We update our previous results for (pseudo-)scalar mesons at zero temperature and finite quark chemical potential and generalize the investigation to include (axial-)vector mesons. We determine bound-state properties such as meson masses and decay constants up to chemical potentials far in the first-order coexistence region. To extract the bound-states properties, we solve the Bethe-Salpeter equation and utilize Landau-gauge quark and gluon propagators obtained from a coupled set of (truncated) Dyson-Schwinger equations with N$_\textup{f}=2+1$ dynamical quark flavors at finite chemical potential and vanishing temperature. For multiple (pseudo-)scalar and (axial-)vector mesons, we observe constant masses and decay constants for chemical potentials up to the coexistence region of the first-order phase transition thus verifying explicitly the Silver-Blaze property of QCD. Inside the coexistence region the pion becomes more massive and its decay constants decrease, whereas corresponding quantities for the (axial-)vector mesons remain (almost) constant.
We study Cabibbo-Kobayashi-Maskawa (CKM) favored weak decays of Bc mesons in the Isgur-Scora-Grinstein-Wise (ISGW) quark model. We present a detailed analysis of the Bc meson decaying to a pseudoscalar meson (P) and an axial-vector meson (A). We also give the form factors involving transition in the ISGW II framework and consequently, predict the branching ratios of decays.
Two body nonleptonic weak decays of bottom mesons to a pseudoscalar meson and an axial-vector meson involving charmed states are studied using the non-relativistic quark model. We calculate the branching ratios of these decays by employing the factorization hypothesis. Obtained results are in good agreement with the existing experimental data. We also calculated the branching ratios in the light of heavy quark symmetry constraints and compared with the exiting theoretical analyses.
The magnetic and quadrupole moments of the vector and axial-vector mesons containing heavy quark are estimated within the light cone sum rules method. Our predictions on magnetic moments for the vector mesons are compared with the results obtained by other approaches.
The axial strange form factor $F^s_A$ of the nucleon is assumed to be dominated at low momentum transfer by the isoscalar axial vector mesons $f_1(1285)$ and $f_1(1420)$. The importance of the $a_0πN$-triangular vertex correction is demonstrated.
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 consider the thermal correlation functions of vector and axial-vector currents and evaluate corrections to the vector and axial-vector meson pole terms to one loop in chiral perturbation theory. As expected, the pole positions do not shift to leading order in temperature. But the residues decrease with temperature.
We evaluate the radiative decay into a pseudoscalar meson and a photon of the whole set of the axial-vector mesons dynamically generated from the vector-pseudoscalar meson ($VP$) interaction. We take into account tree level and loop diagrams coming from the axial-vector decay into a vector and a pseudoscalar meson. We find a large span for the values of the radiative widths of the different axial-vector mesons. In particular, we evaluate the radiative decay into $K γ$ of the two $K_1(1270)$ states, recently claimed theoretically, and discuss the experimental values quoted so far on the assumpt…
A review of effective chiral theory of pseudoscalar, vector, and axial vector mesons is presented. 10 coefficients of the ChPT are predicted. A new symmetry breaking-axial-vector symmetry breaking is found and applied to EW theory. The masses of W and Z are dynamically generated and in agreement with data.
We investigate the weak decays of $B_c$ mesons in Cabibbo-Kobayashi-Maskawa favored and suppressed modes. We present a detailed analysis of the $B_c$ meson decaying to vector meson (V) and axial-vector meson (A) in the final state. We also give the form factors involving $B_c \to A$ transition in the Isgur-Scora-Grinstein-Wise II framework and consequently, predict the branching ratios of $B_c \to V A$ and $AA$ decays.
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.
A quarkonium-gluonium mixing scheme previously developed to describe the characteristic of the pseudoscalar mesons is applied to axial and tensor mesons. The parameters of the model are determined by fitting the eigenvalues of a mass matrix. The corresponding eigenvectors give the proportion of light quarks, strange quarks and glueball in each meson. However the predictions of the model for branching ratios and electromagnetic decays are incompatible with the experimental results. These results suggest the absence of gluonic components in the states of axial and tensor isosinglet mesons analyz…
Recent advances in the development of a chiral linear $σ$-model with (axial-)vector mesons are presented. The model is based on the basic requirements of global chiral symmetry and dilatation invariance. The role of (axial-)vector states turns out to be crucial both in the meson and the baryon sectors. First results at nonzero temperature and density are discussed.
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.
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.
We propose a phenomenological Lagrangian for the decay of the SU(3) nonets of the axial-vector mesons of $J^{PC}=1^{+-},1^{++}$ into a vector meson and a pseudoscalar constructed with tensor fields for the vector and axial-vector mesons. The formulation leads to a good reproduction of the different decay branching ratios and assuming vector meson dominance (VMD) it also leads to good results for the radiative decay of the $a_1$ into pion and photon, and in agreement with the structure proposed in the chiral tensor formulation of radiative decay of axial-vector mesons. The two SU(3) parameters …
While the ground-state tensor ($J^{PC}=2^{++}$) mesons $a_{2}(1320)$, $K_{2}^{\ast}(1430)$, $f_{2}(1270)$, and $f_{2}^{\prime}(1525)$ are well known experimentally and form an almost ideal nonet of quark-antiquark states, their chiral partners, the ground-states axial-tensor ($J^{PC}=2^{--}$) mesons are poorly settled: only the kaonic member $K_2(1820)$ of the nonet has been experimentally found, whereas the isovector state $ρ_2$ and two isoscalar states $ω_2$ and $ϕ_2$ are still missing. Here, we study masses, strong, and radiative decays of tensor and axial-tensor mesons within a chiral mode…
Mass splitting between axial and vector $\bar{Q}q$ mesons is considered within the standard QCD sum rules. In agreement with the first experimental data on the $B_1$ meson ($J^P =1^{+}$) we find that the splitting for B is about the same as for D and show that $1/m_Q$ corrections to the meson masses are small.
In this work, the mass spectrum of the first radial excitation axial vector meson nonet is considered in the framework of the nonrelativistic constituent quark model and Regge phenomenology. After that, we investigate the strong decay characteristics of these states within the $^{3}P_{0}$ model. The results are compared to values from other phenomenological models, and they may be beneficial in the prospective search for $2^{3}P_{1}$ meson nonets.
The first radial excitations of axial-vector mesons are considered in the framework of the extended $U(3)\times U(3)$ Nambu--Jona-Lasinio model. We calculate the mass spectrum of $a_1$, $f_1$, and also strange axial-vector mesons. For description of radially excited states we used the form factors of polynomial type of the second order in transverse quark momentum. For the ground- and the excited-state mesons consisting of light quarks we have calculated the widths of a number of strong and radiative decays. We got satisfactory agreement with experimental data for the ground states. A set of p…
We investigate the effects of (axial)vector mesons on the chiral phase transition in the framework of an SU(3), (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops. We determine the parameters of the Lagrangian at zero temperature in a hybrid approach, where we treat the mesons at tree-level, while the constituent quarks at 1-loop level. We assume two nonzero scalar condensates and together with the Polyakov-loop variables we determine their temperature dependence according to the 1-loop level field equations.
A general expression of the axial-vector current is presented, in which both the effects of the chiral symmetry breaking and the spontaneous chiral symmetry breaking are included. A new resonance formula of the axial-vector meson is derived and in the limit of $q^{2}\rightarrow 0$ this formula doesn't go back to the ``chiral limit``. The studies show that the dominance of the axial-vector meson is associated with the satisfaction of PCAC. The dominance of pion exchange is companied by the strong anomaly of PCAC.
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'.
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.
The radiative decay of the axial-vector resonances into a pseudoscalar meson and a photon is studied using the vector meson Lagrangian obtained from the hidden gauge symmetry (HGS) formalism. The formalism is well suited to study this problem since it deals with pseudoscalar and vector mesons in a unified way, respecting chiral invariance. We show explicitly the gauge invariance of the set of diagrams that appear in the approach and evaluate the radiative decay width of the a1(1260) and b1(1235) axial vector meson resonances into pi gamma. We also include the contribution of loops involving an…
In the covariant level-classification scheme of hadrons proposed recently, the existence of "chiral particles", scalar and axial-vector mesons as the partners of the ground-state pseudo-scalar and vector mesons, respectively, were predicted in the D and B meson systems, realizing a linear representation of chiral symmetry. In this work we reanalyze the D* pi mass spectra obtained through the Upsilon (4S) and Z0 decays to show a possibility for the D_1chi.
By describing within the chiral unitary approach the s-wave interaction of the vector meson nonet with the octet of pseudoscalar Goldstone Bosons, we find that the main component of the axial vector mesons b_1(1235), h_1(1170), h_1(1380), a_1(1260), f_1(1285) and the two states associated to the K_1(1270) does not follow the QCD dependence on the number of colors for ordinary qqbar mesons.
The Lagrangian of pseudoscalar, vector, and axial-vector mesons is determined by the explicit global chiral symmetry and hidden local chiral symmetry. There are fourteen interacting terms up to the dimension-four of covariant derivatives rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. There are only two independent parameters. The three new terms are important in phenomenology.
We reanalyze the D^{*+} pi^- mass spectrum from CLEO II by the VMW method in order to examine the existence of a chiral axial-vector state, which is predicted in a covariant level-classification scheme recently proposed, other than normal orbitally-excited P-wave states in the D meson system. A result of the present analysis seems to suggest that there exists an extra axial-vector meson, in addition to the two normal ones, in a similar mass region.
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.
We study the features of a SU(2) Polyakov-Nambu-Jona-Lasinio model that includes wave function renormalization and nonlocal vector interactions. Within this framework we analyze, among other properties, the masses, width and decay constants of light vector and axial-vector mesons at finite temperature. Then we obtain the corresponding phase diagram in a finite density scenario, after characterizing the deconfinement and chiral restoration transitions.
We investigate the properties of new scalar X_B, X_D and axial-vector X_B*, X_D* mesons, which are recently predicted, in the covariant meson-classification scheme, to exist as the partners of ground-state pseudoscalar B, D and vector B*, D* mesons, respectively, realizing a linear representation of chiral symmetry for the light quark component in heavy-light-quark meson system. The mass splittings between the respective chiral partners are shown to be equal, and the decay widths of one pion emission of X_B, X_D, X_B* and X_D* become to have a common value, due to chiral and heavy quark symmet…
Decay property of hidden-charm tetra-quark mesons is studied. It is seen that estimated width of iso-triplet odd $\mathcal{C}$ partners of X(3872), although still crude, is compatible with the measured ones of Z_c(3900). It is pointed out that confirmation of an eta-pi^0 peak around 3.2 GeV indicated in gamma-gamma collisions gives a clue to select a realistic model of multi-quark mesons.
The new narrow mesons observed recently in the final states Ds+ pi0 and Ds*+ pi0 are pointed out to be naturally assigned as the ground-state scalar and axial-vector chiralons in the c sbar system, which would newly appear in the covariant hadron-classification scheme proposed a few years ago.
In this work, we use the QCD sum rule method to study the radiative decays of the vector and axial-vector $B_c$ mesons to each of three charmed strange mesons, $D_s$, $D^*_s$ and $D_{s1}$, through their dominant weak annihilation channels. We calculate all relevant transition form factors, which are used to estimate the branching fractions at different channels. The order of branching ratios are obtained to be in the order of $ 10^{-6} - 10^{-5} $, which may be checked via differnet experiments.
The axial form factor as well as the axial charge of octet baryons are studied in the perturbative chiral quark model (PCQM) with the quark wave functions predetermined by fitting the theoretical results of the proton charge form factor to experimental data. The theoretical results are found, based on the predetermined quark wave functions, in good agreement with experimental data and lattice values. This may indicate that the electric charge and axial charge distributions of the constituent quarks are the same. The study reveals that the meson cloud plays an important role in the axial charge…
The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model. The preliminary answer for contributions from a1 and f1 mesons to (g-2)_mu is 0.34 x 10^(-11) and does not support the Melnikov-Vainshtein estimate 2.2 x 10^(-11).
Basic features of nonstrange vector and axial vector mesons are analyzed in the framework of a chiral quark model that includes nonlocal four fermion couplings. Unknown model parameters are determined from some input values of masses and decay constants, while nonlocal form factors are taken from a fit to lattice QCD results for effective quark propagators. Numerical results show a good agreement with the observed meson phenomenology.
The level classification of quark-antiquark systems is generally made by the LS-coupling scheme, resorting to the non-relativistic quark model. However, it has been well known that the pi-meson with the (L,S)=(0,0) shows also the properties as a Nambu-Goldstone boson in the case of spontaneous breaking of a relativistic symmetry, the chiral symmetry. In this talk I present a covariant classification scheme for describing both the non-relativistic and the relativistic q q bar-mesons and point out possibility for existence of the new scalar meson nonet (to be assigned to the sigma nonet) and als…
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].
The rates and spectra of the anomalous $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates some low-energy theorems. In this note we point out that a gauge covariant procedure to diagonalize this mixing allows for consistent description of the $η\toπ^+π^-γ$ and $η' \toπ^+π^-γ$ decays.
The renormalized contribution of fermions to the curvature masses of vector and axial-vector mesons is derived with two different methods at leading order in the loop expansion applied to the (2+1)-flavor constituent quark-meson model. The corresponding contribution to the curvature masses of the scalar and pseudoscalar mesons, already known in the literature, is rederived in a transparent way. The temperature dependence of the curvature mass of various (axial-)vector modes obtained by decomposing the curvature mass tensor is investigated along with the (axial-)vector--(pseudo)scalar mixing. A…
In this article, we study the vector and axialvector $B_c$ mesons with the QCD sum rules, and make reasonable predictions for the masses and decay constants, then calculate the leptonic decay widths. The present predictions for the masses and decay constants can be confronted with the experimental data in the future. We can also take the masses and decay constants as basic input parameters and study other phenomenological quantities with the three-point vacuum correlation functions via the QCD sum rules.
Recent reports of the observation of the decay $τ\rarrow ν_τ + K + π+ π$ raise interesting questions. The $u-s$ quark mass difference can induce an effective second-class current in the strange sector and enhance decays to helicity-suppressed scalar states. This suggests searches for scalar strange mesons in the $τ\rarrow ν_τ + K + η' $ and $τ\rarrow ν_τ + K + π$ decay modes. $τ$ decays to axial vector final states may clarify strange meson spectroscopy by analogy with the clarification of the $a_1$ problem in the nonstrange sector. Open questions include mixing effects in the strange axial ve…
We discuss the possible symmetries of the effective lagrangian describing interacting pseudoscalar-, vector-, and axial-vector mesons. Specific choices of the parameters give rise to an $[SU(2)\otimes SU(2)]^3$ symmetry. This symmetry can be obtained either {\it á la} Georgi, with all states in the spectrum remaining massless, or in a new realization, implying decoupling of the pseudoscalar bosons from degenerate vector and axial-vector mesons. This second possibility, when minimally coupled with $SU(2)\otimes U(1)$ electroweak gauge vector bosons, seems particularly appealing. All deviations …
The in-medium behavior of ground-state $q\bar{q}$ mesons, where $q \in \{u,d,s,c\}$, in vector and axial-vector channels is studied based on the spectral analysis for mesonic correlators at finite temperature and zero chemical potential. We first compute the correlators by solving the quark gap equations and the inhomogeneous Bethe-Salpeter equations in the rainbow-ladder approximation. Using a phenomenological ansatz, the spectral functions are extracted by fitting the correlators. By analyzing the evolution of the spectral functions with the temperature, we obtain the dissociation temperatur…
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…
The large branching ratio for B-> K1 gamma recently measured at Belle implies a large B -> K1 transition form factor and large branching ratios for non leptonic B decays involving an axial-vector meson. In this paper we present an analysis of two-body B decays with an axial-vector meson in the final state using naive factorization and the B -> K1 form factors obtained from the measured radiative decays. We find that the predicted B -> J/psi K1 branching ratio is in agreement with experiment. We also suggest that the decay rates of B -> K1 pi, B -> a1 K and B -> b1 K could be used to test the f…
A previous model where the low-lying axial-vector mesons are dynamically generated, implementing unitarity in coupled channels in the vector-pseudoscalar ($VP$) meson interaction, is applied to evaluate the decay widths of the a_1(1260)$ and $b_1(1235)$ axial-vector mesons into $πγ$. Unlike the case of the $a_1$, the $b_1$ radiative decay is systematically underestimated at tree level. In this work we evaluate for the first time the loop contribution coming from an initial $VP$ vertex. Despite the large superficial divergence of the loops, the convergence of the relevant loops can be establish…
A new mathematical framework for the diagonalization of the nondiagonal vector--scalar and axial-vector--pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has unexpected connections with the Hadamard product of $n\times n$ matrices describing the couplings, masses, and fields involved. The approach is shown to be much more efficient as compared with the standard methods employed previously. The difference is especially noticeable if the chiral symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken $SU(3)_L…
The masses and the leptonic decay constants of vector and axial vector heavy-heavy mesons are calculated using the thermal QCD sum rules approach. While obtaining the QCD sum rules, additional operators in the Wilson expansion and also temperature dependency of the continuum threshold are taken into account. The masses and the decay constants remained unchanged up to $T\simeq100~MeV$. After that point, they start to diminish. At the critical temperature, the masses decreased about $3\%$, $5\%$ and $14\%$ for the vector mesons $Υ$, $B_{c}$ and $J/ψ$; $6\%$, $7\%$ and $22\%$ for the axial vector…
The self-consistent chiral soliton of the Nambu--Jona-Lasinio model including the $ω,ρ$ and $a_1$ (axial-) vector meson fields besides the chiral angle is investigated. The resulting energy spectrum of the one particle Dirac Hamiltonian is strongly distorted leading to a polarized Dirac sea which carries the complete baryon number. This supports Witten's conjecture that baryons can be described as topological solitons. The exploration of the isoscalar mean squared radius of the nucleon exhibits that the repulsive character of the isoscalar vector field $ω$ as well as the attractive features of…
We investigate $πρ$ scattering based on the coupled-channel formalism with the $πρ$ and $K\bar{K}^*$ ($\bar{K}K^*$) channels included. We construct the kernel amplitudes by using the meson-exchange model and compute the coupled integral equation for $πρ$ scattering. By performing the partial-wave expansion, we show explicitly that the $a_1(1260)$ meson is dynamically generated by the coupled-channel formalism. The $a_1$ meson only appears by including the $K\bar{K}^*$ ($\bar{K}K^*$) channel. We obtain the pole position of the $a_1$ meson as $\sqrt{s_R} = (1170.7 - i 173.0)$ MeV. We conclude th…
We make a theoretical study of the s-wave interaction of the nonet of vector mesons with the octet of pseudoscalar mesons starting from a chiral invariant Lagrangian and implementing unitarity in coupled channels. By looking for poles in the unphysical Riemann sheets of the unitarized scattering amplitudes, we get two octets and one singlet of axial-vector dynamically generated resonances. The poles found can be associated to most of the low lying axial-vector resonances quoted in the Particle Data Book: $b_1(1235)$, $h_1(1170)$, $h_1(1380)$, $a_1(1260)$, $f_1(1285)$ and two poles to the $K_1(…
We study the properties of axial vector mesons a1 and b1 as relativistic S-wave states which are predicted in the U~(12)-scheme, through the analyses of their radiative and pionic decays. Specifically, partial widths of the strong a1 (b1) -> rho(omega) pi processes, their D/S-wave amplitude ratios, and radiative transition widths of a1(b1) -> pi gamma processes are calculated by using a simple decay interaction model, and made a comparison with the respective experimental values.
We revisit well-known short-distance constraints relating the hadronic light-by light Green's function to the $\langle VVA \rangle$ one, that have been a subject of debate over the past years in the context of the muon $(g-2)$. Specifically, we identify a relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly that, by contrast, has not received attention in the past. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors, but further applications are disc…
In this article, we take the point of view that the charmed axial-vector meson $D_{s1}(2460)$ is the conventional $c\bar{s}$ meson and calculate the strong coupling constant $g_{D_{s1} D^* K}$ in the framework of the light-cone QCD sum rules approach. The numerical values of strong coupling constants $g_{D_{s1} D^* K}$ and $g_{D_{s0} D K}$ are very large, and support the hadronic dressing mechanism. Just like the scalar mesons $f_0(980)$ and $a_0(980)$, the scalar meson $D_{s0}(2317)$ and axial-vector meson $D_{s1}(2460)$ may have small $c\bar{s}$ kernels of the typical $c\bar{s}$ meson size, …
