Impact of J/ψ pair production at the LHC and predictions in nonrelativistic QCD

Abstract

For J/ψ pair production at hadron colliders, we present the full next-to-leading order (NLO) calculations with the color-singlet channel in nonrelativistic QCD. We find that the NLO result can reasonably well describe the LHCb measured cross section, but exhibits very different behaviors from the CMS data in the transverse momentum distribution and mass distribution of J/ψ pair. Moreover, by adding contributions of gluon fragmentation and quark fragmentation, which occur at even higher order in αs, it is still unable to reduce the big differences. In particular, the observed flat distribution in the large invariant mass region is hard to explain. New processes or mechanisms are needed to understand the CMS data for J/ψ pair production. A. INTRODUCTIONNonrelativistic QCD (NRQCD) [1] is widely used in the study of heavy quarkonium physics. In NRQCD a quarkonium production process can be factorized as short-distance parton scattering amplitudes multiplied by long-distance matrix elements (LDMEs). This factorization has been applied in single quarkonium production and tested by various experiments [2][3][4][5][6][7].Besides the single quarkonium production, the multiquarkonuim production provides another ideal laboratory to understand the quarkonium production mechanism that NRQCD assumes. At the LHC, the LHCb Collaboration in 2011 measured the J/ψ pair production for the first time at the center-of-mass energy √ s = 7 TeV with an integrated luminosity of 35.2 pb −1 [8]. In 2013, the CMS Collaboration further released the data of J/ψ pair production[9] with a much larger transverse moment range, providing a good platform for testing the validity of NRQCD in quarkonium pair production.In Refs. [10][11][12], the leading order (LO) calculation of J/ψ pair production in the color singlet model (CSM) is performed. The relativistic correction to the J/ψ pair production is carried out in Ref. [13], where the relativistic correction makes significant improvement for diluting the discrepancy between the shapes of color-singlet (CS) and color-octet (CO) differential cross sections at LO. Furthermore, the partial next-to-leading order (NLO ⋆ ) correction for J/ψ pair production is evaluated by Lansberg and Shao [14]. They argue that the NLO ⋆ yield can approach the full NLO result at large p T , the transverse momentum of one of the two J/ψ's, and thus the NLO ⋆ results give a more precise theoretical prediction than the * Electronic address: sunliping@pku.edu.cn † Electronic address: hao.han@pku.edu.cn ‡ Electronic address: ktchao@pku.edu.cn LO results in this region. All the above works are performed in the single parton scattering (SPS) mechanism, while the contribution of double parton scattering (DPS) is assessed in Refs. [15][16][17], and is expected to be important. As predictions for DPS are very model-dependent [15][16][17], it is needed to have an accurate calculation for SPS contribution before one can extract the DPS contribution.In order to further understand the multi-quarkonium production mechanism, it is neces...

Measurement of the J/ψ pair production cross-section in pp collisions at s = 13 $$ \sqrt{s}=13 $$ TeV

“…The SPS contribution is calculated to be 4.0 ± 1.2 nb [67,68] and 4.6 ± 1.1 nb [39] in the leading-order NRQCD CS approach, and 5.4…”

“…It either describes the production cross-sections and polarisations at large p T or it describes the production cross-section at all p T values, but then fails to predict the polarisation [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. This puzzle can be probed via the production of pairs of quarkonia [34][35][36][37][38][39], where the interpretation of the measured cross-section could be simpler. In quarkonium-pair production, the selection rules in the CS process of leading-order (LO) NRQCD forbid the feed-down from cascade decays of excited C-even states.…”

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.…”

“…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. We will follow the notation from Refs.…”

“…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].…”