Model Independent Results for Heavy Quarkonium

Physical Review D, 1996

We present a method which, starting directly from QCD, permits a systematic gauge-invariant expansion to be made for all hard processes involving quarkonia in powers of the quark relative velocity, a small natural parameter for heavy quark systems. Our treatment automatically introduces soft gluons in the expansion. Corrections arising from the incorporation of gauge symmetry turn out to be important for decay and fragmentation processes involving QQ systems. The contribution of soft gluons is shown to be of higher order in v and so is neglected for calculations done upto and including O(v 2).

Journal of High Energy Physics

In this work we apply effective field theory (EFT) to observables in quarkonium production and decay that are sensitive to soft gluon radiation, in particular measurements that are sensitive to small transverse momentum. Within the EFT framework we study χ Q decay to light quarks followed by the fragmentation of those quarks to light hadrons. We derive a factorization theorem that involves transverse momentum distribution (TMD) fragmentation functions and new quarkonium TMD shape functions. We derive renormalization group equations, both in rapidity and virtuality, which are used to evolve the different terms in the factorization theorem to resum large logarithms. This theoretical framework will provide a systematic treatment of quarkonium production and decay processes in TMD sensitive measurements.

2012

Nuclear Physics B, 2000

Within an effective field theory framework we study heavy-quark-antiquark systems with a typical distance between the heavy quark and the antiquark smaller than 1/Λ QCD . A suitable definition of the potential is given within this framework, while non-potential (retardation) effects are taken into account in a systematic way. We explore different physical systems. Model-independent results on the short distance behavior of the energies of the gluonic excitations between static quarks are obtained. Finally, we show how infrared renormalons affecting the static potential get cancelled in the effective theory.

2000

The effective quark models are employed to describe the hadronization of QCD in the quark sector. They reveal a different structure depending on how the spontaneous chiral symmetry breaking (CSB) is implemented. When the generation of light pseudoscalar mesons is manifestly incorporated one deals with an extension of the chiral quark model (CQM) with the non-linear realization of chiral symmetry. If a model is built at the CSB scale by means of perturbation theory it generalizes the Nambu-Jona-Lasinio (NJL) one with chiral symmetry broken due to attractive 4-fermion forces in the scalar channel. The matching to high-energy QCD is realized at CSB scale by means of Chiral Sum Rules. Two types of models are compared in their fitting of meson physics. In particular, if the lowest scalar meson is sufficiently heavy approaching the mass of heavy \pi'(1300) then QCD favours an effective theory which is dominated by the simplest CQM. On the contrary, the light scalar quarkonium with a mass of order 500MeV, supports the NJL mechanism.

Physical Review D, 2002

We complete the leading-log renormalization group scaling of the nonrelativistic ͑NRQCD͒ Lagrangian at O(1/m 2 ). The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian ͑as far as the singlet is concerned͒ is also obtained in the situation m␣ s ӷ⌳ QCD . As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation m␣ s 2 տ⌳ QCD . When ⌳ QCD Ӷm␣ s 2 , this is equivalent to obtain the whole set of O(m␣ s (nϩ4) ln n ␣ s ) terms in the heavy quarkonium spectrum. The implications of our results in the nonperturbative situation m␣ s ϳ⌳ QCD are also mentioned.

AIP Conference Proceedings, 2000

We discuss the low energy effective action of QCD in the quark sector. When it is built at the CSB (chiral symmetry breaking) scale by means of perturbation theory it has the structure of a generalized Nambu-Jona-Lasinio (NJL) model with CSB due to attractive forces in the scalar channel. We show that if the lowest scalar meson state is sufficiently lighter than the heavy pseudoscalar π ′ then QCD favors a low-energy effective theory in which higher dimensional operators (of the Nambu-Jona-Lasinio type) are dominated and relatively strong. A light scalar quarkonium (m σ = 500 ÷ 600 MeV) would provide an evidence in favor to this NJL mechanism. Thus the non-chiral Quasilocal Quark Models (QQM) in the dynamical symmetry-breaking regime are considered as approximants for low-energy action of QCD. In the mean-field (large-N c) approach the equation on critical coupling surface is derived. The mass spectrum of scalar and pseudoscalar excited states is calculated in leading-log approach which is compatible with the truncation of the QCD effective action with few higher-dimensional operators. The matching to QCD based on the Chiral Symmetry Restoration sum rules is performed and it helps to select out the relevant pattern of CSB as well as to enhance considerably the predictability of this approach.

Nuclear Physics B, 2010

We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the η b decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.

Physical Review D, 1996

We analyse the possible existence of non-perturbative contributions in heavȳ QQ systems (Q and Q need not have the same flavour) which cannot be expressed in terms of local condensates. Starting from QCD, with well defined approximations and splitting properly the fields into large and small momentum components, we derive an effective lagrangian where hard gluons (in the non-relativistic aproximation) have been integrated out. The large momentum contributions (which are dominant) are calculated using Coulomb type states. Besides the usual condensate corrections, we see the possibility of new nonperturbative contributions. We parametrize them in terms of two low momentum correlators with Coulomb bound state energy insertions E n . We realize that the Heavy Quark Effective lagrangian can be used in these correlators. We calculate the corrections that they give rise to in the decay constant, the bound state energy and the matrix elements of bilinear currents at zero recoil. We study the cut-off dependence of the new contributions and we see that it matches perfectly

Physical Review D, 2002

In the framework of potential nonrelativistic QCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy-quarkonium production currents near threshold. This allows us to obtain S-wave heavy-quarkonium production or annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to e ϩ e Ϫ and to two photons. We also compute the O(m␣ 8 ln 3 ␣) corrections to the hydrogen spectrum.