Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals in this class are the two-loop four-point functions where two external lines are on the light-cone and two other external lines have different invariant masses. We compute these and other relevant integrals analytically using differential equations in external kinematic variables and express our results in terms of Goncharov polylogarithms. The case of two equal off-shellnesses, recently considered in Ref. [1], appears as a particular case of our general solution.Comment: 28 pages, many figures; ancillary files included with arXiv submissio

Evaluating single-scale and/or non-planar diagrams by differential equations

We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of the differential equations to single-scale Feynman integrals. Moreover, the information about singular limits significantly simplifies finding boundary constants for the differential equations. To illustrate these points we consider two families of three-loop integrals. The first are form-factor integrals with two external legs on the light cone. We introduce one more scale by taking one more leg off-shell, $p_2^2\neq 0$. We analytically solve the differential equations for the master integrals in a Laurent expansion in dimensional regularization with $\epsilon=(4-D)/2$. Then we show how to obtain analytic results for the corresponding one-scale integrals in an algebraic way. An essential ingredient of our method is to match solutions of the differential equations in the limit of small $p_2^2$ to our results at $p_2^2\neq 0$ and to identify various terms in these solutions according to expansion by regions. The second family consists of four-point non-planar integrals with all four legs on the light cone. We evaluate, by differential equations, all the master integrals for the so-called $K_4$ graph consisting of four external vertices which are connected with each other by six lines. We show how the boundary constants can be fixed with the help of the knowledge of the singular limits. We present results in terms of harmonic polylogarithms for the corresponding seven master integrals with six propagators in a Laurent expansion in $\epsilon$ up to weight six.Comment: 27 pages, 2 figure

Dopamine: A Marker of Psychosis and Final Common Driver of Schizophrenia Psychosis

Our attempt to understand schizophrenia in neurochemical terms began with the landmark studies of Carlsson and Lindqvist (1) in the 1960s. The results of these studies, based on the action of chlorpromazine, were strengthened by the binding studies carried out in both Seeman's (2) and Synder's (3) laboratories, which showed that antipsychotic potency was correlated with dopamine D2 receptor binding. The one major exception to this correlation is clozapine, which appears to be the most effective available drug for treating schizophrenia symptoms. The most recent version of the resulting dopamine hypothesis suggests that genetic, environmental, and developmental variables play major etiological roles in schizophrenia, but that striatal dopamine presynaptic overactivity remains the final trigger resulting in psychosis.....

A planar four-loop form factor and cusp anomalous dimension in QCD

We compute the fermionic contribution to the photon-quark form factor to four-loop order in QCD in the planar limit in analytic form. From the divergent part of the latter the cusp and collinear anomalous dimensions are extracted. Results are also presented for the finite contribution. We briefly describe our method to compute all planar master integrals at four-loop order.Comment: 19 pages, 3 figures, v2: typo in (2.3) fixed and coefficients in (2.6) corrected; references added and correcte

Optimizing Max Camber Points Along Thin Triangular Airfoils for Higher Lift/Drag Ratios

The purpose of this report is to expand knowledge on the lift and drag properties of thin triangular airfoils, and determine whether or not they are a viable option for low-Reynolds number applications. Thin triangular airfoils were thought to be more efficient than standard NACA airfoils under specific conditions. This experiment was performed through the wind tunnel testing of a NACA 2412 and nine thin triangular airfoils with varying max camber points. Between the Reynolds numbers of 30-42,000, lift and drag values were collected at varying angles of attack. Overall, it was found that the thin triangular airfoils proved to have unique lift and drag characteristics when compared to the standard NACA 2412