Relativistic and binding energy corrections to direct photon production inϒdecay

Abstract

A systematic gauge-invariant method, which starts directly from QCD, is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v 2 ) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.

Measurement of the direct photon momentum spectrum inΥ(1S),Υ(2S)Besson1, Henderson2, Pedlar3 et al. 2006Phys. Rev. D27110View full textAdd to dashboardCite

“…These can dominate the background-subtracted spectra for x γ <0.4 and therefore (if not corrected for) lead to an over-estimate of the Υ(1S)→ ggγ branching fraction, and an underestimate of the extracted value of α s . Hoodbhoy and Yusuf [13] also performed a rigorous calculation of the expected Υ(1S)→ ggγ decay rate, by summing all the diagrams contributing to the direct photon final state and treating hard and soft contributions separately. Rather than assuming that the decay occurs via annihilation of two at-rest quarks, the authors smear the annihilation over a size of order 1/m, with a corresponding non-zero velocity.…”

“…Hoodbhoy and Yusuf [13] also performed a rigorous calculation of the expected Υ(1S)→ ggγ decay rate, by summing all the diagrams contributing to the direct photon final state and treating hard and soft contributions separately. Rather than assuming that the decay occurs via annihilation of two at-rest quarks, the authors smear the annihilation over a size of order 1/m, with a corresponding non-zero velocity.…”