arXiv subjects

Wojciech Krolikowski

Publications and source records attributed to Wojciech Krolikowski.

At least 55 records · Page 3Linked to original sources

arXiv2005

Lepton generation-weighting factors and neutrino mass formula

A candidate for the simple empirical neutrino mass formula is found, predicting the mass proportion m_1:m_2:m_3 = 0:4:24 and so, the mass ratio Delta m^2_{32}/Delta m^2_{21} = 35 not inconsistent with its experimental estimate. It involves only one free parameter and three generation-weighting factors suggested by the successful mass formula found previously for charged leptons (the simplest neutrino mass formula would predict m_1:m_2:m_3 = 1:4:24 and thus, Delta m^2_{32}/Delta m^2_{21} \simeq 37). A more involved variation of this equation follows from a special seesaw neutrino model with specifically "conspiring" Dirac and Majorana neutrino mass matrices. In this variation m_1:m_2:m_3 \simeq ε^{(ν)}:4:24, where O(ε^{(ν)}) = 10^{-3}.

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arXiv2005

Embedding the neutrino four-group Z_2 x Z_2 into the alternating group of four objects A_4

If and only if the small neutrino mixing sine s_13 is put zero, the effective neutrino mass matrix M with any mixing sines s_12 and s_23 is invariant under a cyclic group Z_2 of the order two and -- in the limit of m_2 - m_1 --> 0 -- also under the group Z_2 x Z_2 often called the four-group. However, the elements of this group do not build up fully the term of M proportional to m_2 - m_1. When the four-group is embedded into the group of even permutations of four objects A_4 (which is of the order twelve), then the term of M proportional to m_2 - m_1 can be fully constructed from elements of A_4. In contrast, when the four-group is embedded into the dihedral group D_4 of the order eight, then the term of M proportional to m_2 - m_1 cannot be fully built up from elements of D_4.

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arXiv2004

The four-group Z_2 x Z_2 as a discrete invariance group of effective neutrino mass matrix

Two sets of four 3x3 matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3 are constructed, forming two unitarily isomorphic reducible representations 3 of the group Z_2 x Z_2 called often the four-group. They are related to each other through the effective neutrino mixing matrix U with s_{13} = 0, and generate four discrete transformations of flavor and mass active neutrinos, respectively. If and only if s_{13} = 0, the generic form of effective neutrino mass matrix M becomes invariant under the subgroup Z_2 of Z_2 x Z_2 represented by the matrices 1^(3) and varphi_3. In the approximation of m_1 = m_2, the matrix M becomes invariant under the whole Z_2 x Z_2 represented by the matrices 1^(3), varphi_1, varphi_2, varphi_3. The effective neutrino mixing matrix U with s_{13} = 0 is always invariant under the whole Z_2 x Z_2 represented in two ways, by the matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3.

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arXiv2004

Can one of three righthanded neutrinos be light enough to produce a small LSND effect?

It is shown on the ground of a simple 6\times 6 neutrino mixing model that one of three conventional sterile (righthanded) neutrinos, if light enough, may be consistently used for explaining a {\it small} LSND effect. Then, it is still considerably heavier than the three active (lefhanded) neutrinos, so that a kind of {\it soft} seesaw mechanism can work. The usual condition that the Majorana lefthanded component of the overall 6\times 6 neutrino mass matrix ought to vanish, {\it implies} the smallness of active-neutrino masses versus sterile-neutrino masses, when three mixing angles between both sorts of neutrinos are small. In the presented model, the mass spectrum of active neutrinos comes out roughly degenerate, lying in the range (5 - 7.5)\times 10^{-2} eV, {\it if} there is a {\it small} LSND effect with the amplitude of the order 10^{-3} and with the mass-squared splitting \sim 1 eV^2.

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arXiv2004

Two light sterile neutrinos that mix maximally with each other and moderately with three active neutrinos

Since the 3+1 neutrino models with one light sterile neutrino turn out to be not very effective, at least two light sterile neutrinos may be needed to reconcile the solar and atmospheric neutrino experiments with the LSND result, {\it if} this is confirmed by the ongoing MiniBooNE experiment (and when the CPT invariance is assumed to hold for neutrino oscillations). We present an attractive 3+2 neutrino model, where two light sterile neutrinos mix maximally with each other, in analogy to the observed maximal mixing of muon and tauon active neutrinos. But, while the mixing of $ν_e$ and $(ν_μ-ν_τ)/\sqrt2 $ is observed as large (though not maximal), the mixing of $ν_e$ with the corresponding combination of two light sterile neutrinos is expected to be only moderate because of the reported smallness of LSND oscillation amplitude. The presented model turns out, however, not to be {\it more} effective in explaining the hypothetic LSND result than the simplest 3+1 neutrino model. On the other hand, in the considered 3+2 model, the deviations from conventional oscillations of three active neutrinos appear to be {\it minimal} within a larger class of 3+2 models.

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arXiv2003

A proposal of neutrino mass formula

An explicit mass formula is proposed for three active neutrinos and their heavy sterile (righthanded) counterparts in the framework of seesaw mechanism. The formula correlates reasonably the experimental estimates for the solar $Δm^2_{12}$ and atmospheric $Δm^2_{32}$ in the case of hierarchical spectrum $m^2_1 \ll m^2_2 \ll m^2_3 $ of active neutrinos. The lightest heavy neutrino is predicted to be $O(10^5)$ times lighter than the heaviest. An efficient mass formula, proposed previously for charged leptons, is recalled and coordinated with the new mass formula for neutrinos.

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arXiv2003

The LMA solar solution and fermion universality

We suggest that the Large Mixing Angle MSW solar solution, whose unique physical status is confidently supported by the recent results from KamLAND experiments, gets its justification in the fermion universality, interpreted for neutrinos and charged leptons in a straightforward way, most readily in the framework of seesaw mechanism. To this end, we consider an explicit seesaw model, where Dirac and (righthanded) Majorana neutrino masses are simultaneously measurable, and {\it both} are conjectured to be proportional to charged-lepton masses. However, the LMA solar solution is {\it also} not inconsistent with the simple option, where neutrinos are Dirac particles carrying masses proportional to those of charged leptons.

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arXiv2002

ChroNodynamics or a quantum theory involving deviations from uniform run of time

Let us imagine that there is an overall quantum theory (not necessarily recognized yet) of matter and energy ({\it i.e.}, of elementary fermions and bosons) interacting with the physical spacetime (treated on a quantum level). Since states of quantum spacetime are so far not observed directly, they ought to be projected out from the overall Hilbert space (much like states of a quantum medium in the optical model often constructed in nuclear physics). Then, in the reduced Hilbert space only states of quantum matter and energy are left, but now endowed with the energy width that enters through an antiHermitian interaction-like operator, a remainder of their coupling to the quantum spacetime. We postulate that such an energy width involves an averaged coupling of quantum matter and energy to a classical field of time deviations from the uniform time run (in the classical spacetime of special relativity). The well known time-temperature analogy helps us to fix other postulates leading altogether to a quantum theory we call chronodynamics (a loose analogue of thermodynamics of small deviations from thermal equilibrium).

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arXiv2002

Does the LMA MSW solar solution imply the Dirac nature of neutrinos?

Operating with the bilarge neutrino mixing, we show that in the option of Dirac neutrinos the fermion universality -- expressed by the proportionality of neutrino masses to charged-lepton masses -- predicts $Δm_{21}^2$ of the order $10^{-5} {\rm eV}^2$, consistently with the LMA MSW solar solution. In contrast, in the option of Majorana neutrinos the fermion universality -- introduced as the seesaw proportionality of neutrino masses to charged-lepton masses squared -- predicts $Δm_{21}^2$ of the order $10^{-8} {\rm eV}^2$, what is consistent rather with the LOW MSW solar solution. Thus, the favored LMA MSW estimation of $Δm_{21}^2$ might be a signal from the Dirac nature of neutrinos.

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arXiv2002

Explicit seesaw model and deformed fermion universality

In the simple model of neutrino texture presented in this paper, the Majorana left-handed mass matrix is zero, the Majorana righthanded mass matrix - diagonal and degenerate, and the Dirac mass matrix has a hierarchical structure, deformed unitarily by nearly bimaximal mixing. In the case, when the Majorana righthanded term dominates over the Dirac term, the familiar seesaw mechanism leads effectively to the nearly bimaximal oscillations of active neutrinos, consistent with solar and atmospheric neutrino experiments. If the Dirac term, before its unitary deformation, is similar in shape to the known charged-lepton mass matrix, then parameters for solar $ν_e$'s and atmospheric $ν_μ$'s become related to each other, predicting from the SuperKamiokande value of $Δm_{32}^2$ a tiny $Δm_{21}^2$ typical for MSW LOW solar solution rather than for MSW Large Mixing Angle solution. The predicted mass spectrum is then hierarchical. In Appendix a suggestive form of nearly bimaximal effective mass matrix is derived.

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arXiv2002

Explicit seesaw with nearly bimaximal neutrino mixing and no LSND effect

An explicit model of neutrino texture is presented, where in the 6 times 6 mass matrix the Majorana lefthanded component is zero, the Majorana righthanded component - diagonal with equal entries, and the Dirac component gets a hierarchical structure, deformed by nearly bimaximal mixing. If the Majorana righthanded component dominates over the Dirac component, the familiar seesaw mechanism leads effectively to the popular, nearly bimaximal oscillations of active neutrinos. The Dirac component, before its deformation, may be similar in shape to the charged-lepton and quark mass matrices. Then, parameters for solar and atmospheric neutrinos may be related to each other, predicting from the SuperKamiokande value of Delta m_{32}^2 a tiny Delta m_{21}^2, typical for MSW LOW solar solution (rather than for MSW Large Mixing Angle solution).

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arXiv2002

Option of light righthanded neutrinos avoiding oscillations

A new explicit model of neutrino texture is presented, where in the overall 6x6 mass matrix the lefthanded and righthanded Majorana 3x3 components are diagonal with equal entries of opposite sign, while the Dirac 3x3 component is given as a diagonal hierarchical structure (possibly similar to the charged lepton and quark 3x3 mass matrices) deformed by the popular nearly bimaximal 3x3 mixing matrix. Then, all neutrino masses are light and m_1 = -m_4, m_2 = -m_5, m_3 = -m_6. The resulting neutrino oscillation formulae are identical with those working in the effective texture of three active neutrinos, based on this nearly bimaximal mixing matrix. Three (conventional) sterile neutrinos do not oscillate and so, are strictly decoupled. The suggested LSND effect vanishes. The not observed Chooz oscillation effect is consistently negligible.

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arXiv2002

Search for fermion universality of the Dirac component of neutrino mass matrix

An effective texture is presented for six Majorana neutrinos, three active and three (conventional) sterile, based on a 6x6 mass matrix, whose 3x3 active--sterile component (i.e., Dirac component) is conjectured to get a fermion universal form similar to the constructed previously 3x3 mass matrix for charged leptons and 3x3 mass matrices for up and down quarks. This is true, however, when the bimaximal mixing, specific for neutrinos, is transformed out unitarily from the neutrino mass matrix. The 3x3 active--active component (i.e., lefthanded component) of neutrino 6x6 mass matrix is diagonal and gets degenerate entries. It dominates over the whole neutrino mass matrix. In such a texture, three neutrino masses are nearly degenerate, $ m_1 \simeq m_2 \simeq m_3 $, but their mass-squared differences appear hierarchical, $Δm^2_{21} \ll Δm^2_{32} \simeq Δm^2_{31}$, while the remaining three neutrino masses can be constructed to vanish, $ m_4 = m_5 = m_6 = 0 $, in contrast to the familiar seesaw mechanism.

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arXiv2002

Neutrino bimaximal mixing and unitary deformation of fermion universality

An effective texture is presented for six Majorana neutrinos, three active and three (conventional) sterile, based on a 6x6 mass matrix whose 3x3 Dirac component (i.e., active--sterile component) is conjectured to get a hierarchical fermion universal form, similar to the previously constructed 3x3 mass matrices for charged leptons as well as for up and down quarks. However, for neutrinos this form becomes unitarily deformed by the action of bimaximal mixing, specific in their case. The 3x3 lefthanded and righthanded components (i.e., active-active and sterile-sterile components) of the 6x6 mass matrix are diagonal with degenerate entries of opposite sign. They dominate over the 3x3 Dirac component. In such a texture the neutrino masses are $ m_1 = -m_4 \simeq m_2 = -m_5 \simeq m_3 = -m_6 $ with the mass-squared differences $Δm^2_{21} \ll Δm^2_{32} \simeq Δm^2_{31}$ and $Δm^2_{41} = Δm^2_{52} = Δm^2_{63} = 0$. The last equality implies in our texture the absence of oscillations for three (conventional) sterile neutrinos. Thus, these neutrinos are here effectively decoupled, what is realized evidently in another way than through the popular seesaw mechanism. There remain the oscillations of three active neutrinos, getting the form as for bimaximal mixing, but with the mass spectrum following from our texture.

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arXiv2001

Fermion universality manifesting itself in the Dirac component of neutrino mass matrix

An effective texture is presented for six Majorana conventional neutrinos (three active and three sterile), based on a 6x6 neutrino mixing matrix whose 3x3 active-active component arises from the popular bimaximal mixing matrix of active neutrinos $ν_e$, $ν_μ$, $ν_τ$ by three small rotations in the 14, 25, 36 planes of $ν_1$, $ν_2$, $ν_3$ and $ν_4$, $ν_5$, $ν_6$ neutrino mass states. The Dirac component (i.e. 3x3 active-sterile component) of the resulting 6x6 neutrino mass matrix is conjectured to get a structure similar to the charged lepton and quark 3x3 mass matrices, after the bimaximal mixing, specific for neutrinos, is transformed out unitarily {}from the neutrino mass matrix. The charged lepton and quark mass matrices are taken in a universal form constructed previously by the author with a considerable phenomenological success. Then, for the option of $m^2_1\simeq m^2_2\simeq m^2_3\gg m^2_4\simeq m^2_5\simeq m^2_6\simeq0$, the proposed texture {\it predicts} oscillations of solar $ν_e$'s with $Δm^2_{\rm sol}\equivΔm^2_{21}\sim(1.1$ to 1.2)$\times10^{-5}$ eV$^2$, not inconsistent with the LMA solar solution, if the SuperKamiokande value $Δm^2_{\rm atm}\equivΔm^2_{32}\sim$(3 to 3.5)$\times10^{-3}$ eV$^2$ for oscillations of atmospheric $ν_μ$'s is taken as an input.

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arXiv2001

An effective model for quark masses and mixings

By analogy with an effective model of charged-lepton mass matrix that, with the inputs of $m^{exp}_e $ and $m^{exp}_μ$, predicts (in a perturbative zero order) $m_τ= 1776.80 $ MeV close to $m^{exp}_τ= 1777.03^{+0.30}_{-0.26}$ MeV, we construct such a model for quark mass matrices reproducing consistently the bulk of experimental information on quark masses and mixings. In particular, the model predicts $|V_{u b}| = 0.00313$, $γ= - \arg V_{u b} = 63.8^\circ$ and $|V_{t d}| = 0.00785$, $β= - \arg V_{t d} = 20.7^\circ$ (i.e., $\sin 2β= 0.661$ to be compared with the BaBar value $\sin 2β^{exp} = 0.59 \pm 0.14$), if the figures $|V^{exp}_{u s}| = 0.2196$, $|V^{exp}_{c b}| = 0.0402$ and $m^{exp}_{s} = 123$ MeV, $m^{exp}_{c} = 1.25$ GeV, $m^{exp}_{b} = 4.2$ GeV are used as inputs. Also the rest of CKM matrix elements is predicted consistently by the experimental data. Here, quark masses and CKM matrix elements (ten independent quantities) are parametrized by eight independent model constants, what gives two independent predictions, e.g. for $|V_{ub}|$ and $β$. The considered model deals with the fundamental-fermion Dirac mass matrices, so that the neutrino Majorana mass matrix is outside the scheme. Some foundations of the model are collected in Appendix.

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arXiv2001

LSND effect as a Chooz-restricted "sterile" perturbation of three-neutrino texture

Considering the hypothesis of mixing of three active neutrinos with, at least, one sterile neutrino, we report on a simple $4\times 4$ texture whose $ 3 \times 3 $ part arises from the popular bimaximal texture for three active neutrinos $ ν_e, ν_μ, ν_τ$, where $ c_{12} = 1/\sqrt{2} = s_{12}$, $ c_{23} = 1/\sqrt{2} = s_{23}$ and $ s_{13} = 0$. Such a $3\times 3 $ bimaximal texture is perturbed through a rotation in the 14 plane, where $ν_4 $ is the extra neutrino mass state induced by the sterile neutrino $ν_s $ which becomes responsible for the LSND effect. Then, with $m^2_1\simeq m^2_2$ we predict that $\sin^2 2θ_{\rm atm} = {1/2}(1+ c^2_{14}) \sim 0.99$ and $\sin^2 2θ_{\rm LSND} = {1/2}s^4_{14} \sim 4.5\times10^{-4}$, and in addition $ Δm^2_{\rm atm} = Δm^2_{32}$ and $ Δm^2_{\rm LSND} = |Δm^2_{41}|$, where $c^2_{14} = \sin^2 2θ_{\rm sol} \sim 0.97$ and $Δm^2_{21} = Δm^2_{\rm sol} \sim 10^{-7} {\rm eV}^2$ if {\it e.g.} the LOW solar solution is applied. In this four-neutrino texture with $m^2_1 \simeq m^2_2 $ the sum rule $\sin^2 2 θ_{\rm sol} + {1/2}\sin^2 2 θ_{\rm Chooz} + \sin^2 2 θ_{\rm LSND} = 1$ holds in the two-flavor approximation (for each of three cases), leaving room for the LSND effect, depending on the magnitude of Chooz effect that, not observed so far, leads (at present) to the upper bound $\sin^2 2θ_{\rm LSND}\stackrel{<}{\sim} 1.3\times10^{-3}$ and the lower bound $\sin^2 2θ_{\rm sol} \stackrel{>}{\sim} 0.95$. At the end a four-neutrino seesaw mechanism is sketched.

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arXiv2001

Toward neutrino texture dominated by Majorana lefthanded mass matrix

A form of mixing matrix for three active and three sterile, conventional Majorana neutrinos is proposed. Its Majorana lefthanded part arises from the popular bimaximal mixing matrix for three active neutrinos that works satisfactorily in solar and atmospheric experiments if the LSND effect is ignored. One of three sterile neutrinos, effective in the Majorana righthanded and Dirac parts of the proposed mixing matrix, is responsible perturbatively for the possible LSND effect by inducing one of three extra neutrino mass states to exist actively. The corresponding form of neutrino mass matrix is derived. If all three extra neutrino mass states get vanishing masses, the neutrino mass matrix is dominated by its specific Majorana lefthanded part. Then, the observed qualitative difference between mixings of neutrinos and down quarks may be connected with this Majorana lefthanded dominance realized for neutrinos.

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