Two-Loop Maximal Unitarity with External Masses

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.Comment: 41 pages, 7 figures; small corrections, final journal versio

An Overview of Maximal Unitarity at Two Loops

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.Comment: 7 pages, presented at Loops & Legs 2012, Wernigerode, German

Maximal Unitarity for the Four-Mass Double Box

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.Comment: 25 pages, 3 figures; final journal versio

Cross-Order Integral Relations from Maximal Cuts

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.Comment: 58 pages, 19 figures; v2 references adde

Congenital Toxoplasmosis in Austria: Prenatal Screening for Prevention is Cost-Saving

Background: Primary infection of Toxoplasma gondii during pregnancy can be transmitted to the unborn child and may have serious consequences, including retinochoroiditis, hydrocephaly, cerebral calcifications, encephalitis, splenomegaly, hearing loss, blindness, and death. Austria, a country with moderate seroprevalence, instituted mandatory prenatal screening for toxoplasma infection to minimize the effects of congenital transmission. This work compares the societal costs of congenital toxoplasmosis under the Austrian national prenatal screening program with the societal costs that would have occurred in a No-Screening scenario. Methodology/Principal Findings: We retrospectively investigated data from the Austrian Toxoplasmosis Register for birth cohorts from 1992 to 2008, including pediatric long-term follow-up until May 2013. We constructed a decision-analytic model to compare lifetime societal costs of prenatal screening with lifetime societal costs estimated in a No-Screening scenario. We included costs of treatment, lifetime care, accommodation of injuries, loss of life, and lost earnings that would have occurred in a No-Screening scenario and compared them with the actual costs of screening, treatment, lifetime care, accommodation, loss of life, and lost earnings. We replicated that analysis excluding loss of life and lost earnings to estimate the budgetary impact alone. Our model calculated total lifetime costs of €103 per birth under prenatal screening as carried out in Austria, saving €323 per birth compared with No-Screening. Without screening and treatment, lifetime societal costs for all affected children would have been €35 million per year; the implementation costs of the Austrian program are less than €2 million per year. Calculating only the budgetary impact, the national program was still cost-saving by more than €15 million per year and saved €258 million in 17 years. Conclusions/Significance: Cost savings under a national program of prenatal screening for toxoplasma infection and treatment are outstanding. Our results are of relevance for health care providers by supplying economic data based on a unique national dataset including long-term follow-up of affected infants

Impact of mutation rate and selection at linked sites on DNA variation across the genomes of humans and other homininae

DNA diversity varies across the genome of many species. Variation in diversity across a genome might arise from regional variation in the mutation rate, variation in the intensity and mode of natural selection, and regional variation in the recombination rate. We show that both non-coding and non-synonymous diversity are positively correlated to a measure of the mutation rate and the recombination rate and negatively correlated to the density of conserved sequences in 50KB windows across the genomes of humans and non-human homininae. Interestingly, we find that while non-coding diversity is equally affected by these three genomic variables, non-synonymous diversity is mostly dominated by the density of conserved sequences. The positive correlation between diversity and our measure of the mutation rate seems to be largely a direct consequence of regions with higher mutation rates having more diversity. However, the positive correlation with recombination rate and the negative correlation with the density of conserved sequences suggests that selection at linked sites also affect levels of diversity. This is supported by the observation that the ratio of the number of non-synonymous to non-coding polymorphisms is negatively correlated to a measure of the effective population size across the genome. We show these patterns persist even when we restrict our analysis to GC-conservative mutations, demonstrating that the patterns are not driven by GC biased gene conversion. In conclusion, our comparative analyses describe how recombination rate, gene density, and mutation rate interact to produce the patterns of DNA diversity that we observe along the hominine genomes