Perturbative Corrections to ${\Lambda }_b\to \Lambda$ Form Factors from QCD Light-Cone Sum Rules

Abstract

We compute radiative corrections to ${\Lambda }_b\to \Lambda$ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with ${\Lambda }_b$-baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-${\Lambda }_b$-baryon correlation function is justified at leading power in $\Lambda /m_b$, with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-$B$-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at $\mathcal{O}({\alpha }_s)$ shift the ${\Lambda }_b\to \Lambda$ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the ${\Lambda }_b\to \Lambda$ from factors we further investigate several decay observables in the electro-weak penguin ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the ${\Lambda }_b\to \Lambda$ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.

51 pages, 12 figures

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• PQCD Calculation for ${\Lambda }_b\to \Lambda \gamma$ in the Standard Model
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• Rapidity resummation for $B$-meson wave functions

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