Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations

The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically. The system composed by this differential equation with those of the master integrals related to the general massive 2-loop sunrise diagram is numerically solved by the Runge-Kutta method in the complex p^2 plane. A numerical method to obtain results for values of p^2 at and close to thresholds and pseudo-thresholds is discussed in details.Comment: Latex, 20 pages, 7 figure

BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations

Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the epsilon-scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants Zm(OS) and Z2(OS) in dimensional regularization and thus provide the first independent check of the analytical results computed several years ago.Comment: 22 page

Absolute spectroscopy near 7.8 μm with a comb-locked extended-cavity quantum-cascade-laser

We report for the first time the frequency locking of an extended-cavity quantum-cascade-laser (EC-QCL) to a near-infrared frequency comb. The locked laser source is exploited to carry out molecular spectroscopy around 7.8 μm with a line-centre frequency combined uncertainty of ~63 kHz. The strength of the approach, in view of an accurate retrieval of line centre frequencies over a spectral range as large as 100 cm-1, is demonstrated on the P(40), P(18) and R(31) lines of the fundamental rovibrational band of N2O covering the centre and edges of the P and R branches. The spectrometer has the potential to be straightforwardly extended to other spectral ranges, till 12 μm, which is the current wavelength limit for commercial cw EC-QCLs

Radiographic Analysis on the Distortion of the Anatomy of First Metatarsal Head in Dorsoplantar Projection

[Abstract] Background: The diagnostic of flat and crest-shaped of first metatarsal heads has been associated as an important risk factor for hallux deformities, such as hallux valgus and hallux rigidus. The rounded form of the first metatarsal head on the dorsoplantar radiograph of the foot has been believed to be associated with the development of hallux valgus. Purpose: The aim of this study was to clarify the effect of tube angulation on the distortion of first metatarsal head shape, and verify the real shape of the metatarsal head in anatomical dissection after an X-ray has been taken. Materials and Methods: In this prospective study at Universidad Complutense de Madrid, from December 2016 to June 2019, 103 feet from embalmed cadavers were included. We performed dorsoplantar radiograph tube angulation from 0° until 30° every 5° on all specimens; then, two observers verified the shape of the first metatarsal head in the radiographs and after its anatomic dissection. Kappa statistics and McNemar Bowker tests were used to assess and test for intra and interobserver agreement of metatarsal shape. Results: We calculated the intraobserver agreement, and the results showed that the first metatarsal head is distorted and crested only when the angle of the X-ray beam is at 20° of inclination (p < 0.001). The interobserver agreement showed good agreement at 0°, 5°, 10°, 20°, and 25° and was excellent at 30° (p < 0.001). Conclusion: All of the studies that we identified in the literature state that there are three types of shapes of the first metatarsal head and relate each type of head to the diagnosis of a foot pathology, such as hallux valgus or hallux rigidus. This study demonstrates that there is only the round-shaped form, and not three types of metatarsal head shape. Therefore, no diagnoses related to the shape of the first metatarsal head can be made

Hypergeometric representation of the two-loop equal mass sunrise diagram

A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and Appell's F_2 hypergeometric functions is presented. For arbitrary space-time dimension d the imaginary part of the diagram on the cut is found to be the 2F1 hypergeometric function with argument proportional to the maximum of the Kibble cubic form. The analytic expression for the threshold value of the diagram in terms of the hypergeometric function 3F2 of argument -1/3 is given.Comment: 10 page

TSIL: a program for the calculation of two-loop self-energy integrals

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C, C++, or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.Comment: 31 pages. Updated to reflect new functionality through v1.4 May 2016 and new information about use with C++. Source code and documentation are available at http://www.niu.edu/spmartin/TSIL or http://faculty.otterbein.edu/DRobertson/tsil

Finite top quark mass effects in NNLO Higgs boson production at LHC

We present next-to-next-to-leading order corrections to the inclusive production of the Higgs bosons at the CERN Large Hadron Collider (LHC) including finite top quark mass effects. Expanding our analytic results for the partonic cross section around the soft limit we find agreement with a very recent publication by Harlander and Ozeren \cite{Harlander:2009mq}.Comment: 15 page

Non-Singlet Structure Functions at Three Loops: Fermionic Contributions

We compute the fermionic (n_f) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic deep-inelastic scattering at third order of massless perturbative QCD. Complete results are presented for the corresponding nf-parts of the three-loop anomalous dimension and the three-loop coefficient functions for the structure functions F_2 and F_L. Our results agree with all partial and approximate results available in the literature. The present calculation also facilitates a complete determination of the threshold-resummation parameters B_2 and D_2^DIS of which only the sum was known so far, thus completing the information required for the next-to-next-to-leading logarithmic resummation. We find that D_2^DIS vanishes in the MSbar scheme.Comment: 20 pages, LaTeX, 1 eps-figur

Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders

We consider the production of intermediate-mass CP-even and CP-odd Higgs bosons in proton-proton and proton-anti-proton collisions. We extend the recently published results for the complete next-to-next-to-leading order calculation for a scalar Higgs boson to the pseudo-scalar case and present details of the calculation that might be useful for similar future investigations. The result is based on an expansion in the limit of a heavy top quark mass and a subsequent matching to the expression obtained in the limit of infinite energy. For a Higgs boson mass of 120 GeV the deviation from the infinite-top quark mass result is small. For 300 GeV, however, the next-to-next-to-leading order corrections for a scalar Higgs boson exceed the effective-theory result by about 9% which increases to 22% in the pseudo-scalar case. Thus in this mass range the effect on the total cross section amounts to about 2% and 6%, respectively, which may be relevant in future precision studies.Comment: 29 page