Approach to calculation of mass spectra and two-photon decays of cc¯ mesons in the framework of Bethe-Salpeter equation

Abstract

In this work we calculate the mass spectra of charmonium for 1P; …; 4P states of 0 þþ and 1 þþ , for 1S; …; 5S states of 0 −þ , and for 1S; …; 4D states of 1 −− along with the two-photon decay widths of the ground and first excited states of 0 þþ quarkonia for the process O þþ → γγ in the framework of a QCDmotivated Bethe-Salpeter equation (BSE). In this 4 × 4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χ c0 . Our results are in reasonable agreement with data (where available) and other models.

Mass Spectra and Decay Constants of Heavy-Light Axial Quarkonia in the Framework of Bethe-Salpeter Equation

“…with colour, spin and orbital parts respectively. For a kernel with the above spin dependence, we can rewrite the hadron-quark vertex as [29],…”

“…)[g 1 (q, P ) + i P g 2 (q, P ) − i qg 3 (q, P ) + [ P , q]g 4 (q, P )]. (11) Then, making use of the 3D reduction and making use of the fact that q.P = 0, we can write the general decomposition of the instantaneous BS wave function for scalar mesons (J pc = 1 +− ), of dimensionality M 0 being composed of various Dirac structures that are multiplied with scalar functions g i ( q) and various powers of the meson mass M as [29]…”

“…Due to this the confining interaction would dominate over the One-Gluon-Exchange (OGE) interactions for Qq systems. Thus, the perturbative incorporation of OGE term [29,30] is a reasonable approximation for heavy-light quarkonia.…”

Charmonium Properties Using the Discrete Variable Representation (DVR) Method

“…Theoretically, quarkonium systems have been studied by various formalisms based on phenomenological potential models [7][8][9][10][11], effective field theory [12], lattice gauge theory [13][14][15][16], Bethe Salpeter equation [17][18][19][20], etc. Among these, owing to its simplicity, formalism based on potential models is the widely chosen method to investigate quarkonium sys-tems.…”

Decay Constants of S Wave Heavy Quarkonia

“…Lattice QCD provides great hope in this direction and significant results are being reported [1,2]. Various other approaches widely used in the literature to study hadronic systems include QCD sum rules [14][15][16][17][18][19], nonrelativistic and relativistic potential models [20][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36], effective field theory [37][38][39] and formalisms based on Bethe-Salpeter equation and Dyson-Schwinger equation [40][41][42][43][44][45][46][47][48][49]. Among theses QCD inspired potential models have been largely successful in explaining hadronic properties.…”