Reconciling the light-cone and nonrelativistic QCD approaches to calculating e+ e- -> J/psi + eta_c

TL;DR

The paper investigates whether light-cone methods can resolve the mismatch between NRQCD predictions and experimental measurements for e^+e^- → J/ψ + η_c. It derives light-cone distribution amplitudes from a Cornell-potential quarkonium model via the Bethe-Salpeter formalism, and then carefully subtracts the part of the high-momentum tail corresponding to order-α_s NRQCD corrections to avoid double counting. The resulting cross section, after removing the high-momentum contribution and unphysical renormalization factors, is comparable to NRQCD predictions, indicating no large light-cone enhancement. The study concludes that the remaining discrepancy with experimental data likely requires higher-order α_s and relativistic (v^2) corrections, rather than a fundamentally different light-cone treatment.

Abstract

It has been suggested in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] that the disagreement between theoretical calculations and experimental observations for the rate for the process e+ e- -> J/psi + eta_c at the B factories might be resolved by using the light-cone method to take into account the relative momentum of the heavy-quark and antiquark in the quarkonia. The light-cone result for the production cross section in Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] is almost an order of magnitude larger than existing NRQCD factorization results. We investigate this apparent theoretical discrepancy. We compute light-cone distribution functions by making use of quarkonium wave functions from the Cornell potential model. Our light-cone distribution functions are similar in shape to those of Ref. [A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005)] and yield a similar cross section. However, when we subtract parts of the light-cone distribution functions that correspond to corrections of relative-order alpha_s in the NRQCD approach, we find that the cross section decreases by about a factor of three. When we set certain renormalization factors Z_i in the light-cone calculation equal to unity, we find a further reduction in the cross section of about a factor of two. The resulting light-cone cross section is similar in magnitude to the NRQCD factorization cross sections and shows only a modest enhancement over the light-cone cross section in which the relative momentum of the heavy-quark and antiquark is neglected.

Figures (7)

• Figure 1: The dimensionless wave function $u(\rho)$ as a function of the dimensionless variable $\rho$. Input parameters are $m=1.14710$ GeV, $a=2.38139$ GeV$^{-1}$, and $\lambda=0.7$. The wave function at the origin is taken to be $|\psi(0)|=0.18619~\textrm{GeV}^{3/2}$, which is the value for the $J/\psi$ wave function at the origin that is designated as LO in Ref. Braaten:2002fi.
• Figure 2: The light-cone distribution amplitude $\phi(z)$ that is derived from the potential model in this paper and the model light-cone distribution amplitude $\phi_{\rm BC}(z)$ that is used in BC. As is explained in the text, $\phi(z)$ is computed from the potential-model wave function by carrying out the integrations in Eqs. (\ref{['eq:phib-z-exact']}) and (\ref{['eq:phia-z-single']}) numerically, taking $m_c=1.4$ GeV. $\phi_{\rm BC}(z)$ is given in Eq. (\ref{['phi-bc']}).
• Figure 3: Comparison of the light-cone distribution amplitude $\phi_{\rm approx}(z)$ with $\phi(z)$. $\phi_{\rm approx}(z)$ is computed from Eq. (\ref{['eq:phi-z-approx']}), in which the nonrelativistic approximation is used for the light-cone-fraction Jacobian. $\phi(z)$ is computed from the exact expressions in Eqs. (\ref{['eq:phib-z-exact']}) and (\ref{['eq:phia-z-single']}).
• Figure 4: Diagrammatic representation of $\mathcal{M}$, as given in Eq. (\ref{['H-and-wavefn']}). The circle labeled $H$ represents the hard part of the production amplitude, and the oval represents the quarkonium wave function.
• Figure 5: Diagrammatic representation of $\mathcal{M}-\mathcal{M}_0$, as given in Eq. (\ref{['subtraction']}). The circle labeled $H$ represents the hard part of the production amplitude, and the oval represents the quarkonium wave function.