Abstract
In this work we study the effects of new-physics (NP) operators with different Lorentz structures on the inclusive $B \to X_c\tau \bar{\nu}$ decay and make predictions for the ratio of total decay rates $R(X_c)=\frac{\Gamma(B \to X_c\tau \bar{\nu}_\tau)}{\Gamma(B \to X_c \ell \bar{\nu}_\ell)}$ with $\ell=e, \mu$, the differential decay rates, $\frac{d\Gamma}{dq^2}$ and $\frac{d\Gamma}{dE_\tau}$, forward-backward asymmetry $A_{FB}$ and the ratio of the differential decay rates $B(q^2)=\frac{d\Gamma(B \to X_c\tau \bar{\nu}_\tau)/dq^2}{d\Gamma(B \to X_c \ell \bar{\nu}_\ell)/dq^2}$. In addition, we introduce some leptoquark models as explicit models of the NP operators and study their effects on the inclusive decay. We consider $\mathcal{O}(\alpha_s)$ radiative and $1/m_b$ nonperturbative corrections to the Standard Model (SM) decay rate and ignore their small effects in the NP contributions.
Highlights
The b → cτν transitions have attracted a lot of attention recently as there is an excess of τ production compared to Standard Model (SM) predictions
In this work we study the effects of new-physics (NP) operators with different Lorentz structures on the inclusive
The b → cτν transitions have attracted a lot of attention recently as there is an excess of τ production compared to SM predictions
Summary
The b → cτν transitions have attracted a lot of attention recently as there is an excess of τ production compared to SM predictions. For our purpose the calculations in [32] are more useful, where the corrections to the five hadronic structure functions are given and the formulas for the virtual and real gluon corrections are given separately This allows us to calculate the correction to the phenomenological aspects of the inclusive B decay such as q2 and Eτ distributions, the ratio of dΓðB→Xc τντ Þ=dq dΓðB→Xc lνl Þ=dq and the forward-backward asymmetry, AFB. The second order QCD corrections to semileptonic b → c inclusive transitions, not considered here, can be important for the rates and the absolute differential rates [37,38] and so the ratios should be considered cleaner probes of new physics.
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