Modeling theoretical uncertainties in phenomenological analyses for particle physics

Abstract

The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random, nuisance, external) in the frequentist framework, and we derive the corresponding p values. In the case of the nuisance approach where theoretical uncertainties are modeled as biases, we highlight the important, but arbitrary, issue of the range of variation chosen for the bias parameters. We introduce the concept of adaptive p value, which is obtained by adjusting the range of variation for the bias according to the significance considered, and which allows us to tackle metrology and exclusion tests with a single and well-defined unified tool, which exhibits interesting frequentist properties. We discuss how the determination of fundamental parameters is impacted by the model chosen for theoretical uncertainties, illustrating several issues with examples from quark flavor physics.

Constraining the gauge and scalar sectors of the doublet left-right symmetric model

“…We will follow the CKMfitter statistical approach used in flavour physics to combine constraints in a frequentist framework [36,38,78], building a χ 2 function from the likelihoods of the various observables. The theoretical uncertainties are treated following the Rfit scheme corresponding to a modification of the likelihood including a bias parameter left free to vary within the quoted range for the theoretical uncertainty [38]. For a parameter of interest, the χ 2 is considered at different values of this parameter and minimised with respect to the other parameters of the fit.…”

“…In this article, we will discuss three classes of constraints on the DLRM related to the presence of heavy gauge bosons and scalars that affect the dynamics of the light gauge bosons W and Z: the unitarity of the processes involving the scattering of two gauge bosons, the radiative corrections to the muon ∆r parameter, and the electroweak precision observables measured at the Z-pole and at low energies. We will combine these three constraints into a global fit using the frequentist approach of the CKMfitter collaboration [36][37][38] in order to constrain the parameters of the model. We leave the discussion of flavour and the combination of all constraints for future work, due to the large number of additional parameters involved.…”

Disentangling weak and strong interactions in $$B\rightarrow K^{*}(\rightarrow K\pi )\pi $$ B → K ∗

“…On the other hand, we update the hadronic parameters in order to take into account more recent determinations of these quantities; see Appendix B. We use the Rfit scheme to handle theoretical uncertainties [6][7][8]67] (in particular for the hadronic parameters and the 1/m b power-suppressed contributions), and we compute only ratios of hadronic amplitudes using QCD factorisation. We stress that we provide the estimates within QCD factorisation simply to compare the results of our experimental fit for the hadronic amplitudes with typical theoretical expectations concerning the same quantities.…”

What RK and Q5 can tell us about New Physics in b→sℓℓ transitions?

“…This definition, already used in refs. [42][43][44][45], differs from the definition often adopted e.g. in the context of electroweak precision observables [46]: this naive pull is defined as the difference between the experimental value and the theoretical value at the b.f.p., normalised by the uncertainty.…”