Mass matrices and their renormalization

Chiu, Shao-Hsuan; Kuo, T. K.; Lee, Taehun; Xiong, Chi

doi:10.1103/physrevd.79.013012

Cited by 16 publications

(25 citation statements)

References 18 publications

(24 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is the case for electroweak Sudakov processes and also for Regge limits. For the massive case, a regulator which leaves the structure of the theory intact has been proposed in [15], which is not analytic and introduces an additional scale into the effective theory. This complicates the computations and care is needed to avoid double counting.…”

Section: Analytic Regularizationmentioning

confidence: 99%

Analytic regularization in Soft-Collinear Effective Theory

2012

View full text Add to dashboard Cite

In high-energy processes which are sensitive to small transverse momenta, individual contributions from collinear and soft momentum regions are not separately well-defined in dimensional regularization. A simple possibility to solve this problem is to introduce additional analytic regulators. We point out that in massless theories the unregularized singularities only appear in real-emission diagrams and that the additional regulators can be introduced in such a way that gauge invariance and the factorized eikonal structure of soft and collinear emissions is maintained. This simplifies factorization proofs and implies, at least in the massless case, that the structure of Soft-Collinear Effective Theory remains completely unchanged by the presence of the additional regulators. Our formalism also provides a simple operator definition of transverse parton distribution functions.

show abstract

Section: Analytic Regularizationmentioning

confidence: 99%

Analytic regularization in Soft-Collinear Effective Theory

2012

View full text Add to dashboard Cite

show abstract

“…One can easily see that zero-bin subtractions (69) can be also taken into account by changing the sign of the soft contribution in Eq. (62) that was noted already in [34,46]. From considered example we can conclude, that evaluations of integrals using the method of regions in D = 4 with specific regularization, which allows to avoid scaleless integrals, must be carried out with the proper IR-subtractions.…”

Section: Collinear and Soft Contributions In D = 4: One-loop Casementioning

confidence: 54%

“…Then one obtains that corresponding contribution has the leading power suppression Q −6 as in Eq. (46) and can be written as a convolution of hard [...] H and collinear V parts (see details in Appendix C):…”

Section: Overlap Of the Soft And Collinear Regionsmentioning

confidence: 99%

“…These questions have been studied during last years in many publications in connection with the Sudakov form factor, see e.g. [33,46,47]. In [33] a systematic subtraction procedure has been suggested in order to separate contributions of collinear and soft modes in non-inclusive processes.…”

Section: B Calculation Of the Large Logarithmic Term Arising From Thmentioning

confidence: 99%

“…where B µ ⊥ sc denote appropriate part of the total coefficient B µ ⊥ in (46). Computing B µ ⊥ sc we can follow the same line as in the one-loop case and perform all calculations in D = 4.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F1 at large Q2

Kivel

2012

Eur. Phys. J. A

View full text Add to dashboard Cite

In [1] we suggested the factorization formula for the nucleon form factors which consist of the sum of two contributions describing the hard and soft spectator scattering, and we provided a description of the soft rescattering contribution for the FF F1 in terms of convolution integrals of the hard and hard-collinear coefficient functions with the appropriate soft matrix elements.In present paper we investigate the soft spectator scattering contribution for the FF F1. We focus our attention on factorization of the hard-collinear scale ∼ QΛ corresponding to transition from SCET-I to SCET-II. We compute the leading order jet functions and find that the convolution integrals over the soft fractions are logarithmically divergent. This divergency is the consequence of the boost invariance and does not depend on the model of the soft correlation function describing the soft spectator quarks. Using as example a two-loop diagram we demonstrated that such a divergency corresponds to the overlap of the soft and collinear regions. As a result one obtains large rapidity logarithm which must be included in the correct factorization formalism.We conclude that a consistent description of the factorization for F1 implies the end-point collinear divergencies in the hard and soft spectator contributions, i.e. convolution integrals with respect to collinear fractions are not well-defined. Such scenario can only be realized when the twist-3 nucleon distribution amplitude has specific end-point behavior which differs from one expected from the evolution of the nucleon distribution amplitude. Such behavior leads to the violation of the collinear factorization for the hard spectator scattering contribution. We suggest that the soft spectator scattering and chiral symmetry breaking provide the mechanism responsible for the violation of collinear factorization in case of form factor F1.In spite of complexities of the SCET factorization it can be very useful for a phenomenological analysis of hard exclusive reactions. The basis for such approach is provided by universality of the SCET-I form factors which can appear in different hard processes. We show that using, so-called, physical subtraction scheme SCET factorization in some cases allows to perform the systematical analysis of the hadronic processes in the range of moderate values of Q 2 ∼ 5 − 20 GeV 2 where the hard collinear scale ∼ QΛ is still not large

show abstract