Zhe Ren

A bstract: We compute the one-loop mixing of bosonic and two-fermion interactions into two-fermion operators in the dimension-eight Standard Model Effective Field Theory (SMEFT). Together with the results in refs. [ SciPost Phys. 11 (2021) 065, Eur. Phys. J. Plus 137 (2022) 973, JHEP 12 (2024) 214, JHEP 08 (2026) 225], this leaves only the mixing of four-fermion operators into two-fermion ones as the remaining piece to complete the SMEFT renormalization program at this order.

We perform the first computation of phase-transition parameters to cubic order in , where m is the scalar mass and T is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalization-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings and largely surpass those from 3-loop thermal masses.

This is the third of a series of works [1, 2] aimed at renormalizing the Standard Model effective field theory at one loop and to order 1/Λ⁴, with Λ being the new physics cut-off. On this occasion, we concentrate on the running of two-fermion operators induced by pairs of dimension-six interactions. We work mostly off-shell, for which we obtain and provide a new and explicitly hermitian basis of dimension-eight Green’s functions. All our results can be accessed in https://github.com/SMEFT-Dimension8-RGEs.

In the effective field theory (EFT), the positivity bound on dim-8 effective operators tells us that the s² contribution in the scattering amplitude of 2-to-2 process geometrically corresponds to the convex cone composed of the ultraviolet (UV) states as the extremal rays. The J-Basis method can provide a complete group theory decomposition of the scattering amplitude on the direct product of the gauge group and the Lorentz group, thus to search for all UV states. Compared to previous methods, which can only perform direct product decomposition on the gauge groups, the J-Basis method greatly improves the strictness of the restrictions and also provides a systematic scheme for calculating the positivity bounds of the dim-8 operators.

We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We propose an off-shell amplitude formalism such that this new kind of amplitude has a one-to-one correspondence to general operators carrying all kinds of redundancies. The advantage of such formalism is that all kinds of redundancies can be formulated explicitly in terms of the off-shell spinors and thus be removed systematically from the exhaustive list of the general off-shell amplitudes. Following such procedures, redundant operators can be reduced to the ones with the only redundancy from the equation of motion kept, the Green’s basis. We find there are (993+1649) independent (on-shell + off-shell) operators for one generation of fermions and (44807+66197) ones for three generations at dimension 8. This systematic method can be applied to obtain the Green’s basis at any mass dimension for general EFTs.

A bstract: We construct the on-shell amplitude basis and the corresponding effective operators for generic modified gravity theory, such as pure gravity with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking the Weyl tensor as the building block, we utilize the Young tensor technique to obtain independent operators, without equation of motion and total derivative redundancies. We update our algorithm and vastly increase the speed for finding the monomial basis (m-basis) of effective operators expressed in terms of Weyl tensors with Lorentz indices, the familiar form for the General Relativity community. Finally, we obtain the complete and independent amplitude and operator basis for GRSMEFT and GRLEFT up to mass dimension 10.