Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory

We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.Comment: 24 pages, 7 figures; several additions, published versio

Search for ultrahigh energy neutrinos in highly inclined events at the Pierre Auger Observatory

The Surface Detector of the Pierre Auger Observatory is sensitive to neutrinos of all flavors above 0.1 EeV. These interact through charged and neutral currents in the atmosphere giving rise to extensive air showers. When interacting deeply in the atmosphere at nearly horizontal incidence, neutrinos can be distinguished from regular hadronic cosmic rays by the broad time structure of their shower signals in the water-Cherenkov detectors. In this paper we present for the first time an analysis based on down-going neutrinos. We describe the search procedure, the possible sources of background, the method to compute the exposure and the associated systematic uncertainties. No candidate neutrinos have been found in data collected from 1 January 2004 to 31 May 2010. Assuming an E-2 differential energy spectrum the limit on the single-flavor neutrino is E2dN=dE-7GeVcm-2s-1sr-1 at 90% C.L. in the energy range 1 X 1017eV\u3c E 1020eV

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Improved α4\alpha^4 Term of the Electron Anomalous Magnetic Moment

We report a new value of electron $g-2$, or $a_e$, from 891 Feynman diagrams of order $\alpha^4$. The FORTRAN codes of 373 diagrams containing closed electron loops have been verified by at least two independent formulations. For the remaining 518 diagrams, which have no closed lepton loop, verification by a second formulation is not yet attempted because of the enormous amount of additional work required. However, these integrals have structures that allow extensive cross-checking as well as detailed comparison with lower-order diagrams through the renormalization procedure. No algebraic error has been uncovered for them. The numerical evaluation of the entire $\alpha^4$ term by the integration routine VEGAS gives $-1.7283 (35) (\alpha/\pi)^4$, where the uncertainty is obtained by careful examination of error estimates by VEGAS. This leads to $a_e = 1 159 652 175.86 (0.10) (0.26) (8.48) \times 10^{-12}$, where the uncertainties come from the $\alpha^4$ term, the estimated uncertainty of $\alpha^5$ term, and the inverse fine structure constant, $\alpha^{-1} = 137.036 000 3 (10)$, measured by atom interferometry combined with a frequency comb technique, respectively. The inverse fine structure constant $\alpha^{-1} (a_e)$ derived from the theory and the Seattle measurement of $a_e$ is $137.035 998 83 (51)$.Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added after Eq.(40

On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering

We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems with broken time-reversal invariance.Comment: 4 pages, 2 figure

Tumor Necrosis Factor Receptor Superfamily, Member 1B Haplotypes Increase or Decrease the Risk of Inflammatory Bowel Diseases in a New Zealand Caucasian Population

Inflammatory bowel diseases (IBDs) comprising Crohn disease (CD) and ulcerative colitis (UC) are chronic inflammatory conditions with polygenic susceptibility. Interactions between TNF-alpha and TNF-alpha receptor play a fundamental role in inflammatory response. This study investigates the role that selected single nucleotide polymorphisms (SNPs) and haplotypes in the TNF-alpha receptor (TNSFRSF1B) gene play in the risk of IBD in a New Zealand Caucasian population. DNA samples from 388 CD, 405 UC, 27 indeterminate colitis patients, and 293 randomly selected controls, from Canterbury, New Zealand were screened for 3 common SNPs in TNSFRSF1B: rs1061622 (c.676T > C), rs1061624 (c.*1663A > G), and rs3397 (c.*1690T > C), using TaqMan technologies. Carrying the rs1061624 variant decreased the risk of UC in the left colon (OR 0.73, 95% CI = 0.54–1.00) and of being a smoker at diagnosis (OR 0.62; 95% CI = 0.40–0.96). Carrying the rs3397 variant decreased the risk of penetrating CD (OR 0.62, 95% CI = 0.40–0.95). Three marker haplotype analyses revealed highly significant differences between CD patients and control subjects (χ2 = 29.9, df = 7, P = .0001) and UC cases and controls (χ2 = 46.3, df = 7, P < .0001). We conclude that carrying a 3-marker haplotype in the TNSFRSF1B gene may increase (e.g., haplotype of GGC was 2.9-fold more in the CD or UCpatients) or decrease (e.g., TGT was 0.47-fold less in UC patients) the risk of IBD in a New Zealand Caucasian population

Tumor Necrosis Factor Receptor Superfamily, Member 1B Haplotypes Increase or Decrease the Risk of Inflammatory Bowel Diseases in a New Zealand Caucasian Population

Inflammatory bowel diseases (IBDs) comprising Crohn disease (CD) and ulcerative colitis (UC) are chronic inflammatory conditions with polygenic susceptibility. Interactions between TNF-alpha and TNF-alpha receptor play a fundamental role in inflammatory response. This study investigates the role that selected single nucleotide polymorphisms (SNPs) and haplotypes in the TNF-alpha receptor (TNSFRSF1B) gene play in the risk of IBD in a New Zealand Caucasian population. DNA samples from 388 CD, 405 UC, 27 indeterminate colitis patients, and 293 randomly selected controls, from Canterbury, New Zealand were screened for 3 common SNPs in TNSFRSF1B: rs1061622 (c.676T > C), rs1061624 (c.*1663A > G), and rs3397 (c.*1690T > C), using TaqMan technologies. Carrying the rs1061624 variant decreased the risk of UC in the left colon (OR 0.73, 95% CI = 0.54–1.00) and of being a smoker at diagnosis (OR 0.62; 95% CI = 0.40–0.96). Carrying the rs3397 variant decreased the risk of penetrating CD (OR 0.62, 95% CI = 0.40–0.95). Three marker haplotype analyses revealed highly significant differences between CD patients and control subjects (χ2 = 29.9, df = 7, P = .0001) and UC cases and controls (χ2 = 46.3, df = 7, P < .0001). We conclude that carrying a 3-marker haplotype in the TNSFRSF1B gene may increase (e.g., haplotype of GGC was 2.9-fold more in the CD or UCpatients) or decrease (e.g., TGT was 0.47-fold less in UC patients) the risk of IBD in a New Zealand Caucasian population

Testing new physics with the electron g-2

We argue that the anomalous magnetic moment of the electron (a_e) can be used to probe new physics. We show that the present bound on new-physics contributions to a_e is 8*10^-13, but the sensitivity can be improved by about an order of magnitude with new measurements of a_e and more refined determinations of alpha in atomic-physics experiments. Tests on new-physics effects in a_e can play a crucial role in the interpretation of the observed discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large class of models, new contributions to magnetic moments scale with the square of lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in which this scaling is violated and larger effects in a_e are expected. In such models the value of a_e is correlated with specific predictions for processes with violation of lepton number or lepton universality, and with the electric dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde