arXiv subjects

W. Krolikowski

Publications and source records attributed to W. Krolikowski.

28 records · Page 2Linked to original sources

arXiv2003

Bilarge mixing matrix and its invariance under "horizontal conjugation" -- a new discrete transformation for neutrinos

In the first part of the note, we consider a neutrino texture, where the Dirac and righthanded Majorana masses are proportional. If the former are approximately proportional also to the charged lepton masses, then taking $Δm^2_{32}\sim3\times 10^{-3}$ eV$^2$ we estimate approximately that $Δm^2_{21}\sim{\cal O}(10^{-5}$ eV$^2)$, what is not very different from the recent KamLAND estimation $Δm^2_{21}\sim7\times 10^{-5}$ eV$^2$, consistent with the LMA solar solution. In the second part, we show generically that the {\it invariance} of neutrino mixing matrix under the simultaneous discrete transformations $ν_e\to-ν_e$, $ν_μ\toν_τ$, $ν_τ\toν_μ$ and $ν_1\to-ν_1$, $ν_2\to-ν_2$, $ν_3\toν_3$ (neutrino "horizontal conjugation") {\it characterizes} the familiar bilarge form of mixing matrix, favored phenomenologically at present. Then, in the case of this form, the mass neutrinos $ν_1$, $ν_2$, $ν_3$ get a new quantum number, {\it covariant} in their mixings (neutrino "horizontal parity", equal to $-1,-1, 1$, respectively). Conversely, such a covariance may be the {\it origin} of the bilarge mixing matrix. In Section 5, the "horizontal parity" is embedded in a group structure.

hep-ph↗

arXiv2002

Clifford algebra implying three fermion generations revisited

The author's idea of {\it algebraic compositeness} of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. i) For all fundamental particles of matter the Dirac square-root procedure $\sqrt{p^2}\toΓ^{(N)}\cdot p$ works, leading to a sequence $N=1,2,3,...$ of Dirac-type equations, where four Dirac-type matrices $Γ^{(N)}_μ$ are embedded into a Clifford algebra {\it via} a Jacobi definition introducing four "centre-of-mass" and $(N-1)\times$four "relative" Dirac-type matrices. These define one "centre-of-mass" and $N-1$ "relative" Dirac bispinor indices. ii) The "centre-of-mass" Dirac bispinor index is coupled to the Standard Model gauge fields, while $N-1$ "relative" Dirac bispinor indices are all free undistinguishable physical objects obeying Fermi statistics with the Pauli principle which requires the full antisymmetry with respect to "relative" indices. This allows only for {\it three} $N = 1,3,5$ in the case of $N$ odd, implying the existence of {\it three and only three} generations of fundamental fermions.

hep-ph↗

arXiv2000

Two-mixing texture for three active neutrinos

The conjecture that among three massive neutrinos $ν_1, ν_2, ν_3$ there is no direct mixing between $ν_1$ and $ν_3$ leads to a two-mixing texture for three active neutrinos $ν_e, ν_μ, ν_τ$. This texture, much discussed previously, is neatly consistent with the observed deficits of solar $ν_e$'s and atmospheric $ν_μ$'s, but (without extra mixing with at least one sterile neutrino $ν_s$) predicts no LSND effect for accelerator $ν_μ$'s. In this option, the masses $m^2_1\stackrel{<}{\sim} m^2_2 << m^2_3$ are readily estimated. The characteristic feature of the two-mixing neutrino texture that {\it only the close neighbours in the hierarchy of massive neutrinos $ν_1, ν_2, ν_3$ mix significantly} may be physically meaningful. Going out from the notion of mixing matrix we construct an intrinsic occupation-number operator whose {\it eigenvalues} 0, 1, 2 {\it numerate the three generations of massive neutrinos}. Analogical constructions work also for charged leptons as well as for up and down quarks.

hep-ph↗

arXiv2000

Scattering of light by molecules of light

We study the scattering properties of optical dipole-mode vector solitons recently predicted theoretically and generated in a laboratory. We demonstrate that such a radially asymmetric composite self-trapped state resembles ``a molecule of light'' which is extremely robust, survives a wide range of collisions, and displays new phenomena such as the transformation of a linear momentum into an angular momentum, etc.We present also experimental verifications of some of our predictions.

nlin.PS↗

arXiv1999

Fixed points in the evolution of neutrino mixings

We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give $\sin^22θ_{sol}=\sin^22θ_{atm}\sin^2θ_3/ (\sin^2θ_{atm}\cos^2θ_3 + \sin^2θ_3)^2$, consistently with the present experimental information. Further experimental test of this relation is of crucial interest. Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. Several interesting mass patterns show stability in the presence of fixed point solutions for the angles.

hep-ph↗

arXiv1999

An unorthodox alternative for righthanded neutrinos: lefthanded see-saw

A new lefthanded see-saw mechanism is constructed, implying both the smallness of active-neutrino masses and decoupling of heavy passive neutrinos, similarly to the situation in the case of conventional see-saw. But now, in place of the conventional righthanded neutrinos, the lefthanded sterile neutrinos play the role of heavy passive neutrinos, the righthanded neutrinos and righthanded sterile neutrinos being absent. Here, the lefthanded sterile neutrinos are different from charge conjugates of conventional righthanded neutrinos because their lepton numbers differ. In this case, the neutrino mass term is necessarily of pure Majorana type.

hep-ph↗

arXiv1999

Influence of four-wave mixing and walk-off on the self-focusing of coupled waves

Four-wave mixing and walk-off between two optical beams are investigated for fo cusing Kerr media. It is shown that four-wave mixing reinforces the self-focusi ng of mutually-trapped waves by lowering their power threshold for collapse, on ly when their phase mismatch is small. On the contrary, walk-off inhibits the c ollapse by detrapping the beams, whose partial centroids experience nonlinear o scillations.

patt-sol↗

arXiv1998

Hypothetic time -- temperature duality as a hint for modifications in quantum dynamics?

The well-known formal analogy between time and absolute temperature, existing on the quantum level, is considered as a profound duality relationship requiring some modifications in the conventional quantum dynamics. They consist of tiny deviations from uniform time run in the physical spacetime, as well as of tiny deviations from unitary time evolution characteristic for the conventional quantum theory. The first deviations are conjectured to be produced by local changes of total average particle number. Then, they imply the second deviations exerting in turn influence upon this particle number. Two examples of the second deviations are described: hypothetic tiny violation of optical theorem for particle scattering, and hypothetic slow variation of the average number of probe particles contained in a sample situated in proximity of a big accelerator (producing abundantly particles on a target).

hep-th↗

arXiv1998

Texture dynamics including potential sterile neutrino

A unified form of mass matrix proposed previously for all fundamental fermions is extended to include the sterile neutrino $ν_s$, presumed to mix mainly with $ν_e$, while $ν_τ$ mixes strongly with $ν_μ$ (and both $ν_μ$ and $ν_τ$ weakly with $ν_e$ and $ν_s$). It turns out that the former mixing can be responsible for oscillations of solar neutrinos, while the latter for those of atmospheric neutrinos. It is mentioned in a footnote that $ν_s$ is one of two sterile neutrinos, possible from a viewpoint of an algebraic construction. The charged-lepton factor $U^{(e)}$ in the leptonic four-dimensional CKM matrix $V=U^{(ν) \dagger}U^{(e)}$ is determined through the small deviation of our previous prediction $m_τ=1776.80$ MeV (valid at the level of $ U^{(e)} = {\bf 1}$) from the experimental value $m_τ=1777.00^{+0.30}_{-0.27}$ MeV. Then, it gives corrections to the four-dimensional mixing of $ν_e$, $ν_μ$, $ν_τ$, $ν_s$ leading, in particular, to small $ν_e\toν_μ$, $ν_e\to ν_τ$ and $ν_μ\toν_s$ oscillations (absent at the level of $U^{(e)}= 1$). However, the LSND estimates of $\barν_μ\to \barν_e$ and $ν_μ\toν_e$ oscillations are too large to be explained by these corrections, though in the case of $ν_μ\toν_e$ they seem to be at the edge of such possible explanation.

hep-ph↗

arXiv1997

Proposal of unified fermion texture

A unified form of mass matrix is proposed for neutrinos, charged leptons, up quarks and down quarks. Some constraints for the parameters involved are tent% atively postulated. Then, the predictions are neatly consistent with available experimental data. Among the predictions are: (i) $ m_τ\simeq 1776.80 $~MeV (with the inputs of $ m_e $ and $ m_μ$), (ii) $ m_{ν_0} \ll m_{ν_1} \sim (0.6 to 4)\times 10^{-2} $eV and $ m_{ν_2} \sim (0.2 to 1)\times 10^{-1} $eV (with the atmospheric-neutrino inpu% ts of $ |m_{ν_2}^2 - m_{ν_1}^2| \sim (0.0003 to 0.01) eV ^2 $ and the $ν_μ\to ν_τ$ oscillation amplitude $\sim 0.8 $), and also (iii) $ m_s \simeq 270 MeV$, $|V_{ub}/V_{cb}| \simeq 0.082 $ and arg$V_{ub} \simeq -64^\circ $ (with the inputs of $ m_c = 1.3 $ GeV, $ m_b = 4.5 $ GeV, $|V_{us}| = 0.221 $ and $|V_{cb}| = 0.041 $, where $ m_u \ll m_c \ll m_t $ and $ m_d \ll m_s \ll m_b $). All elements of the \CKM matrix are evaluated. All elements of its lepton counterpart are calculated up to an unknown phase (Appendix B). Some items related to dynamical aspects of the proposed fermion "texture" are briefly commented on (Appendix A). In particular, the notion of a novel dark matter, free of any Standard--% Model interactions (and their supersymmetric variants), appears in the case of preon option.

hep-ph↗