# Thesis

Perturbative evaluation of Electroweak Precision Observables in the Standard Model and Beyond

### Details

• Call:

IDPASC Portugal - PHD Programme 2017

2017 / 2018

• Domain:

Theoretical Particle Physics

• Supervisor:

Brigitte Hiller

• Co-Supervisor:

Marcos Rodrigues-Sampaio

• Institution:

A supersymmetric and gauge invariant regularization scheme has not been fully constructed yet. Dimensional sensitive quantum field theories (incompatible with analytical continuation on the spacetime dimension) such as topological, chiral and supersymmetric are particularly affected by regularization ambiguities and at the same time are of paramount phenomenological importance. Some issues are still open problems in the literature: 1- a gauge-invariant prescription for the $\gamma_5$ algebra. In particular, the author of [1,2] presents the so called Rightmost Ordering in which all $\gamma_5$ should be moved to the rightmost position of the amplitude before its dimensionality is altered. Another proposal focuses on an integral representation for the trace involving gamma matrices [3]. Nevertheless, in both cases the authors intend to obtain a prescription which allows dimensional regularization to be applied to dimension specific objects as the $\gamma_5$ matrix. Another proposal, in the case of four-dimensional regularization, was envisaged by the authors of [4]. 2- In the particular instance of supersymmetry breaking, it is neither straightforward nor conclusive that supersymmetry is a symmetry of the full quantum theory in any particular case. However, as discussed in [5], there have been claims about a supersymmetry anomaly which turned out erroneous because of the difficulty to distinguish between a genuine and a spurious anomaly. The latter is an apparent violation of a supersymmetric Ward identity due to use of a regularization method that violates supersymmetry. 3- Electroweak precision observables are extremely well measured data which serve to test Physics beyond the standard model. Examples are the W boson mass, the effective leptonic weak mixing angle, the anomalous magnetic moment of the muon and the mass of the lightest Higgs boson (CP-even) in the Minimal supersymmetric standard model. For instance the muon anomalous magnetic moment a_\mu{exp} measured in the experiment E821 in Brookhaven [6] and theoretical calculations a_mu^{SM} involving the standard Model [7], yield a discrepancy [8] \Delta a_\mu^{today} = a_\mu^{exp} - a_\mu^{SM} = (287 (+\-) 80) 10^{-11}. Such difference can prove supersymmetric models compatible or not with phenomenology. If discarded, extensions in the Higgs sector appear as new possible venues. We intend to apply Implicit Regularization (IR), see e.g. [9-19], to theoretical calculations which need an invariant regularization, particularly to evaluate electroweak precision observables. The basic idea of IR is based on the observation that ultra-violet (UV) singularities are independent of the kinematics. This is used to isolate the UV singular part of loop integrals. In IR, the UV singular part is expressed in terms of implicit integrals and boundary terms (that have to be set to zero to respect gauge invariance). The resulting UV finite integrals are evaluated in strictly four dimensions. Bibliography: [1] E. C. Tsai, Phys. Rev. D83 (2011) 025020. [2] E. C. Tsai, Phys. Rev. D83 (2011) 065011. [3] R. Ferrari, Int. J. Theor. Phys. 56 (2017) 691. [4] G. Cynolter and E. Lendvai, Mod. Phys. Lett. A 26 (2011) 1537. [5] I. Jack, D. R. T. Jones, Perspectives on Supersymmetry (G. L. Kane, ed), hep-ph/97077278. [6] G. Bennett, et al., (Muon $g-2$ collaboration), Phys. Rev. D73 (2006) 072003. [7] The Physics case for the New Muon $g-2$ Experiment, D. W. Hertzog, James P. Miller, Eduardo de Rafael, B. L. Roberts, D. Stockinger, arXiv:0705.4617. [8] Michel Davier et al., Eur.Phys.J. C71 (2011) 1515; Erratum-ibid. C72 (2012) 1874. [9] A.P.B. Scarpelli, M. Sampaio and M.C. Nemes, Phys. Rev. D 63 (2001) 046004. [10] A.L. Cherchiglia, M. Sampaio and M.C. Nemes, Int. J. Mod. Phys. A 26 (2011) 2591. [11] L.C. Ferreira, A.L. Cherchiglia, Brigitte Hiller, Marcos Sampaio and M.C. Nemes, Phys. Rev. D 86 (2012) 025016. [12] A.L. Cherchiglia, L.A. Cabral, M.C. Nemes and M. Sampaio, Phys. Rev. D 87 (2013) no.6, 065011. [13] J.C.C. Felipe, A. R. Vieira, A.L. Cherchiglia, A.P.B. Scarpelli and M. Sampaio, Phys. Rev. D 89 (2014) no.10, 105034. [14] A. R. Vieira, A. L. Cherchiglia and M. Sampaio, Phys. Rev. D 93 (2016) no.2, 025029. [15] A.L. Cherchiglia, A.R. Vieira, B. Hiller, A.P.B. Scarpelli, M. Sampaio, Annals Phys. 351 (2014) 751. [16] O. A. Battistel and G. Dallabona, Eur. Phys. J. C 45 (2006) 721. [17] D.E. Carneiro, A.P.B. Scarpelli, M. Sampaio and M.C. Nemes, JHEP 0312 (2003) 044 [18] H.G. Fargnoli, B. Hiller, A.P.B. Scarpelli, M. Sampaio and M.C. Nemes, Eur. Phys. J. C 71 (2011) 1633. [19] A.L. Cherchiglia, M. Sampaio, B. Hiller and A.P.B. Scarpelli, Eur. Phys. J. C 76 (2016) no.2, 47