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Light-Cone Sum Rules for $B\to K\pi$ Form Factors and Applications to Rare Decays
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abstract
We derive a set of light-cone sum rules relating the hadronic form factors relevant for $B\to K\pi\ell^+\ell^-$ decays to the $B$-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all $B\to K\pi$ form factors of (axial)vector and (pseudo)tensor $b\to s$ currents with a $P$-wave $K\pi$ system. Our results reduce to the known light-cone sum rules for $B\to K^*$ form factors in the limit of a single narrow-width resonance. We update the operator-product expansion for the underlying correlation function by including a more complete set of $B$-meson LCDAs with higher twists, and produce numerical results for all $B\to K^*$ form factors in the narrow-width limit. We then use the new sum rules to estimate the effect of a non-vanishing $K^*$ width in $B\to K^*$ transitions, and find that this effect is universal and increases the factorizable part of the rate of $B\to K^*X$ decays by a factor of $20\%$. This effect, by itself, goes in the direction of increasing the current tension in the differential $B\to K^*\mu\mu$ branching fractions. We also discuss $B\to K\pi$ transitions outside the $K^*$ window, and explain how measurements of $B\to K\pi\ell\ell$ observables above the $K^*$ region can be used to further constrain the $B\to K^*$ form factors.
Forward citations
Cited by 5 Pith papers
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New subleading-power corrections to B to K* form factors from SCET sum rules yield SM branching fractions BR(Bbar0 to Kbar*0 nu nubar)=8.09(96)e-6 and F_L=0.44(4).
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Improved global determination of two-meson distribution amplitudes from multi-body $B$ decays
An improved global fit of two-meson distribution amplitudes in the PQCD framework yields better convergence of the Gegenbauer expansion and resolves the Bs→K*Kbar* polarization puzzle, though the headline results are ...
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Analysis of the $B_{(s)}\rightarrow T(J^P=2^-)$ transition in light cone QCD sum rules
LCSR computation of B(s) -> T(2^-) l+ l- form factors and branching ratios using B-meson DAs up to twist-4, yielding BRs of order 10^-7 to 10^-8.
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