Decay and electromagnetic production of strongly coupled quarkonia in pNRQCD

Abstract

We improve the pNRQCD approach to annihilation processes of heavy quarkonium and make first pNRQCD predictions for exclusive electromagnetic production of heavy quarkonium. We consider strongly coupled quarkonia, i.e., quarkonia that are not Coulombic bound states. Possible strongly coupled quarkonia include excited charmonium and bottomonium states. For these, pNRQCD provides expressions for the decay and exclusive electromagnetic production NRQCD matrix elements that depend on the wavefunctions at the origin and few universal gluon field correlators. We compute electromagnetic decay widths and exclusive production cross sections, and inclusive decay widths into light hadrons for P -wave quarkonia at relative order v 2 and leading order, respectively. We also compute the decay widths of 2S and 3S bottomonium states into lepton pairs and their ratios with the inclusive widths into light hadrons at relative order v 2 . arXiv:2002.07462v2 [hep-ph] 17 Apr 2020 1 The quark-antiquark potential is Coulombic under the condition mv 2 ΛQCD, in which case, v ∼ αs. -4 -, c (T ) J and c (P ) J in eqs. (B.23)-(B.31).

MS renormalization of S-wave quarkonium wavefunctions at the origin

“…The order-α s v 2 contribution to the anomalous dimension in eq. (2.3) is consistent with the known scale dependence of E 3 [40,42]. As a result, the two-loop anomalous dimension in the first term on the right-hand side of eq.…”

“…This wavefunction is an eigensolution of the Schrödinger equation 8) where the potential V (r, ∇) is the one that appears in h S , and we take the wavefunction to be unit normalized ( d 3 r |Ψ n (r)| 2 = 1). The NRQCD LDMEs can be computed in pNRQCD by matching the four-quark operators in the NRQCD Lagrangian to the pNRQCD Hamiltonian h S [39] (alternatively, the same result can be obtained by directly matching the NRQCD LDMEs to pN-RQCD [39,40]). The pNRQCD expression for a decay LDME from a four-quark operator O on a heavy quarkonium state H is given by…”

“…Hence, in this case, the LDMEs H|O|H have the form of squares of quarkonium-to-vacuum matrix elements. The leading-order LDME for a vector quarkonium V is given in strongly coupled pNRQCD to relative order v 2 and Λ 2 QCD /m 2 accuracy by [39,40] 0|χ…”

“…The leading-order LDME for a pseudoscalar quarkonium P is given in strongly coupled pNRQCD to relative order v 2 and Λ 2 QCD /m 2 accuracy by [39,40] 0|χ (2.13) and the order-v 2 LDME is given at leading order in v and Λ QCD /m by…”

“…The dimensionless correlator E 3 in the MS scheme has been determined in ref. [40] from measured decay rates of P -wave charmonia. At the MS scale Λ = 1 GeV, E 3 (1 GeV) = 2.05 +0.…”