Center of mass motion in bag model

TL;DR

This paper addresses the center of mass motion problem in the bag model, proposing a systematic solution that yields consistent calculations of decay constants and form factors, closely matching experimental data.

Contribution

The authors develop a systematic approach to correct the center of mass motion issue in the bag model, enabling consistent computation of decay constants and form factors without free parameters.

Findings

Neutron beta decay form factors match experimental ratios.

Predicted branching ratio for $ ext{Lambda}_b o ext{Lambda} ext{gamma}$ agrees with measurements.

Form factors are determined without free parameters, close to experimental values.

Abstract

Despite the great success on the mass spectra, the reputation of the bag model has been closely followed by the embarrassment from the center of mass motion. It leads to severe theoretical inconsistencies. For instance, the masses and the decay constants would no longer be independent of the momentum. In this work, we provide a systematical approach to resolve this problem. The meson decay constants as well as the baryon transition form factors can be computed consistently in our framework. Notably, the form factors in the neutron $\beta$ decays do not depend on any free parameters, and are determined to be $F^V_1 =1 $ and $F^A_1 = 1.31$ or $F_1^A/F_1^V= 1.31$, which is close the experimental value of $F^A_1/F^V_1 = 1.27$. In addition, we find that ${\cal B} (\Lambda_b \to \Lambda \gamma) = (6.8 \pm 3.3 ) \times 10^{-6} $, which agrees to the experimental value of $(7.1\pm 1.7)\times 10^{-6}$.