Les Houches

[Estimation of the theoretical uncertainties in EFT]

interested people: Olivier Mattelaer, Ken Mimasu, Kentarou Mawatari, Shankha Banerjee, Biplob Bhattacherjee, Francesco Riva, Benjamin Fuks, Ramona Groeber, Julia Harz, Jorge de Blas, Kristin Lohwasser, Alexandra Carvalho… ADD YOUR NAME HERE

A question that often arises is wheter dimension-8 effects compromise present analysis testing dimension-6 ones. Normally this requires a discussion about the expected size of dimension-8 operators under given assumptions (see for instance “On the Validity of the Effective Field Theory Approach to SM Precision Tests” https://arxiv.org/pdf/1604.06444.pdf)

Here we want to compute a class of dimesnion-8 effects that arises after a change of basis, in such a way that their coefficient is uniquely related to the coefficients of dimension-6 operators. The goal of this analysis will be to understand under what conditions we can trust the dimension-6 analysis in the rotated basis.

The project aims to compute a set of observables (cross-sections and differential cross-sections) for a given dimension 6 operator and then compare the predictions obtained in different bases.

A promising operator is HDH \psi gamma \psi. Using the equations of motion, or better phrased field redefinitions) of the form W_\mu→W_\mu + a H D_\mu H this can be converted into 4-fermi operators, operators of the form DW\psi gamma \psi and dimension-8 operators of the form H(HDH)H \psi gamma \psi (the dimension-6 part can be verified with ROSETTA).

Now we can test these operators in \psi\psi → V_L V_L

The contribution of the original O_1= HDH \psi gamma \psi will be equivalent to O_2=DW\psi gamma \psi plus the dimension-8 guy = O_8.

Now, it will be interesting to understand when this dim-8 contribution is important, and in particular if it is important when the square of the dimension-6 becomes bigger than the linear (interference) term. It seems that the dimension-8 is always suppressed by the m/energy, but this needs to be checked.

In practice this project involves the following steps:

1) perform field redefinition to find the coefficient of O_8 as a function of the coefficient of O_1

2) comupte contribution to \psi\psi → V_L V_L from O_1, O_2 and O_8

3) Impose that the quadratic piece be bigger than the linear piece, and test in these conditions how big the dimension-8 contribution becomes

4) Understand wheter this behavior is the same in other processes

Pictures of the blackboard: https://phystev.cnrs.fr/wiki/_media/2017:groups:np:dsc_0151.jpg

References:

“On the Validity of the Effective Field Theory Approach to SM Precision Tests” https://arxiv.org/pdf/1604.06444.pdf

“Rosetta: an operator basis translator for Standard Model effective field theory” https://arxiv.org/pdf/1508.05895.pdf

“Higgs windows to new physics through d=6 operators: constraints and one-loop anomalous dimensions” https://arxiv.org/pdf/1308.1879.pdf