The decay constants and the radiative decay widths of η_b(nS) and η_c(nS) are computed within a semirelativistic quark model, using a potential found through the AdS/QCD correspondence. For η_c, the results are in agreement with experimental data, while in the case of η'_c a discrepancy is found and the possible reasons are discussed.
Rare radiative leptonic decay $B\to l\bar ν_l γ$ is studied in the instantaneous Bethe-Salpeter approach. The results are compared to other relativistic quark model predictions.
We evaluate the complete spectrum of the Bc mesons, below the open flavor BD threshold, in a Bethe-Salpeter model. We make predictions for the radiative decay widths of the Bc excited states. We compare our results with those of other models.
The spectrum of baryons with two heavy quarks is predicted, assuming a configuration of a light quark and a heavy diquark. The masses are computed within a semirelativistic quark model, using a potential obtained in the framework of the AdS/QCD correspondence. All the parameters defining the model are determined fitting the meson spectrum. The obtained mass of Ξ_{cc} is in agreement with the measurements.
In this work we study the radiative decays of heavy-light quarkonia through M1 and E1 transitions, that involve quark-triangle diagrams with two hadron vertices, and are difficult to evaluate in BSE-CIA. We have expressed the transition amplitude, $M_{fi}$ as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadron, with coefficients being related to results of pole integrals over complex $σ$- plane. We evaluate the decay widths for $M1$ transitions ($^3S_1 \rightarrow ^1S_0 +γ$), and $E1$ transition…
This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} γ$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}γ$, and $0^{-+}\rightarrow 1^{+-} γ$ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work,…
The instantaneous formulations for the relativistic Bethe-Salpeter (BS) and the radiative transitions between the bound-states are achieved if the BS kernel is instantaneous. It is shown that the original Salpeter instantaneous equation set up on the BS equation with an instantaneous kernel should be extended to involve the `small (negative energy) component' of the BS wave functions. As a precise example of the extension for the bound states with one kind of quantum number, the way to reduce the novel extended instantaneous equation is presented. How to guarantee the gauge invariance for the …
We interpret the $B_{s1}(5778)$ as an $S$-wave $B^\ast\bar{K}$ molecular state in the Bethe-Salpeter equation approach. In the ladder and instantaneous approximations, and with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the vertex, we find the bound state exists. We also study the decay widths of the decay $B_{s1}(5778)\rightarrow B_s^\astπ$ and the radiative decays $B_{s1}(5778)\rightarrow B_sγ$ and $B_{s1}(5778)\rightarrow B_s^{\ast}γ$, which will be instructive for the forthcoming expe…
We estimate the decay rates of $η_c\rightarrow 2γ$, $η_c'\rightarrow 2γ$, and $J/ψ\rightarrow e^+ e^-$, $ψ^\prime\rightarrow e^+e^-$, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these $c\bar{c}$ states. We find that the relativistic correction to the ratio $R\equiv Γ(η_c \rightarrow 2γ)/ Γ(J/ ψ\rightarrow e^+ e^-)$ is negative and tends to compensate the positive contribut…
We have employed the framework of Bethe-Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like pi, K, D, Ds and B and radiative decay constants of neutral pseudoscalar mesons like pi and etac in two photon decays of these mesons. In the Dirac structure of hadronic BS wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule, order-by-order in powers of inverse of meson mass. The decay constants are calculated with the incorporation of both Leadi…
AdS/QCD correspondence allows to compute the quark-antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schroedinger equation with relativistic kinematics) and a short range hyperfine splitting potential to describe the bound states of quark-antiquark. Comparison with experiment permits to fit the parameters of the model, namely the quark masses and the quark potential parameters. A discussion of heavy tetraquark masses, prompted by the hypothesis of a diquark-antidiquark structure for the puzzling state X(3872), is also presented.
Using the general form of the generalized Bethe-Salpeter wave functions for four-quark states describing the meson-meson molecular structure given in our previous work, we obtain the general formulas for the decay widths of molecular states composed of two vector mesons with arbitrary spin and parity into two photons. Then this general formalism is applied to investigate the radiative two-photon decay of the obeserved \emph{X}(3915) state, where this exotic state \emph{X}(3915) is considered as a molecular state consisting of two heavy vector mesons $D^{*0}\bar{D}^{*0}$. The numerical result o…
We use QCD light-cone sum rules (LCSR) with holographic anti de Sitter/Chromodynamics (AdS/QCD) Distribution Amplitudes (DAs) for the $ρ$ meson to predict the form factors that govern the leading amplitudes of the rare radiative $B -> ργ$ decay and the semileptonic decay $B -> ρl ν$. We test the Isgur-Wise relation between the radiative and semileptonic form factors. We also compute the total width (in units of $|V_{ub}|^2$) for the semileptonic decay $B -> ρl ν$ as well as ratios of partial decay widths which are independent of $|V_{ub}|$.
AdS/QCD correspondence predicts the structure of quark-antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schrödinger equation with relativistic kinematics) and a short range hyperfine splitting potential to determine quark masses and the quark potential parameters from the meson spectrum. The agreement between theory and experimental data is satisfactory provided one considers only mesons comprising at least one heavy quark. We use the same potential (in the one-gluon-exchange approximation) and these data to estimate constituent diq…
In this paper we determine the one loop radiative correction to the higgs potential due to quantum fluctuations about the background metric of Randall-Sundrum model. We then examine the effects of the one loop effective potential on the stability of the classical vacuum paying particular attention to the tadpole terms which could dominate over the classical potential for small field configurations. We find that although the one loop potential due to scale fluctuations could develop a tadpole term in certain regions of the parameter space, it is positive for either sign of H. The quadratic and …
In this work we study the radiative decay widths of vector quarkonia for the process of $J/ψ(nS)\rightarrowη_{c}(nS)γ$ and $Υ(nS)\rightarrowη_{b}(nS)γ$ (for principal quantum numbers $n=1, 2, 3$) in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz using a $4\times 4$ form of BSE. The parameters of the framework were determined by a fit to the mass spectrum of ground states of pseudoscalar and vector quarkonia, such as; $η_{c}$, $η_{b}$, $J/ψ$ and $Υ$. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and exci…
We predict observables in radiative B decays to vector mesons using holographic AdS/QCD Distribution Amplitudes for the vector mesons. We find that end-point divergences can be avoided when computing power-suppressed contributions in the heavy quark limit. The results reported here can be found in references [1] and [2].
We estimate the electromagnetic decay rates of $χ_{c0}\rightarrow γγ$ and $χ_{c2}\rightarrowγγ$ by taking into account both relativistic and QCD radiative corrections. The decay rates are derived in the Bethe-Salpeter formalism and the QCD radiative corrections are included in accordance with factorization assumption. Using a QCD-inspired interquark potential, we obtain relativistic BS wavefunctions of $χ_{c0}$ and $χ_{c2}$ by solving BS equations for the corresponding $^{2S+1}L_J$ states. Our numerical result for the ratio $R=\frac{Γ(χ_{c0}\rightarrowγγ)}{Γ(χ_{c2} \rightarrowγγ)}$ is about $1…
We use AdS/QCD holographic Distributions Amplitudes for the vector mesons $ρ$ and $K^*$ in order to predict the radiative decays $B \to ργ$ and $B \to K^* γ$ as well as the semileptonic decays $B \to ρl ν$ and $B \to K^* μ^+ μ^-$. For the radiative decays, we find that the AdS/QCD DAs offer the advantage of avoiding end-point singularities when computing power suppressed contributions. For the semileptonic decays $B \to ρl ν$ and $B \to K^* μ^+ μ^-$, we compare our predictions to the latest BaBar and LHCb data respectively.
Within the standard model, we calculate the radiative $B\rightarrow K^{\star}γ$ decay rate based on a Bethe-Salpeter description for the meson wave functions and the hadronic matrix elements. With a reasonable choice of parameters the branching ratio BR($B \rightarrow K^{\star}γ$) is found to be $(3.8-4.6)\times 10^{-5}$, which is in agreement with the CLEO experimental data. We also find with $m_{b}=5.12 GeV$ the ratio $R\equiv {Γ(B\rightarrow K^{\star}γ)}/{Γ(b\rightarrow sγ)}=(10-12)\%$, which can be slightly larger if a smaller $m_{b}$ is chosen. In this approach, the light degrees of freed…
Heavy quarkonium decay $V \to ggg$ with both relativistic and QCD radiative corrections
College of Physics and Electronic Science, Hubei Normal University(湖北师范大学物理与电子科学学院);Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University(华中师范大学夸克与轻子物理教育部重点实验室)
Three-gluon decays of radially excited quarkonia $ψ(2S)$ and $Υ(2S)$ with both relativistic and QCD radiative corrections
College of Physics and Electronic Science, Hubei Normal University(湖北师范大学物理与电子科学学院);Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University(华中师范大学夸克与轻子物理教育部重点实验室)
The $P$-wave charmonium decays $h_{c}\rightarrowγη^{(\prime)}$ are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of $η^{(\prime)}$, the relativistic corrections make significant contributions to the decay rates of $h_{c}\rightarrowγη^{(\prime)}$. By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic c…
Casher and Susskind have noted that in the light-front description, spontaneous chiral symmetry breaking in quantum chromodynamics (QCD) is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon QCD condensates are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the AdS/CFT correspondence, and the Bethe-Salpeter/Dyson-Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explici…
Soft-QCD effects of quark-level form factors in $γγ$ decay of $B_s$-mesons via $D{\bar D}$ intermediate states, suggested by Ellis et al, are examined in the "Salpeter" model [reinterpreted in terms of the Markov-Yukawa Transversality Principle (MYTP)] when formulated on a covariant light front (null-plane). The gluonic kernel in the infrared regime which generates the constituent mass via standard $DBχS$, is calibrated to both $q{\bar q}$ and qqq spectra, meson mass splittings, pion form factor,and other parameters. With this check, an exact evaluation of the $D{\bar D}γ$ vertex form factor $…
Radiative E1 decay widths of $\rm X(3872)$ are calculated through the relativistic Salpeter method, with the assumption that $\rm X(3872)$ is the $χ_{c1}$(2P) state, which is the radial excited state of $χ_{c1}$(1P). We firstly calculated the E1 decay width of $χ_{c1}$(1P), the result is in agreement with experimental data excellently, then we calculated the case of $\rm X(3872)$ with the assignment that it is $χ_{c1}$(2P). Results are: $Γ({\rm X(3872)}\rightarrow γ\sl J/ψ)=33.0$ keV, $Γ({\rm X(3872)}\rightarrow γψ(2S))=146$ keV and $Γ({\rm X(3872)}\rightarrow γψ(3770))=7.09$ keV. The ratio ${…
The drag force of charm quarks propagating through a thermalized system of Quark Gluon Plasma (QGP) has been considered within the framework of both conformal/non-conformal Anti de Sitter (AdS) correspondence. Newly derived Einstein Fluctuation-Dissipation relation has been used to calculate the heavy flavor diffusion coefficients. Using the drag and diffusion coefficients as inputs Langevin equation has been solved to study the heavy flavor suppression factor. It has been shown that within conformal AdS correspondence the D-meson suppression at LHC energy can be reproduced where as the non-co…
We report on some recent developments in understanding the nature of the low-lying mesonic resonances $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2'(1525)$, and $K_2^*(1430)$. In particular we show that these five resonances can be dynamically generated from vector meson--vector meson interaction in a coupled-channel unitary approach, which utilizes the phenomenologically very successful hidden-gauge Lagrangians to produce the interaction kernel between two vector mesons, which is then unitarized by the Bethe-Salpeter-equation method. The data on the strong decay branching ratios, total decay wi…
QCD running coupling constant $α_s(m_c)$ and $α_s(m_b)$ are determined from heavy quarkonia $c\overline{c}$ and $b\overline{b}$ decays. The decay rates of $V\rightarrow 3g$ and $V\rightarrow e^+ e^-$ for $V=J/ψ$ and $Υ$ are estimated by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, and the decay rates are estimated by using the meson wavefunctions which are obtained with a QCD-inspired inter-quark potential. For the $V\rightarrow 3g$ decay we find the relativistic correction to be very large and to severel…