The flavor of a minimal composite S1 leptoquark and the $$ b\to c\tau \overline{\nu} $$ anomaly

Abstract

Abstract Several experiments have measured a deviation in B → D(∗) semileptonic decays, that point to new physics at the TeV scale violating lepton flavor universality. A scalar leptoquark S1, with a suitable structure of couplings in flavor space, is known to be able to solve this anomaly modifying $$ b\to c\tau \overline{\nu} $$ b → cτ ν ¯ . In the context of composite Higgs models, we consider a theory containing H and S1 as Nambu-Goldstone bosons (NGBs) of a new strongly interacting sector, with ordinary resonances at a scale $$ \mathcal{O}(10) $$ O 10 TeV. Assuming anarchic partial compositeness of the Standard Model (SM) fermions we calculate the potential of the NGBs that is dominated by the fermions of the third generation, we compute $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ and estimate the corrections to flavor observables by the presence of S1. We find that the SM spectrum and $$ {m}_{S_1} $$ m S 1 ∼ TeV can be obtained with a NGB decay constant of order ∼ 5 TeV. We obtain a robust correlation between the main corrections to $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ , $$ {B}_{K^{\left(\ast \right)}\nu \nu} $$ B K ∗ νν and gτ/gμ, that leads to a sever bound on $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ , roughly 2σ below the experimental value. Besides the bounds on the flavor observables $$ {g}_{\tau}^W $$ g τ W , BR(τ → μγ) and $$ \Delta {m}_{B_s} $$ ∆ m B s are saturated, with the first one requiring a coupling between resonances g* ≲ 2, whereas the second one demands $$ {m}_{S_1} $$ m S 1 ≳ 1.7 TeV, up to corrections of $$ \mathcal{O}(1) $$ O 1 .