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Abstract
Introduction
Nrqcd. How to Build It? General Procedure
Pnrqcd. How to Build It? General Procedure
Summary for the Practitioner
Phenomenological Analysis
Conclusions
References
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Physics
Nuclear and High Energy Physics

Review of heavy quarkonium at weak coupling

Profile image of Antonio Hernandez PinedaAntonio Hernandez Pineda

2012, Progress in Particle and Nuclear Physics

https://doi.org/10.1016/J.PPNP.2012.01.038
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Abstract

We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential non-relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed, and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, non-relativistic sum rules, inclusive decays, and electromagnetic threshold production.

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Joan Soto

Modern Physics Letters A, 2004

We review a number of results for the spectrum and inclusive decays of heavy quarkonium systems which can be derived from QCD under well controlled approximations. They essentially follow from the hierarchy of scales in these systems, which can be efficiently exploited using non-relativistic effective field theories. In particular, we discuss under which conditions non-relativistic potential models emerge as effective theories of QCD.

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Inclusive decays of heavy quarkonium to light particles
Joan Soto

Physical Review D, 2003

We derive the imaginary part of the potential NRQCD Hamiltonian up to order 1/m 4 , when the typical momentum transfer between the heavy quarks is of the order of Λ QCD or greater, and the binding energy E much smaller than Λ QCD. We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to O(mv 3 × (Λ 2 QCD /m 2 , E/m)) and O(mv 5) times a short-distance coefficient, for Sand P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown non-perturbative parameters and, therefore, we obtain new modelindependent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal non-perturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal non-perturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.

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Potential NRQCD: an effective theory for heavy quarkonium
Antonio Hernandez Pineda

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.

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Related topics

  • Effective Field Theory

    • Cited by

    QCD and strongly coupled gauge theories: challenges and perspectives
    Susan Gardner, J. Goity, A. Kronfeld, F. Llanes-estrada, R. Vogt, Elias Kiritsis, H. Sazdjian

    The European Physical Journal C, 2014

    We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

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    Dissociation of heavy quarkonia in an anisotropic hot QCD medium in a quasiparticle model
    Indrani nilima

    Physical Review D

    The present article is the follow-up work of Phys. Rev. D 94, 094006 (2016), where we have extended the study of quarkonia dissociation in (momentum) anisotropic hot QCD medium. As evident by the experimentally observed collective flow at the RHIC and LHC, the momentum anisotropy is present at almost all the stages after the collision, and therefore, it is important to include its effects in the analysis. Employing the in-medium (corrected) potential while considering the anisotropy (both oblate and prolate cases) in the medium, the thermal widths and the binding energies of the heavy quarkonia states (s-wave charmonia and s-wave bottomonia specifically, for radial quantum numbers n ¼ 1 and 2) have been determined. The hot QCD medium effects have been included by employing a quasiparticle description. The presence of anisotropy has modified the potential and then the thermal widths and binding energies of these states in a significant manner. The results show a quite visible shift in the values of dissociation temperatures as compared to the isotropic case. Further, the hot QCD medium interaction effects suppress the dissociation temperature as compared to the case where we consider the medium as a noninteracting ultrarelativistic gas of quarks (antiquarks) and gluons.

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    Heavy quarkonium moving in a quark-gluon plasma
    Massimo Mannarelli

    Physical Review D, 2013

    By means of effective field theory techniques, we study the modifications of some properties of weakly coupled heavy quarkonium states propagating through a quark-gluon plasma at temperatures much smaller than the heavy quark mass, mQ. Two different cases are considered, corresponding to two different hierarchies between the typical size of the bound state, r, the binding energy, E, the temperature, T , and the screening mass, mD. The first case corresponds to the hierarchy mQ ≫ 1/r ≫ T ≫ E ≫ mD, relevant for moderate temperatures, and the second one to the hierarchy mQ ≫ T ≫ 1/r , mD ≫ E, relevant for studying the dissociation mechanism. In the first case we determine the perturbative correction to the binding energy and to the decay width of states with arbitrary angular momentum, finding that the width is a decreasing function of the velocity. A different behavior characterizes the second kinematical case, where the width of s-wave states becomes a non-monotonic function of the velocity, increasing at moderate velocities and decreasing in the ultra-relativistic limit. We obtain a simple analytical expression of the decay width for T ≫ 1/r ≫ mD ≫ E at moderate velocities, and we derive the s-wave spectral function for the more general case T ≫ 1/r , mD ≫ E. A brief discussion of the possible experimental signatures as well as a comparison with the relevant lattice data are also presented.

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    Heavy quarkonium at finite temperature and chemical potential
    Joan Soto

    Physical Review D, 2020

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    Long-range properties of 1 S bottomonium states
    Gastao Krein

    Physical Review D, 2016

    In the framework of weakly coupled potential nonrelativistic QCD, we derive, first, an analytical expression for the chromopolarizability of 1S bottomonium states in agreement with previous determinations. Then we use the QCD trace anomaly to obtain the two-pion production amplitude for the chromopolarizability operator and match the result to a chiral effective field theory with 1S bottomonium states and pions as degrees of freedom. In this chiral effective field theory we compute some long-range properties of the 1S bottomonium generated by the pion coupling such as the leading chiral logarithm to the 1S bottomonium mass and the van der Waals potential between two 1S bottomonium states. Both results improve on previously known expressions.

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