Can NRQCD explain the $\gamma {\gamma }^{\ast }\to {\eta }_c$ transition form factor data?

Abstract

Unlike the bewildering situation in the $\gamma {\gamma }^{\ast }\to \pi$ form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of $\gamma {\gamma }^{\ast }\to {\eta }_c$ transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the $\gamma {\gamma }^{\ast }\to {\eta }_{c,b}$ form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-${\alpha }_s^2$ NRQCD matching coefficient for the ${\eta }_{c,b}\to \gamma \gamma$ process. After including the substantial negative order-${\alpha }_s^2$ correction, the good agreement between NRQCD prediction and the measured $\gamma {\gamma }^{\ast }\to {\eta }_c$ form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium.

6 pages, 3 figures and 1 table; adding Eqs.(8) and (9) as well as some references, correcting errors in Table 1, updating Fig.3 to include the "light-by-light" contributions, devoting a paragraph to discuss why our strategy of interpreting the NNLO corrections is justified; Accepted by PRL

References in corpus (14)

• Big-Bang Nucleosynthesis
• Heavy quarkonium: progress, puzzles, and opportunities
• FIRE5: a C++ implementation of Feynman Integral REduction
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• $Apart: A Generalized Mathematica Apart Function
• QCD corrections to J/psi plus eta_c production in e+e- annihilation at sqrt{s}=10.6 GeV
• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
• Reconciling the light-cone and nonrelativistic QCD approaches to calculating e+ e- -> J/psi + eta_c
• Two Photon Decays of Charmonia from Lattice QCD
• Measurement of the gamma gamma* --> eta_c transition form factor
• Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production
• Two-Loop Matching Coefficients for Heavy Quark Currents
• Two-loop QCD Corrections to $B_c$ Meson Leptonic Decays
• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c$ transition form factor

Cited by in corpus (39)

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• First-principle calculation of ${\eta }_c\to 2\gamma$ decay width from lattice QCD
• Two-loop form factors for pseudo-scalar quarkonium production and decay
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• Next-to-leading-order QCD corrections to gluon fragmentation into ${}^1{S}_0^{(1,8)}$ quarkonia
• Inclusive decays of ${\eta }_c$ and ${\eta }_b$ at NNLO with large $n_f$ resummation
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Photoproduction of C-even quarkonia at EIC and EicC
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• Systematic twist expansion of $({\eta }_c,{\eta }_b)\to {\gamma }^{\ast }\gamma$ transition form factors in light-front quark model
• Bottomonium spectroscopy motivated by general features of pNRQCD
• A solution to the $\gamma {\gamma }^{\ast }\to {\eta }_c$ puzzle using the Principle of Maximum Conformality
• Scale-Fixed Predictions for $\gamma +{\eta }_c$ production in electron-positron collisions at NNLO in perturbative QCD
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• Study on ${\eta }_{c2}({\eta }_{b2})$ electromagnetic decay into double photons
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• Relativistic dynamics of charmonia in strong magnetic fields
• Kinematic distributions of the ${\eta }_c$ photoproduction in $ep$ collisions within the nonrelativistic QCD framework
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• ${\eta }_c$ production associated with light hadrons at the B-factories and the future super B-factories
• Shedding light on charmonium
• Reconsideration of the QCD corrections to the ${\eta }_c$ decays into light hadrons using the principle of maximum conformality
• The $P$-wave charmonium annihilation into two photons ${\chi }_{c0,c2}\to \gamma \gamma$ with high-order QCD corrections
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation
• Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay