B. Machet

Bio: B. Machet is an academic researcher. The author has contributed to research in topics: Cabibbo–Kobayashi–Maskawa matrix. The author has an hindex of 1, co-authored 2 publications receiving 12 citations.

Hierarchies of quark masses and the mixing matrix in the standard theory

Abstract: We study the general dependence of mixing angles on heavy fermion masses when mass hierarchies exist among the fermions. For two generations and small Cabibbo angle, this angle is directly shown to scale like $\mu_1/m_s \pm \mu_2/m_c$, where $|\mu_1| \ll m_s, |\mu_2| \ll m_c$ are independent mass scales. For $n=3$ generations, we extend to the Yukawa matrices of $u$- and $d$-type quarks the property that the $2\times 2$ upper-left sub-matrix of the Cabibbo-Kobayashi-Maskawa matrix $K$ is a good approximation to the Cabibbo matrix $C$. Then, without any additional Ansatz concerning the existence of mass hierarchies or the smallness of the mixing angles, the moduli of its entries $K_{13},K_{23},K_{31},K_{32}$ are shown to scale like $[\beta_{13},\beta_{23},\beta_{31},\beta_{32}] \sqrt{{m_c}/{m_t}} \pm [\delta_{13},\delta_{23},\delta_{31},\delta_{32}] \sqrt{{m_s}/{m_b}}$, where the $\beta$'s and the $\delta$'s are coefficients smaller than 10. This method, when used for two generations, gives a dependence on $m_s$ and $m_c$ ``weaker'' than the one obtained first, but which matches a well known behaviour for the Cabibbo angle: $\theta_c \approx \sqrt{\epsilon_d (m_d/m_s)} - \sqrt{\epsilon_u(m_u/m_c)}$, with $\epsilon_d,\epsilon_u \leq 1$. The asymptotic behaviour in the case of three generations can also be strengthened into a $1/m_{b,t}$ behaviour by incorporating our knowledge about the hierarchies of quark masses and the smallness of the mixing angles.

Binary systems of neutral mesons in Quantum Field Theory

Abstract: Quasi-degenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of ``spurious'' states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parameterization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different ``in'' and ``out'' eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments. The non-vanishing of semi-leptonic asymmetry \delta_S - \delta_L does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and K0bar.

Mixing angles of quarks and leptons in quantum field theory

Abstract: 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 the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ23 is maximal and tan (2θ12)=2. The Cabibbo angle fulfills the condition tan (2θc)=1/2 and θ12 for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θc+θ12=π/4. θ13=±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 broken symmetry of the Standard Model is outlined.

Binary Systems of Neutral Mesons in Quantum Field Theory

Abstract: Quasidegenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of "spurious" states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The KL-KS mass splitting triggers a tiny difference between their CP violating parameters ∊L and ∊S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parametrization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different "in" and "out" eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments; the nonvanishing of the semileptonic asymmetry δS - δL, does not signal, unlike usually claimed, TCP violation, while ATCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and .

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

Abstract: 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".