We propose to measure the $τ^-\to K_1^-ν_τ\to (K^-ω) ν_τ\to (K^- π^+π^-π^0)ν_τ$ decay in order to determine the $K_1$ axial vector mixing angle $θ_{K_1}$. We derive, for the first time, the differential decay rate formula for this decay mode. Using the obtained result, we perform a sensitivity study for the Belle (II) experiment. We will show that the $K^-π^+π^-π^0$ spectrum of the $τ^-\to K_1^-ν_τ\to (K^-ω) ν_τ\to (K^- π^+π^-π^0)ν_τ$ decay can discriminate the two solutions $θ_{K_1}=\sim 30^{\circ}$ or $\sim 60^{\circ}$ observed in the other measurements.
The dispersive approach to QCD, which properly embodies the intrinsically nonperturbative constraints originating in the kinematic restrictions on relevant physical processes and extends the applicability range of perturbation theory towards the infrared domain, is briefly overviewed. The study of OPAL (update 2012) and ALEPH (update 2014) experimental data on inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach is presented.
The dispersive approach to QCD, which extends the applicability range of perturbation theory towards the infrared domain, is developed. This approach properly accounts for the intrinsically nonperturbative constraints, which originate in the low-energy kinematic restrictions on pertinent strong interaction processes. The dispersive approach proves to be capable of describing OPAL (update 2012) and ALEPH (update 2014) experimental data on inclusive tau lepton hadronic decay in vector and axial-vector channels in a self-consistent way.
Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an axial-vector meson are studied. The charm to axial-vector meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole momentum dependence of the $D\to K$ transition form factor and the presence of a sizable long-distance $W$-exchange are the two key ingredients for understanding the data of $D\to \bar Ka_1$. The $K_{1A}-K_{1B}$ mixing angle of the strange axial-vector mesons is found to be $\approx \pm37^\circ$ or $\pm58^\circ$ from $τ\to K_1ν_τ$ decays. The study of $D\to K_1(1270)π…
We discuss the importance of the axialvector meson in chiral phase transition at finite temperature. We show that there exists a significant contribution in the vector spectral function from the axialvector meson through the vector-axialvector mixing in hot matter.
The high statistics COMPASS results on diffractive dissociation $πN \rightarrow πππN$ suggest that the isospin $I=1$ spin-parity $J^{PC}= 1^{++}$ $a_1(1260)$ resonance could be split into two states: $a_1(1260)$ decaying into an S-wave $ρπ$ system, and $a_1^\prime(1420)$ decaying into a P-wave $f_0(980)π$ system. We analyse the reaction by incorporating our previous treatment of resonant re-scattering corrections in the Drell-Deck forward production process. Our results show that the COMPASS results are fully consistent with the existence of a single axial-vector $a_1$ resonance. The character…
In this work we study the axial contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment using the framework of resonance chiral theory. As a result, we obtain $a_μ^{\textrm{HLbL};A} = \left(0.8^{+3.5}_{-0.1}\right)\cdot 10^{-11}$, that might suggest a smaller value than most recent calculations, underlining the need of future work along this direction. In particular, we find that our results depend critically on the asymptotic behavior of the form factors, and as such, emphasizes the relevance of future experiments for large photon virtualities. In addition, we…
We calculate the effects of finite density of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector $\left( D^{\ast}, D_{s}^{\ast}, B^{\ast}, B_{s}^{\ast}\right)$ and axial-vector $\left( D_{1}, D_{1s}, B_{1}, B_{1s}\right)$ mesons using chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift of decay constant of above vector and axial vector mesons. In QCD sum rule approach the properties e.g. masses and decay constants of vector and axial vector mesons are written in terms of …
Various phenomenological studies indicate that the mixing angle $θ_{K_1}$ of $K_{1A}$ and $K_{1B}$, the strange partners of the axial-vector mesons $a_1(1260)$ and $b_1(1235)$, respectively, lies in the vicinity of $35^\circ$ or $55^\circ$, but whether this angle is larger or smaller than $45^\circ$ still remains controversial. When the $f_1(1285)$-$f_1(1420)$ mixing angle $θ_{^3P_1}$ and the $h_1(1170)$-$h_1(1380)$ mixing angle $θ_{^1P_1}$ are determined from the mass relations, they depend on the masses of $K_{1A}$ and $K_{1B}$, which in turn depend on the mixing angle $θ_{K_1}$. We show tha…
We calculate the effects of finite density and temperature of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector $\left( D^{\ast}, D_{s}^{\ast}, B^{\ast}, B_{s}^{\ast}\right)$ and axial-vector $\left( D_{1}, D_{1s}, B_{1}, B_{1s}\right)$ mesons, using chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift in decay constant of above vector and axial-vector mesons. In QCD sum rule approach, the properties, e.g., the masses and decay constants of vector and axial-vector mesons …
We investigate what can be learnt about the $η$ -$η'$ mixing by means of dispersive representation of axial anomaly. We show that our method leads to the strong bounds for the $η-η'$ mixing angle: $θ= -15.3^o \pm 1^o$. Moreover, our result manifests also a dramatic dependence of the width $Γ_{η\to 2γ}$ on the mixing angle $θ$. This property explains how the relatively small mixing strongly effects the decay width.
We study the manifestations of chiral symmetry restoration which have a significance for the parity mixing. Restricting to pions and nucleons we establish a formalism for the expression of the vector correlator, which displays the mixing of the axial correlator into the vector one and unifies the cases of the heat bath and the dense medium. We give examples of mixing cross-sections. We also establish a link between the energy integrated mixing cross-sections and the pion scalar density which governs the quenching factors of coupling constants, such as the pion decay one, as well as the quark c…
Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that …
The new BES measurement on the two-body decays of J/psi and psi' into an axial-vector meson and a pseudoscalar meson is analyzed with the axial-K mixing including the one-photon annihilation contribution. A somewhat puzzling pattern of the K_1^+ K^- decay channels can be understood with no tight constraint on the mixing angle. The branching fractions of the K_1^0 K-bar^0 channels will be the cleanest source of information to determine the mixing angle from the 1^+ 0^- decays of J/psi and psi'.
It is shown that the QCD anomaly may lead to an abnormal mixing behavior of the axial vector mesons similar to the pseudoscalar mesons. These mixing effects, involving a gluonic axial vector state, generate a non-vanishing strange quark component in the nucleon. They reduce the matrix element of the singlet axial vector in comparison to the value obtained in a naive quark model. The results are in agreement with the data obtained in the polarized lepton-nucleon scattering experiments.
In a nonrelativistic constituent quark model we find a constraint on the mixing angle of the strange axial-vector mesons, $35^o\stackrel{<}{\sim } θ_K\stackrel{<}{\sim }55^o,$ determined solely by two parameters: the mass difference of the $a_1$ and $b_1$ mesons and the ratio of the constituent quark masses.
We investigate meson and nucleon dynamics at finite baryon density and temperature by coupling the nucleon field and the omega meson to the three-flavor linear sigma model and calculate hadronic properties around the nuclear liquid-gas transition. We apply the functional renormalization group method, and find that mesonic fluctuations increase the strength of the coefficient of the $U_A(1)$ breaking determinant operator as a function of the chiral condensate. As a consequence, we find that the actual value of the anomaly increases discontinuously at the first order nuclear liquid-gas transitio…
In this work the analysis of mixing parameters of the system involving eta, eta' mesons and some third massive state G is carried out. We use the generalized mixing scheme with three angles. The framework of the dispersive approach to Abelian axial anomaly of isoscalar non-singlet current and the analysis of experimental data of charmonium radiative decays ratio allow us to get a number of quite strict constraints for the mixing parameters. The analysis shows that the equal values of axial current coupling constants f_8 and f_0 are preferable which may be considered as a manifestation of SU(3)…
In this write-up we summarize main results of our recent analyses on the mixing between transverse rho and a1 mesons in hot and/or dense matter. We show that the axial-vector meson contributes significantly to the vector spectral function in hot matter through the mixing. In dense baryonic matter, we include a mixing through a set of omega rho a1 -type interactions. We show that a clear enhancement of the vector spectral function appears below \sqrt{s}=m_ρfor small three-momenta of the rho meson, and thus the vector spectrum exhibits broadening.
We study mixing between conventional and hybrid mesons in vector and axial vector charmonium using QCD Laplace sum-rules. We compute meson-hybrid cross correlators within the operator product expansion, taking into account condensate contributions up to and including those of dimension-six as well as composite operator renormalization-induced diagrams. Using measured masses of charmonium-like states as input, we probe known resonances for nonzero coupling to both conventional and hybrid meson currents, a signal for meson-hybrid mixing.
It is shown that the diagonalization of the axial-vector -- pseudoscalar transitions in the effective meson Lagrangian in presence of electromagnetic interactions leads to a deviation from the vector meson dominance picture which usually arises in the Nambu - Jona-Lasinio model. The essential features of such modification of the theory are studied. Some important examples are considered in detail.
We suggest a rigorous generalization of the pseudoscalar mesons mixing description in SU(3) basis. It is shown that the appearance of extra massive state nicknamed in the paper as glueball is unavoidable in any scheme with more than one angle. In this framework we develop the dispersive approach to Abelian axial anomaly of isoscalar non-singlet current. Combining it with the analysis of experimental data of charmonium radiative decays ratio we get the number of quite strict constraints for mixing parameters. Our analysis favors the equal values of axial currents coupling constants which may be…
We discuss pure $q\bar{q}$ axial-vector mesons in the Tamm-Dancoff approximation of the Coulomb-gauge QCD model from NCSU. While recent studies have put emphasis in configuration mixing with open meson-meson channels, we here concentrate on the simpler closed-channel problem and follow the $1^+$ mixing through a wide range of quark masses. We also examine their radial excitations and discuss with them the concept of insensitivity to chiral symmetry breaking.
The effects of SU(3) symmetry breaking and configuration mixing have been investigated for the weak vector and axial-vector form factors in the chiral constituent quark model (χCQM) for the strangeness changing as well as strangeness conserving semi-leptonic octet baryon decays in the nonperturbative regime. The results are in good agreement with existing experimental data and also show improvement over other phenomenological models.
A model of diffractive neutrino scattering is formulated in terms of the chiral hadronic current which is conserved in the limit of vanishing pion mass. This current has the correct singularity structure and, naturally, does not lead to contradictions with a partial conservation of the axial current (PCAC). In that respect we differ from earlier work in the literature, where a breakdown of PCAC had been reported. We show that such a breakdown of PCAC is an artifact of the hadronic current non-conservation in the model developed there.
The axial-vector emitting weak hadronic decays of $Ω_c^0$ baryon are investigated. After employing the factorization and the pole model framework to predict their branching ratios, we derive the symmetry breaking effects on axial-vector-meson-baryon couplings and effects of flavor dependence on baryon-baryon weak transition amplitudes and, consequently, on their branching ratios. We found that the W-exchange process contributions dominate $p$-wave meson emitting decays of $Ω_c^0$ baryon.
We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay $π^- \to l\,\barν_l$ and discuss the corresponding limits of strong and weak external magnetic fields.
The relation for transition form factors of eta and eta' mesons is obtained by combining the exact nonperturbative QCD sum rule, following from the dispersive representation of axial anomaly, and quark-hadron duality. It is valid at all virtual photon momenta and allows one to express the transition form factors entirely in terms of meson decay constants. This relation is in a good agreement with experimental data.
Interplay between axial anomaly and quark-hadron duality in the presence of strong mixing is considered. The anomaly sum rule for meson transition form factors based on the dispersive representation of axial anomaly and quark-hadron duality in octet channel is analyzed. The comparison of this sum rule to the experimental data on $η$ and $η'$ mesons transition form factors shows that the interval of duality in this channel is rather small, contradicting the usual understanding of quark-hadron duality. The same values of interval of duality are supported by considering the two-point correlator i…
In this write-up we summarize main result of our recent analysis on the mixing between transverse $ρ$ and $a_1$ mesons through a set of $ωρa_1$-type interactions in dense baryonic matter. In the analysis, we showed that a clear enhancement of the vector spectral function appears below $\sqrt{s}=m_ρ$ for small three-momenta of the $ρ$ meson, and thus the vector spectrum exhibits broadening.
I discuss new results on absolute branching ratios of charm mesons into specific exclusive final states, Cabibbo suppressed decay rates, inclusive decays to $s\bar{s}$ mesons, limits on D^0 anti-D^0 mixing, CP violation and T violation. Preliminary results from CLEO-c now dominate the world average absolute branching fractions. For the most important normalization modes involving D^0 and D^+, the averages are B(D^0 -> K^- pi^+ = (3.87 +/- 0.06)%, and B(D^+ -> K^- pi^+ pi^+)= (9.12 +/- 0.19)%. For the Ds^+ CLEO-c measures B(Ds+ -> K^- K^+ pi^+)=(4.54^{+0.44}_{-0.42} =/- 0.25)%. Using this rate,…
The implications of Chiral Quark Model with SU(3) and axial U(1) symmetry breakings as well as configuration mixing generated by one gluon exchange forces ($χ$QM$_{gcm}$) are discussed in context of proton flavor and spin structure as well as hyperon $β$-decay data. Apart from reproducing the success of $χ$QM with symmetry breaking, it is able to improve upon the agreement with data in several cases such as, $G_A/G_V, Δ_8, <A_1^p>$ dependent on spin polarization functions and ($\frac{2 \bar s}{u+d}$), ($\frac{2 \bar s}{\bar u+\bar d}$) and f_s involving the quark distribution functions.
The effect of mixing of the vector and axial vector correlation functions in the nuclear medium arising from the interaction of nuclear pions with corresponding interpolating currents is considered. It is shown that the mass difference between $ρ$ and $a_1$ meson gets smaller with the increase of the nuclear density reflecting the phenomena of partial restoration of chiral symmetry whereas the absolute values of meson masses may both decrease and increase in nuclear medium depending on the model used for the phenomenological spectral density.
Recently the concept of compositeness has been developed so as to distinguish whether interested hadrons are hadronic molecules or not. Here, in terms of compositeness, we investigate $\bar{K} N$ molecular structure of the $Λ(1405)$ resonance with the $Λ(1405)$ radiative decay and $K \bar{K}$ molecular structure of the $a_{0} (980)$ and $f_{0} (980)$ resonances with the $a_{0} (980)$-$f_{0} (980)$ mixing.
We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Fi…
The masses of the $K_1(^3P_1)$ and $K_1(^1P_1)$ are considered in a nonrelativistic constituent quark model, and the absolute value of the $K_1(^3P_1)-K_1(^1P_1)$ mixing angle is determined to be about $59.29^\circ$. Comparison of the theoretical predictions on the strong decay widths of the $K_1(1270)$ and $K_1(1400)$ in the $^3P_0$ decay model as well as the production ratio of these two states in the $τ$ decay between the available experimental data strongly favors that the $K_1(^3P_1)-K_1(^1P_1)$ mixing angle is about $+59.29^\circ$.
In this talk I report on the results of a recent calculation of the α_s corrections to a three-point correlation function at the three-loop level in QCD perturbation theory, which allows one to extract the matrix element of B^0 -\bar B^0 mixing with next-to-leading order accuracy. The evaluation of mixing parameter at NLO allows for a consistent analysis of B^0 -\bar B^0 mixing since the coefficient functions of the effective Hamiltonian for this process are known with the necessary accuracy.
The contribution of the hadronic continuum in the QCD sum rule calculation of the parameters entering in pseudoscalar meson mixing is evaluated by making use of simple integration kernels tailored in order to practically eliminate the contribution of the hadronic continuum. This approach avoids the arbitrariness and instability inherent to previous sum rule calculations. An independent evaluation of the mixed quark gluon condensate $\left\langle QGC\right\rangle =$$\left\langle g\bar{q}σ_{μν}\frac{λ^{a}}{2}G_{μν}^{a}q\right\rangle $ which enters in the calculation is presented as well as the c…
The presence of baryonic matter leads to the mixing between transverse $ρ$ and $a_1$ mesons through a set of $ωρa_1$-type interactions, which results in the modification to the dispersion relation. We show that a clear enhancement of the vector spectral function appears below $\sqrt{s}=m_ρ$ for small three-momenta of the $ρ$ meson, and thus the vector spectrum exhibits broadening. We also discuss its relevance to dilepton measurements.
It is found that in presence of electroweak interactions the gauge covariant diagonalization of the axial-vector -- pseudoscalar mixing in the effective meson Lagrangian leads to a deviation from the vector meson and the axial-vector meson dominance of the entire hadronic electroweak current. The essential features of such a modification of the theory are investigated in the framework of the extended Nambu-Jona-Lasinio model with explicit breaking of chiral $U(2) \times U(2)$ symmetry. The Schwinger-DeWitt method is used as a major tool in our study of the real part of the relevant effective a…
We use lattice QCD to calculate the B-mixing hadronic matrix elements for a basis of effective four-quark operators that spans the space of all possible contributions in, and beyond, the Standard Model. We present results for the SU(3)-breaking ratio and discuss our ongoing calculation of the mixing matrix elements, including the first calculation of the beyond the Standard Model matrix elements from unquenched lattice QCD.
The behavior of the vector Adler function at spacelike momenta is studied in the framework of a covariant chiral quark model with instanton-like quark-quark interaction. The model reproduces the Adler function and $V-A$ correlator extracted from the ALEPH and OPAL data on hadronic $τ$ lepton decays, transformed into the Euclidean domain via dispersion relations. The leading order contribution from hadronic part of the photon vacuum polarization to the anomalous magnetic moment of the muon, $a_μ^{\mathrm{hvp}(1)} $, is estimated.
Three-quark nucleon interpolating fields in QCD have well-defined SU_L(2) x SU_R(2) and U_A(1) chiral transformation properties. Mixing of the [(1,1/2) + (1/2,1)] chiral multiplet with one of [(1/2,0) + (0,1/2)] or [(0,1/2) + (1/2,0)] representation can be used to fit the isovector axial coupling g_A(1) and thus predict the isoscalar axial coupling g_A(0) of the nucleon, in reasonable agreement with experiment. We also use a chiral meson-baryon interaction to calculate the masses and one-pion-interaction terms of J=1/2 baryons belonging to the [(0,1/2) + (1/2,0)] and [(1,1/2) + (1/2,1)] chiral…
We study a chiral quark model of $π$, $σ$, $ρ$, and $a_1$ mesons in the large-$N_c$ limit. We show that the quadratic $a_1-π$ mixing can be set to zero at zero momentum, thus protecting the $g_{σππ}$ and $g_{ρππ}$ couplings from being contaminated by the corresponding vertices with one or both pions replaced by the axial-vector meson. We further require the chiral-quark Lagrangian to feature an approximate classical scale invariance, the latter being only broken by dimension-two mass terms, and that the longitudinal vector meson scattering amplitudes grow at most like $s$, where $\sqrt{s}$ is …
It is shown, that the correlators of vector and axial-vector currents at finite temperature T in order T^2 reduce to mixing of vacuum VV and AA correlators with universal mixing coefficient given by the parameter ε= T^2/6 F^2_π, unlike the claim in the recent paper by Mallik and Sarkar [1].
Long-distance contributions to the $D^0$-$\bar D^0$ mixing parameters $x$ and $y$ are evaluated using latest data on hadronic $D^0$ decays. In particular, we take on two-body $D \to PP$ and $VP$ decays to evaluate the contributions of two-body intermediate states because they account for $\sim 50%$ of hadronic $D^0$ decays. Use of the diagrammatic approach has been made to estimate yet-observed decay modes. We find that $y$ is of order a few $\times 10^{-3}$ and $x$ of order $10^{-3}$ from hadronic $PP$ and $VP$ modes. These are in good agreement with the latest direct measurement of $D^0$-$\b…
We study the vector-axialvector mixing in a hot medium and its evolution toward the chiral phase transition using different symmetry restoration scenarios based on the generalized hidden local symmetry framework. We show that the presence of the $a_1$ meson reduces the vector spectral function around $ρ$ meson mass and enhances it around $a_1$ meson mass. The coupling strength of $a_1$ to $ρ$ and $π$ vanishes at the critical temperature due to the degenerate $ρ$-$a_1$ masses. This feature holds rigorously in the chiral limit and still stays intact to good approximation for the physical pion ma…
The extraction of CKM-matrix-element information from hadronic B-decays generally suffers from discrete ambiguities, hampering the diagnosis of physics beyond the Standard Model. We show that a measurement of the rate asymmetry, which is CP-violating, in $B^{\pm}\toρ^{\pm}ρ^0(ω)\toρ^{\pm}π^+π^-$, where the invariant mass of the $π^+π^-$ pair is in the vicinity of the $ω$ resonance, can remove the mod($π$) uncertainty in $α\equiv arg [-V_{td} V_{tb}^\ast/(V_{ud}V_{ub}^\ast)]$ present in standard analyses.
Comparing the results of finite energy and Borel transformed sum rules for the difference of vector and axial vector current correlators we evaluate the instanton contributions to the $τ$ hadronic width. In contrast to an explicit theoretical calculation we find that the instanton contributions to the $τ$ hadronic width are much smaller than the standard nonperturbative corrections.
We study the decays of the lightest axial-vector and pseudovector mesons, interpreted as quark-antiquark states, into a vector and a pseudoscalar meson. We show that the quarkonium assignment delivers a good description of the decays and allows also to make further testable predictions. In the kaonic sector, the physical resonances $K_{1}(1270)$ and $K_{1}(1400)$ emerge as mixed objects of an axial vector state $K_{1,A}$ and a pseudovector state $K_{1,B}$. We determine the mixing angle as $\left\vert θ_{K}\right\vert=\left(33.6\pm4.3\right) ^{\circ}$, a value compatible with previous studies b…
The SM predictions for CP violating effects in D meson systems are highly suppressed at the per mill level. Therefore, any experimental evidence for a sizable CP violation in D0-D0bar mixing would unambiguously point towards a New Physics (NP) signal. Within supersymmetric scenarios, the popular alignment models can naturally account for large, non-standard effects in D0-D0bar mixing. We demonstrate that, within alignment models, detectable CP violating effects in D0-D0bar mixing would unambiguously imply a lower bound for the electric dipole moment (EDM) of hadronic systems, like the neutron …
We present the general ansatz, the energy density and the Chern-Simons charge for static axially symmetric configurations in the bosonic sector of the electroweak theory. Containing the sphaleron, the multisphalerons and the sphaleron-antisphaleron pair at finite mixing angle, the ansatz further allows the construction of the sphaleron and multisphaleron barriers and of the bisphalerons at finite mixing angle. We conjecture that further solutions exist.
In the Randall-Sundrum model, the radion-Higgs mixing is weakly suppressed by the effective electroweak scale. One of its novel features would be a sizable three-point vertex of KK graviton-Higgs-radion. We explored the potential of the Fermilab Tevatron and the CERN LHC in probing the radion-Higgs mixing via the associated production of the radion with the Higgs boson. The observation of the rare decay of the KK gravitons into a Higgs and a radion is then the direct and exclusive signal of the radion-Higgs mixing. We also studied all the partial decay widths of the KK gravitons in the presenc…
We present a systematic study of the vector--axial-vector mixing (V-A mixing) in the current correlation functions and its evolution with temperature within an effective field theory. The $a_1$-$ρ$-$π$ coupling vanishes at the critical temperature $T_c$ and thus the V-A mixing also vanishes. A remarkable observation is that even for finite $m_π$ the $ρ$ and $a_1$ meson masses are almost degenerate at $T_c$. The vanishing V-A mixing at $T_c$ stays approximately intact.
We investigate the correlations between the scalar meson configurations and Okuba-Zweig-Iizuka (OZI) rule violations in the hadronic decays of heavy quarkonia, e.g. $J/ψ$ and $Υ$, into isoscalar vector meson ($ϕ$ and $ω$) and scalar mesons ($f_0(1710)$, $f_0(1500)$, and $f_0(1370)$). It shows that the dramatic change of the values of the branching ratio fraction of $ϕf_0/ωf_0$ from low (e.g. in $J/ψ$ decays) to high energies (e.g. in $Υ$ decays) will not only test the glueball-$Q\bar{Q}$ mixings, but also provide important information about the mysterious OZI-rule violations within the scalars…
