The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c$ transition form factor

Abstract

We study the ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c$ transition form factor, $F_{{\eta }_c\gamma \gamma }(Q_1^2,Q_2^2),$ with the local-duality (LD) version of QCD sum rules. We analyse the extraction of this quantity from two different correlators, $<PVV>$ and $<AVV>,$ with $P,$ $A,$ and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for $F_{{\eta }_c\gamma \gamma }(Q_1^2,Q_2^2)$ allows us to fix the effective continuum thresholds for the $<PVV>$ and $<AVV>$ correlators at large values of $Q^2=Q_2^2$ and some fixed value of $\beta \equiv Q_1^2/Q_2^2$. We give arguments that, in the region $Q^2\ge 10$--$15Ge{V}^2$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for $F_{{\eta }_c\gamma \gamma }(Q_1^2,Q_2^2).$ We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for $F_{{\eta }_c\gamma }(Q^2)\equiv F_{{\eta }_c\gamma \gamma }(0,Q^2)$ may be well approximated by the simple monopole formula $F_{{\eta }_c\gamma }(Q^2)=2e_c^2{N}_c{f}_P(M_V^2+Q^2{)}^{-1},$ where $f_P$ is the ${\eta }_c$ decay constant, $e_c^2$ is the $c$-quark charge, and the parameter $M_V$ lies in the mass range of the lowest $\bar{c}c$ vector states.

9 pages

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• Spacelike and timelike form factors for the $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }\gamma$ transitions in the light-front quark model
• Universal behaviour of the ${\gamma }^{\ast }\gamma \to ({\pi }^0,\eta ,{\eta }^{\prime })$ transition form factors
• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c(1S,2S)$ transition form factors for spacelike photons
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• On properties of the exotic hadrons from QCD sum rules
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