Theory for quarkonium: from NRQCD factorization to soft gluon factorization

Abstract

We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to the nonrelativistic QCD (NRQCD) factorization for heavy quarkonium production or decay, which means that for any given process these two factorization theories are either both valid or both violated. We use two methods to achieve this conclusion. In the first method, we apply the two factorization theories to the physical process $J/\psi \to e^{+}{e}^{-}$. Our explicit calculation shows that both SGF and NRQCD can correctly reproduce low energy physics of full QCD, and thus the two factorizations are equivalent. In the second method, by using equations of motion we successfully deduce SGF from NRQCD effective field theory. By identifying SGF with NRQCD factorization, we establish relations between the two factorization theories and prove the generalized Gremm-Kapustin relations as a by product. Comparing with the NRQCD factorization, the advantage of SGF is that it resums the series of relativistic corrections originated from kinematic effects to all powers, which gives rise to a better convergence in relativistic expansion.

15 pages, 1 figure

References in corpus (8)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Potential-model calculation of an order-v^2 NRQCD matrix element
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• NRQCD Factorization and Velocity-dependence of NNLO Poles in Heavy Quarkonium Production
• Improvement for Color Glass Condensate factorization: single hadron production in pA collisions at next-to-leading order
• Order-alpha_s corrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity
• The color-singlet contribution to e^+ e^- ->J/psi + X at the endpoint

Cited by in corpus (5)

• Conceptual design of the Spin Physics Detector
• Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections
• Fragmentation function of $g\to Q\bar{Q}{(}^3{S}_1^{[8]})$ in soft gluon factorization and threshold resummation
• Color-octet contributions for $J/\psi$ inclusive production at B factories in soft gluon factorization
• Resolving negative cross section of quarkonium hadroproduction using soft gluon factorization