Field redefinitions in effective theories at higher orders

Criado, Juan Carlos; Pérez-Victoria, M.

doi:10.1007/jhep03(2019)038

Cited by 66 publications

(59 citation statements)

References 84 publications

(176 reference statements)

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“…The field redefinition for n + A c is fixed only up to residual gauge transformation and the above relations hold only for a specific, non-covariant gauge choice. In practice, we want to use a covariant gauge fixing in the original fields to ensure that the SCET LSZ Zfactor of the collinear fields as well as the MS field renormalization factor does not receive any O(λ) contribution at one-loop, 8 such that the LSZ Z-factor remains the same with the above field redefinition. This choice allows to directly compare the on-shell Green functions computed with the original fields to those computed with the redefined fields.…”

Section: Extension Of Soft Mixing To the Non-abelian Casementioning

confidence: 99%

“…Moreover, a well-known result due to Kluberg-Stern and Zuber [3] states that eom operators (also termed "class II") do not mix into physical ("class I") operators under renormalization (see also [1,4] and [5][6][7][8] for other aspects of the statement), which implies a triangular structure of the operator anomalous dimension matrix (ADM). This does not mean that eom operators can always be ignored in ADM computations.…”

Section: Introductionmentioning

confidence: 99%

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Violation of the Kluberg-Stern-Zuber theorem in SCET

Beneke

Garny

Szafron

et al. 2019

J. High Energ. Phys.

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A classic result, originally due to Kluberg-Stern and Zuber, states that operators that vanish by the classical equation of motion (eom) do not mix into "physical" operators. Here we show that and explain why this result does not hold in soft-collinear effective theory (SCET) for the renormalization of power-suppressed operators. We calculate the non-vanishing mixing of eom operators for the simplest case of N -jet operators with a single collinear field in every direction. The result implies that-for the computation of the anomalous dimension but not for on-shell matrix elements-there exists a preferred set of fields that must be used to reproduce the infrared singularities of QCD scattering amplitudes. We identify these fields and explain their relation to the gauge-invariant SCET Lagrangian. Further checks reveal another generic property of SCET beyond leading power, which will be relevant to resummation at the next-to-leading logarithmic level, the divergence of convolution integrals with the hard matching coefficients. We propose an operator solution that allows to consistently renormalize such divergences. arXiv:1907.05463v1 [hep-ph]

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Section: Extension Of Soft Mixing To the Non-abelian Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Violation of the Kluberg-Stern-Zuber theorem in SCET

Beneke

Garny

Szafron

et al. 2019

J. High Energ. Phys.

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“…The decision of using the equations of motion is left to the user, as it may be convenient to work with redundant bases in some cases (see ref. [5]). It is also possible not only to compute invariants but to generate all covariant operators, classified by their irreps.…”

Section: Discussionmentioning

confidence: 99%

“…This means that some operators with derivatives can be rewritten in terms of others. Moreover, at each order in the effective Lagrangian, the addition of an operator proportional to the equations of motion does not change the S matrix up to higher order effects [1][2][3][4][5]. It follows that the equations of motion can be used, for example, to obtain a basis in which all the operators proportional to the functional derivative of the kinetic term have been removed [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

BasisGen: automatic generation of operator bases

Criado

2019

Eur. Phys. J. C

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BasisGen is a Python package for the automatic generation of bases of operators in effective field theories. It accepts any semisimple symmetry group and fields in any of its finite dimensional irreducible representations. It takes into account integration by parts redundancy and, optionally, the use of equations of motion. The implementation is based in well-known methods to generate and decompose representations using roots and weights, which allow for fast calculations, even with large numbers of fields and high-dimensional operators. BasisGen can also be used to do some representation-theoretic operations, such as finding the weight system of an irreducible representation from its highest weight or decomposing a tensor product of representations.

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“…An example of a system which initially appears to generate just such problems is reduction of type IIA supergravity on a non-compact H (2,2) A recent list of some of the literature on field redefinitions in effective theories may be found in [2]. 2 The various problems involving technically inconsistent dimensional reduction are a large topic. Older literature on problems of consistent and technically inconsistent Kaluza-Klein reductions can be found in Refs [4].…”

mentioning

confidence: 99%