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Title: Heavy quarkonium decays and transitions in the language of effective field theories

Abstract

Heavy quarkonium decays and transitions are discussed in the framework of non-relativistic effective field theories. Emphasis is put on the matching procedure in the non-perturbative regime. Some exact results valid for the magnetic dipole couplings are discussed.

Authors:
 [1];  [2]
  1. Dipartimento di Fisica dell'Universita di Milano, via Celoria 16, 20133 Milano (Italy)
  2. (Italy)
Publication Date:
OSTI Identifier:
20787642
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 806; Journal Issue: 1; Conference: International workshop on quantum chromodynamics: Theory and experiment, Conversano, Bari (Italy), 16-20 Jun 2005; Other Information: DOI: 10.1063/1.2163767; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COUPLING; HADRONIC PARTICLE DECAY; MAGNETIC DIPOLES; MESONS; QUANTUM CHROMODYNAMICS; QUARKONIUM; RELATIVISTIC RANGE; RESONANCE PARTICLES

Citation Formats

Vairo, Antonio, and INFN, via Celoria 16, 20133 Milan. Heavy quarkonium decays and transitions in the language of effective field theories. United States: N. p., 2006. Web. doi:10.1063/1.2163767.
Vairo, Antonio, & INFN, via Celoria 16, 20133 Milan. Heavy quarkonium decays and transitions in the language of effective field theories. United States. doi:10.1063/1.2163767.
Vairo, Antonio, and INFN, via Celoria 16, 20133 Milan. Thu . "Heavy quarkonium decays and transitions in the language of effective field theories". United States. doi:10.1063/1.2163767.
@article{osti_20787642,
title = {Heavy quarkonium decays and transitions in the language of effective field theories},
author = {Vairo, Antonio and INFN, via Celoria 16, 20133 Milan},
abstractNote = {Heavy quarkonium decays and transitions are discussed in the framework of non-relativistic effective field theories. Emphasis is put on the matching procedure in the non-perturbative regime. Some exact results valid for the magnetic dipole couplings are discussed.},
doi = {10.1063/1.2163767},
journal = {AIP Conference Proceedings},
number = 1,
volume = 806,
place = {United States},
year = {Thu Jan 12 00:00:00 EST 2006},
month = {Thu Jan 12 00:00:00 EST 2006}
}
  • This article reviews recent theoretical developments in heavy-quarkonium physics from the point of view of effective-field theories of QCD. We discuss nonrelativistic QCD and concentrate on potential nonrelativistic QCD. The main goal will be to derive Schroedinger equations based on QCD that govern heavy-quarkonium physics in the weak- and strong-coupling regimes. Finally, the review discusses a selected set of applications, which include spectroscopy, inclusive decays, and electromagnetic threshold production.
  • QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. Here I summarize few relevant concepts and some of the interesting physical applications (spectrum, decays, production) of NREFT.
  • In the traditional non-relativistic bound state calculation, the two-photon decay amplitudes of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} states depend on the derivative of the wave function at the origin which can only be obtained from potential models. However by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation. Following the same line as in recent work for the two-photon decays of the S-wave {eta}{sub c} and {eta}{sub b}more » quarkonia, we show that the effective Lagrangian for the two-photon decays of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} is given by the heavy quark energy-momentum tensor local operator or its trace, the {anti Q}Q scalar density and that the expression for {chi}{sub c0} two-photon and two-gluon decay rate is given by the f{sub {chi}{sub c0}} decay constant and is similar to that of {eta}{sub c} which is given by f{sub {eta}{sub c}}. From the existing QCD sum rules value for f{sub {chi}{sub c0}}, we get 5 keV for the {chi}{sub c0} two-photon width, somewhat larger than measurement, but possibly with large uncertainties.« less
  • In the traditional nonrelativistic bound state calculation, the two-photon decay amplitudes of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} states depend on the derivative of the wave function at the origin, which can only be obtained from potential models. However, by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with the QCD sum rules technique or lattice simulation. Following the same lines as in recent work for the two-photon decays of the S-wave {eta}{sub c} and {eta}{submore » b} quarkonia, we show that the effective Lagrangian for the two-photon decays of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} states is given by the heavy quark energy-momentum tensor local operator or its trace, the QQ scalar density, and that the expression for {chi}{sub c0} two-photon and two-gluon decay rates is given by the f{sub {chi}{sub c}{sub 0}} decay constant and is similar to that of {eta}{sub c} which is given by f{sub {eta}{sub c}}. From the existing QCD sum rules value for f{sub {chi}{sub c}{sub 0}}, we get 5 keV for the {chi}{sub c0} two-photon width, somewhat larger than the measurements, but possibly with large uncertainties.« less
  • The mechanism of dipion transitions nS {sup {yields}}n'S {pi}{pi} (n = 3, 2; n' = 2, 1) in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of {pi}(K, {nu}), and not containing fitting parameters. The transition amplitude contains two terms: M = a - b, where the first term (a) refers to subsequent one-pion emission, {Gamma} (nS) {yields} {pi} B bar B {yields} {pi} {Gamma} (n'S){pi} , and the second term (b) refers to two-pion emission, {Gamma} (nS) {yields} {pi} {pi} B bar B {yields} {pi} {pi} {Gamma}more » (n'S). The one parameter formula for the dipion mass distribution is derived, dw/dq {approx} (phase space) x vertical bar {eta} - x vertical bar {sup 2}, where x = (q{sup 2} - 4m{sub {pi}}{sup 2})/(q{sub max}{sup 2} - 4m{sub {pi}}{sup 2}), q{sup 2} m= M{sub {pi}{pi}}{sup 2}. The parameter {nu} dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a and b. The resulting dipion mass distributions are in agreement with experimental data.« less