Two-, three-, and four-body decays in the constructive standard model

Christensen, Neil D.; Field, Bryan; Moore, Annie; Pinto, S. E. S.

doi:10.1103/physrevd.101.065019

Cited by 22 publications

(17 citation statements)

References 27 publications

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“…Hilbert series (more generally, the mathematical structure of polynomial rings) have recently been utilized to organize and ameliorate the difficulties surrounding the construction of EFT operator bases and to study the structure of EFTs [81][82][83][84][85][86][87] (see also the developments [33,[88][89][90][91][92][93][94][95][96][97]). The scalar EFTs we consider fall into the class where their operator bases are controlled by an underlying conformal representation theory, which can be directly used in the construction of a Hilbert series.…”

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%

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Renormalization and non-renormalization of scalar EFTs at higher orders

Cao

Herzog

Melia

et al. 2021

J. High Energ. Phys.

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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.

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Section: Jhep09(2021)014mentioning

confidence: 99%

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.

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show abstract

“…[3,7], we will not report it explicitly here. Useful formulas for the computation of the squared matrix element with spinor variables can be found in [44].…”

Section: Oscillations From the 4-point Amplitudementioning

confidence: 99%

An on-shell perspective on neutrino oscillations and non-standard interactions

Alves,

Bertuzzo,

Salla

2021

Preprint

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We apply on-shell amplitude techniques to the study of neutrino oscillations in vacuum, focussing on processes involving W bosons. We start by determining the 3-point amplitude involving one neutrino, one charged lepton and one W boson, highlighting all the allowed kinematic structures. The result we obtain contains terms generated at all orders in an expansion in the cutoff scale of the theory, and we explicitly determine the lower dimensional operators behind the generation of the different structures. We then use this amplitude to construct the 4-point amplitude in which neutrinos are exchanged in the s-channel, giving rise to oscillations. We also study in detail how flavor enters in the amplitudes, and how the PMNS matrix emerges from the on-shell perspective.

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“…However, they narrow down the form of the amplitude to a finite number of terms. For an exhaustive analysis, we refer the reader to [18] and [36,37]. In this paper, we will discuss only the amplitudes relevant to us.…”

Section: Scattering Amplitudes As Little Group Tensorsmentioning

confidence: 99%

On-shell electroweak sector and the Higgs mechanism

Bachu

Srikant

2020

J. High Energ. Phys.

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We describe a new approach towards the development of an entirely on-shell description of the bosonic electroweak sector of the Standard Model and the Higgs mechanism. We write down on-shell three particle amplitudes consistent with Poincaré invariance and little group covariance. Tree-level, four particle amplitudes are determined by demanding consistent factorization on all poles and correct UV behaviour. We present expressions for these 2 → 2 scattering amplitudes using massive spinor helicity variables. We show that on-shell consistency conditions suffice to derive relations between the masses of the W ± , Z, the Weinberg angle and the couplings. This provides a completely on-shell description of the Higgs mechanism without any reference to the vacuum expectation value of the Higgs field.

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Two-, three-, and four-body decays in the constructive standard model

Cited by 22 publications

References 27 publications

Renormalization and non-renormalization of scalar EFTs at higher orders

Renormalization and non-renormalization of scalar EFTs at higher orders

An on-shell perspective on neutrino oscillations and non-standard interactions

On-shell electroweak sector and the Higgs mechanism

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