Heavy quarkonium effective theory

Abstract

We formulate a QCD-based effective theory approach to heavy quarkonia-like systems ascc andbb resonances and B c states. We apply the method to inclusive decays, working out a few examples in detail.

Color-singlet relativistic correction to inclusiveJ/ψproduction associated with light hadrons atBfactories

“…As noted in Ref. [15] (see also [16]), these cms-derivative operators, though nominally of higher-order than the relative momentum operators in NRQCD expansion, can be of dynamical significance near the kinematic endpoint of quarkonium spectrum. Upon expansion of the δ-function in q 1 + q 2 , the resulting power series in v 2 make increasingly singular contributions near the boundary of partonic phase space, which signals that NRQCD expansion may break down near the endpoint region.…”

“…The shape function is of greatest utility to improve the predictions for inclusive quarkonium production in the color-octet channel [15,16,39]. Nevertheless, it can also play a nontrivial role even for the color-singlet channel, which is relevant to our case.…”

“…A more serious problem is that since each NRQCD matrix element is a number instead of a distribution, so NRQCD factorization makes rather restrictive predictions to the various J/ψ energy spectra. It has long been suggested that in certain kinematic region of quarkonium production, resummation of a class of enhanced nonperturbative effects is crucial to make reliable prediction, which effectively promotes the local NRQCD matrix element to a nonperturbative shape function [15,16]. It is also worth noting that, there is also an ongoing endeavor to circumvent the velocity expansion framework of NRQCD, by introducing a more general set of fragmentation functions in conventional perturbative QCD (pQCD) factorization base to describe inclusive quarkonium production at large p t [17].…”

Nonperturbative effects in semileptonicBcdecays

“…In fact, the non-relativistic approximation (8) can generate bound states of (inverse) size m Qv and of binding energy m Qv 2 which introduce two more, dynamically generated scales into the problem. This fact makes the construction of an effective field theory approach more complicated.…”

“…Our procedure follows the strategy of Heavy Quarkonia Effective Theory (HQQET) [8,9]. We just eliminate some redundancies and rotate the operator basis into the familiar one of NRQCD.…”