arXiv subjects

Quentin Duret

Publications and source records attributed to Quentin Duret.

9 recordsLinked to original sources

arXiv2010

Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities. The case of a single fermion-antifermion pair

Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.

hep-ph↗

arXiv2009

Mixing angles of quarks and leptons in Quantum Field Theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2)_L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2)_f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns: on one hand, the three quark mixing angles; on the other hand, a neutrino-like pattern in which theta_{23} is maximal and tan(2 theta_{12})=2. The Cabibbo angle fulfills the condition tan (2 theta_c)=1/2 and theta_{12} for neutrinos satisfies accordingly the "quark-lepton complementarity condition" theta_c + theta_{12}= π/4. theta_{13} = +- 5.7 10^{-3} are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly brokensymmetry of the Standard Model is outlined.

hep-ph↗

arXiv2008

Quark Lagrangian diagonalization versus non-diagonal kinetic terms

Loop corrections induce a dependence on the momentum squared of the coefficients of the Standard Model Lagrangian, making highly non-trivial (or even impossible) the diagonalization of its quadratic part. Fortunately, the introduction of appropriate counterterms solves this puzzle.

hep-ph↗

arXiv2007

Magnetic fields in noncommutative quantum mechanics

We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature.

quant-ph↗

arXiv2007

Mixing angles of quarks and leptons as an outcome of SU(2) horizontal symmetries

We show that all mixing angles are determined, within experimental uncertainty, by a product of SU(2) horizontal symmetries intimately linked to the algebra of weak neutral currents. This concerns: on one hand, the three quark mixing angles; on the other hand, a neutrino-like pattern in which theta_{23} is maximal and tan (2 theta_{12}) = 2. The latter turns out to exactly satisfy the ``quark-lepton complementarity condition'' theta_c + theta_{12} = pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise, which satisfy the bound sin^2(theta_{13}) \leq 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717.

hep-ph↗

arXiv2007

The neighborhood of the Standard Model: mixing angles and quark-lepton complementarity for three generations of non-degenerate coupled fermions

We investigate the potential (small) deviations from the unitarity of the mixing matrix that are expected to occur, because of mass splittings, in the Quantum Field Theory of non-degenerate coupled systems. We extend our previous analysis concerning mixing angles, which led to a precise determination of the Cabibbo angle, to the case of three generations of fermions. We show that the same condition for neutral currents of mass eigenstates, i.e. that universality of diagonal currents is violated with the same strength as the absence of non-diagonal ones, is satisfied: on one hand, by the three CKM mixing angles with a precision higher than the experimental uncertainty; on the other hand, by a neutrino-like mixing pattern in which theta_{23} is maximal, and tan (2 theta_{12})=2. This last pattern turns out to satisfy exactly the "quark-lepton complementarity condition" theta_c + theta_{12}= pi/4. Moreover, among all solutions, two values for the third neutrino mixing angle arise which satisfy the bound sin^2(theta_{13}) < 0.1: theta_{13} = +/- 5.7 10^{-3} and theta_{13} = +/- 0.2717. The so-called "Neighborhood of the Standard Model" is thus confirmed to exhibit special patterns which presumably originate in physics "Beyond the Standard Model".

hep-ph↗

arXiv2006

The emergence of the Cabibbo angle in non-degenerate coupled systems of fermions

Investigating, in direct continuation of our previous paper hep-ph/0606303 the implications of the non-unitarity of mixing matrices for non-degenerate coupled systems that we demonstrated there, we examine more accurately the vicinity of Cabibbo-like mixing in quantum field theory. We show that it is possible to preserve one of its main features, namely that, in the space of mass eigenstates, the two requirements -- of universality for weak diagonal currents and -- of the absence of their non-diagonal counterparts, although not fulfilled separately any more, can however reduce to a single condition for a unique mixing angle theta\_c. This leads to tan (2 theta\_c)=+/- 1/2, or cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the argumentation.

hep-ph↗

arXiv2006

The Cabibbo angle : an algebraic calculation

We show that the Cabibbo angle theta\_c satisfies the relation tan(2 theta\_c)=-+/- 1/2 when universality for diagonal neutral currents of mass eigenstates is satisfied at the same level of accuracy as the absence of their off-diagonal counterparts. The predicted value is cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio appears in the calculation. theta\_c occurs a priori for both quark species, and, showing that one recovers the standard dependence of leptonic and semi-leptonic decays of pseudoscalar mesons, we advocate, like for neutrinos and charged leptons, for a symmetrical treatment of u and d-type quarks.

hep-ph↗

arXiv2006

Mixing Angles and Non-Degenerate Systems of Particles

Defining, in the framework of quantum field theory, their mass eigenstates through their matricial propagator, we show why the mixing matrices of non-degenerate coupled systems should not be parametrized as unitary. This is how, for leptonic binary systems, two-angles solutions with discrete values pi/4 [pi/2] and pi/2 [pi] (in addition to the trivial case 0 [pi]) arise when weak leptonic currents of mass eigenstates approximately satisfy the two properties of universality and vanishing of their non-diagonal neutral components. Charged weak currents are also discussed, which leads to a few remarks concerning oscillations. We argue that quarks, which cannot be defined on shell because of the confinement property, are instead more naturally endowed with unitary Cabibbo-like mixing matrices, involving a single unconstrained mixing angle. The similarity between neutrinos and neutral kaons is outlined, together with the role of the symmetry by exchange of families.

hep-ph↗