Neutrino production coherence and oscillation experiments

Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.Comment: LaTeX, 40 pages, 4 figures. v2: minor typos correcte

Fermionic decays of scalar leptoquarks and scalar gluons in the minimal four color symmetry model

Fermionic decays of the scalar leptoquarks $S=S_1^{(+)}, S_1^{(-)}, S_m$ and of the scalar gluons $F=F_1, F_2$ predicted by the four color symmetry model with the Higgs mechanism of the quark-lepton mass splitting are investigated. Widths and branching ratios of these decays are calculated and analysed in dependence on coupling constants and on masses of the decaying particles. It is shown that the decays $S_1^{(+)}\to tl^+_j, S_1^{(-)}\to \nu_i\tilde b, S_m\to t\tilde \nu_j, F_1\to t\tilde b, F_2\to t\tilde t$ are dominant with the widths of order of a few GeV for $m_S, m_F<1$ TeV and with the total branching ratios close to 1. In the case of $m_S < m_t$ the dominant scalar leptoquark decays are S_1^{(+)}\to cl_j^+, S_1^{(-)}\to \nu_i\tilde b, S_m\to b\l_j^+, S_m\to c\tilde \nu_j with the total branching ratios $Br(S_1^{(+)}\to cl^+) \approx$ $Br(S_1^{(-)}\to \nu\tilde b) \approx 1$, $Br(S_m\to bl^+) \approx 0.9$ and $Br(S_m\to c\tilde \nu) \approx 0.1.$ A search for such decays at the LHC and Tevatron may be of interest.Comment: 11 pages, 1 figure, 1 table, to be published in Modern Physics Letters

On a possible manifestation of the four color symmetry Z′Z' boson in μ+μ−\mu^+\mu^- events at the LHC

The cross section of the $\mu^+\mu^-$ pair production in $pp$-collisions at the LHC is calculated with acount of the $Z'$ boson induced by the minimal four color quark-lepton symmetry($MQLS$). The $\mu^+\mu^-$ invariant mass spectrum with account of the $MQLS$ $Z'$ boson is analysed in dependence on the $Z'$ mass. The mass region for the $MQLS$ $Z'$ boson observable at the LHC is found in dependence on the significance and on the integrated luminosity.Comment: 11 pages, 2 figures, accepted for publication in Modern Physics Letters

On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients

We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U_q(su(3)). We obtain a very compact general analytical formula for the U_q(su(3)) CGCs in terms of the U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei), (2001