Can Nonrelativistic QCD Explain the γγ^{*}→η_{c} Transition Form Factor Data?

Area of Science:

• High Energy Physics
• Quantum Chromodynamics (QCD)
• Particle Physics

Background:

• The transition form factor for gamma gamma* to eta_c is crucial for understanding charmonium interactions.
• Previous studies suggested perturbative QCD and nonrelativistic QCD (NRQCD) factorization could explain experimental measurements.
• A discrepancy exists in the gamma gamma* to pi form factor, unlike the eta_c case.

Purpose of the Study:

• To investigate the next-to-next-to-leading-order perturbative corrections to the gamma gamma* to eta_c,b form factor within the NRQCD framework.
• To calculate the most precise order-alpha_s^2 NRQCD matching coefficient for the eta_c,b to gamma gamma process.
• To re-evaluate the agreement between theoretical predictions and BABAR experimental data for the gamma gamma* to eta_c form factor.

Main Methods:

• Application of the nonrelativistic QCD (NRQCD) factorization framework.
• Calculation of perturbative QCD corrections up to the next-to-next-to-leading-order (order-alpha_s^2).
• Derivation of the NRQCD matching coefficient for the eta_c,b to gamma gamma process.

Main Results:

• The study provides the most precise order-alpha_s^2 NRQCD matching coefficient for the eta_c,b to gamma gamma process to date.
• Inclusion of the substantial negative order-alpha_s^2 correction significantly disrupts the agreement between NRQCD predictions and the measured gamma gamma* to eta_c form factor.
• The discrepancy is observed over a wide range of momentum transfer squared.

Conclusions:

• The previously good agreement between NRQCD predictions and experimental data for the gamma gamma* to eta_c form factor is lost after incorporating higher-order corrections.
• The significant discrepancy raises doubts about the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.
• Further theoretical and experimental investigations are needed to resolve this issue in charmonium physics.