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 with axial vector particle heavier than vector particle, 2. possible technicolor model with vector particle heavier than the axial vector one, 3. the unphysical QCD case where both the KSRF and Weinberg relations hold. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) theglobal region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of bare sigma mass parameter for describing these two regions. If a reasonable globa fit is made, there is some loss of precision in the near threshold region.
We study the beta functions of the leading, two-derivative terms of the left-gauged SU(N) nonlinear sigma-model in d dimensions. In d>2, we find the usual Gaussian ultraviolet fixed point for the gauge coupling and an attractive non-Gaussian fixed point for the Goldstone boson coupling. The position of the latter fixed point controls the chiral expansion, unitarity and the strength of the tree-level Goldstone boson scattering amplitudes. Attention is paid to the gauge- and scheme-dependence of the results.
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.
The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson-quark Lagrangian, with the quark (q) and meson ($σ,π$) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be $m_q = f_πg, m_π= 0, m_σ= 2m_q$, and we also find that the quark-meson coupling $g = 2π/sqrt{N_c}$, the three-meson coupling is $g' = m_σ^2/2f_π= 2gm_q$ and the four-meson coupling is $λ= 2g^2 = g'/f_π$, where $f_π\simeq 90$ MeV is the pion decay constant and $N_c = 3$ is the color number. By g…
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.
The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons. The validity of this theorem within the standard model with a heavy Higgs boson and within the gauged nonlinear sigma-model (in which the Higgs boson is absent) is shown. Furthermore it is examined to what extent also internal lines other than scalar lines can be neglected. A simple power-counting method is developed which determines th…
We consider vector and axialvector mesons in the framework of a gauged linear sigma model with chiral $U(N_f)_R \times U(N_f)_L$ symmetry. For $N_f=2$, we investigate the behavior of the chiral condensate and the meson masses as a function of temperature by solving a system of coupled Dyson-Schwinger equations derived via the 2PI formalism in double-bubble approximation. We find that the inclusion of vector and axialvector mesons tends to sharpen the chiral transition. Within our approximation scheme, the mass of the $ρ$ meson increases by about 100 MeV towards the chiral transition.
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.
The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are presented. The complete set of seven coupled non-linear field equations of the gauged non-linear sigma model together with the corresponding Maxwell equations are reduced in a self-consistent way to just one linear Schrodinger-like equation in two dimensions. The corresponding two dimensional periodic potential can be computed explicitly in terms of the solitons …
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.
The linear $σ$-model with a chemical potential for hypercharge is a toy model for the description of the dynamics of the kaon condensate in high density QCD. We analyze the dynamics of the gauged version of this model. It is shown that spontaneous breakdown of $SU(2) \times U(1)_{Y}$ symmetry, caused by the chemical potential, is always accompanied by spontaneous breakdown of both rotational symmetry and electromagnetic $U(1)_{em}$. The spectrum of excitations in this model is rich and, because of rotational symmetry breakdown, anisotropic. It is shown that there exist excitation branches that…
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 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.
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…
Magnetized Baryonic layer and a novel BPS bound in the gauged-Non-Linear-Sigma-Model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation
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…
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 calculate pion-pion scattering lengths and sigma, rho and a1 decay widths from a gauged linear sigma model with two flavours and its globally invariant generalisation.
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 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…
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.
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.
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.
The pion-nucleon sigma term is a quantity involved in many important aspects of particle and nuclear physics. In this review I show its origin and how it is connected to important questions as the origin of mass of the ordinary matter, studies of dark matter detection and nucleosynthesis. I mention the most common methods used to obtain the sigma term, and comment on the extracted values. As it is shown, the accepted value of the sigma term has been moving from relatively low ($\sim 40$ MeV) to larger ones ($\sim 60$ MeV) until today, where this controversy still persist.
In this paper we address the question how to discriminate whether the gauged isometry group G_Sigma of the Kahler manifold Sigma that produces a D-type inflaton potential in a Minimal Supergravity Model is elliptic, hyperbolic or parabolic. We show that the classification of isometries of symmetric cosets can be extended to non symmetric Sigma.s if these manifolds satisfy additional mathematical restrictions. The classification criteria established in the mathematical literature are coherent with simple criteria formulated in terms of the asymptotic behavior of the Kahler potential K(C) = 2 J(…
We investigate the influence of new GRAAL Sigma-beam asymmetry measurements on the neutron in multipole fits to the single-pion photoproduction database. Results are compared to those found with the addition of a double-polarization quantity associated with the sum rule.
We present an extraction of the pion-nucleon ($πN$) scattering lengths from low-energy $πN$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $πN$ $σ$-term, $σ_{πN}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.
