Constructing general partial waves and renormalization in EFT

Shu, Jiwu; Xiao, Ming-Lei; Zheng, Yinqiang

doi:10.48550/arxiv.2111.08019

Cited by 9 publications

(18 citation statements)

References 9 publications

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“…However, at this point, for simplicity, we take Λ → ∞ and consider only renormalizable interactions. One can check that the two terms above reproduce, by construction, the correct high energy amplitudes for the little-group indices (1,2,11), (2,1,11), and similarly for (1 ↔ 2). With the LE amplitude eq.…”

Section: 10)mentioning

confidence: 95%

“…For the remaining six choices of little-group indices, namely (1, 2, {12}), (2,2,11), (2,2,22) (plus 1 ↔ 2), the amplitudes vanish at O(m 0 ): the global charges of the massless particles involved forbid these amplitudes from appearing in the high-energy theory. These components arise from amplitudes with additional Higgs legs.…”

Section: O(m): Massive Amplitudes Arising From He Four-point Amplitudesmentioning

confidence: 99%

“…These additional non-renormalizable interactions also contribute mass-suppressed corrections to other components of the massive amplitude. 11 Here, we limit our discussion to one choice of little-group indices, namely (2,2,11), for which the matching has some novel features. The dipole interactions generate the following O(m 3 ) correction to this component,…”

Section: Including Non-renormalizable Interactionsmentioning

confidence: 99%

“…In the context of the standard-model EFT (SMEFT), similar selection rules beautifully relate the non-renormalization of various operators at the one-loop level to the allowed helicity amplitudes arising in unitarity cuts [2], and dictate the (non-)interference of tree-level SMEFT and SM amplitudes [3]. This approach has been recently extended to calculate the anomalous dimensions of operators in the SMEFT and other EFTs at the one-loop level [4][5][6][7][8], and to relate these to the partial-wave decomposition of the amplitudes [9][10][11]. Unitarity was further used to prove general nonrenormalization theorems in ref.…”

Section: Introductionmentioning

confidence: 99%

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On-shell Higgsing for EFTs

Balkin,

Durieux,

Kitahara

et al. 2021

Preprint

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We study the on-shell version of the Higgs mechanism in effective theories (EFTs) containing particles of different spins, focusing on contact terms as a simple starting point. We derive the massive contact terms and their coefficients from the massless amplitudes of the EFT above the symmetry breaking scale, by covariantizing the massless contact terms under the massive little group. In the little-group-covariant massive-spinor formalism, this notationally amounts to bolding spinor labels. Mass-suppressed contributions to the contact-term coefficients arise from higher-point contact terms with additional soft Higgs legs. We apply this procedure to obtain massive four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the standard-model EFT. The subleading helicityflipped components of each massive contact term, which are dictated by little-group covariance, are associated with the residues of factorizable massless amplitudes. Extra "frozen" Higgses emitted from each leg of a massless contact term supply the additional light-like momentum component, needed to form a massive leg of the same polarization. As another application, we derive various components of massive three-point amplitudes from massless amplitudes with up to three additional Higgses, in a standard-model-like toy model.

show abstract

Section: 10)mentioning

confidence: 95%

Section: O(m): Massive Amplitudes Arising From He Four-point Amplitudesmentioning

confidence: 99%

Section: Including Non-renormalizable Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On-shell Higgsing for EFTs

Balkin,

Durieux,

Kitahara

et al. 2021

Preprint

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show abstract

“…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

Self Cite

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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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On-shell Higgsing for EFTs

Balkin

Durieux

Kitahara

et al. 2022

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the on-shell version of the Higgs mechanism in effective theories (EFTs) containing particles of different spins, focusing on contact terms as a simple starting point. We derive the massive contact terms and their coefficients from the massless amplitudes of the EFT above the symmetry breaking scale, by covariantizing the massless contact terms under the massive little group. In the little-group-covariant massive-spinor formalism, this notationally amounts to bolding spinor labels. Mass-suppressed contributions to the contact-term coefficients arise from higher-point contact terms with additional soft Higgs legs. We apply this procedure to obtain massive four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the standard-model EFT. The subleading helicity-flipped components of each massive contact term, which are dictated by little-group covariance, are associated with the residues of factorizable massless amplitudes. Extra “frozen” Higgses emitted from each leg of a massless contact term supply the additional light-like momentum component, needed to form a massive leg of the same polarization. As another application, we derive various components of massive three-point amplitudes from massless amplitudes with up to three additional Higgses, in a standard-model-like toy model.

show abstract

Constructing general partial waves and renormalization in EFT

Cited by 9 publications

References 9 publications

On-shell Higgsing for EFTs

On-shell Higgsing for EFTs

Constructing Generic Effective Field Theory for All Masses and Spins

On-shell Higgsing for EFTs

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