Anomalous dimensions of effective theories from partial waves

Baratella, Pietro; Fernandez, Clara; Harling, Benedict von; Pomarol, Alex

doi:10.1007/jhep03(2021)287

Cited by 25 publications

(45 citation statements)

References 21 publications

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“…[23], and in part to understand underlying structures in EFT and in calculational approaches to them more generally e.g. [24][25][26][27][28][29][30][31][32][33].…”

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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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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“…[23], and in part to understand underlying structures in EFT and in calculational approaches to them more generally e.g. [24][25][26][27][28][29][30][31][32][33].…”

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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“…On-shell scattering amplitude is efficient in dealing with some problems of EFT, such as calculating the running of EFT operators [13][14][15][16][17][18][19], deriving EFT selecting rules [20][21][22], and constructing scalar EFT with nontrivial soft-limit [23][24][25][26]. Especially it is very efficient in constructing EFT bases of massless fields (called amplitude bases) [19,[27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Constructing Generic Effective Field Theory for All Masses and Spins

Dong¹,

Ma²,

Shu³

et al. 2022

Preprint

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We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude bases at any given dimension through semi-standard Young tableaus of Lorentz subgroup SU (2)r and global symmetry U (N ) (N is the number of external legs), which can be directly mapped into physical operator bases. We first construct a complete set of monomial bases whose dimension is not the lowest and a redundant set of bases that always contains a complete set of amplitude bases with the lowest dimension. Then we decompose the bases of the redundant set into the monomial bases from low to high dimension and eliminate the linear correlation bases. Finally, the bases with the lowest dimension can be picked up. We also propose a matrix projection method to construct the massive amplitude bases involving identical particles. The operator bases of a generic massive effective field theory can be efficiently constructed by the computer programs. A complete set of four-vector operators at dimensions up to six is presented.

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“…Recently, there has been raising interest about theoretical constraints on effective field theories from the principle of unitarity, while partial wave analysis tends to provide a tighter bound than a general analysis [1,2]. There are also observations of new selection rules and computational techniques [3,4] for anomalous dimensions based on partial waves. It is hence instructive to implement a complete study on the partial waves in general for scattering problems.…”

Section: Introductionmentioning

confidence: 99%

“…which provides algebraic method of computing the Anomalous Dimension Matrix (ADM) for effective operators. As we generalize the partial wave basis, we are not restricted to 2 → 2 scattering [4], and we also adopt the BCFW momenta shift to eliminate the possible IR divergence. THEREFORE, the ADM is a sum over various unitarity cuts, while each can be directly read off from the partial waves of tree-level sub-amplitudes.…”

Section: Introductionmentioning

confidence: 99%

“…(5.8) is confirmed by the orthonormality of Wigner d-functions. Which has been used to compute the anomalous dimension in[4].5.2 Example of 2-to-3 scatteringIn this section, we calculate the anomalous dimension of O eH = ( leH)(H † H) and show how partial-wave expansion works. We consider only the renormalization from O He = (ēγ µ e)(H † i ← → D µ H) and other SM interactions.…”

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confidence: 99%

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Constructing general partial waves and renormalization in EFT

Shu¹,

Xiao²,

Zheng³

2021

Preprint

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We construct the general partial wave amplitude basis for the N → M scattering, which consists of Poincaré Clebsch-Gordan coefficients whose Lorentz covariant form is given in terms of the spinor-helicity variables. The inner product of the Clebsch-Gordan coefficients is defined, converting on-shell phase space integration into an algebraic problem. We also develop the technique of partial wave expansions of arbitrary IR finite amplitudes, including those with massless poles. These are applied to the computation of anomalous dimension matrix for general effective operators, where unitarity cuts for the loop amplitudes, with arbitrary number of external particles, are obtained via partial wave expansion.

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Anomalous dimensions of effective theories from partial waves

Cited by 25 publications

References 21 publications

Renormalization and non-renormalization of scalar EFTs at higher orders

Renormalization and non-renormalization of scalar EFTs at higher orders

Constructing Generic Effective Field Theory for All Masses and Spins

Constructing general partial waves and renormalization in EFT

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