Reparameterization Invariance for Collinear Operators

By A. Manohar, Thomas Mehen, D. Pirjol, Iain W. Stewart. 2002

146 citations recorded by the source corpus.

We discuss restrictions on operators in the soft-collinear effective theory (SCET) which follow from the ambiguity in the decomposition of collinear momenta and the freedom in the choice of light-like basis vectors n and n. Invariance of SCET under small changes in n and/or n implies a symmetry of the effective theory that constrains the form of allowed operators with collinear fields. The restrictions occur at a given order in the power counting as well as between different orders. As an example, we present the complete set of higher order operators that are related to the collinear quark kinetic term.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8b192c468ea13a71b1ced1dfa1f0a132f0fed769

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In Nuclear and High Energy Physics

1. A. Larkoski
2. D. Neill
3. W. Waalewijn
4. Jesse Thaler
5. I. Moult
6. F. Tackmann
7. Iain W. Stewart
8. A. Broggio

Citations in the corpus

• Jet shapes and jet algorithms in SCET (2010, background): “The residual and soft momenta appearing in the exponentials can be reabsorbed into the label momenta by a series of reparameterizations of the label momenta and directions, under which the SCET Lagrangian is invariant [70].”
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, methodology): “can choose any n that satises nn = 2. The precise choice of these parameters should not aect our calculations, providing us with additional symmetries known as reparametrization invariance (RPI) [139]. We will often use RPI-III that transforms n!enand n!e n. As an example, an RPI-III invariant funct”
• An effective field theory for forward scattering and factorization violation (2016, background): “However, all such enhanced graphs, which attempt to use Glauber interactions to join a disconnected set of n-collinear fields, vanish by RPI-III invariance symmetry [89].”
• A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory (2012, background): “Since dimensional regularization preserves boost invariance and is the only regularization required to separate modes in SCETI, each sector individually remains RPIIII invariant.”
• Factorization at the LHC: From parton distribution functions to initial state jets (2010, background): “By Lorentz invariance (or reparameterization invariance of na,b and n̄a,b [139]), the scalar coefficients can only depend on b̃a · b̃b = xaxbE cm = q2.”
• Introduction to Soft-Collinear Effective Theory (2014, background): “The most general infinitesimal transformation is a linear combination of the these three types of transformations [27]”
• Jet shapes with the broadening axis (2014, methodology): “Having identified the relevant modes, we are free to use reparametrization invariance (RPI) of the effective theory [52, 53] to perform small changes in the jet axis directions.”
• The quark beam function at NNLL (2010, background): “Dimensional analysis and RPI-III invariance imply that the single logarithm multiplying 2Γicusp scales like ln(y − a y − b μ 2).”