Aspects of the gauge hierarchy of the standard model

The standard model (SM) is a huge success, being able to explain particle physics phenomenology up to the energy scales accessible nowadays (up to 13 TeV). Albeit this huge feat, the SM is not considered to provide an ultimate description of nature. Many extensions of the standard model have been motivated by the so-called hierarchy problem. While this does not characterize an incosistency of the standard model, it rather refers to the aesthetics of the theory, or its naturalness. This issue is often paraphrased as: How can the Higgs mass stay small compared to an UV cutoff while it receives radiative corrections which are naively of order cutoff squared? In this work functional renormalization group techinques are employed to provide a new perspective on the gauge hierarchy of various toy models mimicking parts of the standard model. First a Z2-symmetric toy model containing one real scalar field and one Dirac fermion is studied, especially focussing on the dependence of the scale separation on the IR observables top mass and Higgs mass. Then a model containing Nf = 6 Fermions transforming in the fundamental representation of SU(3), gauge bosons, and one scalar SU(2) doublet is investigated. The strong interaction forces spontaneous chiral symmetry breaking which will be accounted for by partial bosonization of the theory, in addition to the the usual electroweak symmetry breaking in the scalar sector. The hierarchy of the emerging scales is studied, namely the UV cutoff, the electroweak scale and in the latter model also the QCD scale for different values of the parameters of the models. The goal is to study the phase transition or crossover of this standard-model-like system from a “deeply-Higgsed” into a pure QCD-type phase. From the renormalization group perspective, the rapidness of this transition is quantitatively related to the severity of the naturalness problem

Interplay of Chiral Transitions in the Standard Model

We investigate nonperturbative aspects of the interplay of chiral transitions in the standard model in the course of the renormalization flow. We focus on the chiral symmetry breaking mechanisms provided by the QCD and the electroweak sectors, the latter of which we model by a Higgs-top-bottom Yukawa theory. The interplay becomes quantitatively accessible by accounting for the fluctuation-induced mixing of the electroweak Higgs field with the mesonic composite fields of QCD. In fact, our approach uses dynamical bosonization and treats these scalar fields on the same footing. Varying the QCD scale relative to the Fermi scale we quantify the mutual impact of the symmetry-breaking mechanisms, specifically the departure from the second order quantum phase transition of the pure Yukawa sector in favor of a crossover upon the inclusion of the gauge interactions. This allows to discuss the ``naturalness'' of the standard model in terms of a pseudo-critical exponent which we determine as a function of the ratio of the QCD and the Fermi scale. We also estimate the minimum value of the $W$ boson mass in absence of the Higgs mechanism.Comment: 25 pages, 13 figure

Ω-Arithmetization of Ellipses

International audienceMulti-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs. Moreover, we give a global condition for the connectivity of the discrete curves generated by the method at every scale

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Measurement of the W-boson mass in pp collisions at √s=7 TeV with the ATLAS detector

A measurement of the mass of the W boson is presented based on proton–proton collision data recorded in 2011 at a centre-of-mass energy of 7 TeV with the ATLAS detector at the LHC, and corresponding to 4.6 fb−1 of integrated luminosity. The selected data sample consists of 7.8×106 candidates in the W→μν channel and 5.9×106 candidates in the W→eν channel. The W-boson mass is obtained from template fits to the reconstructed distributions of the charged lepton transverse momentum and of the W boson transverse mass in the electron and muon decay channels, yielding mW=80370±7 (stat.)±11(exp. syst.) ±14(mod. syst.) MeV =80370±19MeV, where the first uncertainty is statistical, the second corresponds to the experimental systematic uncertainty, and the third to the physics-modelling systematic uncertainty. A measurement of the mass difference between the W+ and W−bosons yields mW+−mW−=−29±28 MeV