scholarly journals Factorization at subleading power, Sudakov resummation, and endpoint divergences in soft-collinear effective theory

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Ze Long Liu ◽  
Bianka Mecaj ◽  
Matthias Neubert ◽  
Xing Wang
Keyword(s):  
Effective Theory ◽  
Soft Collinear Effective Theory

Effective Field Theory in Particle Physics and Cosmology

2020 ◽  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Large Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Soft Collinear Effective Theory ◽  
Multiple Length Scales ◽  
Cosmological Observations ◽  
Standard Models

Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.

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.

scholarly journals Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ze Long Liu ◽  
Bianka Mecaj ◽  
Matthias Neubert ◽  
Xing Wang
Keyword(s):  
Decay Amplitude ◽  
Factorization Theorem ◽  
Effective Theory ◽  
Operator Matrix ◽  
Quark Loop ◽  
Perfect Agreement ◽  
Soft Collinear Effective Theory ◽  
Convolution Integrals ◽  
Factorization Formula ◽  
Massless Quark

Abstract Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

scholarly journals Soft Wilson lines in the soft-collinear effective theory

2005 ◽  
Vol 71 (5) ◽  
Author(s):  
Junegone Chay ◽  
Chul Kim ◽  
Yeong Gyun Kim ◽  
Jong-Phil Lee
Keyword(s):  
Effective Theory ◽  
Soft Collinear Effective Theory

scholarly journals Soft-collinear effective theory: BRST formulation

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Sudhaker Upadhyay ◽  
Bhabani Prasad Mandal
Keyword(s):  
Degrees Of Freedom ◽  
Brst Symmetry ◽  
Symmetry Transformation ◽  
Gauge Condition ◽  
Effective Theory ◽  
Hard Interaction ◽  
Soft Collinear Effective Theory ◽  
Parameter Field ◽  
Definite Structure ◽  
Gauge Conditions

AbstractWe provide a BRST formalism for the soft-collinear effective theory describing interactions of soft and collinear degrees of freedom in the presence of a hard interaction. In particular, we develop a BRST symmetry transformation for SCET theory. We further generalize the BRST formulation by making the transformation parameter field dependent. This establishes a mapping between several SCET actions consistently when defined in different gauge conditions. In fact, a definite structure of gauge-fixed actions corresponding to any particular gauge condition can be generated for SCET theory using our formulation.

Soft-Collinear Effective Theory

2020 ◽  
pp. 307-361 ◽  
Author(s):  
Thomas Becher
Keyword(s):  
Cross Sections ◽  
Vector Current ◽  
Jet Physics ◽  
Effective Theory ◽  
Event Shape ◽  
Sudakov Form Factor ◽  
Shape Variable ◽  
Soft Collinear Effective Theory ◽  
Jet Cross Sections ◽  
Event Shape Variable

The lectures that appear within this chapter provide an introduction to soft-collinear effective theory (SCET). It begins by discussing resummation for soft-photon effects in QED, including soft photons in electron–electron scattering and the expansion of loop integrals and the method of regions event-shape variables. It then covers SCET specifically, including the method of regions for the Sudakov form factor, effective Lagrangians, the vector current in SCET, and resummation by renormalization group (RG) evolution. It covers applications of SCET in jet physics, describes the characteristic feature in jet processes of Sudakov logarithms, and discusses factorization for the event-shape variable thrust and factorization and resummation for jet cross sections.

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