### Abstract

We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parametrizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parametrizations. We include higher resonances in the hadronic sum that, together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors in B̄→Dℓν̄ and can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parametrization of one of the Λ_{b}→Λ_{c}ℓν̄ from factors, together with heavy quark symmetry relations valid to order 1/m^{2}, describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantity Λ̄_{Λ}≈M_{Λb}-m_{b}. We discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimental B̄→D*ℓν̄ and B̄→Dℓν̄ data to the improved one-parameter expansion.

Original language | English (US) |
---|---|

Pages (from-to) | 6895-6911 |

Number of pages | 17 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 56 |

Issue number | 11 |

State | Published - Dec 1 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*56*(11), 6895-6911.

**Precision corrections to dispersive bounds on form factors.** / Boyd, C. Glenn; Grinstein, Benjamín; Lebed, Richard.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 56, no. 11, pp. 6895-6911.

}

TY - JOUR

T1 - Precision corrections to dispersive bounds on form factors

AU - Boyd, C. Glenn

AU - Grinstein, Benjamín

AU - Lebed, Richard

PY - 1997/12/1

Y1 - 1997/12/1

N2 - We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parametrizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parametrizations. We include higher resonances in the hadronic sum that, together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors in B̄→Dℓν̄ and can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parametrization of one of the Λb→Λcℓν̄ from factors, together with heavy quark symmetry relations valid to order 1/m2, describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantity Λ̄Λ≈MΛb-mb. We discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimental B̄→D*ℓν̄ and B̄→Dℓν̄ data to the improved one-parameter expansion.

AB - We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parametrizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parametrizations. We include higher resonances in the hadronic sum that, together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors in B̄→Dℓν̄ and can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parametrization of one of the Λb→Λcℓν̄ from factors, together with heavy quark symmetry relations valid to order 1/m2, describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantity Λ̄Λ≈MΛb-mb. We discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimental B̄→D*ℓν̄ and B̄→Dℓν̄ data to the improved one-parameter expansion.

UR - http://www.scopus.com/inward/record.url?scp=0001514365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001514365&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001514365

VL - 56

SP - 6895

EP - 6911

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 11

ER -