Erratum to: electromagnetic quarkonium decays at order v 7

Abstract

We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M 4 in the heavy-quark mass expansion, which includes center of mass operators, and at order α 2 s in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order 1/M 6 and at order α 2 s that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at order v 7 in the heavy-quark velocity expansion. If we count α s (M ) ∼ v 2 , the calculation provides the complete next-to-leading order corrections to the P-wave hadronic widths, and in the original NRQCD power counting, the complete next-to-leading order corrections to the vector S-wave widths, and part of the next-to-next-to leading order corrections to the pseudoscalar S-wave widths. In the S-wave case, we confirm previous findings and add new terms in a more conservative power counting. In the P-wave case, our results are in disagreement with previous ones. Constraints induced by Poincaré invariance on the NRQCD four-fermion sector are studied for the first time and provide an additional check of the calculation. Perspectives for phenomenological applications are discussed.

New developments in FeynCalc 9.0

“…These matching coefficients have been calculated in the framework of NRQCD multiple times [16,32,61,62,63], with many of these calculations carried out in a fully covariant way using the covariant projector technique [33]. Nevertheless, for pedagogical reasons we want to stick to the explicit non-covariant matching in the spirit of [16] and [62].…”

On HQET and NRQCD operators of dimension 8 and above

“…The main reason is that the one heavy fermion sector can be considered as interacting with another heavy fermion leading to, e.g. higher power NRQCD and NRQED four-fermion operators, see [9,[23][24][25], or as interacting with a relativistic fermion leading to the four-fermion operators QED-NRQED operators, see [9,14]. Each case should be considered separately depending on the application and is beyond the scope of this paper.…”

“…Results for each case were presented in the literature [9,14,[23][24][25], but not for an arbitrary operator dimension.…”

Relativistic correction to J/ψ and $ \varUpsilon $ pair production

“…In general, the intermediate state can be in a conventional color-singlet or a color-octet state. By introducing the color-octet mechanism, one can get the infrared-safe calculations for the decay rates of P-wave quarkonium states [2][3][4][5][6][7][8][9] and D-wave [10][11][12] decay widths. Besides, one may also explain the Tevatron data on the surplus production of J/ψ and ψ ′ at large p T by fitting the data and extracting the color-octet long-distance NRQCD matrix elements.…”