Beyond SMEFT with $b \to c \,\tau^- {\bar\nu}$

Abstract

Electroweak interactions assign a central role to the gauge group $SU(2)_L \times U(1)_Y$, which is either realized linearly (SMEFT) or nonlinearly (e.g., HEFT) in the effective theory obtained when new physics above the electroweak scale is integrated out. Although the discovery of the Higgs boson has made SMEFT the default assumption, nonlinear realization remains possible. The two can be distinguished through their predictions for the size of certain low-energy dimension-6 four-fermion operators: for these, HEFT predicts $O(1)$ couplings, while in SMEFT they are suppressed by a factor $v^2/\Lambda_{\rm NP}^2$, where $v$ is the Higgs vev. One such operator, $O_V^{LR} \equiv ({\bar \tau} \gamma^\mu P_L \nu )\, ( {\bar c} \gamma_\mu P_R b )$, contributes to $b \to c \,\tau^- {\bar\nu}$. We show that present constraints permit its non-SMEFT coefficient to have a HEFTy size. We also note that the angular distribution in ${\bar B} \to D^* (\to D \pi') \, \tau^{-} (\to \pi^- \nu_\tau) {\bar\nu}_\tau$ contains enough information to extract the coefficients of all new-physics operators. Future measurements of this angular distribution can therefore tell us if non-SMEFT new physics is really necessary.