Effective Lagrangian for Two-photon and Two-gluon Decays of P-wave Heavy Quarkonium chi_c(0,2) and chi_(b0,2) states

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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} ... continued below

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5 pages

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Lansberg, J. P. & Pham, T. N. June 3, 2009.

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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} 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.

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5 pages

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  • Journal Name: Phys.Rev.D79:094016,2009

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  • Report No.: SLAC-PUB-13566
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 953850
  • Archival Resource Key: ark:/67531/metadc934205

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  • June 3, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Aug. 1, 2017, 1:27 p.m.

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Lansberg, J. P. & Pham, T. N. Effective Lagrangian for Two-photon and Two-gluon Decays of P-wave Heavy Quarkonium chi_c(0,2) and chi_(b0,2) states, article, June 3, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc934205/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.