Two-photon width of singlet positronium and quarkonium with arbitrary total angular momentum

Ackleh, E.S.; Barnes, T.

doi:10.1103/physrevd.45.232

Cited by 73 publications

(97 citation statements)

References 17 publications

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“…The [16] independently developed a similar approach to the one we developed for positronium decay [15] and then applied it to spin singlet quarkonium decay into two gammas. As in our approach, they include the effects of the bound state wave function on the initial decaying particle.…”

Section: A Charmoniummentioning

confidence: 99%

“…[16] which uses p 0 i = m 2 + p 2 i ). The amplitude we use incorporates an off-mass-shell assumption which is true for constituent particles of the bound state.…”

Section: Positronium Decaysmentioning

confidence: 99%

“…Independent treatments by Crater [15] and Ackleh and Barnes [16] develop related (but distinctly different) approaches for folding in the effect of the Yukawa fermion exchange mass, giving a smearing of the singularity over the corresponding Compton wave length. We give a brief review of the first of these approaches and how we extend it to include the effects of the full sixteen component Two-Body Dirac wave function.…”

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confidence: 99%

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Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons

2006

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Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schrödinger equation. Here we begin important tests of the relativistic sixteen component wave function solutions obtained in a recent work on meson spectroscopy, extending a method developed previously for positronium decay into two photons. Preliminary to this we examine the positronium decay in the 3 P0,2 states as well as the 1 S0. The two-gamma quarkonium decays that we investigate are for the η c , η ′ c , χ c0 , χ c2 , π 0 , π2, a2,and f ′ 2 mesons. Our results for the four charmonium states compare well with those from other quark models and show the particular importance of including all components of the wave function as well as strong and CM energy dependent potential effects on the norm and amplitude. The results for the π 0 , although off the experimental rate by 15%, is much closer than the usual expectations from a potential model. We conclude that the Two-Body Dirac equations lead to wave functions which provide good descriptions of the two-gamma decay amplitude and can be used with some confidence for other purposes.

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Section: A Charmoniummentioning

confidence: 99%

“…[16] which uses p 0 i = m 2 + p 2 i ). The amplitude we use incorporates an off-mass-shell assumption which is true for constituent particles of the bound state.…”

Section: Positronium Decaysmentioning

confidence: 99%

mentioning

confidence: 99%

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Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons

2006

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“…(20). Equation (15) is still general (up to the absence of exchange currents) and we may study it in both limits: case A (Eq.…”

Section: Bethe-salpeter Approachmentioning

confidence: 99%

“…There exists a prescription to calculate the two-photon decay amplitude by contracting the on-shell decay amplitude with the bound-state wave function ψ( k) (see, e.g. [20]):…”

Section: Case a In The Weak Coupling Limitmentioning

confidence: 99%

Two-photon decays of hadronic molecules

Hanhart

Kalashnikova²,

Kudryavtsev³

et al. 2007

Phys. Rev. D

119

139

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In many calculations of the two-photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force 1/β. In the leading order one gets the well-known pointlike limit answer. We estimate, in a self-consistent and gauge invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small, of order O(mε/β 2 ), where m and ε denote the mass of the constituents and the binding energy, respectively. The role of possible shortranged operators and of the width of the scalars remains to be investigated.

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Annihilation rate of 2−+ charmonium and bottomonium

Wang

et al. 2013

J. High Energ. Phys.

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The 1 1 D 2 (cc) state is the ground state of spin-singlet D-wave charmonia. Although it has not been found yet, the experimental data accumulate rapidly. This charmonium attracts more and more attention, especially when the BaBar Collaboration finds that the X(3872) particle has negative parity. In this paper we calculate the double-gamma and double-gluon annihilation processes of 1 D 2 charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. We find the relativistic corrections make the decay widths of 1 1 D 2 (cc) 2∼5 times smaller than the non-relativistic results. If this state is below the D 0 D 0 * threshold, we can use the sum of annihilation widths and EM transition widths to estimate the total decay width. Our result for 1 1 D 2 (cc) with m = 3820 GeV is Γ = 432 keV. The dominant decay channel 1 1 D 2 (cc) → h c γ, whose branching ratio is about 90%, can be used to discover this state.

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Two-photon width of singlet positronium and quarkonium with arbitrary total angular momentum

Cited by 73 publications

References 17 publications

Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons

Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons

Two-photon decays of hadronic molecules

Annihilation rate of 2−+ charmonium and bottomonium

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