Study On Eta(C2) (Eta(B2)) Electromagnetic Decay Into Double Photons

Within the framework of nonrelativistic QCD factorization formalism, we compute the helicity amplitude as well as the decay width of eta(Q2) (Q = c, b) electromagnetic decay into two photons up to next-to-next-to-leading order in alpha(s) expansion. For the first time, we verify the validity of nonrelativistic QCD factorization for the D-wave quarkonium decay at next-to-next-to-leading order. We find that the O(alpha(s)) and O(alpha(2)(s)) corrections to the helicity amplitude are negative and moderate, nevertheless both corrections combine to suppress the leading-order prediction for the decay width significantly. By approximating the total decay width of eta(Q2) as the sum of those for the hadronic decay and the electric El transition, we obtain the branching ratios Br(eta(c2) -> 2 gamma) approximate to 5 x 10(-6) and Br(eta(b2) -> 2 gamma) approximate to 4 x 10(-7). To explore the potential measurement on eta(Q2), we further evaluate the production cross section of eta(Q2) at LHCb at the lowest order in alpha(s) expansion. With the kinematic constraint on the longitudinal rapidity 4.5 > y > 2 and transverse momentum P-T > (2-4)m(Q) for eta(Q2), we find the cross section can reach 2-50 nb for eta(c2), and 1-22 pb for eta(b2). Considering the integrated luminosity L = 10 fb(-1) at root s = 7, 13 TeV, we estimate that there are several hundreds events of pp -> eta(c2) -> 2 gamma. Since the background is relatively clean, it is promising to reconstruct eta(c2) through its electromagnetic decay. On the other hand, due to the small branching ratio and production cross section, it is quite challenging to detect eta(b2) -> 2 gamma at LHCb.