Calculation of the annihilation rate of P wave quark-antiquark bound states

Barbieri, Riccardo; Gatto, R.; Kögerler, Reinhart

doi:10.1016/0370-2693(76)90419-6

Cited by 229 publications

(107 citation statements)

References 8 publications

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“…In parallel with positronium decay, the leading-order NRQCD prediction to χ c0,2 → γγ in the nonrelativistic limit is extremely simple, yields R = 4/15 ≈ 0.27 [16]. This is impressively consistent with the measurement (2a).…”

supporting

confidence: 81%

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

et al. 2016

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We calculate the next-to-next-to-leading-order (NNLO) perturbative corrections to P -wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD (NRQCD) factorization. The order-α 2 s short-distance coefficients associated with each helicity amplitude are presented in a semi-analytic form, including the "light-by-light" contributions. With substantial NNLO corrections, we find disquieting discrepancy when confronting our state-of-the-art predictions with the latest BESIII measurements, especially fail to account for the measured χc2 → γγ width. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative NRQCD matrix elements of χc0 and χc2 toward the wrong direction. We also present the order-α 2 s predictions to χ b0,2 → γγ, which await the future experimental test. Charmonium decay has historically played an important role in establishing the asymptotic freedom of QCD, and served as a clean platform to probe the interplay between pertubative and nonperturbative dynamics [1,2]. Among them, the electromagnetic decay χ c0,2 → γγ provide a particularly interesting, and, rich testing ground of QCD [3,4]. In the past decades, these decay channels have been extensively studied from various theoretical angles, such as nonrelativistic potential model [5,6], relativistic quark model [7][8][9], Bethe-Salpeter approach [10], nonrelativistic QCD (NRQCD) factorization [11,12], as well as lattice QCD [13]. On the experimental side, they were previously measured by . BESIII experiment [15] has recently reported their high precision results, Γ γγ (χ c0 ) = (2.33 ± 0.20 ± 0.13 ± 0.17) keV, (1a) Γ γγ (χ c2 ) = (0.63 ± 0.04 ± 0.04 ± 0.04) keV. (1b)

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confidence: 81%

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

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“…As stressed in [40] the inclusion of the small components of the wave functions is essential for this decay. For the 3 P 2 amplitude j = 2, l = j − 1 = 1, j ′ = 0, 2, 4.…”

Section: Positronium Decaysmentioning

confidence: 99%

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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“…In spite of the fact that this wave function was not computable from perturbative QCD (pQCD), it canceled in suitable ratios, and hence predictions depending on pQCD only could be put forward. Nevertheless, it was soon noticed that the above framework had difficulties due to the infrared divergences which showed up at higher orders of s m [2]. The introduction of color octet operators in the framework of nonrelativistic QCD (NRQCD) [3] provided a rigorous way to understand and to deal with these divergences [4].…”

mentioning

confidence: 99%

“…Later on, it was pointed out that of the hierarchy of relevant scales in heavy quarkonium m mv mv 2 , v being the relative velocity, only the first inequality was exploited in NRQCD and that the velocity counting proposed in [3] did not necessarily follow from it. It was also shown how the last inequality could be exploited by constructing a further effective theory, namely, potential NRQCD (pNRQCD) [5,6](see [7] for a review).…”

mentioning

confidence: 99%

“…The interplay of QCD with the scales mv and mv 2 above dictates the degrees of freedom of pNRQCD. Two regimes have been identified: (i) the weak coupling regime, QCD & mv 2 , and (ii) the strong coupling regime mv 2 QCD & mv. In the weak coupling regime, the relevant degrees of freedom are a singlet and an octet wave function fields interacting with (perturbative) potentials and with ultrasoft gluons.…”

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Radiative Decays and the Nature of Heavy Quarkonia

Tormo

Soto

2006

Phys. Rev. Lett.

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We argue that the photon spectra in radiative decays of various heavy quarkonium states provide important information on their nature. If two of these states are in the strong coupling regime, we are able to produce a parameter-free model-independent formula, which holds at next-to-leading order and includes both direct and fragmentation contributions. When the formula is checked against recent CLEO data it favors 2S and 3S in the strong coupling regime and disfavors 1S in it. DOI: 10.1103/PhysRevLett.96.111801 PACS numbers: 13.20.Gd, 12.39.St Heavy quarkonium systems have played a major role in our understanding of QCD (see [1] for a review). Inclusive heavy quarkonium decays to light particles involve a short distance process, in which the heavy quark and antiquark annihilate into gluons or photons, and a long distance process, which takes into account that the heavy quark and antiquark are bound in a color singlet state. Because of the asymptotic freedom of QCD the short distance process can be calculated using perturbation theory in s m , m being the heavy quark mass. It was believed for some time that in order to have a color singlet state the heavy quark and antiquark in it had to be in a color singlet state themselves. This allowed us to parameterize the long distance process by a wave function at the origin (or derivatives of it). In spite of the fact that this wave function was not computable from perturbative QCD (pQCD), it canceled in suitable ratios, and hence predictions depending on pQCD only could be put forward. Nevertheless, it was soon noticed that the above framework had difficulties due to the infrared divergences which showed up at higher orders of s m [2]. The introduction of color octet operators in the framework of nonrelativistic QCD (NRQCD) [3] provided a rigorous way to understand and to deal with these divergences [4]. The price to be paid was the introduction of new nonperturbative parameters, the color octet matrix elements, which made predictions depending on pQCD only more difficult to obtain.Later on, it was pointed out that of the hierarchy of relevant scales in heavy quarkonium m mv mv 2 , v being the relative velocity, only the first inequality was exploited in NRQCD and that the velocity counting proposed in [3] did not necessarily follow from it. It was also shown how the last inequality could be exploited by constructing a further effective theory, namely, potential NRQCD (pNRQCD) [5,6](see [7] for a review). The interplay of QCD with the scales mv and mv 2 above dictates the degrees of freedom of pNRQCD. Two regimes have been identified: (i) the weak coupling regime, QCD & mv 2 , and (ii) the strong coupling regime mv 2 QCD & mv. In the weak coupling regime, the relevant degrees of freedom are a singlet and an octet wave function fields interacting with (perturbative) potentials and with ultrasoft gluons. The original NRQCD counting [3] belongs to this regime. Moreover, the use of diagrammatic and quantum mechanical methods allows us to carry out explicit calculations ...

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Calculation of the annihilation rate of P wave quark-antiquark bound states

Cited by 229 publications

References 8 publications

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

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

Radiative Decays and the Nature of Heavy Quarkonia

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