Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass

We describe details of the renormalization of two-loop integrals relevant to the calculation of the nucleon mass in the framework of manifestly Lorentz-invariant chiral perturbation theory using infrared renormalization. It is shown that the renormalization can be performed while preserving all relevant symmetries, in particular chiral symmetry, and that renormalized diagrams respect the standard power counting rules. As an application we calculate the chiral expansion of the nucleon mass to order O(q^6).Comment: Version accepted for publication in Nucl. Phys. A, missing one-loop diagram added, minor changes in notation, discussion of results improve

Virtual QCD corrections to Higgs boson plus four parton processes

We report on the calculation of virtual processes contributing to the production of a Higgs boson and two jets in hadron-hadron collisions. The coupling of the Higgs boson to gluons, via a virtual loop of top quarks, is treated using an effective theory, valid in the large top quark mass limit. The calculation is performed by evaluating one-loop diagrams in the effective theory. The primary method of calculation is a numerical evaluation of the virtual amplitudes as a Laurent series in $D-4$, where $D$ is the dimensionality of space-time. For the cases $H \to q\bar{q}q\bar{q}$ and $H \to q\bar{q}q'\bar{q}'$ we confirm the numerical results by an explicit analytic calculation.Comment: 21 pages, 2 figures. v2 modifies the text to agree with published version and corrects typos in the analytical expressions for the four quark amplitude

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

We have completed the evaluation of all mass-dependent $\alpha^4$ QED contributions to the muon $g-2$, or $a_\mu$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\alpha^4$ term $A_2^{(8)} (m_\mu / m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)} (m_\mu / m_e, m_\mu / m_\tau)$ is 0.0376 (1). The term $A_2^{(8)} (m_\mu / m_\tau)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_\mu$ is $116 584 719.58 (0.02)(1.15)(0.85) \times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\alpha^4$ and $\alpha^5$ terms and 0.85 is from the uncertainty in $\alpha$ measured by atom interferometry. This raises the Standard Model prediction by $13.9 \times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_\mu$. It is within the noise of current uncertainty ($\sim 100 \times 10^{-11}$) in the estimated hadronic contributions to $a_\mu$.Comment: Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PR

Reduction schemes for one-loop tensor integrals

We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e+ e- -> 4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex.Comment: 55 pages, latex, some references updated and few comments added, version to appear in Nucl. Phys.

D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops

The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large N_c) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.Comment: 31 pages, revtex, 12 figure

Asymptotic thermal quark masses and the entropy of QCD in the large-N_f limit

We study the thermodynamics of QCD in the limit of large flavor number (N_f) and test the proposal to resum the physics of hard thermal loops (HTL) through a nonperturbative expression for the entropy obtained from a Phi-derivable two-loop approximation. The fermionic contribution to the entropy involves a full next-to-leading order evaluation of the asymptotic thermal quark mass, which is non-local, and for which only a weighted average value was known previously. For a natural choice of renormalization scale we find remarkably good agreement of the next-to-leading-order HTL results for the fermion self energy and in turn for the entropy with the respective exact large-N_f results even at very large coupling.Comment: REVTEX, 31 pages, 16 figure