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 $$ 1/{N}_c^2 $$ 1 / N c 2 . 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.

P-wave quarkonium wavefunctions at the origin in the $$ \overline{\mathrm{MS}} $$ scheme

“…While the binding energy for the 2P state is also consistent with the mass of the X(3872), we do not identify the 2P states with the X(3872) or other states of similar masses, because those states have masses that are heavier than the open flavor threshold, and are unlikely to be pure quarkonium states. 9 Unsurprisingly, our results for |R LO (0)| for charmonium states are much larger than what we obtain in perturbative QCD, where the long-distance nonperturbative effects in the potentials are neglected. For the 1P state, a perturbative QCD calculation at same values of α s and m gives a value of |R LO (0)| that is only a few percent of our result in table 1.…”

“…This way, nonrelativistic effective field theory methods eliminate the need for ad hoc remedies for cutting off singularities, and make possible computations of production and decay rates of P -wave heavy quarkonia based on first principles. Ongoing experimental activities in lepton and hadron colliders call for continued theoretical efforts for making accurate QCD-based predictions of P -wave quarkonium production and decay [5][6][7][8][9].…”

The static force from generalized Wilson loops using gradient flow

“…Gauge link ensembles and their parameters have been calculated up to one-loop level in Ref. [19]. This calculation will be important for the final extraction of the static force at finite flow time on the lattice.…”

“…The continuum and zero flow time limits are left for a later publication. These limits and the strong coupling extraction could be improved further with the recent perturbative calculation of the flowed static force at one loop level [19].…”

Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections

“…being incapable to describe the J/ψ-pair hadroproduction [22], single J/ψ hadroproduction at large p T [22] or e + e − → J/ψ + c + c cross section [3]. Moreover, recent theoretical developments, such as potential-NRQCD [23] or soft-gluon factorisation [24][25][26] stay within the non-relativistic paradigm for the bound-state and try to either reduce number of free parameters in NRQCD or more accurately treat the kinematic effects of soft gluon emissions at hadronisation stage.…”