Feynman rules for the rational part of the Electroweak 1-loop amplitudes

We present the complete set of Feynman rules producing the rational terms of kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard Model. Our results are given both in the 't Hooft-Veltman and in the Four Dimensional Helicity regularization schemes. We also verified, by using both the 't Hooft-Feynman gauge and the Background Field Method, a huge set of Ward identities -up to 4-points- for the complete rational part of the Electroweak amplitudes. This provides a stringent check of our results and, as a by-product, an explicit test of the gauge invariance of the Four Dimensional Helicity regularization scheme in the complete Standard Model at 1-loop. The formulae presented in this paper provide the last missing piece for completely automatizing, in the framework of the OPP method, the 1-loop calculations in the SU(3) X SU(2) X U(1) Standard Model.Comment: Many thanks to Huasheng Shao for having recomputed, independently of us, all of the ${\rm R_2}$ effective vertices. Thanks to his help and by comparing with an independent computation we performed in a general $R_\xi$ gauge, we could fix, in the present version, the following formulae: the vertex $A l \bar l$ in Eq. (3.6), the vertex $Z \phi^+ \phi^-$ in Eq. (3.8), Eqs (3.16), (3.17) and (3.18

The SM and NLO multileg working group: Summary report

This report summarizes the activities of the SM and NLO Multileg Working Group of the Workshop "Physics at TeV Colliders", Les Houches, France 8-26 June, 2009.Comment: 169 pages, Report of the SM and NLO Multileg Working Group for the Workshop "Physics at TeV Colliders", Les Houches, France 8-26 June, 200

On the singular behaviour of scattering amplitudes in quantum field theory

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop-tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences

Counting to one: reducibility of one- and two-loop amplitudes at the integrand level

Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially, the reduction at the integrand level technique, improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one- and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams

Birth outcome in women with breast cancer

We investigated whether maternal breast cancer affects birth outcome in a nationwide cohort study of 695 births from 1973 to 2002 of women with breast cancer with respect to preterm birth, low birth weight at term, stillbirth and congenital abnormalities as well as mean birth weight, compared with the outcomes of 33 443 births from unaffected mothers. There was no excess risk of adverse birth outcome for the 216 newborns of women with breast cancer before pregnancy. Stratification by mother's treatment did not change the results. For 37 newborns of women diagnosed during pregnancy, the prevalence ratio (PR) of preterm birth was 8.1 (95% confidence interval (CI): 3.8–17). However, 10 of the 12 preterm deliveries among these women were elective early deliveries. Among 442 births of women diagnosed in the 2 years from time of delivery, the PR of preterm birth was 1.4 (95% CI: 1.0–2.0), and the PR of low birth weight at term for boys was 2.9 (95% CI: 1.3–6.3). Overall, our results are reassuring regarding the risks of adverse birth outcome for breast cancer patients