1-loop quantum corrections are shown to induce large effects on the refraction index n inside a graphene strip in the presence of an external magnetic field B orthogonal to it. To this purpose, we use the tools of Quantum Field Theory to calculate th
e photon propagator at 1-loop inside graphene in position space, which leads to an effective vacuum polarization in a brane-like theory of photons interacting with massless electrons at locations confined inside the thin strip (its longitudinal spread is considered to be infinite). The effects factorize into quantum ones, controlled by the value of B and that of the electromagnetic coupling alpha, and a transmittance function U in which the geometry of the sample and the resulting confinement of electrons play the major roles. We consider photons inside the visible spectrum and magnetic fields in the range 1-20 Teslas. At B=0, quantum effects depend very weakly on alpha and n is essentially controlled by U; we recover, then, an opacity for visible light of the same order of magnitude pi * alpha_{vac} as measured experimentally.
The Glashow-Salam-Weinberg model for N=2 generations is extended to 8 composite Higgs multiplets by using a one-to-one correspondence between its complex Higgs doublet and very specific quadruplets of bilinear quark operators. This is the minimal num
ber required to suitably account, simultaneously, for the pseudoscalar mesons that can be built with 4 quarks and for the masses of the $W$ gauge bosons. They are used as input, together with elementary low energy considerations, from which all other parameters, masses and couplings can be calculated. We focus in this work on the spectrum of the 8 Higgs bosons, on the mixing angles, and on the set of horizontal and vertical entangled symmetries that, within the chiral $U(4)_L times U(4)_R$ group, strongly frame this extension of the Standard Model. In particular, the $u-c$ ($theta_u$) and $d-s$ ($theta_d$) mixing angles satisfy the robust relation $tan(theta_d+theta_u)tan(theta_d-theta_u) = Big(frac{1}{m_{K^pm}^2}-frac{1}{m_{D^pm}^2}Big) big/ Big(frac{1}{m_{pi^pm}^2}-frac{1}{m_{D_s^pm}^2}Big)$. Light scalars (below $90 MeV$) arise and the mass of (at least) one of the Higgs bosons grows like that of the heaviest $bar qgamma_5 q$ bound state. $theta_u$ cannot be safely tuned to zero and several parameters have no reliable expansion in terms of small parameters like $m_pi$ or the mixing angles. This study does not call for extra species of fermions. The effective couplings of scalars, which depend on the non-trivial normalization of their kinetic terms, can be extremely weak. For the sake of (relative) brevity, their rich content of non-standard physics (including astrophysics), the inclusion of the 3rd generation and the taming of quantum corrections are left for a subsequent work.
Maximally extending the Higgs sector of the Glashow-Salam-Weinberg model by including all scalar and pseudoscalar J=0 states expected for 2 generations of quarks, I demonstrate that the Cabibbo angle is given by tan^2(theta_c) = (1/m_K^2-1/m_D^2)/(1/
m_pi^2-1/m_{D_s}^2) approx (m_pi^2 /m_K^2)(1-m_K^2/m_D^2 + m_pi^2/m_{D_s}^2).
We continue investigating the Standard Model for one generation of fermions and two parity-transformed Higgs doublets K and H advocated for in a previous work, using the one-to-one correspondence, demonstrated there, between their components and bili
near quark operators. We show that all masses and couplings, in particular those of the two Higgs bosons $varsigma$ and $xi$, are determined by low energy considerations. The mass of the quasi-standard Higgs boson, $xi$, is $m_xi approx m_pi$; it is coupled to u and d quarks with identical strengths. The mass of the lightest one, $varsigma$, is $m_varsigma approx m_pi frac{f_pi}{2sqrt{2}m_W/g} approx 34,KeV$; it is very weakly coupled to matter except hadronic matter. The ratio of the two Higgs masses is that of the two scales involved in the problem, the weak scale $sigma=frac{2sqrt{2}m_W}{g}$ and the chiral scale $v=f_pi$, which are also the respective vacuum expectation values of the two Higgs bosons. They can freely coexist and be accounted for. The dependence of $m_varsigma$ and $m_xi$ on $m_pi$, that is, on quark masses, suggests their evolution when more generations are added. Fermions get their masses from both Higgs multiplets. The theory definitely stays in the perturbative regime.
A very specific two-Higgs-doublet extension of the Glashow-Salam-Weinberg model for one generation of quarks is advocated for, in which the two doublets are parity transformed of each other and both isomorphic to the Higgs doublet of the Standard Mod
el. The chiral group U(2)_L X U(2)_R gets broken down to U(1) X U(1)_{em}. In there, the first diagonal U(1) is directly connected to parity through the U(1)_LX U(1)_R algebra. Both chiral and weak symmetry breaking can be accounted for, together with their relevant degrees of freedom. The two Higgs doublets are demonstrated to be in one-to-one correspondence with bilinear quark operators.
We show that, unlike mass matrices, the fermionic gauge currents of the Standard Model exhibit, at the quantum level, remarkable SU(2)_f flavor properties at the observed values of the mixing angles. They accommodate all measured mixing for three fam
ilies of quarks, and, for neutrinos, maximal theta_{23}, quark-lepton complementarity tan(2 theta_c)=1/2 <--> tan (2 theta_{12})=2, and a not so small sin^2(2 theta_{13}) = .267 within the present 90% c.l. interval of the T2K experiment.
We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: Phi(z) = e/|z| [ 1- exp(-sqrt{6m_e^2}|z|) + exp(
-sqrt{(2/pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulombs law becomes essential for B > 3pi B_{cr}/alpha = 3 pi m_e^2/e^3 approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 pi B_{cr}/alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.
Starting from Wigners 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 sp
inors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightmans 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.
Flavor mixing is scrutinized at 1-loop in a SU(2)_L gauge theory of massive fermions. The main issue is to cope with kinetic-like, momentum (p^2) dependent effective interactions that arise at this order. They spoil the unitarity of the connection be
tween flavor and mass states, which potentially alters the standard Cabibbo-Kobayashi-Maskawa (CKM) phenomenology by giving rise, in particular, to extra flavor changing neutral currents (FCNC). We explore the conservative requirement that these should be suppressed, which yields relations between the CKM angles, the fermion and $W$ masses, and a renormalization scale $mu$. For two generations, two solutions arise: either the mixing angle of the fermion pair the closer to degeneracy is close to maximal while, inversely, the mass and flavor states of the other pair are quasi-aligned, or mixing angles in both sectors are very small. For three generations, all mixing angles of neutrinos are predicted to be large (theta_{23}, close to maximal, is the largest) and the smallness of their mass differences induces mass-flavor quasi-alignment for all charged leptons. The hadronic sector differs in that the top quark is twice as heavy as the W. The situation is, there, bleaker, as all angles come out too large, but, nevertheless, encouraging, because theta_{12} decreases as the top mass increases. Whether other super-heavy fermions could drag it down to realistic values stays an open issue, together with the role of higher order corrections. The same type of counterterms that turned off the 4th order static corrections to the quark electric dipole moment are, here too, needed, in particular to stabilize quantum corrections to mixing angles.
We show that 1-loop transitions between two quasi-degenerate fermions can induce a potentially large renormalization of their mixing angle, and a large renormalized Cabibbo (or PMNS) angle when the second fermion pair in the same two generations is f
ar from degeneracy. At the resonance, the Cabibbo angle gets maximal and simply connected to masses without invoking any new physics beyond the standard model. This solution appears as the only one perturbatively stable (mixing angles are then renormalized with respect to their classical values by small amounts).
