Simple one-dimensional integral representations for two-loop self-energies: the master diagram

The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a one-dimensional integral representation is derived. This representation uses only elementary functions and is thus well suited for a numerical calculation of the master diagram.     

Exploiting the 1, 440-fold symmetry of the master two-loop diagram

The 1, 440-element symmetry group of the generic two-loop diagram of massless scalar field theory in 4-2ω dimensions is computed, using tetrahedral symmetry and star-triangle duality. Constructing all quadratic and quartic polynomial invariants, we expand the diagram throughO(ω ⁵), where one first encounters a coefficient that does not appear to be expressible in terms of the Riemann zeta function, thereby strengthening previous suspicions that genuinely new calculational comoplexity arises at the level of 6-loop renormalization.     

Z 2×S 6 symmetry of the two-loop diagram

The generic two-loop diagram of massless scalar field theory ind dimensions, with propagators raised to powers {α _i |i=1,5} is shown to have a symmetry groupZ ₂×S ₆ corresponding to reflection and permutation of six linear combinations of the six parameters. The expansion about α _i =d/4=1 is given to the level required for six-loop renormalization. All but five of the coefficients are obtained from products of one-loop diagrams. All but one are expressed in terms of the Riemann zeta function.     

Annihilation diagram contribution to charmonium masses

In this work, we generate gauge configurations with \begin{document}$ N_f = 2 $\end{document} dynamical charm quarks on anisotropic lattices. The mass shift of \begin{document}$ 1S $\end{document} and \begin{document}$ 1P $\end{document} charmonia due to the charm quark annihilation effect can be investigated directly in a manner of unitary theory. The distillation method is adopted to treat the charm quark annihilation diagrams at a very precise level. For \begin{document}$ 1S $\end{document} charmonia, the charm quark annihilation effect barely changes the \begin{document}$ J/\psi $\end{document} mass, but lifts the \begin{document}$ \eta_c $\end{document} mass by approximately 3–4 MeV. For \begin{document}$ 1P $\end{document} charmonia, this effect results in positive mass shifts of approximately 1 MeV for \begin{document}$ \chi_{c1} $\end{document} and \begin{document}$ h_c $\end{document}, but decreases the \begin{document}$ \chi_{c2} $\end{document} mass by approximately 3 MeV. We did not obtain a reliable result for the mass shift of \begin{document}$ \chi_{c0} $\end{document}. In addition, we observed that the spin averaged mass of the spin-triplet \begin{document}$ 1P $\end{document} charmonia is in good agreement with \begin{document}$ h_c $\end{document}, as expected by the non-relativistic quark model and measured by experiments.     

Infrared quasi-fixed point structure of the fermion masses in the standard model: The two-loop analysis

In the standard model, the renormalization group equation for the Yukawa couplings has the infrared quasi-fixed point which determines the upper bound for the masses of fermions present in the theory. We analyse this effect within the two loop approximation and report the 15% increase of the quark bound compared to the one loop results. We notice and investigate the strong dependence of the bound on the precise value of the Weinberg angle. The detailed study of the Yukawa coupling evolution is also included.     

Analytic two-loop master integrals for tW production at hadron colliders: I

We present the analytic calculation of two-loop master integrals that are relevant for tW production at hadron colliders. We focus on the integral families with only one massive propagator. After selecting a canonical basis, the differential equations for the master integrals can be transformed into the d ln form. The boundaries are determined by simple direct integrations or regularity conditions at kinematic points without physical singularities. The analytical results in this work are expressed in terms of multiple polylogarithms, and have been checked via numerical computations.     

The massless two-loop two-point function

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter . As a side product, we show that in the Laurent expansion of the two-loop integral only rational numbers and multiple zeta values occur. Our method of calculation obtains the two-loop integral as a convolution product of two primitive one-loop integrals. We comment on the generalization of this product structure to higher loop integrals.Received: 1 September 2003, Revised: 30 September 2003, Published online: 12 November 2003     

Heavy-to-light-quark decays with two-loop accuracy

We present a determination of a new class of three-loop Feynman diagrams describing heavy-to-light transitions. We apply it to find the O(alpha2(s)) corrections to the top quark decay t --> bW and to the distribution of lepton invariant mass in the semileptonic b quark decay b --> ulnu. We also confirm the previously determined total rate of that process as well as the O(alpha2) corrections to the muon lifetime.     

The two-loop β-function in models with extended rigid supersymmetry

The two-loop propagators and β-function of a general N =2 supersymmetric model comprising N = 2 Yang-Mills coupled to sets of N = 2 hypermultiplets are calculated by N = 1 supergraph techniques. It is shown that all such models are finite at two loops while a subset is also finite at the one-loop level. The calculation thus confirms the finiteness theorems, and shows that they are valid at the two-loop level even if the hypermultiplet is in a complex representation of the gauge group.     

The masses of the neutral {\cal CP}-even Higgs bosons in the MSSM: Accurate analysis at the two-loop level

We present detailed results of a diagrammatic calculation of the leading two-loop QCD corrections to the masses of the neutral -even Higgs bosons in the Minimal Supersymmetric Standard Model (MSSM). The two-loop corrections are incorporated into the full diagrammatic one-loop result and supplemented with refinement terms that take into account leading electroweak two-loop and higher-order QCD contributions. The dependence of the results for the Higgs-boson masses on the various MSSM parameters is analyzed in detail, with a particular focus on the part of the parameter space accessible at LEP2 and the upgraded Tevatron. For the mass of the lightest Higgs boson, , a parameter scan has been performed, yielding an upper limit on which depends only on . The results for the Higgs-boson masses are compared with results obtained by renormalization group methods. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account. Received: 11 January 1999 / Published online: 28 May 1999     

The two-loop effective potential of the Wess-Zumino model

An unconstrained component field formalism of the Wess-Zumino (WZ) model is used to calculate the effective potential to two-loop order. It is found that both one- and two-loop contributions are bounded below however they may become negative. Nonetheless the summed effective potential does respect positive definiteness.     

Pentagonal two-loop ring interferometer

Results of work on the assembly and adjustment of an original pentagonal, two-loop interferometer are reported; the interferometer is a passive version of a compact laser gravitational wave detector. It is shown that the correlative automatic noise-compensation system developed for the project is capable of lowering the phase noise level in the resultant signal channel of the detector by two orders of magnitude. Zh. Tekh. Fiz. 68, 121–125 (May 1998)     

The two-loop vector form factor in the Sudakov limit

Recently two-loop electroweak corrections to the neutral current four-fermion processes at high energies have been presented. The basic ingredient of this calculation is the evaluation of the two-loop corrections to the Abelian vector form factor in a spontaneously broken SU(2) gauge model. Whereas the final result and the derivation of the four-fermion cross sections from evolution equations have been published earlier, the calculation of the form factor from the two-loop Feynman diagrams is presented for the first time in this paper. We describe in detail the individual contributions to the form factor and their calculation with the help of the expansion by regions method and Mellin–Barnes representations.     

The two-loop self-energy: diagrams in the coordinate-momentum representation

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Zα) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.     

The Skyrme model with pion masses

We study the SU(2) × SU(2) Skyrme model with an explicit chiral breaking term. The new quantities that we evaluate are the pion-nucleon sigma term and the isovector charge radii, whose values come out in reasonable agreement with experiment. The other static properties of nucleons differ by a few percent from the corresponding values in the chiral limit.     

Testing QED screening and two-loop contributions with He-Like ions

We report wavelength measurements of H-like and He-like ions obtained with a novel x-ray spectrometer at the Heidelberg Electron Beam Ion Trap. The experimental uncertainty for the Lyman-alpha1 wavelength in Cl16+ is reduced by a factor of 3 and, as expected, excellent agreement with theory is maintained. For the resonance line in He-like Ar16+, an uncertainty of only deltalambda/lambda=2x10(-6) was achieved. This is the most precise x-ray wavelength reported for highly charged ions to date, and allows to test recent predictions on QED two-electron and two-photon radiative corrections for He-like ions. The results also point to the advantages of establishing absolute x-ray wavelength standards using Lyman-alpha transitions (in the present case Ar17+ Lyman-alpha1) to supersede the current ones.     

A note on two-loop superloop

We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang–Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the null polygonal super Wilson loop at two loops restricting the contour kinematics to a two-dimensional subspace. This allows one to perform all computations in a concise analytical form and trace the pattern of cancellations between individual Feynman graphs in a transparent fashion. As a consequence of our consideration we obtain a dual conformally invariant result for the remainder function in agreement with one-loop NMHV amplitudes.