10,392 research outputs found
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
Solar neutrinos: global analysis and implications for SNO
We present a global analysis of all the available solar neutrino data
treating consistently the 8B and hep neutrino fluxes as free parameters. The
analysis reveals at 99.7% C.L. eight currently-allowed discrete regions in
two-neutrino oscillation space, five regions corresponding to active neutrinos
and three corresponding to sterile neutrinos. Most of the allowed solutions are
robust with respect to changes in the analysis procedure, but the traditional
vacuum solution is fragile. The globally-permitted range of the 8B neutrino
flux, 0.45 to 1.95 in units of the BP2000 flux, is comparable to the 3 sigma
range allowed by the standard solar model. We discuss the implications for SNO
of a low mass, Delta m^2 ~ 6 times 10^{-12} eV^2, vacuum oscillation solution,
previously found by Raghavan, and by Krastev and Petcov, but absent in recent
analyses that included Super-Kamiokande data. For the SNO experiment, we
present refined predictions for the charged-current rate and the ratio of the
neutral-current rate to charged-current rate. The predicted charged-current
rate can be clearly distinguished from the no-oscillation rate only for the LMA
solution. The predicted ratio of the neutral-current rate to charged-current
rate is distinguishable from the no-oscillation ratio for the LMA, SMA, LOW,
and VAC solutions for active neutrinos.Comment: viewgraphs and related material at http://www.sns.ias.ed
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