Denis Parganlija, Francesco Giacosa, Dirk H. Rischke
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.
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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…
We evaluate the nucleon sigma term and in-medium quark condensate in the modified quark-meson coupling model which features a density-dependent bag constant. We obtain a nucleon sigma term consistent with its empirical value, which requires a significant reduction of the bag constant in the nuclear medium similar to those found in the previous works. The resulting in-medium quark condensate at low densities agrees well with the model independent linear order result. At higher densities, the magnitude of the in-medium quark condensate tends to increase, indicating no tendency toward chiral symm…
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
The coupling constant g_{rho sigma gamma} is determined from light cone QCD sum rules. A comparison of our result with the ones existing in literature is presented.
The strong coupling constants g_{K LAMBDA N} and g_{K SIGMA N} for the structure (sigma_{mu,nu} gamma_5) are calculated within light cone QCD sum rules. A comparison of our results on these couplings with predictions from traditional QCD sum rules is presented.
The long-range $ΛN-ΣN$ interaction is modeled by a configuration space meson-exchange potential matrix coupling to channels with $Δ$ and $Σ(1385)$ isobars. An inner boundary condition, based on $R$-matrix theory, replaces form factors for short-range effects and includes the effects of free quark configurations. An excellent fit is obtained to the available data, with only the energy-independent boundary conditions as free parameters. The effect of isobar thresholds is shown to be substantial in several partial waves and is crucial to the understanding of the higher energy $ΛN$ elastic scatter…
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.
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 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.
The quark-meson coupling (QMC) model, which has been successfully used to describe the properties of both infinite nuclear matter and finite nuclei, is applied to a systematic study of $Λ, Σ$ and $Ξ$ hypernuclei. Assumptions made in the present study are, (i) the (self-consistent) exchanged scalar, and vector, mesons couple only to the u and d quarks, and (ii) an SU(6) valence quark model for the bound nucleons and hyperon. The model automatically leads to a very weak spin-orbit interaction for the $Λ$ in a hypernucleus. Effects of the Pauli blocking at the quark level, particularly in the ope…
The tricritical line of the first-order chiral phase transition is investigated in the U(Nf)xU(Nf) sigma model by means of the ring improved one-loop finite temperature effective potential. To locate the tricritical line in the space of the coupling constants, we expand the effective potential up to third order in the high temperature expansion, and up to sixth order in the order parameter expansion. In this approximation, the tricritical line can be evaluated to the lowest order of the coupling constants and it follows an analytic relation between the tree-level masses of the scalar bosons. T…
We extract the K+K- couplings of the isoscalar scalar mesons sigma/f_0(600) and f_0(980) from pi pi to pi pi / K K scatterings and found: |g_{sigma K+K-}|/ |g_{sigma pi+pi-}|= 0.8 and |g_{f_0 K+K-}|/ |g_{f_0 pi+pi-}|= 1.7. These results, together with the tiny "direct" gamma gamma width of the sigma and its large hadronic width, are a strong indication for the gluonium/glueball nature of the sigma-meson, as predicted by QCD spectral sum rules (QSSR) + some low-energy theorems (LET), while some other assignements (pi pi molecule, tetraquark state and ordinary qq meson) do not satisfy simultaneo…
We compute the magnetic field-induced modifications to the boson self-coupling and the boson-fermion coupling, in the static limit, using an effective model of QCD, the linear sigma model with quarks. The former is computed for arbitrary field strengths as well as using the strong field approximation. The latter is obtained in the strong field limit. The arbitrary field result for the boson self-coupling depends on the ultraviolet renormalization scale and this dependence cannot be removed by a simple vacuum subtraction. Using the strong field result as a guide, we find the appropriate choice …
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…
It is known that supersymmetric nonlinear sigma models for the compact Kahler manifolds G/H cannot be consistently coupled to supergravity, since the Kahler potentials are not invariant under the G transformation. We show that the supersymmetric nonlinear sigma models can be deformed such that the Kahler potential be exactly G-invariant if and only if one enlarges the manifolds by dropping all the U(1)'s in the unbroken subgroup H. Then, those nonlinear sigma models can be coupled to supergravity without losing the G invariance.
The pi pi scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the sigma meson which is observed as the lowest scalar-isoscalar resonance. We compare several models with different origins of the sigma meson, such as the chiral partner of the pion and the dynamically generated pi pi molecule. We find that the dynamically generated sigma meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. Thi…
We explore the nature of running couplings in the higher derivative linear and nonlinear sigma models and show that the results in dimensional regularization for the physical running couplings do not always match the values quoted in the literature. Heat kernel methods identify divergences correctly, but not all of these divergences are related to physical running couplings. Likewise the running found using the Functional Renormalization Group does not always appear as running couplings in physical processes, even for the case of logarithmic running. The basic coupling of the higher derivative…
Recently there are several evidences of the hadronic total cross section sigma(tot) to be proportional to B (log s)2 consistent with the Froissart unitarity bound. The COMPETE collaborations have further assumed sigma(tot) = B (log s/s0)2 + Z to extend its universal rise with the common value of B and s0 for all hadronic scatterings to reduce the number of adjustable parameters. The coefficient B was suggested to be universal in the arguments of colour glass condensate (CGC) of QCD in recent years. There has been, however, no rigorous proof yet based only on QCD. We attempt to investigate the …
In this talk, we present an explanation for the Delta I = 1/2 rule in K-decays based on the premise of an infrared fixed point alpha_IR in the running coupling alpha_s of quantum chromodynamics (QCD) for three light quarks u,d,s. At the fixed point, the quark condensate spontaneously breaks scale and chiral SU(3)_L x SU(3)_R symmetry. Consequently, the low-lying spectrum contains nine Nambu-Goldstone bosons: pi,K,eta and a QCD dilaton sigma. We identify sigma as the f_0(500) resonance and construct a chiral-scale perturbation theory CHPT_sigma for low-energy amplitudes expanded in alpha_s abou…
The reducible Kähler coset space G/S\otimesU(1)^k is discussed in a geometrical approach. We derive the formula which expresses the Riemann curvature of the reducible Kähler coset space in terms of its Killing vectors. The formula manifests the group structure of G. On the basis of this formula we establish an algebraic method to evaluate the four-fermi coupling of the supersymmetric non-linear sigma-model on G/S\otimesU(1)^k at the low-energy limit. As an application we consider the supersymmetric non-linear sigma-model on E_7/SU(5)\otimesU(1)^3 which contains the three families of {10} + {5^…
Under the assumption of the Abelian dominance in QCD, we show that chiral condensate is locally present around a QCD monopole. The appearance of the chiral condensate around a GUT monopole was shown in the previous analysis of the Rubakov effect. We apply a similar analysis to the QCD monopole. It follows that the condensation of the monopole carrying the chiral condensate leads to the chiral symmetry breaking as well as quark confinement. To realize the result explicitly, we present a phenomenological linear sigma model coupled with the monopoles, in which the monopole condensation causes the…
We estimate the coupling of the K* vector meson to the N-->Theta+ transition employing unitary symmetry, vector meson dominance, and results from the GRAAL Collaboration for eta photoproduction off the neutron. Our small numerical value for the coupling constant is consistent with the non-observation of the Theta+ in recent CLAS searches for its photoproduction. We also estimate the K*-coupling for the N-->Sigma* excitation, with Sigma* being the Sigma-like antidecuplet partner of the Theta+-baryon.
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…
Recently there are several evidences of the increase of the total cross section sigma(tot) to be log2 s consistent with the Froissart unitarity bound, and the COMPETE collaborations in the PDG have further assumed sigma(tot) = B log2(s/s0) to extend its universal rise with a common value of B for all the hadronic scatterings. However, there is no rigorous proof yet based only on QCD. Therefore, it is worthwhile to prove this universal rise of sigma(tot) even empirically. In this letter we attempt to obtain the value of B for pi p scattering, B(pi p), with reasonable accuracy by taking into acc…
Based on the strong coupling expansion, we reinvestigate two dimensional O(N) sigma model by the use of Pade-Borel approximants. The conventional strong coupling expansion of the mass square M in momentum space in beta=1/g^2 is inverted to give beta expanded in 1/M. Borel transform of beta with respect to M is carried out and the result is improved as the rational function by Pade method. We find the behavior of Pade-Borel transformed bare coupling at 18th order is consistent for N>=3 with that of continuum scaling to the four-loop perturbation theory. We estimate non-perturbative mass gap at …
We analyze the one loop corrections to leptonic W and Z decays in an R-parity violating extension to the Minimal Supersymmetric Standard Model (MSSM). We find that lepton universality violation in the Z line-shape variables alone would strengthen the bounds on the magnitudes of the lambda' couplings, but a global fit on all data leaves the bounds virtually unchanged at |lambda'_{33k}| < 0.42 and |lambda'_{23k}| < 0.50 at the 2 sigma level. Bounds from W decays are less stringent: |lambda'_{33k}| < 2.4 at 2 sigma, as a consequence of the weaker Fermilab experimental bounds on lepton universalit…
Linkage is demonstrated between the quark mass, quark condensate and coupling strength in the infrared limit of QCD and in the quark-level linear sigma model.
We calculate the one loop beta functions for nonlinear sigma models in four dimensions containing general two and four derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N \geq 4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2,3. In the approximation considered, the four derivative couplings are asymptotically free but the coupling in the two derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymp…
Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kaehler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U(1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted gamma_5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of …
We propose a new method that fixes the coupling to two photons of the recently found lightest QCD resonance, the sigma. This coupling provides crucial information for discriminating the yet unknown nature of this special state. Our method uses available data on the nucleon polarizabilities together with analyticity and unitarity. Taking into account all the uncertainties, our result is Gamma_{pole}= 1.2 +- 0.4 keV.
The lightest QCD resonance, the sigma, has been recently fixed in the pi-pi scattering amplitude. The nature of this state remains nowadays one of the most intriguing and difficult issues in particle physics. Its coupling to photons is crucial to discriminate its structure. We propose a new method that fixes this coupling using only available precise experimental data on the proton electromagnetic polarizabilities together with analyticity and unitarity. Taking into account the uncertainties in the analysis and in the parameter values, our result is Gamma_{pole}(sigma -> gamma gamma) = (1.2 +-…
A recent analysis of the LEP data shows an interesting deviation from lepton universality in W boson decays. An excess at the level of 2.8 sigma is found in the tau mode branching ratio with respect to the other two modes. It is suggested that this seeming lepton non-universality might stem from pair production of charged Higgs bosons almost degenerate with W, that preferentially decay to heavy fermions. It is shown that the deviation can be reduced to 1.4 sigma in two Higgs doublet model I without any conflict with the existing direct or indirect constraints. This conclusion is largely indepe…
Topological and self-dual vortices in a double sigma model with Maxwell coupling
本文研究了双O(3)-σ模型与Maxwell场耦合下的自对偶磁漩涡存在性，揭示了两种σ场属于同一拓扑sector，势能呈余弦型，并通过数值验证了BPS结构的一致性与渐进行为。
The coupling constants G_(K N Lambda) and G_(K N Sigma) are obtained from the Goldberger-Treiman relation in the strange channel with chiral symmetry breaking taken into account. The results, G_(K N Lambda)=-12.3+-1.2 and G_(K N Sigma)=5.5+-.5 come close to the SU(3) values.
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 calculate the CP-violating polarization asymmetry of tt-bar, delta =[ sigma(ee-bar --> t(-)t-bar(-))-sigma(ee-bar --> t(+)t-bar(+)) ]/ sigma(ee-bar --> tt-bar), for the most general tt-bar gamma/Z couplings without dropping any non-standard contribution. We find that one term which is usually neglected increases with s and will eventually become non-negligible at very high energy.
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…
We consider the existence of the state X^0 (214 MeV) in Sigma^+ -> p mu^+ mu^- decay found by the HyperCP collaboration. We assume that a fundamental spin zero boson X^0 coupled to quarks leads to flavor changing s -> d X^0 process. We estimate the scalar and pseudoscalar coupling constants by considering Sigma^+ -> p X^0 and K^+ -> pi^+ X^0 processes, and find that pseudoscalar coupling dominates. We then evaluate the branching ratios for K_L -> pi^0 pi^0 X^0, pi^+ pi^- X^0 and Omega^- -> Xi^- X^0 decays. All these rates are found to be in the measurable ranges. We also comment on X^0 couplin…
Top pair production at LHC is the ideal place to search for nonstandard Wtb couplings in t -> W b -> l nu b decays. The lb forward-backward asymmetry in the W rest frame is very sensitive to sigma_{mu nu} couplings, and can spot one-loop QCD corrections to the decay vertex with more than 5 sigma statistical significance. We discuss the potential of this asymmetry to signal nonstandard gamma_mu and sigma_{mu nu} couplings and compare with top-antitop spin correlation asymmetries, which have a lower sensitivity. We also briefly summarise the results for Tevatron.
We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi…
In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs,at one loop level,on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use o…
Coupling of `t Hooft's determinant term is investigated in the framework of the three flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field dependent correction to the coupling of the conventional U_A(1) breaking determinant term. It is found that at low temperatures mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid-gas transition.
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 determine the next-to-leading logarithmic (NLL) QCD corrections to the cross section sigma(e+e- to t bar t H) for center-of-mass energies up to 500 GeV. The dynamics is dominated by nonrelativistic effects, and the summation of terms singular in the relative t bar t velocity is mandatory to all orders in the strong coupling constant alpha_s using an effective theory. The summations lead to an enhancement of the tree level predictions by about a factor of two and are important for the determination of the top Yukawa coupling. We also study the impact of polarization of the electron-positron …
We consider the renormalization group(RG) improved inflaton potential in unitarized Higgs inflation where the original Higgs inflation is unitarized by the addition of a real singlet scalar of sigma-model type. The sigma field coupling to the Higgs, which is introduced to reproduce a large non-minimal coupling of the Higgs below the sigma scalar threshold, also improves the Standard Model vacuum stability due to the RG running. Furthermore, the same sigma field coupling determines the reheating temperature or the number of efoldings. Considering the uncertainties in the number of efoldings in …
We study the potential to use measurements of extra neutral gauge bosons (Z') properties in pp collisions at the Large Hadron Collider to unravel the underlying physics. We focus on the usefulness of third generation final states (tau, b, t) in distinguishing between models with non-universal Z'-fermion couplings. We present an update of discovery limits of Z's including the 2010-2011 LHC run and include models with non-universal couplings. We show how ratios of sigma(pp -> Z' -> ttbar), sigma(pp -> Z' -> bbbar), and sigma(pp -> Z' -> tau^+tau^-) to sigma(pp -> Z' -> mu^+mu^-) can be used to d…
We briefly review the nonlinear sigma model approach for the subject of increasing interest: "two-step" phase transitions in the Gross-Neveu and the modified Nambu-Jona-Lasinio models at low $N$ and condensation from pseudogap phase in strong-coupling superconductors. Recent success in describing "Bose-type" superconductors that possess two characterstic temperatures and a pseudogap above $T_c$ is the development approximately comparable with the BCS theory. One can expect that it should have influence on high-energy physics, similar to impact of the BCS theory on this subject. Although first …
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