qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminate

Determination of a time-shift in the OPERA set-up using high energy horizontal muons in the LVD and OPERA detectors

The purpose of this work is to report the measurement of a time-shift in the OPERA set-up in a totally independent way from Time Of Flight (TOF) measurements of CNGS neutrino events. The LVD and OPERA experiments are both installed in the same laboratory: LNGS. The relative position of the two detectors, separated by an average distance of ~ 160 m, allows the use of very high energy horizontal muons to cross-calibrate the timing systems of the two detectors, using a TOF technique which is totally independent from TOF of CNGS neutrino events. Indeed, the OPERA-LVD direction lies along the so-called "Teramo anomaly", a region in the Gran Sasso massif where LVD has established, many years ago, the existence of an anomaly in the mountain structure, which exhibits a low m. w. e. thickness for horizontal directions. The "abundant" high-energy horizontal muons (nearly 100 per year) going through LVD and OPERA exist because of this anomaly in the mountain orography. The total live time of the data in coincidence correspond to 1200 days from mid 2007 until March 2012. The time coincidence study of LVD and OPERA detectors is based on 306 cosmic horizontal muon events and shows the existence of a negative time shift in the OPERA set-up of the order of deltaT(AB) = - (73 \pm 9) ns when two calendar periods, A and B, are compared. This result shows a systematic effect in the OPERA timing system from August 2008 until December 2011. The size of the effect is comparable with the neutrino velocity excess recently measured by OPERA. It is probably interesting not to forget that with the MRPC technology developed by the ALICE Bologna group the TOF world record accuracy of 20 ps was reached. That technology can be implemented at LNGS for a high precision determination of TOF with the CNGS neutrino beams of an order of magnitude smaller than the value of the OPERA systematic effect

Observation of a first ντ\nu_\tau candidate in the OPERA experiment in the CNGS beam

The OPERA neutrino detector in the underground Gran Sasso Laboratory (LNGS) has been designed to perform the first detection of neutrino oscillations in direct appearance mode through the study of the $\nu_\mu\rightarrow\nu_\tau$ channel. The hybrid apparatus consists of an emulsion/lead target complemented by electronic detectors and it is placed in the high energy long-baseline CERN to LNGS beam (CNGS) 730 km away from the neutrino source. Runs with CNGS neutrinos were successfully carried out in 2008 and 2009. After a brief description of the beam, the experimental setup and the procedures used for the analysis of the neutrino events, we describe the topology and kinematics of a first candidate $\nu_\tau$ charged-current event satisfying the kinematical selection criteria. The background calculations and their cross-check are explained in detail and the significance of the event is assessed.Comment: 19 pages, 3 figure