Relativistic corrections to double charmonium production in high energy proton-proton interaction

Abstract

On the basis of perturbative QCD and the relativistic quark model, we calculate relativistic corrections to the process of pair J=c production in proton-proton collisions at LHC energy ffiffiffi S p ¼ 7 TeV. Relativistic terms in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave functions to the reference frame of moving J=c mesons are taken into account. For the gluon and quark propagators entering the amplitude, we use a truncated expansion in relative quark momenta up to the second order. Relativistic corrections to the quark bound state wave functions are considered by means of the Breit-like potential. It turns out that the examined effects decrease initial nonrelativistic cross section more than two times. The final result lies below the experimental value measured by LHCb.

Pair double heavy diquark production in high energy proton–proton collisions

“…The quasipotential wave functions of double heavy diquarks are obtained by numerical solution of the Schrödinger equation with effective relativistic Hamiltonian based on the QCD generalization of the Breit potential completed by scalar and vector exchange confinement terms, as is described in detail in our previous work [27][28][29]40]. We present the values of the diquark masses and relativistic parameters (22), (23) in Table 1.…”

“…According to the quasipotential approach the double heavy diquark production amplitude for the gluonic subprocess gg → D bc +Dbc can be expressed as a convolution of the perturbative production amplitude of (bc) and (bc) quark and antiquark pairs T ( p 1 , p 2 ; q 1 , q 2 ) and the quasipotential wave functions of the final diquarks D [14][15][16][17][18][19][20][27][28][29]:…”

“…At collider energies, double charmonium production occurs for the most part through the gluon-gluon channel. The theoretical description of charmonium pair production was carried out in this case in a nonrelativistic approximation in [22][23][24][25][26] and with the account of relativistic corrections in [27][28][29][30]. Note that an additional uncertainty occurs in the ppinteraction due to the double parton scattering mechanism [31,32].…”

Double heavy quarkonium production in diffractive processes at the Run 2 LHC energy

“…The leading-order color-singlet and color-octet contributions for the differential cross sections of the gg → H 1 H 2 subprocess were calculated by several authors in the nonrelativistic approximation [7][8][9][10][11][12][13][14] and more recently by taking into account the relativistic effects [15,17] and higher-order corrections [16,19,20]. As the impact of the relativistic effects is still a theme of debate [15,17] and the higher-order corrections are predicted to modify the transverse momentum distribution at large p T [16,19,20], in our calculations for the diffractive production, we will estimate the differential cross sections at leading order, disregarding these corrections.…”

“…Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). The recent theoretical and experimental advances were strongly motivated by the large contribution of multiple parton interactions at the LHC energies [22].…”