Inclusive Production of Heavy Quarkonia in pNRQCD

Abstract

We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order 1/N 2 c . These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of P -wave charmonia and bottomonia at the LHC, and find good agreement with measurements.

Quarkonium production in pNRQCD: the $P$-wave case

“…Following [6,7], we find that after matching with pNRQCD the contact terms O ( ) ( , ∇ ) projecting on -wave states read up to higher order corrections…”

“…In this contribution, instead, we summarize the work done in the last two years to provide, under some circumstances, a description of quarkonium production cross sections also in the ultimate EFT listed in figure 1, i.e. potential NRQCD (pNRQCD) [5][6][7].…”

“…Following [7], the correlator E can be fitted to the ratio 21 = ( 2 (1 ) / )/( 1 (1 ) / ), which does not depend (at leading order in ) on the wavefunction. In order to compare to measurements, we compute 21 multiplied with 2 (1 ) / 1 (1 ) , where…”

“…The ratio of the 2 (1 ) and 1 (1 ) differential cross sections times 2 (1 ) / 1 (1 ) at the LHC center of mass energy √ = 7 TeV and in the rapidity range | | < 0.75, with fitted E, compared to CMS [30] and ATLAS [31] data. From [7].…”

“…For -wave bottomonium, we show in figure 10 the differential production cross section ratio ( 2 (1 ) / )/( 1 (1 ) / ), which does not depend at leading order in and 1/ on TeV and in the rapidity range 2 < < 4.5 compared with LHCb [35] and CMS [36] data. From [7].…”