Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the critical temperature.
We study the effects of CP violation on the nature of the chiral transition within the linear sigma model with two flavors of quarks. The finite-temperature effective potential containing contributions from nontrivial values for the parameter $θ$ is computed to one loop order and their minima structure is analyzed. Motivated by the possibility of observing the formation of CP-odd domains in high-energy heavy ion collisions, we also investigate the behavior of the effective potential in the presence of a strong magnetic background. We find that the nature of the chiral transition is influenced …
We show a general form of neutrino mass matrix (M), whose matrix elements are denoted by M_{ij} (i.j=e, mu, tau) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of M_{mu mu}, M_{tau tau} and M_{mu tau}+sigma M_{ee} (sigma =\pm 1) turn out to be completely determined by M_{e mu} and M_{e tau} for given mixing angles. The appearance of CP violation is found to originate from the interference between the mu-tau symmetric part of M and its breaking part. If |M_{e mu}|=|M_{e tau}|, giving either M_{e mu}=-sigma e^{i theta} M_{e…
We investigate the consequences of replacing the continuous flavour symmetry of minimal flavour violation by a discrete group. Goldstone bosons, resulting from the breaking of the continuous flavour symmetry, generically lead to bounds on new flavour structure by many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitutes the primary motivation of our work. The four crystal-like groups Sigma(168), Sigma(72phi), Sigma(216phi) and Sigma(360phi)$ provide enough protection for a discrete TeV-scale MFV scenario in the case where Delta F = 2 proc…
On general grounds based on quantum field theory the decay amplitude for $Σ^0 \to Λγ$ consists of a parity conserving magnetic and a parity violating electric dipole transition moment. Because of the subsequent self-analyzing weak decay of the $Λ$ hyperon the interference between magnetic and electric dipole transition moment leads to an asymmetry in the angular distribution. Comparing the decay distributions for the $Σ^0$ hyperon and its antiparticle gives access to possible C and CP violation. Based on flavor SU(3) symmetry the present upper limit on the neutron electric dipole moment can be…
Expecting the forthcoming experiment at the upgraded Fermilab Tevatron, we calculated CP-violating polarization asymmetry of t t-bar, A_{CP}= [sigma(p p-bar --> t(-) t-bar(-) X) - sigma(p p-bar --> t(+) t-bar(+) X)]/ sigma(p p-bar --> t t-bar X), due to possible anomalous chromomagnetic (kappa) and chromoelectric (tilde{kappa}) couplings of the gluon to the top quark. Since kappa and tilde{kappa} are sensitive to a contribution from new physics beyond standard model, this observable is useful to search for a signal of new physics. It was seen that the magnitude of A_{CP} depends only on Im(til…
We investigate the consequences of replacing the global flavour symmetry of Minimal Flavour Violation (MFV) SU(3)_QxSU(3)_UxSU(3)_Dx..., by a discrete D_QxD_UxD_Dx.. symmetry. Goldstone bosons resulting from the breaking of the flavour symmetry generically lead to bounds on new flavour structure many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitute the \emph{primary} motivation of our work. Less symmetry implies further invariants and renders the mass flavour basis transformation observable in principle and calls for a hierarchy in the…
We study genuine CP-odd observables at the LHC to test the CP property of the ZZH interaction for a Higgs boson with mass below the threshold to a pair of gauge bosons via the process p,p -> Z,H -> l+,l-,b,bbar. We illustrate the analysis by including a CP-odd ZZH coupling, and show how to extract the CP asymmetries in the signal events. After selective kinematical cuts to suppress the SM backgrounds plus an optimal Log-likelihood analysis, we find that, with a CP violating coupling btilde = 0.25, a CP asymmetry may be established at a 3 sigma (5 sigma) level with an integrated luminosity of a…
We reconstruct the neutrino mass matrix in the flavor basis, using all available experimental data on neutrino oscillations. Majorana nature of neutrinos, normal mass hierarchy (ordering) and validity of the LMA MSW solution of the solar neutrino problem are assumed. We study dependences of the mass matrix elements, m_{alpha beta}, on the CP violating Dirac, delta, and Majorana, rho, sigma, phases, for different values of the mixing angle theta_{13} and of the absolute mass scale, m_1. The contours of constant mass in the rho-sigma plane have been constructed for all m_{alpha beta}. These rho-…
My recent fit of the light scalar mesons is discussed in the light of the U3 x U3 linear sigma model. The argument for why there exists a light and broad sigma meson is explained in more detail, and the mechanism of spontaneous symmetry breaking is discussed.
We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu-Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the c…
I present the status of the elements and parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and summarise the related theoretical progress since "Lepton-Photon 2003". One finds |V_{us}| = 0.2227 +/- 0.0017 from K and tau decays and |V_{cb}| = (41.6 +/- 0.5) * 10^{-3} from inclusive semileptonic B decays. The unitarity triangle can now be determined from tree-level quantities alone and the result agrees well with the global fit including flavour-changing neutral current (FCNC) processes, which are sensitive to new physics. From the global fit one finds the three CKM angles theta_{12}=12.9…
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.
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.
The spatial momentum dependence of the spectral function for pi and sigma at finite temperature is studied by employing the O(4) linear sigma model and adopting a resummation technique called optimized perturbation theory (OPT).
Recent data from long-baseline neutrino oscillation experiments have provided new information on θ_{13}, hinting that 0.01\lesssim sin^2 2θ_{13} \lesssim 0.1 at 2 sigma C.L. Confirmation of this result with high significance will have a crucial impact on the optimization of the future long-baseline oscillation experiments designed to probe the neutrino mass ordering and leptonic CP violation. In this context, we expound in detail the physics reach of an experimental setup where neutrinos produced in a conventional wide-band beam facility at CERN are observed in a proposed Giant Liquid Argon de…
We discuss an Nf=3 linear sigma model with vector and axial-vector mesons (extended Linear Sigma Model - eLSM). We present first results regarding the masses of axial-vector mesons determined from the extended model.
The lightest scalar and pseudoscalar nonets are discussed within the [A framework of the broken old UxU3 linear sigma model, and it is shown that already at the tree level this model works remarkably well predicting scalar masses and couplings not far from present experimental values, when all parameters are fixed from the pseudoscalar masses and decay constants. The linear sigma model is the simplest way to implement chiral symmetry together with the broken SU3 of the quark model, and this, not well known, success in understanding experiment is comparable to that of the naive quark model for …
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.
We show that therecently observed pion invariant mass distribution of the phi ->pi0 pi0 gamma decay can be satisfactorily described by the chiral U(3) X U(3) Linear Sigma Model.
Soft-photon emission rates are calculated within the linear sigma model. The investigation is aimed at answering the question to which extent the emissivities map out the phase structure of this particular effective model of strongly interacting matter.
The recent measurement of the like-sign dimuon charge asymmetry in semileptonic b-hadron decays by the D0 Collaboration is about 3 sigmas away from the standard-model prediction, hinting at the presence of CP-violating new physics in the mixing of B_s mesons. We consider the possibility that this anomalous result arises from the contribution of a light spin-1 particle. Taking into account various experimental constraints, we find that the effect of such a particle with mass below the b-quark mass can yield a prediction consistent with the anomalous D0 measurement within its one-sigma range.
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.
We have investigated the phase transition and disoriented chiral condensate domain formation in linear sigma model. Solving the equation of motion for the sigma model fields in contact with a heat bath, we have shown that the fields undergo phase transition above a certain critical temperature(T_c). It was also shown that when the fields thermalised at temperature above T_c are cooled down sufficiently rapidly, disoriented chiral condensate domains are formed quite late in the evolution.
We consider techniques (based on an ultraviolet cutoff) used to prove that the pure boson ($ϕ^4)_4$ field theory is trivial and apply them instead to the dynamically generated quark-level linear sigma model. This cutoff approach leads to the conclusion that the latter field theory is in fact nontrivial.
We study the BRST symmetries in the SU(3) linear sigma model which is constructed through introduction of a novel matrix for the Goldstone boson fields satisfying geometrical constraints embedded in SU(2) subgroup. To treat these constraints we exploit the improved Dirac quantization scheme. We also discuss phenomenological aspacts in the mean field approach to this model.
We study the chiral symmetry structure in a linear sigma model with fermions in the presence of an external, uniform magnetic field in the 'effective potential' approach at the one loop level. We also study the chiral phase transition as a function of density in the core of magnetized neutron stars.
We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term are recovered. We calculate the coefficient of the next to leading term and investigate the spectrum beyond the low energy regime.
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.
The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall-Jackiw-Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The BEC is discussed in chiral limit and non-chiral limit at Hartree approximation and also at large N approximation.
The nucleon sigma term of the isoscalar and isovector quark chromo-magnetic dipole moments are essential inputs for the determination of the CP-odd pion-nucleon couplings induced by quark chromo-electric dipole moments. We demonstrate that the former can be mapped to the third moment of the nucleon twist-three chiral-odd distribution functions $e^q(x)$ which are in principle measurable in semi-inclusive deep inelastic scattering processes. We perform a survey on existing model calculations as well as experimental data on $e^u(x)+e^d(x)$ and derive a predicted range for the isoscalar chromo-mag…
We have attempted an approach to the chiral phase transition of QCD using the linear sigma model as an effective theory. In order to get some insight into how the phase transition could proceed, we have calculated the finite temperature effective potential of this model in the Hartree and large N approximations using the Cornwall-Jackiw-Tomboulis formalism of composite operators.
A self-consistent strategy to complete the dynamical generation of Quark-Level-Linear-Sigma-Model-like Lagrangean theories beyond one loop as proposed in more detail in our manuscript arXiv:0802.1540 [hep-ph] is shortly outlined.
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.
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.
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 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.
In this letter we explore the temperature and isospin chemical potential ($μ_I$) dependence of the vacuum structure and the meson masses in the linear sigma model, at the one loop level. The sigma meson mass grows steadily with temperature. This behavior does not agree with previous mean field calculations. For the pion our results show the same behavior as the mean field approach. The stability of the vacuum has a very soft dependence on $μ_I$ since this is a second order effect in the tadpole diagrams.
We construct the electromagnetic anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four quark content. We compute in the leading order of this framework the decays into two photons of six pseudoscalars: $π_0(137)$, $π_0(1300)$, $η(547)$, $η(958)$, $η(1295)$ and $η(1760)$. Our results agree well with the available experimental data.
The linear sigma model with broken U3xU3 is compared with data on the lightest scalar and pseudoscalar mesons. When 5 of the 6 parameters are fixed by the pseudoscalar masses and decay constants one finds that, already at the tree level, a reasonable description for the 4 scalar masses, mixing and up to 8 tri-linear couplings of lightest scalars, taken as a0(980), f0(980), sigma(500) and K*0(1430). This clearly indicates that these scalars are the chiral partners of the pi, eta, eta', K and strongly suggests that they like the latter are (unitarized) quark-antiquark states.
We study the QCD phase diagram using the linear sigma model coupled to quarks. We compute the effective potential at finite temperature and quark chemical potential up to ring diagrams contribution. We show that, provided the values for the pseudo-critical temperature $T_c = 155$ MeV and critical baryon chemical potential $μ_{Bc} \simeq 1$ GeV, together with the vacuum sigma and pion masses. The model couplings can be fixed and that these in turn help to locate the region where the crossover transition line becomes first order.
Recently two hints for new physics have emerged: The B_s mixing phase phi_s and the rate of D_s -> (mu,tau) nu exposing a discrepancy of \sim 3 sigma and 3.8 sigma deviation from the Standard Model respectively. Moreover the difference of the CP asymmetries in B -> K pi between the charged and neutral modes is at the 5.3 sigma level which is somewhat larger than expected. New physics in phi_s or A_CP(B -> K pi) would be in contradiction with the minimal flavour violation hypothesis. The latter has recently attracted attention because of the absence of deviation in CP and flavour violation in t…
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.
As is well known, one can arrange the parameters of the O(N) non-linear sigma model to reproduce the low energy S-matrix elements of the renormalizable O(N) linear sigma model. In this note we provide details which are necessary in order to obtain the off-shell equivalence between the two theories.
We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the $R^2$ term and the tracker…
A simple approximate treatment of statistical equilibrium is developed within the linear sigma sigma model by means of the Hartree factorization technique, providing a simple means for sampling initial configurations of the chiral field. These are then subjected to pseudo-expansions and their non-equilibrium relaxation towards the normal vacuum is studied.
We discuss the phenomenology of the axial-vector mesons within a three-flavour Linear Sigma Model containing scalar, pseudoscalar, vector and axial-vector degrees of freedom.
We have investigated the phase transition properties of classical linear sigma model. The fields were kept in contact with a heat bath for sufficiently long time such that fields are equilibrated at the temperature of the heat bath. It was shown that the sigma model fields undergoes phase transition, but the transition temperature depend crucially on the lattice spacing. In the continuum limit, the transition temperature tends to zero or at least to a very low value.
Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint H_{}^2=\pm M^2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity theory, which mimics linearized general relativity in Minkowski space-time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Loren…
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…
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.
We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.
We outline the extension of the globally chirally invariant Nf = 2 linear sigma model with vector and axial-vector degrees of freedom to Nf=3. We present preliminary results concerning the scalar meson masses.
A symmetry conserving, non-perturbative treatment based on a variational squeezed vacuum state in conjunction with a well-defined class of RPA fluctuations is applied to the SU(3) linear-sigma-model. It is shown that the Goldstone theorem holds exactly both at zero and finite temperature. The approach represents a systematic procedure which avoids problems of the Gaussian Functional with the symmetries.
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…
It is well-known that the standard BCFW construction cannot be used for on-shell amplitudes in effective field theories due to bad behavior for large shifts. We show how to solve this problem in the case of the SU(N) non-linear sigma model, i.e. non-renormalizable model with infinite number of interaction vertices, using scaling properties of the semi-on-shell currents, and we present new on-shell recursion relations for all on-shell tree-level amplitudes in this theory.
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses.
The finite-temperature effective potential of the O(N) linear σmodel is studied, with emphasis on the implications for the investigation of hot hadron dynamics. The contributions from all the ``bubble diagrams'' are fully taken into account for arbitrary N; this also allows to address some long-standing issues concerning the use of non-perturbative approaches in (finite-temperature) field theory.
