An exactly solvable limit of low energy QCD

Starting from the QCD Hamiltonian, we derive a schematic Hamiltonian for low energy quark dynamics with quarks restricted to the lowest s-level. The resulting eigenvalue problem can be solved analytically. Even though the Hamiltonian exhibits explicit chiral symmetry the severe restriction of the number of degrees of freedom breaks the pattern of chiral symmetry breaking for finite quark masses.Comment: 7 page

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

Pion-Nucleon Scattering Relations at Next-to-Leading Order in 1/N_c

We obtain relations between partial-wave amplitudes for pi-N-->pi-N and pi-N-->pi-Delta directly from large N_c QCD. While linear relations among certain amplitudes holding at leading order (LO) in 1/N_c were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large N_c expansion. At LO we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at leading order (LO) and thus have little additional predictive power. However, three NLO relations for the pi-N-->pi-Delta reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment. These relations describe experiment dramatically better than their LO counterparts.Comment: 8 pages, 2 figures; references adde

Semiclassical Analysis of the Wigner 12j12j Symbol with One Small Angular Momentum

We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. When applying the same technique to the $12j$ symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram for a $9j$ symbol. This illustrates a general geometric connection between asymptotic limits of the various $3nj$ symbols. This work contributes the first known asymptotic formula for the $12j$ symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner $15j$ symbol with two small angular momenta.Comment: 15 pages, 14 figure

Three Additional Quiescent Low-Mass X-ray Binary Candidates in 47 Tucanae

We identify through their X-ray spectra one certain (W37) and two probable (W17 and X4) quiescent low-mass X-ray binaries (qLMXBs) containing neutron stars in a long Chandra X-ray exposure of the globular cluster 47 Tucanae, in addition to the two previously known qLMXBs. W37's spectrum is dominated by a blackbody-like component consistent with radiation from the hydrogen atmosphere of a 10 km neutron star. W37's lightcurve shows strong X-ray variability which we attribute to variations in its absorbing column depth, and eclipses with a probable 3.087 hour period. For most of our exposures, W37's blackbody-like emission (assumed to be from the neutron star surface) is almost completely obscured, yet some soft X-rays (of uncertain origin) remain. Two additional candidates, W17 and X4, present X-ray spectra dominated by a harder component, fit by a power-law of photon index ~1.6-3. An additional soft component is required for both W17 and X4, which can be fit with a 10 km hydrogen-atmosphere neutron star model. X4 shows significant variability, which may arise from either its power-law or hydrogen-atmosphere spectral component. Both W17 and X4 show rather low X-ray luminosities, Lx(0.5-10 keV)~5*10^{31} ergs/s. All three candidate qLMXBs would be difficult to identify in other globular clusters, suggesting an additional reservoir of fainter qLMXBs in globular clusters that may be of similar numbers as the group of previously identified objects. The number of millisecond pulsars inferred to exist in 47 Tuc is less than 10 times larger than the number of qLMXBs in 47 Tuc, indicating that for typical inferred lifetimes of 10 and 1 Gyr respectively, their birthrates are comparable.Comment: Accepted for publication in ApJ. 13 pages, 7 figures (2 color

Semi-relativistic description of quasielastic neutrino reactions and superscaling in a continuum shell model

The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(\nu_\mu,\mu^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(\nu_\mu,\mu^-)$ cross sections.Comment: 33 pages, 10 figures, to appear in PR

Search For Hole Mediated Ferromagnetism In Cubic (Ga,Mn)N

Results of magnetisation measurements on p-type zincblende-(Ga,Mn)N are reported. In addition to a small high temperature ferromagnetic signal, we detect ferromagnetic correlation among the remaining Mn ions, which we assign to the onset of hole-mediated ferromagnetism in (Ga,Mn)N.Comment: 2 pages, 1 figure, proc. ICPS 27, Flagstaff '0

Stellar Variability in the Globular Cluster Terzan 5

We present the results of a search for variability in and near the core of the metal-rich, obscured globular cluster Terzan 5, using NICMOS on HST. This extreme cluster has approximately solar metallicity and a central density that places it in the upper few percent of all clusters. It is estimated to have the highest interaction rate of any galactic globular cluster. The large extinction towards Terzan 5 and the severe stellar crowding near the cluster center present a substantial observational challenge. Using time series analysis we discovered two variable stars in this cluster. The first is a RRab Lyrae variable with a period of ~0.61 days, a longer period than that of field stars with similar high metallicities. This period is, however, shorter than the average periods of RR Lyraes found in the metal-rich globular clusters NGC 6441, NGC 6388 and 47 Tuc. The second variable is a blue star with a 7-hour period sinusoidal variation and a likely orbital period of 14 hours. This star is probably an eclipsing blue straggler, or (less likely) the infrared counterpart to the low mass X-ray binary known in Terzan 5. Due to the extreme crowding and overlapping Airy profile of the IR PSF, we fall short of our original goal of detecting CVs via Palpha emission and detecting variable infrared emission from the location of the binary MSP in Terzan 5.Comment: 17 pages including 12 figures. Accepted for publication in Ap