Search for B + → ℓ + ν ℓ γ decays with hadronic tagging using the full Belle data sample

We derive a set of light-cone sum rules relating the hadronic form factors relevant for B → Kπ + − decays to the B-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all B → Kπ form factors of (axial)vector and (pseudo)tensor b → s currents with a P -wave Kπ system. Our results reduce to the known light-cone sum rules for B → 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 → 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 → K * transitions, and find that this effect is universal and increases the factorizable part of the rate of B → 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 → K * µµ branching fractions. We also discuss B → Kπ transitions outside the K * window, and explain how measurements of B → Kπ observables above the K * region can be used to further constrain the B → K * form factors.

Section: Numerical Input and Strategysupporting

confidence: 82%

“…We refrain from replacing f + (s) by its model expression (40), since one may choose to use another model or a direct experimental determination of f + (s) inside the integral in Eq. (45). In deriving Eq.…”

Section: Resonance Models For B → Kπ Form Factorsmentioning

confidence: 99%

Light-cone sum rules for B → K π form factors and applications to rare decays

Descotes-Genon

Khodjamirian

Virto

2019

“…In order to perform the numerical analysis of the newly derived expressions for F V (n · p) and F A (n · p) in (4.12) and (4.13), we will proceed by specifying the nonperturbative models for the two-particle and three-particle DAs of the B-meson, determining the sum rule parameters and setting the hard and hard-collinear scales. Taking advantage of the new measurements of the partial branching fractions of B → γ ν from the Belle Collaboration [35], theory constraints of the inverse moment of the leading-twist DA φ + B (ω, µ) will be further addressed with the updated predictions for the B → γ form factors presented above.…”

Section: Numerical Analysismentioning

confidence: 99%

“…Since the factorization formula for the decay amplitude A(B − → γ ν) was established with the power counting scheme n · p ≡ 2E γ ∼ O(m b ), the phase-space cut on the photon energy needs to be introduced in the definition of the integrated decay rate 12) in order to facilitate the comparison of the experimental measurements from the Belle Collaboration [35] and the theoretical predictions displayed in figure 9. The main observations can be summarized as follows.…”

Section: Nlpll V2pmentioning

confidence: 99%

Factorization and dispersion relations for radiative leptonic B decay

Wang

2016

Applying the dispersion approach we compute perturbative QCD corrections to the power suppressed soft contribution of B → γ ν at leading twist. QCD factorization for the B → γ * form factors is demonstrated explicitly for the hard-collinear transverse polarized photon at one loop, with the aid of the method of regions. While the one-loop hard function is identical to the matching coefficient of the QCD weak currentūγ µ⊥ (1 − γ 5 )b in soft-collinear effective theory, the jet function from integrating out the hard-collinear fluctuations differs from the corresponding one entering the factorization formula of B → γ ν, due to the appearance of an additional hard-collinear momentum mode. Furthermore, we evaluate the sub-leading power contribution to the B → γ form factors from the three-particle B-meson distribution amplitudes (DAs) at tree level, with the dispersion approach. The soft contribution to the B → γ form factors from the three-particle B-meson DAs is shown to be of the same power compared with the corresponding hard correction, in contrast to the two-particle counterparts. Numerically the next-to-leading-order QCD correction to the soft two-particle contribution in B → γ form factors will induce an approximately (10 ∼ 20)% shift to the tree-level contribution at λ B (µ 0 ) = 354 MeV. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the B → γ form factors by an amount of (10 ∼ 30)% with the same value of λ B (µ 0 ). Employing the phenomenological model of the three-particle B-meson DAs inspired by a QCD sum rule analysis, the three-particle contribution to the B → γ form factors is predicted to be of O(1%), at leading order in α s , with the default theory inputs. Finally, we explore theory constraints on the inverse moment of the leading-twist B-meson DA λ B from the recent Belle measurements of the partial branching fractions of B → γ ν, taking into account the newly computed contributions to the B → γ form factors at subleading power.

“…It can be observed that the integrated branching fractions BR(B → γ ν, E γ ≥ E cut ) grow rapidly with the decrease of the inverse moment due to the dependence of the two form factors on 1/λ B (µ 0 ) at leading-power in Λ/m b . Since the photon-energy cut E γ ≥ 1 GeV implemented in the Belle measurements [47] is not sufficiently large to perform perturbative QCD calculations of the B → γ form factors, we will not employ the experimental bound BR(B → γ ν, E γ ≥ E cut ) < 3.5 × 10 −6 with the full Belle data sample reported in [47] for the determination of λ B (µ 0 ) at the moment. Instead, we prefer to explore the solid theory constraints on the first inverse moment by comparing our predictions of the (partially) integrated branching fractions with the improved measurements at the Belle II experiment, with the tighter phase-space cut on the photon energy, thanks to the much higher designed luminosity of the SuperKEKB accelerator.…”

Section: Jhep05(2018)184mentioning

confidence: 99%

Subleading-power corrections to the radiative leptonic B → γℓν decay in QCD

Wang

Shen

2018

Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic B → γ ν decay from the twist-two hadronic photon contribution at next-to-leading order in QCD; and further evaluate the higher-twist "resolved photon" corrections at leading order in α s , up to twist-four accuracy. QCD factorization for the vacuum-to-photon correlation function with an interpolating current for the B-meson is established explicitly at leading power in Λ/m b employing the evanescent operator approach. Resummation of the parametrically large logarithms of m 2 b /Λ 2 entering the hard function of the leading-twist factorization formula is achieved by solving the QCD evolution equation for the light-ray tensor operator at two loops. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two B → γ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30% correction to the leading-power "direct photon" effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of O(3 ∼ 5%) with the light-cone sum rule approach. We further predict the partial branching fractions of B → γ ν with a photonenergy cut E γ ≥ E cut , which are of interest for determining the inverse moment of the leading-twist B-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.