Gluon Exchange Interaction Research Articles

Electromagnetic and strong isospin breaking in light meson masses

We study electromagnetic as well as strong isospin breaking effects in the isospin mass splittings of light pseudoscalar and vector mesons. To this end we employ a coupled system of quark Dyson-Schwinger and meson Bethe-Salpeter equations whose interaction kernels contain gluon, pion and photon exchange interactions. In bound states, QCD-induced isospin breaking is manifest on different levels. On the one hand, a different explicit up- and down-quark mass directly affects the propagators of the constituent quarks. On the other hand, it leads to different interaction kernels within the isospin multiplets. In addition, electromagnetic isospin breaking is induced via a photon exchange diagram. Using the kaon iso-doublet and the charged pion masses as input to determine the up, down and strange quark masses we find for the pion, kaon and rho meson mass splittings different patterns each. In particular, our results provide evidence that the effects from two sources of mass splittings, the different quark masses and the different quark charges, do not add up linearly.

Radiative M1 transitions of heavy baryons: Effective quark mass scheme

We calculate the magnetic moments of ground state ${J}^{P}={\frac{1}{2}}^{+}$ and ${J}^{P}={\frac{3}{2}}^{+}$ heavy flavor charm and bottom baryon states employing the concept of effective mass based on single gluon exchange interaction coupling to the spectator quarks in the nonrelativistic quark model. We exploit the current experimental information in the heavy flavor sector to estimate the interaction contributions to get the effective masses of the quarks inside the baryons. We study the spin ${\frac{1}{2}}^{\ensuremath{'}+}\ensuremath{\rightarrow}{\frac{1}{2}}^{+}$, ${\frac{3}{2}}^{+}\ensuremath{\rightarrow}{\frac{1}{2}}^{+}$, and ${\frac{3}{2}}^{+}\ensuremath{\rightarrow}{\frac{1}{2}}^{\ensuremath{'}+}$ transition moments for these baryons. We make robust predictions of the radiative $M1$ decay widths of singly, doubly, and triply heavy flavored baryons.

Bottomonium spectrum with a Dirac potential model in the momentum space

We study the bottomonium spectrum using a relativistic potential model in the momentum space. This model is based on a complete one gluon exchange interaction with a momentum dependent screening factor to account for the effects due to virtual pair creation that appear close to the decay thresholds. The overall model does not make use of nonrelativistic approximations. We fit well established bottomonium states below the open bottom threshold and predict the rest of the spectrum up to approx 11200 MeV and J^{PC}=3^{--}. Uncertainties are treated rigorously and propagated in full to the parameters of the model using a Monte Carlo to identify if which deviations from experimental data can be absorbed into the statistical uncertainties of the models and which can be related to physics beyond the bbar{b} picture, guiding future research. We get a good description of the spectrum, in particular the Belle measurement of the eta _b(2S) state and the varUpsilon (10860) and chi _b(3P) resonances.

Masses of tetraquark states in the hidden charm sector above D − D⁎ threshold

In the diquark-antidiquark composition, we study the masses of hidden charm tetraquark systems (cqc¯q¯, csc¯s¯ and csc¯q¯) using a linear confinement potential. In this study, we have factorized the four body system into three subsequent two body systems. To remove degeneracy in the S and P wave masses of mesons and tetraquark states, the spin-spin, spin orbit and tensor components of the confined one gluon exchange interactions are employed. In this attempt, we have been able to assign the ψ(4230) as pure cqc¯q¯ tetraquark state. ψ(4360) and ψ(4390) as pure csc¯q¯ tetraquark states. According to our analysis ψ(4260) is found to be an admixture of two P11cqc¯q¯ tetraquark states having mass 4259 MeV. Additionally, we have been able to predict the radiative decay width Γ(ψ→J/ψγ), leptonic decay width Γe+e− and hadronic decays of 1−− tetraquark states. The status of X(3872) and Zcs are also identified as compact tetraquark states. Additionally, we have been able to predict the radiative decay width Γ(ψ→J/ψγ), leptonic decay width Γe+e− and hadronic decays of 1−− tetraquark states.

Bc mesons and their properties on the light front

We investigate the unequal mass relativistic bound state system, the $B_c$ mesons, in a light-front Hamiltonian formalism. We adopt an effective Hamiltonian based on soft-wall light-front holography, together with a longitudinal confinement that was first introduced for heavy quarkonium. We also include the one gluon-exchange interaction with a running coupling, which produces the spin structure. We present the mass spectrum and light-front wave functions. We also use the light-front wave functions to calculate decay constants, charge and momentum densities, as well as distribution amplitudes. The results are compared with experiments and other theoretical approaches, all of which are in reasonable agreement.

Possible ferromagnetism of dense quark matter

The cardinal focus of the present review is to investigate the possibility of the para-ferro phase transition of dense quark matter. For these, the calculation of the single-particle energies, ground state energy (GSE) densities, and spin susceptibility χ of degenerate quark matter with one gluon exchange interaction in terms of spin-dependent Landau parameters (LPs) have been presented. The expressions for the GSE and χ of cold and dense spin-polarized quark matter have been derived with corrections due to correlation. Furthermore, the magnetic properties of spin polarized quark matter have been discussed by evaluating the magnetization ⟨M⟩ and magnetic susceptibility χM in terms of LPs. Finally, the possibility of magnetic instability has been revealed by studying the density dependence of ⟨M⟩ and χM.

Qbar{Q} (Qin {b, c}) spectroscopy using the Cornell potential

The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schrödinger equation to obtain their mass spectra using only four parameters namely quark mass (m_c, m_b) and confinement strength (A_{cbar{c}}, A_{bbar{b}}). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited S, P, D and F states. Digamma, digluon and dilepton decays of these mesons are computed using the model parameters and numerical wave functions. The predicted spectroscopy and decay properties for quarkonia are found to be consistent with available data from experiments, lattice QCD and other theoretical approaches. We also compute mass spectra and life time of the B_c meson without additional parameters. The computed electromagnetic transition widths of heavy quarkonia and B_c mesons are in tune with available experimental data and other theoretical approaches.

Tetraquark states in the bottom sector and the status of the $$Y_b$$ Y b (10890) state

We have done the exploratory study of bottom tetraquarks ($[bq\bar b \bar q];{q\in u,d}$) in the diquark-antidiquark framework with the inclusion of spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction. Our focus here is on the $Y_b$(10890) and other exotic states in the bottom sector. We have predicted some of the bottom counterparts to the charm tetraquark candidates. Our present study shows that if $Z_b(10610)$ and $Z_b(10650)$ are diquark-diantiquark states then they have to be first radial excitations only and we have predicted $Z_b(10650)$ state as first radial excitation of tetraquark state $X_b$ (10.143-10.230). We have identified $X_b$ state with $J^{PC}= 1^{+-}/0^{++}$ as being the analogue of $Z_c(3900)$. An observation of the $X_b$ will provide a deeper insight into the exotic hadron spectroscopy and is helpful to unravel the nature of the states connected by the heavy quark symmetry. We particularly focus on the lowest P wave $[bq][\bar b\bar q]$ states with $J^{PC}=1^{--}$ by computing their leptonic, hadronic and radiative decay widths to predict the status of still controversial $Y_b$(10890) state. Apart from this, we have also shown here the possibility of mixing of P wave states. In the case of mixing of $1^{--}$ state with different spin multiplicities, we found that predicted masses of the mixed P states differ from $Y_b$(10890) state only by $\pm20$ MeV energy difference which can be helpful to resolve further the structure of $Y_b$(10890).

Decay rates of charmonia within a quark-antiquark confining potential**Supported by Major Research Project NO. F. 40-457/2011(SR), UGC, India

In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of the non-relativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and a few low-lying P and D waves. The resultant wave functions at zero inter-quark separation as well as some finite separations are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states using the conventional Van Royen-Weisskopf formula. The di-gamma and di-leptonic decay widths are also computed by incorporating the relativistic corrections of order v4 within the NRQCD formalism. We have observed that the NRQCD predictions with their matrix elements computed at finite radial separation yield results which are found to be in better agreement with experimental values for both di-gamma and di-leptonic decays. The same scenario is seen in the case when di-gamma and di-leptonic decay widths are computed with the Van Royen-Weisskopf formula. It is also observed that the di-gluon decay width with the inclusion of binding energy effects are in better agreement with the experimental data available for 1S-2S and 1P. The di-gluon decay width of 3S and 2P waves waves are also predicted. Thus, the present study of decay rates clearly indicates the importance of binding energy effects.

Operator analysis of effective spin-flavor interactions forL=1excited baryons

We match the non-relativistic quark model, with both flavor dependent and flavor independent effective quark-quark interactions, to the spin-flavor operator basis of the 1/Nc expansion for the L=1 non-strange baryons. We obtain analytic expressions for the coefficients of the 1/Nc operators in terms of radial integrals that depend on the shape and relative strength of the spin-spin, spin-orbit and tensor interactions of the model, which are left unspecified. We obtain several new, parameter-free relations between the seven masses and the two mixing angles that can discriminate between different spin-flavor structures of the effective quark-quark interaction. We discuss in detail how a general parametrization of the mass matrix depends on the mixing angles and is constrained by the assumptions on the effective quark-quark interaction. We find that, within the present experimental uncertainties, consistency with the best values of the mixing angles as determined by a recent global fit to masses and decays does not exclude any of the two most extreme possibilities of flavor dependent (independent) quark-quark interactions, as generated by meson (gluon) exchange interactions.

QCD Kondo effect: Quark matter with heavy-flavor impurities

We show that the Kondo effect occurs in light quark matter which contains heavy quarks as impurities. We consider a scattering between a heavy-flavor impurity and a light quark near a Fermi surface which is mediated by gluon-exchange interactions. We find that the scattering amplitude has a logarithmic infrared divergence originating from imperfect cancellation between quark-impurity and hole-impurity scatterings in a loop integral, implying the presence of a strongly coupled regime near the Fermi surface. Renormalization group method is used to find the Kondo scale where a running coupling constant hits a Landau pole. Following an illustration by a simple contact-interaction model, we examine gluon-exchange interactions on the basis of high density QCD.

Cc¯interaction above threshold and the radiative decayX(3872)→J/ψγ

Radiative decays of $X(3872)$ are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels $D\bar D^*$ are described with the string breaking mechanism. In SCA the transition rate $\tilde{\Gamma}_2=\Gamma(2\,{}^3P_1 \rightarrow \psi\gamma)=71.8$~keV and large $\tilde{\Gamma}_1=\Gamma(2\,{}^3P_1\rightarrow J/\psi\gamma)=85.4$~keV are obtained, giving for their ratio the value $\tilde{R_{\psi\gamma}}=\frac{\tilde{\Gamma}_2}{\tilde{\Gamma}_1}=0.84$. In the CC approach three factors are shown to be equally important. First, the admixture of the $1\,{}^3P_1$ component in the normalized wave function of $X(3872)$ due to the CC effects. Its weight $c_{\rm X}(E_{\rm R})=0.200\pm 0.015$ is calculated. Secondly, the use of the multipole function $g(r)$ instead of $r$ in the overlap integrals, determining the partial widths. Thirdly, the choice of the gluon-exchange interaction for $X(3872)$, as well as for other states above threshold. If for $X(3872)$ the gluon-exchange potential is taken the same as for low-lying charmonium states, then in the CC approach $\Gamma_1= \Gamma(X(3872)\rightarrow J/\psi\gamma) \sim 3$~keV is very small, giving the large ratio $R_{\psi\gamma}=\frac{\mathcal{B}(X(3872)\rightarrow \psi(2S)\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi\gamma)}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case $\Gamma_1=42.7$~keV, $\Gamma_2= 70.5$~keV, and $R_{\psi\gamma}=1.65$ are predicted for the minimal value $c_{\rm X}({\rm min})=0.185$, while for the maximal value $c_{\rm X}=0.215$ we obtained $\Gamma_1=30.8$~keV, $\Gamma_2=73.2$~keV, and $R_{\psi\gamma}=2.38$, which agrees with the LHCb data.

Beyond Rainbow-Ladder in a covariant three-body Bethe-Salpeter approach: Baryons

We report on recent results of a calculation of the nucleon and delta masses in a covariant bound-state approach, where to the simple rainbow-ladder gluon-exchange interaction kernel we add a pion-exchange contribution to account for pion cloud effects. We observe good agreement with lattice data at large pion masses. At the physical point our masses are too large by about five percent, signaling the need for more structure in the gluon part of the interaction.

Spin interactions in mesons in strong magnetic field

Spin interactions in relativistic quark-antiquark system in magnetic field is considered in the framework of the relativistic Hamiltonian, derived from the QCD path integral. The formalism allows to separate spin-dependent terms from the basic spin-independent interaction, contained in the Wilson loop, and producing confining and gluon exchange interaction. As a result one obtains relativistic spin-spin interaction $V_{ss}$, generalizing its nonrelativistic analog. It is shown, that in large magnetic field $eB, V_{ss}$ modifies and produces hyperfine shifts which grow linearly with $eB$ and preclude the use of perturbation theory. We also show, that tensor forces for $eB \neq 0$ are active in all meson states, but do not grow with $eB$

Meson spectrum in strong magnetic fields

We study the relativistic quark-antiquark system embedded in magnetic field. The Hamiltonian containing confinement, one gluon exchange and spin-spin interaction is derived. We analytically follow the evolution of the lowest meson states as a functions of MF strength. Calculating the one gluon exchange interaction energy <V_OGE> and spin-spin contribution <a_SS> we have observed, that these corrections remain finite at large magnetic fields, preventing the vanishing of the total rho-meson mass at some B_crit, as previously thought. We display the rho masses as functions of magnetic field in comparison with recent lattice data.

Asymptotic Freedom in Strong Magnetic Fields

Perturbative gluon exchange interaction between quark and antiquark, or in a 3q system, is enhanced in a magnetic field and may cause vanishing of the total qq[over ¯] or 3q mass, and even unlimited decrease of it-recently called the magnetic collapse of QCD. The analysis of the one-loop correction below shows a considerable softening of this phenomenon due to qq[over ¯] loop contribution, similar to the Coulomb case of QED, leading to approximately logarithmic damping of gluon exchange interaction (<V>≈O(1/ln|eB|)) at large magnetic field.

The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark gluon plasma($QGP$) as well as its phase diagram are calculated as a function of baryon density (chemical potential) and temperature. The $QGP$ is assumed to be composed of the light quarks only, i.e. the up and the down quarks, which interact weakly and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (${\cal B}$) for the nonperturbative part and the quantum chromodynamics ($QCD$) coupling is assumed to be constant i.e. no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the $QGP$ phase diagram are shown and discussed. It is demonstrated that the one gluon exchange interaction for the massless quarks has considerable effect on the $QGP$ phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase-diagram. Our results depend on the values of bag pressure and the $QCD$ coupling constant which the latter does not have a dramatic effect on our calculations . Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice $QCD$ prediction for the $QGP$ transition critical temperature.

Critical Exponents of Quark Matter

I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.

Heavy meson interquark potential

The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We calculate the interquark static potential for heavy mesons by assuming that it is given by a massive One Gluon Exchange interaction and compare with phenomenologyical fits inspired by lattice QCD. We apply these potential forms to the description of quarkonia and conclude that, even though some aspects of the confinement mechanism are absent in the Dyson-Schwinger formalism, the spectrum can be reasonably reproduced. We discuss possible explanations for this outcome.

Quark-diquark model description for double charm baryons

We report here the mass spectrum and magnetic moments of ccq(q ∊ u,d,s) systems in the potential model framework by assuming the inter-quark potential as the colour coulomb plus power form with power index ν varying between 0.1 to 2.0. Here the two charm quarks are considered for the diquark states. The conventional one gluon exchange interaction has been employed to get the hyperfine and the fine structure between different states. We have predicted many low-lying states whose experimental verification can exclusively support the quark-diquark structure of the baryons.