Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

Exactly solvable model of superstring in Ramond-Ramond plane wave background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.Comment: 33 pages, latex. v4: minor sign corrections in (1.5) and (3.62), to appear in PR

The Shapes of Dirichlet Defects

If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.Comment: 24 pages, RevTeX, 21 eps figure

Cohort studies of fat intake and the risk of breast cancer--a pooled analysis.

Cohort studies of fat intake and the risk of breast cancer--a pooled analysis. Hunter DJ, Spiegelman D, Adami HO, Beeson L, van den Brandt PA, Folsom AR, Fraser GE, Goldbohm RA, Graham S, Howe GR, et al. Department of Epidemiology, Harvard School of Public Health, Boston, MA, USA. BACKGROUND. Experiments in animals, international correlation comparisons, and case-control studies support an association between dietary fat intake and the incidence of breast cancer. Most cohort studies do not corroborate the association, but they have been criticized for involving small numbers of cases, homogeneous fat intake, and measurement errors in estimates of fat intake. METHODS. We identified seven prospective studies in four countries that met specific criteria and analyzed the primary data in a standardized manner. Pooled estimates of the relation of fat intake to the risk of breast cancer were calculated, and data from study-specific validation studies were used to adjust the results for measurement error. RESULTS. Information about 4980 cases from studies including 337,819 women was available. When women in the highest quintile of energy-adjusted total fat intake were compared with women in the lowest quintile, the multivariate pooled relative risk of breast cancer was 1.05 (95 percent confidence interval, 0.94 to 1.16). Relative risks for saturated, monounsaturated, and polyunsaturated fat and for cholesterol, considered individually, were also close to unity. There was little overall association between the percentage of energy intake from fat and the risk of breast cancer, even among women whose energy intake from fat was less than 20 percent. Correcting for error in the measurement of nutrient intake did not materially alter these findings. CONCLUSIONS. We found no evidence of a positive association between total dietary fat intake and the risk of breast cancer. There was no reduction in risk even among women whose energy intake from fat was less than 20 percent of total energy intake. In the context of the Western lifestyle, lowering the total intake of fat in midlife is unlikely to reduce the risk of breast cancer substantially

Photospheric and Subphotospheric Dynamics of Emerging Magnetic Flux

Magnetic fields emerging from the Sun's interior carry information about physical processes of magnetic field generation and transport in the convection zone. Soon after appearance on the solar surface the magnetic flux gets concentrated in sunspot regions and causes numerous active phenomena on the Sun. This paper discusses some properties of the emerging magnetic flux observed on the solar surface and in the interior. A statistical analysis of variations of the tilt angle of bipolar magnetic regions during the emergence shows that the systematic tilt with respect to the equator (the Joy's law) is most likely established below the surface. However, no evidence of the dependence of the tilt angle on the amount of emerging magnetic flux, predicted by the rising magnetic flux rope theories, is found. Analysis of surface plasma flows in a large emerging active region reveals strong localized upflows and downflows at the initial phase of emergence but finds no evidence for large-scale flows indicating future appearance a large-scale magnetic structure. Local helioseismology provides important tools for mapping perturbations of the wave speed and mass flows below the surface. Initial results from SOHO/MDI and GONG reveal strong diverging flows during the flux emergence, and also localized converging flows around stable sunspots. The wave speed images obtained during the process of formation of a large active region, NOAA 10488, indicate that the magnetic flux gets concentrated in strong field structures just below the surface. Further studies of magnetic flux emergence require systematic helioseismic observations from the ground and space, and realistic MHD simulations of the subsurface dynamics.Comment: 21 pages, 15 figures, to appear in Space Science Review

Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS

We present the results of a search for new, heavy particles that decay at a significant distance from their production point into a final state containing charged hadrons in association with a high-momentum muon. The search is conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS detector operating at the Large Hadron Collider. Production of such particles is expected in various scenarios of physics beyond the standard model. We observe no signal and place limits on the production cross-section of supersymmetric particles in an R-parity-violating scenario as a function of the neutralino lifetime. Limits are presented for different squark and neutralino masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final version to appear in Physics Letters

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter

Measurement of the inclusive isolated prompt photon cross-section in pp collisions at sqrt(s)= 7 TeV using 35 pb-1 of ATLAS data

A measurement of the differential cross-section for the inclusive production of isolated prompt photons in pp collisions at a center-of-mass energy sqrt(s) = 7 TeV is presented. The measurement covers the pseudorapidity ranges |eta|<1.37 and 1.52<=|eta|<2.37 in the transverse energy range 45<=E_T<400GeV. The results are based on an integrated luminosity of 35 pb-1, collected with the ATLAS detector at the LHC. The yields of the signal photons are measured using a data-driven technique, based on the observed distribution of the hadronic energy in a narrow cone around the photon candidate and the photon selection criteria. The results are compared with next-to-leading order perturbative QCD calculations and found to be in good agreement over four orders of magnitude in cross-section.Comment: 7 pages plus author list (18 pages total), 2 figures, 4 tables, final version published in Physics Letters