Factorization at subleading power and irreducible uncertainties in $ \bar{B} \to {X_s}\gamma $ decay

Abstract

Using methods from soft-collinear and heavy-quark effective theory, a systematic factorization analysis is performed for theB → X s γ photon spectrum in the endpoint region m b − 2E γ = O(Λ QCD ). It is proposed that, to all orders in 1/m b , the spectrum obeys a novel factorization formula, which besides terms with the structure H J ⊗ S familiar from inclusiveB → X u lν decay distributions contains "resolved photon" contributions of the form H J ⊗ S ⊗J and H J ⊗ S ⊗J ⊗J. Here S andJ are new soft and jet functions, whose form is derived. These contributions arise whenever the photon couples to light partons instead of coupling directly to the effective weak interaction. The new contributions appear first at order 1/m b and are related to operators other than Q 7γ in the effective weak Hamiltonian. They give rise to non-vanishing 1/m b corrections to the total decay rate, which cannot be described using a local operator product expansion. A systematic analysis of these effects is performed at tree level in hard and hard-collinear interactions. The resulting uncertainty on the decay rate defined with a cut E γ > 1.6 GeV is estimated to be approximately ±5%. It could be reduced by an improved measurement of the isospin asymmetry ∆ 0− to the level of ±4%. We see no possibility to reduce this uncertainty further using reliable theoretical methods.

B→Xdγand constraints on new physics

“…Including the improved determination of V td and the reduced hadronic uncertainties [10,11] We found constraints on the parameters δ d LR,RL 13 of the MSSM squark mass matrices which are more stringent than the ones obtained from B−B mixing. Also, an effective right-handed W coupling to the top and down quarks is severely constrained: |V R td | ≤ 1.5 × 10 −4 .…”

“…However, it has been only recently realized that most of these uncertainties drop out in the CP-averaged branching ratio [10,11]. Thus, the SM prediction for B → X d γ can in principle be calculated with the same accuracy as B → X s γ.…”

A complete basis of helicity operators for subleading factorization

“…The description of observables with more complicated dynamics typically relies on factorization theorems and much less is known about the structure of power corrections in these cases. Power corrections have been considered for Drell-Yan [11][12][13][14][15] at O(Λ 2 QCD /Q 2 ), for inclusive B decays in the endpoint region at O((1−z) 0 , (Λ QCD /m b ) 1,2 ) [16][17][18][19][20][21][22][23][24], for exclusive B decays at O(Λ QCD /m b ) [25][26][27][28][29][30][31][32][33], for event shapes τ in e + e − , ep, and pp collisions at O(Λ k QCD /(Qτ ) k ) [13,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], and at O((1 − z) 0 ) for threshold resummation [49][50][51][52][53][54][55][56]…”

News on penguins

“…While non-perturbative corrections to this decay mode are subleading and recently estimated to be well below 10% [6], perturbative QCD corrections are the most important corrections. Within a global effort, a perturbative QCD calculation to the next-to-next-to-leading-logarithmic order level (NNLL) has quite recently been performed and has led to the first NNLL prediction of theB → X s γ branching fraction [7] with a photon cut at E γ = 1.6GeV (including the error due to nonperturbative corrections):…”