### Abstract

Using methods from soft-collinear and heavy-quark effective theory, a systematic factorization analysis is performed for the B̄ → 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 inclusive B̄ → X_{u}lv̄ decay distributions contains "resolved photon" contributions of the form H J ⊗ S ⊗ J̄ and H J ⊗ S ⊗ J̄ ⊗ J̄. Here S and J̄ 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} > 1.6GeV is estimated to be approximately ±5%. It could be reduced by an improved measurement of the isospin asymmetry δ_{0-} to the level of ±4%. We see no possibility to reduce this uncertainty further using reliable theoretical methods.

Original language | English |
---|---|

Article number | 99 |

Journal | Journal of High Energy Physics |

Volume | 2010 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2010 Dec 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- B-Physics
- Heavy Quark Physics
- Nonperturbative Effects

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

_{s}γ decay.

*Journal of High Energy Physics*,

*2010*(8), [99]. https://doi.org/10.1007/JHEP08(2010)099

**Factorization at subleading power and irreducible uncertainties in B̄ → X _{s}γ decay.** / Benzke, Michael; Lee, Seung Joon; Neubert, Matthias; Paz, Gil.

Research output: Contribution to journal › Article

_{s}γ decay',

*Journal of High Energy Physics*, vol. 2010, no. 8, 99. https://doi.org/10.1007/JHEP08(2010)099

_{s}γ decay. Journal of High Energy Physics. 2010 Dec 1;2010(8). 99. https://doi.org/10.1007/JHEP08(2010)099

}

TY - JOUR

T1 - Factorization at subleading power and irreducible uncertainties in B̄ → Xsγ decay

AU - Benzke, Michael

AU - Lee, Seung Joon

AU - Neubert, Matthias

AU - Paz, Gil

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Using methods from soft-collinear and heavy-quark effective theory, a systematic factorization analysis is performed for the B̄ → X sγ photon spectrum in the endpoint region mb-2E γ = O(ΛQCD). It is proposed that, to all orders in 1/mb, the spectrum obeys a novel factorization formula, which besides terms with the structure H J⊗S familiar from inclusive B̄ → Xulv̄ decay distributions contains "resolved photon" contributions of the form H J ⊗ S ⊗ J̄ and H J ⊗ S ⊗ J̄ ⊗ J̄. Here S and J̄ 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/mb and are related to operators other than Q7γ in the effective weak Hamiltonian. They give rise to non-vanishing 1/mb 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 Eγ > 1.6GeV is estimated to be approximately ±5%. It could be reduced by an improved measurement of the isospin asymmetry δ0- to the level of ±4%. We see no possibility to reduce this uncertainty further using reliable theoretical methods.

AB - Using methods from soft-collinear and heavy-quark effective theory, a systematic factorization analysis is performed for the B̄ → X sγ photon spectrum in the endpoint region mb-2E γ = O(ΛQCD). It is proposed that, to all orders in 1/mb, the spectrum obeys a novel factorization formula, which besides terms with the structure H J⊗S familiar from inclusive B̄ → Xulv̄ decay distributions contains "resolved photon" contributions of the form H J ⊗ S ⊗ J̄ and H J ⊗ S ⊗ J̄ ⊗ J̄. Here S and J̄ 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/mb and are related to operators other than Q7γ in the effective weak Hamiltonian. They give rise to non-vanishing 1/mb 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 Eγ > 1.6GeV is estimated to be approximately ±5%. It could be reduced by an improved measurement of the isospin asymmetry δ0- to the level of ±4%. We see no possibility to reduce this uncertainty further using reliable theoretical methods.

KW - B-Physics

KW - Heavy Quark Physics

KW - Nonperturbative Effects

UR - http://www.scopus.com/inward/record.url?scp=78651070821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651070821&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2010)099

DO - 10.1007/JHEP08(2010)099

M3 - Article

AN - SCOPUS:78651070821

VL - 2010

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 99

ER -