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

Abstract

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)

Next-to-next-to-leading-order radiative corrections to e+e− → χcJ + γ at B factory

“…The LDME is determined to be O( 3 PJ ) = 0.060 +0.043 −0.029 GeV 5 [13], which seems to be considerably smaller than the values given by potential models. Nevertheless, the O(α 2 s ) corrections χc0,2 → γγ turns out to be substantial [28]. For consistency, we will not use the fitted value of LDME in [13] for m = 1.68 GeV.…”

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

“…To date, perturbative calculations beyond NLO have been conducted only for a few exclusive processes involving quarkonium, exemplified by O(α 2 s ) corrections to Υ(J/ψ) → e + e − [11,12] (Notice the O(α 3 s ) coefficients were also available recently [13,14]), η b,c → γγ [15,16], χ c0,2 → γγ [17], and B c → ℓν [18,19], as well as the O(α 2 s ) correction to the γγ * → η c,b transition form factor [16]. Only two-loop virtual corrections are required in calculating these hard matching coefficients, since they correspond to exclusive quarkonium decays or productions.…”

The P-wave charmonium annihilation into two photons $$\chi _{c0, c2}\rightarrow \gamma \gamma $$ with high-order QCD corrections

“…Refs. [5][6][7][8][9][10][11][12][13][14][15][16] and references therein. Within the framework of NRQCD factorization theory, one has observed that the leading-order (LO) prediction is close to the experimental measurements, but this process is extremely sensitive to highorder QCD corrections and relativistic corrections, due to the fact that the typical magnitude of strong coupling constant and the squared relative velocity of the charm quark in charmonium, α s (m c ) ∼ v 2 c ∼ 0.3, are comparatively large.…”

“…In year 2016, the NNLO QCD corrections to the P-wave charmonium χ c0,c2 → γ γ have been done by Ref. [16], which however show large renormalization scale dependence, and the predicted R-ratio cannot explain the above BESIII value. It is important to show what's the reason for such discrepancy.…”

“…The amplitude of the P-wave quarkonium electromagnetic decays χ c0,c2 → γ γ can be expressed as [16] A…”