Photonic production of a pair of Bc mesons

Abstract

We study the pair production of B c mesons in the photon-photon interaction in the framework of perturbative quantum chromodynamics and the relativistic quark model. The production amplitudes of a pair of pseudoscalar and vector B c mesons are constructed in the nonrelativistic approximation and taking into account relativistic effects. Relativistic corrections related to the relative motion of heavy quarks in the production amplitude, as well as in the wave function of the bound state of heavy quarks, are taken into account. Analytical expressions are constructed for the relativistic differential and total cross sections for the pair B c meson production. Based on them, numerical values of the production cross sections are obtained for various energies and scattering angles.

Higgs boson decay to the pair of S- and P-wave $B_c$ mesons

“…We study the relativistic corrections both in the production amplitude of two quarks and antiquarks, and in the transformation law of the wave functions of B c mesons during the transition from the rest frame to the moving reference frame. As known from our previous studies the corrections of these types significantly contribute to the production cross section of a pair of heavy quarkonia [11][12][13].…”

“…Initially it can be written as a convolution of perturbative production amplitude of free quarks and antiquarks and the quasipotential wave functions of B c mesons moving with four-momenta P and Q. Using then the transformation law of the bound state wave functions from the rest frame to the moving one with fourmomenta P and Q we can present the meson production amplitude in the form [11,12,21]:…”

Associated Charmonium-Bottomonium Production in a Single Boson e+e− Annihilation

“…It is known that accounting for such effects can crucially change the predictions, especially for the charmonium-pair production in the e + e − annihilation, where accounting for the relativistic effects decreases the virtuality of the intermediate gluon, and therefore essentially increases the cross section value (see for example [9][10][11][12][13][14][15][16][17][18][19][20][21]). Another example of the influence of the relativistic effects on the paired quarkonium production could be found in [29][30][31][32]. For the processes discussed in this study, we do not expect such a huge change of the cross section due to relativistic effects, as for the paired charmonium production, but, of course, it does not eliminate the problem, and such effects should be thoroughly investigated.…”

Higgs boson decay to paired $B_c$: relativistic and one-loop corrections

“…Initially it can be written as a convolution of perturbative production amplitude of free quarks and antiquarks and the quasipotential wave functions of B c mesons moving with four-momenta P and Q. Using then the transformation law of the bound state wave functions from the rest frame to the moving one with four-momenta P and Q we can present the meson production amplitude in the form [4,13,14]: ×Sp Ψ P,V Bc (p, P )Γ ν 1 (p, q, P, Q)Ψ P,V Bc (q, Q)γ ν + Ψ P,V Bc (−p, P )Γ ν 2 (p, q, P, Q)Ψ P,V Bc (−q, Q)γ ν , where a superscript P indicates a pseudoscalar B c meson, a superscript V indicates a vector 4). The method for producing the amplitudes in the form (2) is described in detail in our previous studies [3,4,15].…”

“…In other terms of the Hamiltonians ( 23) and ( 24) we use the leading order approximation for α s . The typical momentum transfer scale in a quarkonium is of order of double reduced mass, so we set the renormalization scale µ = 2m The numerical values of the relativistic parameters entering the cross sections (13), and ( 15) are obtained by the numerical solution of the Schrödinger equation [32]. They are…”