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, Adam Falkowski… ADD YOUR NAME HERE

A question that often arises is whether 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 dimension-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 → Francesco

2) comupte contribution to \psi\psi → V_L V_L from O_1, O_2 and O_8 Use Re-Weighting method to avoid statistical error in the various generation → Model and param_card created by Ken + Ramona → Run by Olivier

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

4) Understand wheter this behavior is the same in other processes → Shankha: O_W, O_B and O_WB and O_phi_1 (this one is strongly constrained by custodial symmetry, that's what I remember) (Eq. 2 in Ref. https://arxiv.org/pdf/1211.4580.pdf) which modify the ZWW/ gamma WW couplings as given in Eqs. 27 and 28. → Ken and Ramona for generating the model, Biplob and Shankha for the generation/comparaison

Another possibly interesting question would be the EFT effect included in the definition of the dependent electroweak parameters. This is assumed to be super small, but we may want to verify it quantitatively. After all, this is also part of the dim8 effects that we are after. I honestly think it is small, but i have never seen anything where this was tested.

Todo:

1) generate the model with and without those contributions → Benj

* Here is a model fully truncated at the dim 6 level.

2) generate p p > W W (same process as above) and compare the various results. Use Re-Weighting method to avoid statistical error in the various generation → Ken and Olivier

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

“Dimension-Six Terms in the Standard Model Lagrangian” https://arxiv.org/pdf/1008.4884.pdf