Abstract
A branching fraction measurement of the {{B} ^0} {rightarrow }{{D} ^+_{s}} {{pi } ^-} decay is presented using proton–proton collision data collected with the LHCb experiment, corresponding to an integrated luminosity of 5.0,text {fb} ^{-1} . The branching fraction is found to be {mathcal {B}} ({{B} ^0} {rightarrow }{{D} ^+_{s}} {{pi } ^-} ) =(19.4 pm 1.8pm 1.3 pm 1.2)times 10^{-6}, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the {{B} ^0} {rightarrow }{{D} ^-} {{pi } ^+} , {{D} ^+_{s}} {rightarrow }{{K} ^+} {{K} ^-} {{pi } ^+} and {{D} ^-} {rightarrow }{{K} ^+} {{pi } ^-} {{pi } ^-} branching fractions. This is the most precise single measurement of this quantity to date. As this decay proceeds through a single amplitude involving a b{rightarrow }u charged-current transition, the result provides information on non-factorisable strong interaction effects and the magnitude of the Cabibbo–Kobayashi–Maskawa matrix element V_{ub}. Additionally, the collision energy dependence of the hadronisation-fraction ratio f_s/f_d is measured through {{overline{B}} {}^0_{s}} {rightarrow }{{D} ^+_{s}} {{pi } ^-} and {{B} ^0} {rightarrow }{{D} ^-} {{pi } ^+} decays.
Highlights
To test the Cabibbo–Kobayashi–Maskawa (CKM) sector of the Standard Model (SM), it is crucial to perform accurate measurements of the quark-mixing matrix elements
The form factor and the decay constant can be obtained from light-cone sum rules [3,4] and lattice QCD calculations [5,6], and since |Vcs| is known to be close to unity, the B0→Ds+π − branching fraction can be used to probe the product |Vub||aNF|
This mostly cancels in the ratio of B0→D−π + and B0→Ds+π − efficiencies, but the difference of one final-state particle is sensitive to this detection asymmetry
Summary
To test the Cabibbo–Kobayashi–Maskawa (CKM) sector of the Standard Model (SM), it is crucial to perform accurate measurements of the quark-mixing matrix elements. Where is a phase-space factor, F(B0→π −) is a form factor, f Ds+ is the Ds+ decay constant, Vcs is the CKM matrix element representing c→s transitions, and |aNF| encapsulates non-factorisable effects. B meson decays into a heavy and a light meson, where the W emission of the decay corresponds to the light meson and the spectator quark forms part of the heavy meson This is not the case for the B0→Ds+π − decay, as shown, and |aNF| may be significantly different from unity [7]. Fd is proportional to the relative production ratio and its dependence on the centre-of-mass energy is reported here This is measured using B0s →Ds+π − and B0→D−π + decays. Where R is defined in Eq (5), the numerical factor takes phase-space effects into account, Na describes nonfactorisable SU(3) breaking effects, NF is the ratio of the form factors, NE takes into account the contribution of the W -exchange diagram in the B0→D−π + decay, and τBd (τBs ) is the B0 (Bs0) lifetime
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