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Wojciech Krolikowski

Publications and source records attributed to Wojciech Krolikowski.

69 records · Page 4Linked to original sources
arXiv2001

Prediction of LSND effect as a "sterile" perturbation of the bimaximal texture for three active neutrinos

As a contribution to the hypothesis of mixing of three active neutrinos with, at least, one sterile neutrino, we report on a simple $4\times4$ texture whose $3\times3$ 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 $\sin^2 2θ_{\rm atm} = {1/2}(1+ c^2_{14}) \sim 0.95$ and $\sin^2 2θ_{\rm LSND} = {1/2}s^4_{14} \sim 5\times10^{-3}$, and in addition $Δm^2_{\rm atm} = Δm^2_{32}$ and $Δm^2_{\rm LSND} = |Δm^2_{41}|$, where $c^2_{14} = \sin^2 2θ_{\rm sol} \sim 0.9$ and $Δm^2_{21} = Δm^2_{\rm sol} \sim 10^{-7} {\rm eV}^2$ if e.g. the LOW solar solution is applied.

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arXiv2001

Possible LSND effect as a small perturbation of the bimaximal texture for three active neutrinos

A particular form of mixing matrix for three active and one sterile neutrinos is proposed. Its $3\times 3 $ part describing three active neutrinos arises from the popular bimaximal mixing matrix that works satisfactorily in solar and atmospheric experiments if the LSND effect is ignored. Then, the sterile neutrino, effective in the fourth row and fourth column of the proposed mixing matrix, is responsible for the possible LSND effect by inducing one extra neutrino mass state to exist actively. The LSND effect, if it exists, turns out to reveal its {\it perturbative} nature related to small mixing of three active neutrinos with their sterile partner.

hep-ph↗
arXiv2000

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 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. Also, the respective neutrino oscillation probabilities are calculated.

hep-ph↗
arXiv2000

An alternative: two-mixing texture for three neutrinos or three-mixing texture for four neutrinos

The alternative formulated in the title has a chance to be settled, when the existence of the LSND effect is experimentally excluded or confirmed. The first option, much discussed in literature, works in the case of three active neutrinos $ν_e, ν_μ, ν_τ$, when among their massive states $ν_1, ν_2, ν_3$ there is no direct mixing between $ν_1$ and $ν_3$, and the mass hierarchy $m^2_1 < {\sim} m^2_2 \ll m^2_3$ holds. This option is consistent with the observed deficits of solar $ν_e$'s and atmospheric $ν_μ$'s, if $Δm^2_{21} \leftrightarrow Δm^2_{\rm sol}$ and $ Δm^2_{32} \leftrightarrow Δm^2_{\rm atm}$. On the other hand, the second option is an extension of the idea of the former to the case of four neutrinos $ν_s, ν_e, ν_μ, ν_τ$ (including one sterile neutrino $ν_s$), when among their massive states $ν_0, ν_1, ν_2, ν_3$ there are no direct mixings between $ν_0$ and $nu_2$, $ν_0$ and $ν_3$, $ν_1$ and $ν_3$, and the mass hierarchy $m^2_0 < {\sim} m^2_1 \ll m^2_2 < {\sim} m^2_3$ is now valid. Such an option, belonging to a class of textures widely discussed in literature, may be consistent with the observed deficits of solar $ν_e$'s and atmospheric $ν_μ$'s as well as with the LSND appearance of $ν_e$'s in the beam of accelerator $ν_μ$'s, if now $Δm^2_{10} \leftrightarrow Δm^2_{\rm sol}$, $Δm^2_{32} \leftrightarrow Δm^2_{\rm atm}$ and $Δm^2_{21} \leftrightarrow Δm^2_{\rm LSND}$.

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arXiv2000

Two sterile neutrinos as a consequence of matter structure

An algebraic argument based on a series of generalized Dirac equations, truncated by an "intrinsic Pauli principle", shows that there should exist two sterile neutrinos as well as three families of leptons and quarks. Then, the influence of these additional neutrinos on neutrino oscillations is studied. As an example, a specific model of effective five-neutrino texture is proposed, where only the nearest neighbours in the sequence of five neutrinos ordered as $ν_s, ν'_s, ν_e, ν_μ, ν_τ$ are coupled through the 5x5 mass matrix. Its diagonal elements are taken as negligible in comparison with its nonzero off-diagonal entries.

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arXiv2000

A four-neutrino texture implying bimaximal flavor mixing and reduced LSND effect

A four-neutrino effective texture is described, where a sterile neutrino mixes nearly maximally with the electron neutrino and so, is responsible for the deficit of solar $ν_e $'s (according to the large-angle MSW solution or vacuum solution, of which the former is selected a posteriori). But, while maximal mixing of muon neutrino with tauon neutrino causes the deficit of atmospheric $ν_μ$'s, the original magnitude of LSND effect is reduced by as much as four orders, becoming unobservable.

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arXiv1999

Option of three pseudo--Dirac neutrinos

As an alternative for popular see-saw mechanism, the option of three pseudo% -Dirac neutrinos is discussed, where ${1/2}(m^{(L)} + m^{(R)}) \ll m^{(D)}$ for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product $ M^{(ν)} \otimes {(\{array} {cc} λ^{(L)} & 1 1 & λ^{(R)} \{array})}$, where $ M^{(ν)}$ is a neutrino family mass matrix ($ M^{(ν) \dagger} = M^{(ν)}$) and $λ^{(L,R)} \equiv m^{(L,R)}/m^{(D)}$ with $ m^{(L)}$, $ m^{(R)}$ and $ m^{(D)} $ being taken as universal for three neutrino families. It is shown that three neutrino effects (deficits of solar $ν_e $'s and atmospheric $ ν_μ$'s as well as the possible LSND excess of $ν_e $'s in accelerator $ν_μ$ beam) can be nicely described by the corresponding neutrino oscillations, though the LSND effect may, alternatively, be eliminated (by a parameter choice). Atmospheric $ν_μ$'s oscillate dominantly into $ν_τ$'s, while solar $ν_e $'s - into (existing here automatically) Majorana sterile counterparts of $ν_e $'s. A phenomenological texture for neutrinos, compatible with the proposed description, is briefly presented.

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arXiv1999

An 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. In this case, the neutrino mass term is necessarily of pure Majorana type.

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arXiv1999

Oscillations of the mixed pseudo--Dirac neutrinos

Oscillations of three pseudo--Dirac flavor neutrinos $ν_e, ν_μ, ν_τ$ are considered: $0 < m^{(L)} = m^{(R)} \ll m^{(D)}$ for their Majorana and Dirac masses taken as universal before family mixing. The actual neutrino mass matrix is assumed to be the tensor product $ M^{(ν)} \otimes {(\begin{array}{cc} λ^{(L)} & 1 1 & λ^{(R)} \end{array})}$, where $M^{(ν)}$ is a neutrino family mass matrix ($ M^{(ν) \dagger} = M^{(ν)}$) and $λ^{(L,R)} = m^{(L,R)}/m^{(D)}$. The $ M^{(ν)}$ is tried in a form proposed previously for charged leptons $e, μ, τ$ for which it gives $m_τ= 1776.80$ MeV versus $m^{exp}_τ= 1777.05^{+0.29}_{-0.20}$ MeV (with the experimental values of $m_e$ and $m_μ$ used as inputs). However, in contrast to the charged -lepton case, in the neutrino case its off-diagonal entries dominate over diagonal. Then, it is shown that three neutrino effects (the deficits of solar $ν_e$'s and atmospheric $ν_μ$'s as well as the possible LSND excess of $ν_e$'s in accelerator $ν_μ$ beam) can be explained by neutrino oscillations though, alternatively, the LSND effect may be eliminated (by a parameter choice). Atmospheric $ν_μ$'s oscillate dominantly into $ν_τ$'s, while solar $ν_e$'s -- into (automatically existing) Majorana sterile counterparts of $ν_e$'s.

hep-ph↗
arXiv1999

Fermion texture and sterile neutrinos

An explicit form of charged--lepton mass matrix, predicting $m_τ= 1776.80$ MeV from the experimental values of $m_e$ and $m_μ$ (in good agreement with the experimental figure $m_τ= 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $ν_e, ν_μ, ν_τ$ in order to correlate tentatively their masses and mixing parameters. It is suggested that for neutrinos the diagonal elements of the mass matrix are small versus its off-diagonal elements. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino oscillation probabilities are calculated in the corresponding lowest perturbative order. Then, the nearly maximal mixing of $ν_μ$ and $ν_τ$ is predicted in consistency with the observed deficit of atmospheric $ν_μ$'s. However, the predicted deficit of solar $ν_e$'s is much too small to explain the observed effect, what suggests the existence of (at least) one sort, $\enu$, of sterile neutrinos, whose mixing with $ν_e$ would be responsible for the observed deficit. Perspectives for applying the same form of mass matrix to quarks are also outlined. Two independent predictions of $|V_{ub}|/|V_{cb}| = 0.0753 \pm 0.0032$ and unitary angle $γ\simeq 70^\circ$ are deduced from the experimental values of $|V_{us}|$ and $|V_{cb}|$ (with the use of quark masses m_s, m_c and m_b). In the last three Sections, the option of two sorts, $\enu$ and $\mnu$, of sterile neutrinos is considered. They may dominate neutrino mixing, and even cause that two extra neutrino mass states (arising then) are agents of some tiny neutrino instability and related damping of $ν_e$ and $ν_μ$ oscillations. In Appendix, three conventional Majorana sterile neutrinos are discussed.

hep-ph↗
arXiv1998

Explicit lepton texture

An explicit form of charged--lepton mass matrix, predicting $ m_τ= 1776.80 $~MeV from the experimental values of $ m_e $ and $ m_μ$ (in good agreement with the experimental figure $ m_τ= 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $ν_e $, $ν_μ$, $ν_τ$ in order to correlate tentatively their masses and mixing parameters. While for charged leptons the off--diagonal mass--matrix elements turn out to be small {\it versus} its diagonal elements, it is suggested that for neutrinos the situation is inverse. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino oscillation probabilities are calculated in the corresponding lowest (and the next to lowest) perturbative order. Then, the nearly maximal mixing of $ν_μ$ and $ν_τ$ is predicted in consistency with the observed deficit of atmospheric $ν_μ$'s. However, the predicted deficit of solar $ν_e $'s is much too small to explain the observed effect, what suggests the existence of (at least) one sort, $ν_s $, of sterile neutrinos, whose mixing with $ν_e$ would be responsible for the observed deficit. In the last Section, promising perspectives for applying the same form of mass matrix to quarks are outlined. Two independent predictions of $|V_{ub}|/|V_{cb}| = 0.0753 \pm 0.0032 $ and unitary angle $γ\simeq 70^\circ $ are deduced from the experimental values of $|V_{us}|$ and $|V_{cb}|$ (with the use of quark masses $ m_s $, $ m_c $ and $ m_b $).

hep-ph↗
arXiv1998

Are there two sterile neutrinos cooscillating with $ν_e$ and $ν_μ$?

The existence of two sterile neutrinos $ν_s$ and $ν'_s$ (blind to all Standard-Model interactions) is shown to be implied by a model of fermion "texture" that we develop since some time. They may mix nearly maximally with two of three conventional neutrinos, say $ν_e$ and $ν_μ$, thus leading to neutrino oscillations, say $ν_e \to ν_s$ and $ν_μ\to ν'_s$, with nearly maximal amplitudes. Then, they can be responsible for the observed deficits of solar $ν_e$'s and atmospheric $ν_μ$'s, respectiv% ely, but by themselves do not help to explain the LSND results for $ν_μ\to ν_e$ oscillations. On the other hand, they are consistent with the CHOOZ negative result. At the moment, the experiment cannot decide, whether the deficit of atmospheric $ν_μ$'s, confirmed by the recent \SK findings, has to be related to the oscillations $ν_μ\to ν_τ$ or $ν_μ\to ν'_s$. In the last Section of the paper, a new notion of "non-Abelian spin-1/2 fermions" is presented in the context of a composite option for fermion families.

hep-ph↗
arXiv1998

Two hypothetic sterile neutrinos which want to mix with $ν_e $ and $ν_μ$

It is argued that the observed deficit of solar and atmospheric neutrinos can be explained by neutrino oscillations $ν_e \to ν_s $ and $ν_μ\to ν'_{s}$ involving two hypothetic sterile neutrinos $ν_s $ and $ν'_{s} $ (blind to all Standard--Model interactions). They are keen to mix nearly maximally with $ν_{e}$ and $ν_μ$, respectively, to form neutrino mass states $ν_1$, $ν_4 $ and $ν_2 $, $ν_5 $. Our argument is presented in the framework of a model of fermion "texture" formulated previously, which implies the existence of two sterile neutrinos beside the three conventional.

hep-ph↗
arXiv1997

Texture dynamics for neutrinos

An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation) $m_τ\simeq1776.80$ MeV from the experimental values of $m_e$ and $m_μ$, in agreement with $m_τ^{exp}= 1777.00^{+0.30}_{-0.27}$ MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations $ν_μ\toν_τ$ is $\sim 1/2$ and $|m^2_{ν_τ}-m^2_{ν_μ}|\sim(0.0003 to 0.01) eV^2$, as seems to follow from atmospheric-neutrino experiments, this ansatz predicts $m_{ν_e}\ll m_{ν_μ}\sim(0.2 to 1)\times 10^{-2} $ eV and $m_{ν_τ}\sim(0.2 to 1)\times 10^{-1} eV$, and also the amplitude of neutrino oscillations $ν_e \to ν_μ\sim 2^{+4}_{-2}\times 10^{-4}$ (in the vacuum). Such a very small amplitude for $ν_e \to ν_μ$ is implied by the value of $ m_τ^{exp} - 1776.80 $ MeV used to determine the deviation of the diagonalizing matrix $\hat{U}^{(e)}$ from $\hat{1}$ in the lepton Cabibbo-Kobayashi- Maskawa matrix $\hat{V} = \hat{U}^{(ν) \dagger}\hat{U}^{(e)}$. Here, $\hat{U}^{(ν)}$ by itself gives practically no oscillations $ν_e \toν_μ$, while it provides the large oscillations $ν_μ\toν_τ$.

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