Abstract
Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of noncanceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quarkonium production contains derivative operators, the gauge links are necessary to make it gauge invariant and be consistent with the factorization of such non-canceling infrared divergences at all orders in coupling constant.
Highlights
Where the orbital angular momentum quantum number L = 0 corresponds to S-wave heavy quarkonium such as ηc, j/ψ and L = 1 corresponds to P-wave heavy quarkonium such as hc, χJ where S and J are the spin and total angular momentum quantum numbers of the heavy quarkonium
One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of noncanceling infrared divergences due to real soft gluons exchange, no such infrared divergences are present in the color singlet S-wave heavy quarkonium
We find that the correct definition of the gauge invariant non-perturbative matrix element of the color singlet P-wave heavy quarkonium production which is consistent with factorization of infrared divergences is given by
Summary
We find that the correct definition of the gauge invariant non-perturbative matrix element of the color singlet P-wave heavy quarkonium production which is consistent with factorization of infrared divergences is given by In this paper we will derive the correct definition of the gauge invariant color singlet P-wave non-perturbative matrix element which cancels these infrared divergences at all order in coupling constant in QCD.
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