scholarly journals Consistent treatment of rapidity divergence in soft-collinear effective theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Junegone Chay ◽  
Chul Kim
Keyword(s):  
Heavy Quark ◽  
Soft Mode ◽  
Form Factors ◽  
Effective Theory ◽  
Large Rapidity ◽  
Soft Modes ◽  
Heavy Quark Mass ◽  
Soft Collinear Effective Theory ◽  
Matching Procedure ◽  
Consistent Treatment

Abstract In soft-collinear effective theory, we analyze the structure of rapidity divergence due to the collinear and soft modes residing in disparate phase spaces. The idea of an effective theory is applied to a system of collinear modes with large rapidity and soft modes with small rapidity. The large-rapidity (collinear) modes are integrated out to obtain the effective theory for the small-rapidity (soft) modes. The full SCET with the collinear and soft modes should be matched onto the soft theory at the rapidity boundary, and the matching procedure becomes exactly the zero-bin subtraction. The large-rapidity region is out of reach for the soft mode, which results in the rapidity divergence. The rapidity divergence in the collinear sector comes from the zero-bin subtraction, which ensures the cancellation of the rapidity divergences from the soft and collinear sectors. In order to treat the rapidity divergence, we construct the rapidity regulators consistently for all the modes. They are generalized by assigning independent rapidity scales for different collinear directions. The soft regulator incorporates the correct directional dependence when the innate collinear directions are not back-to-back, which is discussed in the N-jet operator. As an application, we consider the Sudakov form factor for the back-to-back collinear current and the soft-collinear current, where the soft rapidity regulator for a soft quark is developed. We extend the analysis to the boosted heavy quark sector and exploit the delicacy with the presence of the heavy quark mass. We present the resummed results of large logarithms in the form factors for various currents with the light and the heavy quarks, employing the renormalization group evolution on the renormalization and the rapidity scales.

Symmetry-breaking corrections to the form factors for heavy-to-heavy B-meson at large recoil

2019 ◽  
Vol 34 (08) ◽  
pp. 1950046
Author(s):  
Saba Shafaq ◽  
Ishtiaq Ahmed ◽  
M. Jamil Aslam
Keyword(s):  
Perturbation Theory ◽  
Symmetry Breaking ◽  
Heavy Quark ◽  
B Meson ◽  
Form Factors ◽  
Heavy Meson ◽  
Effective Theory ◽  
Vertex Corrections ◽  
Soft Collinear Effective Theory ◽  
Heavy Quark Limit

The present study investigates the decay of B to heavy meson using the soft collinear effective theory. By assigning different loop momenta, the factorization has been tested and it is found to be valid to all orders in the perturbation theory. It is noted that theory contains one hard collinear and two soft modes depending upon virtuality of different momenta. In the next step, symmetry-conserving relations (in heavy quark limits) to the form factors have been studied. These relations are then used to parametrize the form factors to get symmetry-breaking corrections. These symmetry-breaking corrections can be calculated using perturbative (vertex corrections) as well as nonperturbative (hard spectator interactions) QCD. It is found that in the heavy quark limit, these symmetry contributions do not contribute to the form factors that appear in physical observables for the case of [Formula: see text] decays which are contrary to the heavy-to-light meson decays.

IMPACT OF POSITIVE PARITY HEAVY MESONS ON CHARM MESON DECAYS

2008 ◽  
Vol 23 (21) ◽  
pp. 3196-3199 ◽  
Author(s):  
SVJETLANA FAJFER ◽  
JERNEJ F. KAMENIK
Keyword(s):  
Heavy Quark ◽  
Form Factors ◽  
Negative Parity ◽  
Heavy Meson ◽  
Effective Theory ◽  
Charm Meson ◽  
Soft Collinear Effective Theory ◽  
Heavy Quark Symmetry ◽  
The Impact

We discuss strong decays of positive and negative parity charmed mesons within heavy meson chiral perturbation theory and study the impact of excited charm states on the determination of the effective meson couplings. Motivated by recent experimental results we also reconsider semileptonic D → Plνl and D → Vlνl decays within a model which combines heavy quark symmetry and properties of the chiral Lagrangian. Using limits of soft collinear effective theory and heavy quark effective theory we parametrize the semileptonic form factors. We include excited charm meson states in our Lagrangian and determine their impact on the charm meson semileptonic form factors.

scholarly journals HQET form factors for Bs → Klv decays beyond leading order

2018 ◽  
Vol 175 ◽  
pp. 13025
Author(s):  
Debasish Banerjee ◽  
Mateusz Koren ◽  
Hubert Simma ◽  
Rainer Sommer
Keyword(s):  
Form Factor ◽  
Heavy Quark ◽  
Form Factors ◽  
Good Control ◽  
Effective Theory ◽  
Ratio Method ◽  
Heavy Quark Effective Theory ◽  
Leading Order ◽  
Decay Form ◽  
Static Order

We compute semi-leptonic Bs decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the 1 /mb expansion, one has to take into account not only the leading static order but also the terms arising at O (1/mb): kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to O (1/[see formula in PDF]) corrections and without O (αs(mb)n) corrections.

B → K* ℓ+ ℓ- DECAYS WITH POLARIZED K*

2003 ◽  
Vol 18 (08) ◽  
pp. 1443-1448
Author(s):  
C. H. CHEN ◽  
C. Q. GENG
Keyword(s):  
Standard Model ◽  
Heavy Quark ◽  
B Meson ◽  
Form Factors ◽  
Decay Chain ◽  
New Physics ◽  
Effective Theory ◽  
Heavy Quark Effective Theory ◽  
B Meson Decays ◽  
The Standard Model

We study the exclusive decays of B → K* ℓ+ ℓ- within the framework of the PQCD. We obtain the form factors for the B → K* transition in the large recoil region, where the PQCD for heavy B meson decays is reliable. We find that the form factors at q2 = 0 are consistent with those from the large energy effective theory combined with the heavy quark effective theory and the experiment of B → K*γ. Via the decay chain of B → K* (Kπ) ℓ+ ℓ-, we can study many physical observables which are related to the different helicity combinations of B → K* ℓ+ ℓ-, such as the forward-backward asymmetries (FBAs). In particular, we can study the T violating effect which is small in the standard model but can be up to 10% in models with new physics.

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