# A High-Statistics Lattice Calculation of $\lambda_1$ and $\lambda_2$ in the $B$ meson

## TL;DR

This paper reports a high-statistics lattice QCD calculation of the kinetic and chromo-magnetic energy parameters in the B meson, providing results relevant for phenomenology and highlighting discrepancies with experimental data.

## Contribution

The study presents the first high-statistics lattice calculation of $ ext{lambda}_1$ and $ ext{lambda}_2$ in the B meson using improved lattice actions and a large gauge configuration sample.

## Key findings

- Estimated $- ext{lambda}_1$ as $-0.09 ext{ GeV}^2$ with large uncertainty
- Calculated $ ext{lambda}_2$ as $0.07 ext{ GeV}^2$, about half the experimental value
- Identified a discrepancy between lattice results and experimental measurements

## Abstract

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $\beta=6.0$, on a lattice volume $24^3 \times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060 $ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.