Leptonic Decays of Charged Pseudoscalar Mesons - 2015

TL;DR

This paper reviews leptonic decays of charged pseudoscalar mesons, discussing how experimental data and lattice-QCD calculations of decay constants help determine CKM matrix elements and test the Standard Model's flavor structure.

Contribution

It provides a comprehensive review of leptonic decay measurements, decay constants from lattice QCD, and their implications for CKM matrix determination and Standard Model tests.

Findings

Decay constants can be precisely calculated with lattice QCD.

Experimental decay rates enable CKM matrix element extraction.

Results are consistent with Standard Model unitarity constraints.

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 antiquark wave-functions in the meson, called the decay constant $f_P$. The leptonic decay constants for $\pi^\pm$, $K^\pm$, $D^{\pm}$, $D_s^\pm$, and $B^\pm$ mesons can be obtained with controlled theoretical uncertainties and high precision from {\it ab initio} lattice-QCD simulations. The combination of experimental leptonic decay-rate measurements and theoretical decay-constant calculations enables the determination of several elements of the CKM matrix within the standard model. These determinations are competitive with those obtained from semileptonic decays, and also complementary because they are sensitive to different quark flavor-changing currents. They can also be used to test the unitarity of the first and second rows of the CKM matrix. Conversely, taking the CKM elements predicted by unitarity, one can infer "experimental" values for $f_P$ that can be compared with theory. These provide tests of lattice-QCD methods, provided new-physics contributions to leptonic decays are negligible at the current level of precision. This review is the basis of the article in the Particle Data Group's 2016 edition, updating the versions in Refs. [1-3].