Algorithms to Evaluate Multiple Sums for Loop Computations

We present algorithms to evaluate two types of multiple sums, which appear in higher-order loop computations. We consider expansions of a generalized hypergeometric-type sums, \sum_{n_1,...,n_N} [Gamma(a1.n+c1) Gamma(a2.n}+c2) ... Gamma(aM.n+cM)] / [Gamma(b1.n+d1) Gamma(b2.n+d2) ... Gamma(bM.n+dM)] x1^n1...xN^nN with $ai.n=\sum_{j=1}^N a_{ij}nj$, etc., in a small parameter epsilon around rational values of ci,di's. Type I sum corresponds to the case where, in the limit epsilon -> 0, the summand reduces to a rational function of nj's times x1^n1...xN^nN; ci,di's can depend on an external integer index. Type II sum is a double sum (N=2), where ci,di's are half-integers or integers as epsilon -> 0 and xi=1; we consider some specific cases where at most six Gamma functions remain in the limit epsilon -> 0. The algorithms enable evaluations of arbitrary expansion coefficients in epsilon in terms of Z-sums and multiple polylogarithms (generalized multiple zeta values). We also present applications of these algorithms. In particular, Type I sums can be used to generate a new class of relations among generalized multiple zeta values. We provide a Mathematica package, in which these algorithms are implemented.Comment: 30 pages, 2 figures; address of Mathematica package in Sec.6; version to appear in J.Math.Phy

Significance of myocardial tenascin-C expression in left ventricular remodelling and long-term outcome in patients with dilated cardiomyopathy

Aim Dilated cardiomyopathy (DCM) has a variety of causes, and no useful approach to predict left ventricular (LV) remodelling and long-term outcome has yet been established. Myocardial tenascin-C (TNC) is known to appear under pathological conditions, possibly to regulate cardiac remodelling. The aim of this study was to clarify the significance of myocardial TNC expression in LV remodelling and the long-term outcome in DCM. Methods and results One hundred and twenty-three consecutive DCM patients who underwent endomyocardial biopsy for initial diagnosis were studied. Expression of TNC in biopsy sections was analysed immunohistochemically to quantify the ratio of the TNC-positive area to the whole myocardial tissue area (TNC area). Clinical parameters associated with TNC area were investigated. The patients were divided into two groups based on receiver operating characteristic analysis of TNC area to predict death: high TNC group with TNC area ≥2.3% (22 patients) and low TNC group with TNC area <2.3% (101 patients). High TNC was associated with diabetes mellitus. Comparing echocardiographic findings between before and 9 months after endomyocardial biopsy, the low TNC group was associated with decreased LV end-diastolic diameter and increased LV ejection fraction, whereas the high TNC group was not. Survival analysis revealed a worse outcome in the high TNC group than in the low TNC group (P < 0.001). Multivariable Cox regression analysis revealed that TNC area was independently associated with poor outcome (HR = 1.347, P = 0.032). Conclusions Increased myocardial TNC expression was associated with worse LV remodeling and long-term outcome in DCM

Violation of Casimir Scaling for Static QCD Potential at Three-loop Order

We compute the full ${\cal O}(\alpha_s^4)$ and ${\cal O}(\alpha_s^4\log\alpha_s)$ corrections to the potential $V_R(r)$ between the static color sources, where $V_R(r)$ is defined from the Wilson loop in a general representation $R$ of a general gauge group $G$. We find a violation of the Casimir scaling of the potential, for the first time, at ${\cal O}(\alpha_s^4)$. The effect of the Casimir scaling violation is predicted to reduce the tangent of $V_R(r)/C_R$ proportionally to specific color factors dependent on $R$. We study the sizes of the Casimir scaling violation for various $R$'s in the case $G=SU(3)$. We find that they are well within the present bounds from lattice calculations, in the distance region where both perturbative and lattice computations of $V_R(r)$ are valid. We also discuss how to test the Casimir scaling violating effect.Comment: 20 pages, 7 figures, v2: a typo in eq.(13) correcte

Orbital Degeneracy and Peierls Instability in Triangular Lattice Superconductor Ir1−x_{1-x}Ptx_xTe2_2

We have studied electronic structure of triangular lattice Ir$_{1-x}$Pt$_x$Te$_2$ superconductor using photoemission spectroscopy and model calculations. Ir $4f$ core-level photoemission spectra show that Ir $5d$ $t_{2g}$ charge modulation established in the low temperature phase of IrTe$_2$ is suppressed by Pt doping. This observation indicates that the suppression of charge modulation is related to the emergence of superconductivity. Valence-band photoemission spectra of IrTe$_2$ suggest that the Ir $5d$ charge modulation is accompanied by Ir $5d$ orbital reconstruction. Based on the photoemission results and model calculations, we argue that the orbitally-induced Peierls effect governs the charge and orbital instability in the Ir$_{1-x}$Pt$_x$Te$_2$.Comment: 5 pages,4 figure

Fermi-surface reconstruction involving two Van Hove singularities across the antiferromagnetic transition in BaFe2As2

We report an angle-resolved photoemission study of BaFe2As2, a parent compound of iron-based superconductors. Low-energy tunable excitation photons have allowed the first observation of a saddle-point singularity at the Z point, as well as the Gamma point. With antiferromagnetic ordering, both of these two van Hove singularities come down below the Fermi energy, leading to a topological change in the innermost Fermi surface around the kz axis from cylindrical to tear-shaped, as expected from first-principles calculation. These singularities may provide an additional instability for the Fermi surface of the superconductors derived from BaFe2As2.Comment: 14 pages, 4 figures, 1 tabl