Reparameterization invariant operator basis for NRQED and HQET

Kobach, Andrew; Pal, Sridip

doi:10.1007/jhep11(2019)012

Cited by 11 publications

(9 citation statements)

References 36 publications

(77 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[37] which counts the number of independent gauge-invariant chiral operators in supersymmetric gauge theories, HS has been applied to a wide range of formal theories [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. The construction of all (linearly-) independent gauge-and Lorentzinvariant effective operators at certain mass dimension in the effective field theories is also a standard example in the invariant theory and has been developed a lot by the tool of HS in recent years [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68], which provides a cross-check to the traditional group theory method. In addition, HS also plays a role in some interesting physical processes like the tidal effects [69,70].…”

Section: Jhep09(2021)053 B Invariant Theory and Hilbert Seriesmentioning

confidence: 99%

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

Wang

Zhou

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

In the present paper, we carry out a systematic study of the flavor invariants and their renormalization-group equations (RGEs) in the leptonic sector with three generations of charged leptons and massive Majorana neutrinos. First, following the approach of the Hilbert series from the invariant theory, we show that there are 34 basic flavor invariants in the generating set, among which 19 invariants are CP-even and the others are CP-odd. Any flavor invariants can be expressed as the polynomials of those 34 basic invariants in the generating set. Second, we explicitly construct all the basic invariants and derive their RGEs, which form a closed system of differential equations as they should. The numerical solutions to the RGEs of the basic flavor invariants have also been found. Furthermore, we demonstrate how to extract physical observables from the basic invariants. Our study is helpful for understanding the algebraic structure of flavor invariants in the leptonic sector, and also provides a novel way to explore leptonic flavor structures.

show abstract

Section: Jhep09(2021)053 B Invariant Theory and Hilbert Seriesmentioning

confidence: 99%

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

Wang

Zhou

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…We emphasize that both the Hilbert series and R* techniques we develop are general, and can apply beyond the scalar EFTs we consider here. In particular, for Hilbert series, applications to spin [82][83][84][85], non-linearly realized internal symmetries [83,86], gravity [99] and non-relativistic EFTs [100,101], have all been developed. The R* method has already found application in gauge theories and the SM EFT, as already mentioned above.…”

Section: Jhep09(2021)014mentioning

confidence: 99%

“…Indeed, the R* method has, for instance, already been widely applied to gauge theories. Also Hilbert series technology can encompass spin [82][83][84][85], non-linearly realized internal symmetries [83,86], gravity [99] and non-relativistic EFTs [100,101], and the systematic construction of operators that involve particles of higher spin via the study of polynomial rings and conformal representation theory has recently been studied in detail [84,85], and by related methods [33,[88][89][90][91][92][93][94][95][96][97]. We expect that such on-shell techniques, and their development to off-shell objects of interest that was presented here, could also be of use in studying full loop amplitudes in EFT, i.e.…”

Section: Jhep09(2021)014mentioning

confidence: 99%

Renormalization and non-renormalization of scalar EFTs at higher orders

Cao

Herzog

Melia

et al. 2021

J. High Energ. Phys.

View full text Add to dashboard Cite

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a ‘non-renormalization’ rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing n- and (n− 2)-field operators, with n the maximal number of fields at a fixed mass dimension. The first appears only when the (n− 2)-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.

show abstract

“…We emphasize that both the Hilbert series and R* techniques we develop are general, and can apply beyond the scalar EFTs we consider here. In particular, for Hilbert series, applications to spin [79][80][81][82], non-linearly realized internal symmetries [80,83], gravity [96] and non-relativistic EFTs [97,98], have all been developed. The R* method has already found application in gauge theories and the SM EFT, as already mentioned above.…”

mentioning

confidence: 99%

Renormalization and non-renormalization of scalar EFTs at higher orders

Cao

Herzog

Melia

et al. 2021

Preprint

View full text Add to dashboard Cite

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a 'non-renormalization' rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing n-and (n − 2)-field operators, with n the maximal number of fields at a fixed mass dimension. The first appears only when the (n − 2)-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.

show abstract

Reparameterization invariant operator basis for NRQED and HQET

Cited by 11 publications

References 36 publications

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

Renormalization and non-renormalization of scalar EFTs at higher orders

Renormalization and non-renormalization of scalar EFTs at higher orders

Contact Info

Product

Resources

About