Renormalization of higher-dimensional operators from on-shell amplitudes

We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.

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“…In ref. [49] all one-loop anomalous dimensions of the SU(2) L dipole operator of the electron (up to self-renormalisation) are reproduced.…”

Section: Discussionmentioning

confidence: 86%

“…Simultaneously with the submission of this preprint ref. [49] appeared where the renormalisation of higher-dimensional operators from on-shell amplitudes is presented from a slightly different perspective. In ref.…”

Section: Discussionmentioning

confidence: 99%

EFT anomalous dimensions from the S-matrix

Miró

Ingoldby

Riembau

2020

J. High Energ. Phys.

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“…[77][78][79][80][81][82][83][84][85]) and consider their renormalization using both conventional and on-shell formalism (see e.g. [86][87][88][89][90][91][92][93][94]). While the state-of-the-art computation is mostly at one-loop order, it would be worth extending the method developed in this paper to general two-loop renormalization in SMEFT (see also [95]).…”

Section: Discussionmentioning

confidence: 99%

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

Jin

Ren

Yang

2021

J. High Energ. Phys.

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We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.

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“…The resulting operators will then be evolved to the scale appropriate for the measurement using renormalization group equations (RGE) [45][46][47][48][49][50]. Recently, a deeper connection has been established between the helicity amplitude structures of SMEFT and the RGEs of the operator coefficients [38,[51][52][53][54][55][56][57][58]. In short, an operator is only renormalized by another if the latter contributes at one…”

Section: Robustness Of the Sum Rulesmentioning

confidence: 99%

Sum rules in the standard model effective field theory from helicity amplitudes

Wang

2021

J. High Energ. Phys.

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The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.

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Renormalization of higher-dimensional operators from on-shell amplitudes

Cited by 53 publications

References 15 publications

EFT anomalous dimensions from the S-matrix

EFT anomalous dimensions from the S-matrix

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

Sum rules in the standard model effective field theory from helicity amplitudes

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