G. Erkol, M. Oka
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.
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A three flavor linear sigma model with vector and axial-vector mesons is discussed. Preliminary results concerning on the symmetry breaking pattern, the question of parameterization, as well as the resulting meson masses are presented.
The hypothesis of sigma meson pole dominance in the Delta I = 1/2 K -> pi pi amplitudes is tested by using the K_L-K_S mass difference.
The propagation of sigma meson in nuclear matter is studied in the Walecka model, assuming that the sigma couples to a pair of nucleon-antinucleon states and to particle-hole states, including the in medium effect of sigma-omega mixing. We have also considered, by completeness, the coupling of sigma to two virtual pions. We have found that the sigma meson mass decreases respect to its value in vacuum and that the contribution of the sigma omega mixing effect on the mass shift is relatively small.
We study the effect of sigma meson on the $D_1(2430) \to Dππ$ decay by constructing an effective Lagrangian preserving the chiral symmetry and the heavy quark symmetry. The sigma meson is included through a linear sigma model, in which both the $q\bar{q}$ and $qq\bar{q}\bar{q}$ states are incorporated respecting their different $U(1)_{A}$ transformation properties. We first fit the sigma meson mass and $σ$-$π$-$π$ coupling constant to the I=0, $S$-wave $π$-$π$ scattering data. Then, we show how the differential decay width $dΓ(D_1 \to D(ππ)_{I = 0, L =0})/d m_{ππ}$ depends on the quark structu…
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…
Expansion of model Nambu-Jona-Lasinio is considered and on its basis an effective lagrangian for mesons, baryons and baryon - meson interaction has been obtained.
In the present work, the temperature dependence of the scalar mesons parameters is investigated in the framework of thermal QCD sum rules. We calculate sigma-pole and the non-resonant two-pion continuum contributions to the spectral density. Taking into account additional operators appearing at finite temperature, the thermal QCD sum rules are derived. The temperature dependence of the shifts in the mass and leptonic decay constant of scalar sigma(600) meson is calculated.
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.
Zero temperature properties of an (axial-) vector meson extended linear sigma model are discussed, concerning on the possible different realizations of the axial anomaly term. The different anomaly terms are compared with each other on the basis of a chi^2 minimalization process. It is found that there is no essential difference among the different realizations. This means that any of them can be equally used from phenomenological point of view.
We calculate the branching ratio of omega --> pi^+ pi^- gamma decay in a phenomenological framework in which the contributions of VMD, chiral loops, sigma-meson intermediate state amplitudes and the effects of omega-rho mixing are considered. We conclude that the sigma-meson intermediate state amplitude and omega-rho mixing make substantial contribution to the branching ratio.
We use QCD sum rule approach to calculate the masses of the ground-state Lambda_Q and Sigma_Q^(*) baryons. Contributions of the operators up to dimension six are included in operator product expansion. The resulting heavy baryonic masses from the calculations are m_{Lambda_b}=5.69 +/- 0.13 GeV, and m_{Lambda_c}=2.31 +/- 0.19 GeV for Lambda_Q; m_{Sigma_b}=5.73 +/- 0.21 GeV, m_{Sigma_b^*}=5.81 +/- 0.19 GeV, m_{Sigma_c}=2.40 +/- 0.31 GeV and m_{Sigma_c^*}=2.56 +/- 0.24 GeV for Sigma_Q^(*), respectively, which are in good agreement with the experimental values.
We study the radiative $ρ^0\to π^+π^-γ$ and $ρ^0\to π^0π^0γ$ decays and we calculate their branching ratios using a phenomenological approach by adding to the amplitude calculated within the framework of chiral perturbation theory and vector meson dominance the amplitude of $σ$-meson intermediate state. Our results for the branching ratios are in good agreement with the experimental values.
We comment on the recent paper by N.A. Tornqvist and M. Roos published in Phys. Rev. Lett. 76, 1575 (1996).
We extend the three-flavor linear sigma model with (axial-)vector mesons to four flavors. We compute the masses of (pseudo)scalar and (axial-)vector mesons including open and hidden charmed mesons as well as weak decay constants. The results are in good agreement with experimental data.
We reply to the preceding Comment by E. van Beveren et al., arXiv:0811.2589 [hep-ph].
Using recent experimental evidence from E791 on the sigma meson in D \to 3πdecays, we study the relevant couplings in D \to σπand σ\to π pi within the accepted theoretical framework for non leptonic D decays. We also review the linear sigma model, finding that it gives a description which is consistent with the experimental data.
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 show that the non-strange scalar $σ$ meson, as now reported in the 1996 PDG tables, is a natural consequence of crossing symmetry as well as chiral dynamics for both strong interaction low energy $ππ$ scattering and also $K \to 2π$ weak decays.
We reply to the comment of Harada, Sannino and Schechter (hep-ph/9609428) on our recent paper in the Phys. Rev. Letters on the sigma meson. This concerns the question, raised by Isgur and Speth in another comment, of whether a detailed crossing symmetric form is necessary to understand the data. The discussion gives further support on the existence of the broad sigma near 500 MeV.
The pi0 pi0 mass spectra and angular distributions around KKbar -threshold and at 1.5 GeV in ppbar (at rest) --> 3 pi0 in the Crystal Barrel experiment are reanalyzed by applying the new method, which is consistent with unitarity of S-matrix and expressed directly by resonance parameters. The effects of light sigma-meson production are clearly seen to improve the fit with sigma, in comparing with the fit without sigma.
Applying the effective amplitude, which is evidently consistent with general constraints from chiral symmetry, the pipi spectra in the relevant processes are analyzed, leading to a strong evidence for existence of the light sigma meson. It is also pointed out that the pipi scattering process, which had been one of the main sources for PDG table for these many years, is, in principle, exceptionally difficult to investigate the property of sigma-meson.
An important role of the scalar isoscalar sigma-meson in the low-energy physics is discussed. The behavior of the sigma-meson in the hot and dense medium is studied. It is shown that in the vicinity of critical values of temperature(T) and chemical potential(m) the sigma-meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes pi pi -> gamma gamma and pi pi-> pi pi near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and phase transition of…
We present an updated analysis of meson-baryon sigma terms in the perturbative chiral quark model, which is based on effective chiral Lagrangian. The new feature concerns the inclusion of excited states in the quark propagator. Its influence on meson loops is shown to lead in particular for the pion-nucleon sigma term to an enhancement relevant for the current evaluation of this quantity. We also determine various flavor combinations of the scalar nucleon form factors and their respective low-momentum transfer limits.
Properties and temperature behavior of pi and sigma bound states are studied in the framework of the nonlocal model with a separable interaction kernel based on the quark Dyson-Schwinger and the meson Bethe-Salpeter equations. M_pi(T), f_pi(T), M_sigma(T) and Gamma_{sigma -> pi pi}(T) are considered above and below the deconfinement and chiral restoration transitions.
In the framework of the dispersion relation N/D-approach, we restore the low-energy pi-pi (IJ^{PC}=00^{++})-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450-1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane near the pi-pi threshold, that is the light sigma meson.
We include instanton effects in QCD sum rules for coupled scalar glueballs and mesons. We find a light glueball/sigma as in earlier studies without instantons, but in a lattice-type pure instanton model the light glueball/sigma is not found. In the 1-2 Gev region we now find that lightest I=0 meson, in the region of the f$_o$(1370), has no direct glueball mixing, with the instanton loop replacing the glueball component. The lightest scalar mainly glueball in the region of the f$_o$(1500) is sensitive to the choice of nonperturbative gluonic parameters.
The SU(3) linear sigma model is dynamically generated in loop-order using the nonstrange-strange basis. Only self-consistent logarithmic divergent graphs are needed, with quadratic divergent graphs replaced by SU(3) mass-shell equal splitting laws. The latter lead to an eta'-eta mixing angle of 41.84 deg which is consistent with phenomenology. Finally this above SU(3) linear sigma model in turn predicts strong decay rates which are all compatible with data.
The pion-baryon sigma terms and the strange-quark condensates of the octet and the decuplet baryons are calculated by employing the method of quantum chromodynamics (QCD) sum rules. We evaluate the vacuum-to-vacuum transition matrix elements of two baryon interpolating fields in an external isoscalar-scalar field and use a Monte Carlo-based approach to systematically analyze the sum rules and the uncertainties in the results. We extract the ratios of the sigma terms, which have rather high accuracy and minimal dependence on QCD parameters. We discuss the sources of uncertainties and comment on…
The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized 2+1 flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare 2+1 quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in quark meson linear sigma model together wit…
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.
A baryonic chemical potential is included in the linear sigma model at finite temperature. The effective mesonic potential is numerically calculated using the midpoint technique. The meson masses are investigated as functions of the temperature at fixed value of baryonic chemical potential. The pressure and energy density are investigated as functions of temperature at fixed value of chemical potential. The obtained results are in good agreement in comparison with other techniques. We conclude that the calculated effective potential successfully predicts the meson properties and thermodynamic …
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…
In this paper we give a computation of the mass spectrum of mesons and baryons. By this computation we show that there is a consecutive numbering of the mass spectrum of mesons and baryons. We show that in this numbering many stable mesons and baryons are assigned with a prime number. PACS numbers: 12.40.Yx, 14.20Gk, 14.40A, 14.40Cs.
In the framework of an SU(3) (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops, we investigate the effects of (axial)vector mesons on the chiral phase transition. The parameters of the Lagrangian are set at zero temperature and we use a hybrid approach where in the effective potential the constituent quarks are treated at one-loop level and all the mesons at tree-level. We have four order parameters, two scalar condensates and two Polyakov loop variables and their temperature and baryochemical potential dependence are determined from the corr…
We study the SU(3) linear sigma model for the pseudoscalar mesons in the Gaussian Functional Approximation (GFA). We use the SU(3) linear sigma model Lagrangian with nonet scalar and pseudo-scalar mesons including symmetry breaking terms. In the GFA, we take the Gaussian Ansatz for the ground state wave function and apply the variational method to minimize the ground state energy. We derive the gap equations for the dressed meson masses, which are actually just variational parameters in the GFA method. We use the Bethe-Salpeter equation for meson-meson scattering which provides the masses of t…
We compute the polarization of the final-state baryon, in its rest frame, in low-energy meson--baryon scattering with unpolarized initial state, in Unitarized BChPT. Free parameters are determined by fitting total and differential cross-section data (and spin-asymmetry or polarization data if available) for $pK^-$, $pK^+$ and $pπ^+$ scattering. We also compare our results with those of leading-order BChPT.
In this talk I review recent advances on the structure of the meson and baryon resonances which can be dynamically generated from the interaction of mesons or mesons and baryons. Particular emphasis is put on results involving vector mesons, which bring new light into the nature of some of the observed higher mass mesons and baryons and make predictions for new states.
We show that energetically favored meson-baryon fluctuations present in the light-cone wave function of a transversely polarized proton can account for the left-right asymmetries measured in inclusive meson production processes.
We present an effective model, which is an extension of the usual linear sigma model, that contains a low energy multiplet for every hadronic particle type. These multiplets are a scalar nonet, a pseudoscalar nonet, a vector nonet, an axialvector nonet, a baryon octet and a baryon decuplet. Tree level baryon masses and possible two body decuplet decays are calculated. The baryon masses are generated through spontaneous symmetry breaking. The calculated quantities are used to determine the model parameters through a multiparametric minimalization process, which compares the calculated physical …
We develop an ansatze of the sigma enhancement of the I=0, L=0 $π$-$π$ scattering amplitude as arising from a low-energy glueball pole. Using this picture we estimate the $π^0π^0$ to $π^0$ branching ratio for the decays of the Roper resonance, which we previously found to be a hybrid in our QCD sum rule calculation. We find that the sigma decay might be a good signal for gluonic components of hadrons.
We formulate an extended linear $σ$ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) field to study the low-lying scalar meson. Chiral symmetry and $U_A(1)$ symmetry and their breaking play important role to shape the scalar meson spectrum in our work. Based on our study we will comment on what may be the mass of the lowest possible scalar and pseudoscalar glueball states. We will also discuss on what may be the nature of the sigma or $f_0(600)$ meson.
An extended linear sigma model with mesons (q\bar{q} states) and baryons (qqq states) is presented. The model contains a low energy multiplet for every hadronic particle type, namely a scalar, a pseudoscalar, a vector, and an axialvector nonet, an baryon octet and a baryon decuplet. The model parameters are determined through a multiparametric minimalization with the help of well known physical quantities. It is found that the considered zero temperature quantities (masses and decay widths) can be described well at tree-level and are in good agreement with the experimental data.
The original results for the baryon-pion couplings in the large $N_c$ QCD can be understood in a simpler way in the Hartree-Fock picture. The large $N_c$ relation and its $1/N_c$ correction between the heavy baryon-meson coupling and the light baryon-meson coupling are emphasized. Application to the baryon-$ρ$ meson interactions is straightforward. The implications of recent experimental result for the strong coupling constants of the heavy baryon chiral lagrangian are discussed.
We compute the spin asymmetry and polarization of the final-state baryon in its rest frame in two-body meson--baryon low-energy scattering with unpolarized initial state, to lowest non-trivial order in BChPT. The required absorptive amplitudes are obtained analytically at one-loop level. We discuss the polarization results numerically for several meson--baryon processes. Even at low energies above threshold, where BChPT can reasonably be expected to be applicable, sizable values of polarization are found for some processes.
Using the calculated values of the strong coupling constants of the heavy sextet spin-3/2 baryons to sextet and antitriplet heavy spin-1/2 baryons with light mesons within the light cone QCD sum rules method, and vector meson dominance assumption, the radiative decay widths are calculated. These widths are compared with the "direct" radiative decay widths predicted in the framework of the light cone QCD sum rules.
In the light scalar meson sector (M < 1.8 GeV) one expects at least one q qbar nonet and a glueball, possibly also multi-quark states. We discuss the present phenomenological evidence for sigma and kappa particles; if real, they could be members of the lightest (quark or multi-quark) nonet together possibly with a_0(980) and f_0(980). Alternatively, the lightest nonet could include f_0(980) but not sigma and kappa. Future decisive experimental studies, concerning tests of symmetry relations, especially in B-decays, are outlined.
We study the spectra of mesons and baryons, composed of light quarks, in the framework of a semirelativistic potential model including instanton induced forces. We show how a simple modification of the instanton interaction in the baryon sector allows a good description of the meson and the baryon spectra using an interaction characterized by a unique set of parameters.
The recent experimental data of both pipi / Kpi scattering and production processes, suggesting the existence of scalar sigma and kappa mesons, are reviewed. In many pipi /Kpi production processes the direct effects of their productions are observed, while they are, because of chiral symmetry, hidden in scattering processes, and now sigma(500--600) and kappa(800--900) are considered to be confirmed experimentally. The recent criticism on our method of analyses, which is based on the long believed prejudice of universal pipi / Kpi phase through scattering and production amplitudes, is explained…
We study the chiral phase transition in the linear sigma model with 2 quark flavors and $N_c$ colors. One-loop calculations predict a first-order phase transition at both $μ=0$ and $μ\neq 0$. We also discuss the phase diagram and make a comparison with a thermal parametrization of existing heavy-ion experimental data.
A new crossing symmetric unitarization scheme conveniently applied to meson-meson and meson-baryon scattering amplitudes is shortly proposed which can be not only used by theoreticians to unitarize arbitrary theoretical reaction amplitudes resulting from phenomenological Lagrangeans for mesons and baryons, yet also by experimentalists to generate realistic unitary fitting formulae for meson-meson and meson-baryon scattering observables sharing on one hand all the features of the underlying theoretical amplitudes, on the other hand allowing direct comparison to these amplitudes. The new unitari…
The phenomenologically observed property of sigma(600) in our recent analyses of various pi pi-scattering and -production processes is reviewed and compared with the prediction of SU(2) linear sigma model. Furthermore, a possibility of the scalar sigma-nonet (sigma (600), kappa (900), f_0(980) and a_0(980)) forming with the pseudoscalar pi-nonet a linear representation of SU(3) chiral symmetry is investigated. The origin of repulsive background phase shift delta_BG, which is essential to lead us to the sigma-existence in our phase shift analysis, is shown to come from the repulsive lambda phi^…
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.
It is pointed out that the hadron spectroscopy should be a study of the structure of the QCD vacuum, low-energy elementary excitations on top of which are hadrons. Concentrating on the dynamical breaking of the chiral symmetry in the QCD vacuum, we emphasize the importance to clarify what is going on with mesons in the $I=J=0$-channel, i.e., the sigma meson channel, because it is connected to the quantum fluctuations of the chiral order parameter. After summarizing the significance of the sigma meson in QCD and low-energy hadron phenomenology, we give a review on some theoretical and experimen…
The chiral constituent quark model ($χ$CQM) has been extended to calculate the flavor structure of the nucleon through the meson-nucleon sigma terms which have large contributions from the quark sea and are greatly affected by chiral symmetry breaking and SU(3) symmetry breaking. The hidden strangeness component in the nucleon has also been investigated and its significant contribution is found to be consistent with the recent available experimental observations.
We enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark according to the global $U(4)_r\times U(4)_l$ chiral symmetry. In the eLSM, besides scalar and pseudoscalar mesons, also vector and axial-vector mesons are present. Almost all the parameters of the model were fixed in a previous study of mesons below 2 GeV. In the extension to the four-flavor case, only three additional parameters (all of them related to the bare mass of the charm quark) appear. We compute the (OZI-dominant) strong decays of open charmed mesons. The results are compatible with the experime…
We investigate f_0-sigma mixing in the framework of light cone QCD sum rules and by employing the experimental results about the decay widths and the masses of these scalar mesons we estimate the scalar mixing angle by using sigma meson data and f_0 meson data. The two values we thus obtain of the scalar mixing angle are not entirely consistent with each other, possibly indicating that the structure of these mesons cannot be simple quark-antiquark states.
The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and with the octet and decuplet baryons is considered. The leading two-body counter terms involving two baryon fields and two $D$ meson fields are constructed in the open-charm sector. There are 26 terms. A combined expansion in the inverse of the charm quark mass and in the inverse of the number of colors provides sum rules that reduce the number of free parameter down to 5 only. Our result shows the feasibility of a systematic computation of the open-charm baryon spectrum based on coupled-channel dynamics.
A constituent-quark (CQ) mapping of all the baryon and meson resonances is listed for < 3000 MeV. The Isotopic Tables of the Baryons and Mesons (2003) are based upon the CQ Model of M. H. Mac Gregor. Hadrons in boldface are predictions of Mac Gregor. Hadrons in blue indicate rotational states. Predicted hadrons and their spins are indicated in red color. Underlined baryons indicate SU(3) decuplet for J = 3/2. The tables may be extended to charmed and bottom baryons or mesons at a later date. The table for the baryons is expanded to incorporate the recently discovered S = + 1 baryon. Additional…
In the framework of the $U(2)_{R}\times U(2)_{L}$ symmetric linear sigma model with (axial)vector mesons generalized by including a dilaton field we study the phenomenology of the scalar-isoscalar resonances below 2 GeV. It turns out that, in our favoured scenario, the resonance $f_{0}(1370)$ is predominantly a $\bar{q}q$ state and $f_{0}(1500)$ is predominantly a glueball state. Additionally we are able to calculate the value of the gluon condensate, which is in agreement with lattice QCD results.
Whether the $σ-meson$ ($f_0(600)$) exists as a real particle is a long-standing problem in both particle physics and nuclear physics. In this work, we analyze the deuteron binding energy in the linear $σ$ model and by fitting the data, we are able to determine the range of $m_σ$ and also investigate applicability of the linear $σ$ model for the interaction between hadrons in the energy region of MeV's. Our result shows that the best fit to the data of the deuteron binding energy and other experimental data about deuteron advocates a narrow range for the $σ-$meson mass as $520\leq m_σ\leq 580$ …
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