Is there really a $W\to \tau \nu$ puzzle?

Abstract

According to the Particle Data Group, the measurements of $\mathcal{B}(W^{+}\to {\tau }^{+}{\nu }_{\tau })$ and $\mathcal{B}(W^{+}\to {\ell }^{+}{\nu }_{\ell })$ ($\ell =e,\mu$) disagree with one another at the $2.3\sigma$ level. In this paper, we search for a new-physics (NP) explanation of this $W\to \tau \nu$ puzzle. We consider two NP scenarios: (i) the $W$ mixes with a $W^{\prime }$ boson that couples preferentially to the third generation, (ii) ${\tau }_{L,R}$ and ${\nu }_{\tau L}$ mix with isospin-triplet leptons. Unfortunately, once other experimental constraints are taken into account, neither scenario can explain the above experimental result. Our conclusion is that the $W\to \tau \nu$ puzzle is almost certainly just a statistical fluctuation.

Comments: 14 pages; references and discussion added; journal version