Theory tables

Each experimental dataset is associate with a corresponding theory table which has to be provided by the user. Theory tables are json files containing the following information:

  • best standard model predictions for each datapoint: provided as a list [best_sm_prediction_1, ... ,best_sm_prediction_N] with N being the number of datapoints

  • theory covariance matrix for the specific dataset considered: provided as a N x N matrix like [[th_cov_11, ... ,th_cov_1N], ... , [th_cov_N1, ... ,th_cov_NN]] with N being the number of data points

  • LO and NLO predictions with linear and quadratic SMEFT corrections: provided as two independent dictionaries LO: {} and NLO: {} each containing

    • SM predictions obtained at that specific order SM: [sm_prediction_1, ... , sm_prediction_N]

    • linear terms for each operator involved in the computation Opi: [linear_term_Opi_1, ..., linear_term_Opi_N]

    • quadratic terms for each couple of operators (when present) Opi*Opj: [quad_term_Opi*Opj_1, ..., quad_term_Opi*Opj_N]

The EFT corrections should always be provided in the Warsaw basis. In order to produce a fit with a different basis, the corresponding rotation matrix has to be provided externally, see here for more details.

The above information are used to build the theory predictions for the different observables entering the \(\chi^2\). As default theory predictions are expressed as

\[\sigma=\sigma_{\rm SM}^{\rm best} + \sum_i^{N_{d6}}{\kappa_i}^{\rm LO/NLO} \frac{c_i}{\Lambda^2} + \sum_{i,j}^{N_{d6}} \widetilde{\kappa}_{ij}^{\rm LO/NLO} \frac{c_ic_j}{\Lambda^4} \, ,\]

The user can also choose to use the relation

\[\sigma=\sigma_{\rm SM}^{\rm best}\left(1 + \sum_i^{N_{d6}}\frac{{\kappa_i}^{\rm LO/NLO}}{\sigma_{\rm SM}^{\rm LO/NLO}} \frac{c_i}{\Lambda^2} + \sum_{i,j}^{N_{d6}} \frac{\widetilde{\kappa}_{ij}^{\rm LO/NLO}}{\sigma_{\rm SM}^{\rm LO/NLO}} \frac{c_ic_j}{\Lambda^4}\right) \, ,\]

instead by setting in the runcard use_multiplicative_prescription: True. The reason to take the ratios \(\frac{{\kappa_i}^{\rm LO/NLO}}{\sigma_{\rm SM}^{\rm LO/NLO}}\) and \(\frac{\widetilde{\kappa}_{ij}^{\rm LO/NLO}}{\sigma_{\rm SM}^{\rm LO/NLO}}\) is to reduce the dependence on the specific set of parton distribution functions used to computed the LO and NLO predictions.