities and radiative transitions for Sigma hyperons. The polarizabilities can test predictions of baryon chiral perturbation theory. The radiative transitions to the Sigma*(1385…
We studied chiral phase transition in the linear sigma model within the Tsallis nonextensive statistics in the case of small deviation from the Boltzmann-Gibbs (BG) statistics. The statistics has two parameters: the temperature $T$ and the entropic parameter $q$. The normalized $q$-expectation value and the physical temperature $\Tph$ were employed in this study. The normalized $q$-expectation value was expanded as a series of the value $(1-q)$, where the absolute value $|1-q|$ is the measure of the deviation from the BG statistics. We applied the Hartree factorization and the free particle ap…
We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach. The one-loop pion-pion scattering amplitude in Chiral Perturbation Theory at finite temperature is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the rho and sigma widths. The masses decrease slightly for high T, while the rho-pion-pion coupling increases. The rho behavior seems to be favored by experimental results. In the sigma case, it signals chiral symmetry restoration.
The pion-nucleon $σ$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3σ$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.
Fits of the p^4 covariant SU(2) baryon chiral perturbation theory to lattice QCD nucleon mass data from several collaborations for 2 and 2+1 flavors are presented. We consider contributions from explicit Delta(1232) degrees of freedom, finite volume and finite spacing corrections. We emphasize here our Nf=2+1 study. We obtain low-energy constants of natural size that are compatible with the rather linear pion-mass dependence of the nucleon mass observed in lattice QCD. We report a value for the pion-nucleon sigma term of 41(5)(4) MeV for the 2 flavor case and 52(3)(8) MeV for 2+1 flavors.
We have reanalyzed the $π^{\pm} p$ scattering data at low energy in the Coulomb-nuclear interference region as measured by the CHAOS group at TRIUMF with the aim to determine the pion-nucleon $σ$ term. The resulting value $σ=(44\pm 12)$ MeV, while in agreement with lattice QCD calculations and compatible with other recent analyses, is significantly lower than that from the GWU-TRIUMF analysis of 2002.
For a long time doubts have existed on the existence of the f0(1370) meson as an individual object distinct and separated from the sigma meson. Decays into two charged pions of the f0(1370) are the main source of an isolated structure localized between 1.2 and 1.5 GeV in the two charged pions mass spectrum measured in pp Central Exclusive Production (CEP) at 200 GeV at very low four momentum transfer squared ltl. These data confirm in the two charged pions decay channel the existence of the f0(1370) as an isolated well identified structure that was previously observed in K+K-, KsKs, 4 neutral …
The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_σ-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_π^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated fo…
A modified linear sigma model that allows for $g_A = 1.26$ by addition of vector and pseudovector $πN$ coupling terms was discussed by Bjorken and Nauenberg and by Lee. In this extended linear sigma model the elastic $π$N scattering amplitudes satisfy the relevant chiral low-energy theorems, such as the Weinberg-Tomozawa relation for the isovector scattering length and in some cases Adler's "consistency condition". The agreement of the isospin symmetric $πN$ scattering length with experiment is substantially improved in this extended sigma model as compared with the original one. We show that …
We compute the neutral pion mass dependence on a magnetic field in the weak field approximation at one-loop order. The calculation is carried out within the linear sigma model coupled to quarks and using Schwinger's proper-time representation for the charged particle propagators. We find that the neutral pion mass decreases with the field strength provided the boson self-coupling magnetic field corrections are also included. The calculation should be regarded as the setting of the trend for the neutral pion mass as the magnetic field is turned on.
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