Leptonic Decays of Charged Pseudoscalar Mesons

TL;DR

This paper reviews the physics of purely leptonic decays of charged pseudoscalar mesons, discussing how experimental measurements relate to theoretical parameters like decay constants and CKM matrix elements, highlighting current challenges in testing predictions.

Contribution

It provides a comprehensive review of leptonic meson decays, comparing experimental data with theoretical predictions, and emphasizes the need for improved tests in the charm and bottom sectors.

Findings

Experimental decay rates are related to CKM elements and decay constants.

Current tests of theoretical predictions are unsatisfactory, especially in the bottom sector.

Lighter mesons like π and K offer precise comparisons between theory and experiment.

Abstract

We review the physics of purely leptonic decays of $\pi^\pm$, $K^\pm$, $D^{\pm}$, $D_s^\pm$, and $B^\pm$ pseudoscalar mesons. The measured decay rates are related to the product of the relevant weak-interaction-based CKM matrix element of the constituent quarks and a strong interaction parameter related to the overlap of the quark and anti-quark wave-functions in the meson, called the decay constant $f_P$. The interplay between theory and experiment is different for each particle. Theoretical predictions of $f_B$ that are needed in the $B$ sector can be tested by measuring $f_{D^+}$ and $f_{D_s^+}$ in the charm sector. Currently, these tests are unsatisfactory. The lighter $\pi$ and $K$ mesons provide stringent comparisons between experiment and theory due to the accuracy of both the measurements and the theoretical predictions. An abridged version of this review was prepared for the Particle Data Group's 2010 edition.