Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes

M. Beneke; S. Jager (RWTH Aachen)

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Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes

M. Beneke, S. Jager (RWTH Aachen)

High Energy Physics - Phenomenology · Submitted 28 Dec 2005

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The authors' main claim The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order.

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arXiv IDhep-ph/0512351 (version 1)

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CitationM. Beneke, S. Jager (RWTH Aachen). "Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes." arXiv:hep-ph/0512351 (2005). https://pith.science/paper/VHNJUXFH

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We compute the 1-loop (alpha_s^2) correction to hard spectator scattering in non-leptonic B decay tree amplitudes. This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries. Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators. The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order. Depending on the values of hadronic input parameters, the new 1-loop correction may have a significant impact on tree-dominated decays such as B -> pi pi.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the 1-loop (alpha_s^2) correction to hard spectator scattering in non-leptonic B decay tree amplitudes.	contribution 1.00	0.97	0.11	asserted 1.00
s1	This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries.	interpretation 0.68	0.75	0.35	asserted 1.00
s2	Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators.	method 0.94	0.78	0.03	asserted 0.67
s3	The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order.	result 0.52	0.93	0.31	asserted 1.00
s4	Depending on the values of hadronic input parameters, the new 1-loop correction may have a significant impact on tree-dominated decays such as B -> pi pi.	interpretation 0.98	0.57	0.15	hedged possibility 1.00

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Original abstract

We compute the 1-loop (alpha_s^2) correction to hard spectator scattering in non-leptonic B decay tree amplitudes. This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries. Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators. The infrared finiteness of our result establishes factorization of spectator scattering at the 1-loop order. Depending on the values of hadronic input parameters, the new 1-loop correction may have a significant impact on tree-dominated decays such as B -> pi pi.

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References

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Cited by 10 Pith papers

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36 arXiv papers cite this in 72 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Builds on it 1 paper

Generalizing from the pure QCD case [ref] , the matching equation then takes the form [equation] with $t̂ = n_- q t = m_B t$, $ŝ = n_+ p' s = m_B s$, and $p' (q)$ the momentum of the $M_1(M_2)$ meson.

QED factorization of non-leptonic $B$ decays · $SCET_I$ operators · 0.91

Uses its method or tool 2 papers

Following the first paper of [ref] , we implement the spectator scattering contribution to the topological tree amplitudes as[One should keep in mind that the Wilson coefficients in the spectator scattering term refer to a different operator basis than the one used in the current work (namely the Fierz-symmetric traditional basis that we denoted by a tilde in [ref] ).] [equation] Since the spectator scattering starts at $()$, the resummation is required here in the next-to-leading-logarithmic (NLL) approximation.

NNLO vertex corrections in charmless hadronic B decays: Real part · Implementation of spectator scattering · 0.98
In ([ref]) the resummation is encoded in [equation] with the Sudakov factor $S$ given in LL approximation in equation (106) of [ref] and the kernels $r_i$ in equations (38) and (39) of [ref] .

NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part · Implementation of Spectator Scattering · 0.93

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The dominant NLO QCD corrections to Wilson Coefficients given in Refs. [ref] ) are taken into account in our analysis.

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In contrast, values of$|C/T|$calculated in QCD, using a heavy-quark expansion and various assumptions about$Λ_QCD/m_b$corrections, do not exceed 0.6 [ref] .

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As the spectator term is the main source for the uncertainties from the hadronic input parameters, we also obtain smaller error bars than [ref] .

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The calculations in [ref] are done in the SCET framework, whereas [ref] employs factorization in full QCD.

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This can be done, because it can be shown [ref] that these convolutions are convergent to all orders in perturbation theory, which has been confirmed explicitly by one-loop calculations [ref] .

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Anyway, the study of hadronic $B$ decays favors a relative small value of $λ_B$ $≈$ 200 MeV to achieve a satisfactory description of color-suppressed tree decay modes [ref] .

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Details have been worked out for $B→Vγ$ in [ref] , for heavy-to-light form factors in [ref] , and for $B→PP$ in [ref] .

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Both in QCDF and SCET the hard kernels are known to NLO in $α_S(m_b)$ [ref] , with partial results already known at NNLO [ref] .

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Three different approaches to factorization in $B$ decays have been put forward: the so-called QCD factorization [ref] , perturbative QCD (PQCD) [ref] and Soft-Collinear Effective Theory (SCET) [ref] .

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