arXiv subjects

B. Machet

Publications and source records attributed to B. Machet.

At least 19 recordsLinked to original sources

arXiv2018

Resonances in positron scattering on a supercritical nucleus and spontaneous production of $e^{+}e^{-}$ pairs

We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase $δ_{\varkappa}$ and its dependence on the energy $\varepsilon$ of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential $Zα/r$ is rounded to the constant $Zα/R$ for $r < R$. We confirm the resonant behavior of $δ_{\varkappa}$ that we investigate in details. In addition to solving the Dirac equation for an electron, we solve it for a positron, in the field of the same nucleus. This clarifies the interpretation of the resonances. Our results are compared with claims made in previous works.

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arXiv2012

Critical nucleus charge in a superstrong magnetic field: effect of screening

A superstrong magnetic field stimulates the spontaneous production of positrons by naked nuclei by diminishing the value of the critical charge Z_{cr} . The phenomenon of screening of the Coulomb potential by a superstrong magnetic field which has been discovered recently acts in the opposite direction and prevents the nuclei with Z<52 from becoming critical. For Z>52 for a nucleus to become critical stronger B are needed than without taking screening into account.

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arXiv2005

Binary systems of neutral mesons in Quantum Field Theory

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 ε_L and ε_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 δ_S - δ_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.

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arXiv2003

CP non-invariance from scaling violations

In the framework of a renormalizable quantum field theory and taking the example of neutral kaons, CP violation is shown to be a dynamical consequence of the anomalous scaling of the fields; its connection to the mass splitting is exhibited. It is also shown to be compatible with the normality condition [M,M^\dagger]=0 for the renormalized mass matrix.

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arXiv2003

About neutral kaons and similar systems; from quantum field theory to effective mass matrices

Systems of neutral interacting mesons are investigated, concerning in particular the validity of their description by an effective hamiltonian. First, I study its connection to quantum field theory and show that the spectrum of such systems cannot be reduced in general to the one of a single constant effective mass matrix. Choosing nevertheless to work in this customary formalism, one then faces several ways to diagonalize a complex matrix, which lead to different eigenvalues and eigenvectors. Last, and it is the main subject of this work, because K0 and its charge conjugate K0bar are also connected, in quantum field theory, by hermitian conjugation, any constant effective mass matrix is defined, in this basis, up to arbitrary diagonal antisymmetric terms; I use this freedom to deform the mass matrix in various ways and study the consequences on its spectrum. Emphasis is put on the role of discrete symmetries throughout the paper. That the degeneracy of the eigenvalues of the full renormalized mass matrix can be a sufficient condition for the outcome of CP violation is outlined in an appendix. In the whole work, the dual formalism of |in> and <out| states and bi-orthogonal basis, suitable for non-normal matrices, is used.

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arXiv2002

Neutrino mixing angles and eigenstates; CP properties and mass hierarchies

In the presence of independent generations of leptons, I show that the same type of ambiguity in the mass spectrum arises as was discussed in ref.[1] for neutral kaons. It results from the freedom to add to their Majorana mass matrix, usually taken to be symmetric, an antisymmetric term which vanishes as soon as fermions belonging to different generations anticommute. In the simple examples proposed, dealing with two generations, this procedure introduces an extra (mass) parameter $ρ$, which is shown to connect the (CP violating) mixing angle to the hierarchy of neutrino masses. We use this opportunity to investigate the relations between the two; in particular, large hierarchies are no longer preferentially attached to small mixing angles; this can be relevant for the ``Large Mixing Angle'' solution strongly advocated by recent experiments on neutrinos oscillations. I discuss how the $ρ$ parameter could be fixed, which appears, in the absence of a substructure for leptons, still more delicate than for kaons.

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arXiv2001

Mass matrices and eigenstates for scalars / pseudoscalars; indirect CP violation, mass hierarchies and symmetry breaking

I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)^2 of the CP eigenstates K^0_1, K^0_2, and for certain ranges of values of the CP-violating parameter, a negative (mass)^2 can arise in the CP-violating basis. Under certain conditions, even a small perturbation, by lifting the ambiguity, can strongly alter the pattern of masses. These investigations extend in a natural way to indirect CP violation among a set of Higgs-like doublets. The C-odd commutator [K^0, K^0 bar], or its equivalent for Higgs multiplets, plays an important role. The condition for its vanishing and its consequences are among the main concerns of this work.

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arXiv2001

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

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 $μ_1/m_s \pm μ_2/m_c$, where $|μ_1| \ll m_s, |μ_2| \ll m_c$ 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 $[β_{13},β_{23},β_{31},β_{32}] \sqrt{{m_c}/{m_t}} \pm [δ_{13},δ_{23},δ_{31},δ_{32}] \sqrt{{m_s}/{m_b}}$, where the $β$'s and the $δ$'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: $θ_c \approx \sqrt{ε_d (m_d/m_s)} - \sqrt{ε_u(m_u/m_c)}$, with $ε_d,ε_u \leq 1$. 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.

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arXiv2000

Gauge bosons in an SU(2)right x SU(2)left x G(leptonique) electroweak model

By considering its generalization to composite J=0 mesons proposed in a previous work [1], I show how and why a chiral extension of the Glashow-Salam-Weinberg standard model of electroweak interactions calls, there, for right-handed charged W_R's coupled with g_R = e/cos(theta_W), and the masses of which are related to the ones of the left-handed W_L's through the relation M_L^2 + M_R^2 = M_Z^2. The mesonic sector, having vanishing baryonic and leptonic number, is neutral with respect to the corresponding U(1) symmetries, making the natural chiral gauge group to be [SU(2)left x SU(2)right], blind to the presence of extra Z's. The W_R gauge bosons cannot have been detected in hadronic colliders and can be very elusive in electroweak processes involving, in particular, pseudoscalar mesons. Present data select one among two possible extensions for which, in the right sector: - a specific breaking of universality occurs between families of quarks, which belong to inequivalent representations of SU(2)right; - the mixing angle is a free parameter, constrained to be smaller than the Cabibbo angle by the box diagrams controlling the K_L-K_S mass difference; this also minimizes contributions to muon -> electron + photon. The relation g_L^2/M_L^2 = g_R^2/M_R^2 implements left-right symmetry for low energy charged effective weak interactions. For the sake of simplicity, this study is performed for two generations only.

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arXiv2000

Extending the Standard Model: an upper bound for a neutrino mass from the rare decay K+ -> Pi+ neutrino antineutrino

The standard model seeming at a loss to account for the present experimental average rate for the rare decay K+ -> Pi+ neutrino antineutrino, I tackle the question with the extension of the Glashow-Salam-Weinberg model to an SU(2)left x U(1) gauge theory of J=0 mesons proposed by the author in [Phys. Lett. B 385 (1996) 198], in which, in addition, the neutrinos are given Dirac masses from Yukawa couplings to the Higgs boson. The latter triggers a new contribution to this decay through flavor changing neutral currents that arise in the quartic term of the symmetry breaking potential; it becomes sizeable for a neutrino mass in the $MeV$ range; the experimental upper limit for the decay rate translates into an upper bound of 5.5 MeV for the mass of the neutrino, three times lower than present direct bounds.

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arXiv1999

Mass hierarchies and mixing angles

The paper has been withdrawn

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arXiv1999

Large breaking of isospin symmetry in an electroweak SU(2)left x U(1) gauge theory of J=0 mesons: the case of K -> Pi Pi decays

K -> Pi Pi decays are investigated in the framework of the SU(2)left x U(1) gauge theory of J=0 mesons proposed in ref.[1], to which is added an interaction between mesons respecting the two symmetries generally attributed to strong interactions, flavour symmetry and parity conservation. It is shown that the damping of the K+ -> Pi+ Pi0 amplitude with respect to the ones of Kshort -> Pi Pi results from a cancelation between the W and Z gauge bosons. The ratio of the two types of amplitudes is sensitive to the spectrum of electroweak (pseudoscalar and scalar) mass eigenstates, an in particular to the mass of the Higgs boson. In the case where scalars and pseudoscalars are degenerate, the amplitudes satisfy the lower bound |(Kshort -> Pi+ Pi-) / (K+ -> Pi+ Pi0)| > 1/tan(Weinberg angle)^2.

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arXiv1999

The decays "neutrino{heavy} -> neutrino{light} + photon" and "neutrino{heavy} -> neutrino{light} e+ e-" of massive neutrinos

If, as recently reported by the Super-Kamiokande collaboration, the neutrinos are massive, the heaviest one would not be stable and, though chargeless, could in particular decay into a lighter neutrino and a photon by quantum loop effects. The corresponding rate is computed in the standard model with massive Dirac neutrinos as a function of the neutrino masses and mixing angles. The lifetime of the decaying neutrino is estimated to be approximately 10^44 years for a mass 5 10^{-2} eV. If kinematically possible, the decay of a heavy neutrino into a lighter one plus an e+ e- pair occurs at tree level and its one-loop radiative corrections get enhanced by a large logarithm of the electron mass acting as an infrared cutoff. It then largely dominates the photonic mode by several orders of magnitude, corresponding to a lifetime approximately equal to 10^{-2} year for a mass 1.1 MeV.

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arXiv1999

Some aspects of electroweak physics for a composite Higgs boson: application to the Z gauge boson decaying into two leptons and two pseudoscalar mesons

I study phenomenological aspects of the SU(2)L x U(1) electroweak physics of a Higgs boson transforming like a quark-antiquark pair. A correspondence is established between its flavour content, the hierarchy of quark condensates, and the leptonic decay constants f of pseudoscalar mesons; the Higgs-mesons couplings coming from the symmetry-breaking scalar potential can then be expressed in terms of the f's, of the Cabibbo-Kobayashi-Maskawa mixing angles, and of the mass of the Higgs boson. Application is made to the decays of a Z boson into two leptons and two charged pseudoscalar mesons, more specially $e^+e^- B^+B^-, e^+e^- D_s^+D_s^-$ and $e^+e^- K^\pm π^\mp$; the last channel, involving new types of flavour changing neutral currents in the scalar sector, is characteristic of this approach. Unlike in the standard model for quarks, the detection of two outgoing charged $B$ mesons is hopeless, like, unfortunately, that of $K^\pm π^\mp$; the channel $D_s^+ D_s^-$ could have been missed in present experiments for a Higgs mass lower than $65 GeV$ because of insufficient statistics. For higher masses this Higgs becomes undetectable from such channels. This shows that too drastic conclusions should not be drawn from an eventual negative outcome from searches for the standard Higgs boson, that simple variants of it are more elusive, may have escaped detection, and could still escape in the near future.

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arXiv1998

Indirect CP violation in an electroweak SU(2)left x U(1) gauge theory of chiral mesons

Indirect CP violation is analyzed in the framework of the electroweak gauge theory of J=0 mesons proposed in ref.[1], in which they transform like composite fermion-antifermion operators by the chiral U(N)left x U(N)right group and by the SU(2)left x U(1) gauge group of the Glashow-Salam-Weinberg model. It is shown that, in this model where, in particular, mass terms can be introduced for the mesons themselves, and unlike what happens in the standard model for fermions: - electroweak mass eigenstates can differ from CP eigenstates even in the case of two generations; - the existence of a complex entry in the mixing matrix for the constituent fermions is no longer a sufficient condition for indirect CP violation to occur at the mesonic level.

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arXiv1997

An electroweak SU(2)left x U(1) gauge theory of J=0 mesons

I build a SU(2)left x U(1) electroweak gauge theory of J=0 mesons, which transform like sets of fermion-antifermion composite fields. SU(2)left x U(1) is embedded in a natural way, compatible with the Glashow-Salam-Weinberg model for quarks, into the chiral group U(N)left x U(N)right, N being the (even) number of ``flavours''. The Lagrangian exhibits a chiral SU(2)left x SU(2)right symmetry at the limit when the hypercharge coupling g' goes to zero. It is spontaneously broken down to its diagonal SU(2)v subgroup; as the latter includes the U(1) group of electromagnetism, this provides an explanation for the quantization of the electric charge. Comparison with recent works by Cho et al. unraveling dyon-like solution is an electroweak model with the same structure suggests that electric-magnetic duality may be realized here, with the occurrence of a strongly interacting sector. Chiral are electroweak spontaneous breaking are identical. Consequences for the nature of the Goldstone bosons are examined. The mass spectrum is analysed. It bears no special connection with the nature of the ``fermionic content'' of the mesons and shares with the leptonic sector the same arbitrariness. No information on the mass of the Higgs boson can be expected without additional input. New results about CP violation are obtained: ``indirect'' CP violation appears to results from P violation (unitarity compels the electroweak mass eigenstates to be C eigenstates), and the role of the Kobayashi-Maskawa mixing matrix for fermions fades away: mesonic mass eigenstates can still be CP eigenstates despite the presence of a complex phase. I briefly show how the customary results for the leptonic decays of pseudoscalar mesons are recovered. The extension to leptons is discussed.

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arXiv1997

Two results concerning CP violation for J=0 mesons

I show, in the framework of a SU(2)left x U(1) gauge theory for J=0 mesons expressed as scalar or pseudoscalar di-quark fields, that: - the existence, at the fermionic level, of a complex mixing matrix of the Kobayashi-Maskawa type is not a sufficient condition for electroweak mass eigenstates to be different from CP eigenstates; - unitarity constrains this phenomenon to arise from an admixture of states with different parities, and present experiments probing ``indirect'' CP violation are likely to be interpreted with P violation only.

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arXiv1996

CP violation with two generations and pseudoscalar mesons revisited

After developing in ref.[1] a SU(2)left x U(1) gauge theory for J=0 mesons, I show in the case of two generations that: - the electroweak mass eigenstates differ, especially in the K and D sector, from what they are assumed to be on the basis of a classification by the SU(4) group of flavour; - a new mechanism for CP violation springs out, different from that of the standard model for quarks which requires at least three generations, and I construct a SU(2)left x U(1) gauge invariant Lagrangian which is not invariant by CP.

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