Electroweak radiative corrections to single top production

Fortran subroutines to calculate helicity amplitudes with massive spin-3/2 particles, such as massive gravitinos, which couple to the standard model and supersymmetric particles via the supercurrent, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external gravitinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the gauge invariance of the helicity amplitudes.     

K^{-} nuclear quasi-bound states in a chirally motivated coupled-channel approach

K ^?? nuclear optical potentials are constructed from in-medium ${\bar K}N$ scattering amplitudes within a chirally motivated coupled-channel model. The strong energy and density dependence of the scattering amplitudes at and below threshold leads to K ^?? potential depths ?Re $V_{K^-}(\rho_0) \approx 80 -100$ ?MeV. Self consistent calculations of K ^?? nuclear quasi-bound states are discussed.     

General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in $$\mathcal {}$$-cut representation

In this paper, we give the general expressions for a special series of tree amplitudes of the Yang–Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive helicity gluons. With special helicity choices, we use the spinor helicity formalism to express these n-point amplitudes in compact forms, and find a clever way to use the BCFW recursion relations to prove the results. Then these amplitudes are used to form the complete 1-loop all-plus integrand with any number of gluons, expressed in the \(\mathcal {Q}\)-cut representation.     

Automated one-loop calculations with GoSam

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the?loop.     

Resonance Conversion as the Predominant Decay Mode of ^{229m}Th

Calculations performed within the advanced MCDF method show that the probability of decay of the 3.5-eV level of $^{229m}$ Th through the resonance electronic bridges exceeds the direct radiative nuclear decay width by a factor of around $5\cdot 10^3$ . Experimental consequences for detection of the delayed soft photons or $\alpha$ particles from the decay of the isomer are discussed.     

The\overline {MS} and on-shell renormalization schemes in the analysis of neutrino scattering experiments

The relationship between the \(\overline {MS} \) and on-shell renormalization schemes is discussed and the correction, for finite top quark mass, to the formula connecting sin² θ _W =1?M _W ² /M _Z ² and sin² \(\widehat\theta _W (M_W )\) is given. A table is presented to allow easy conversion. The relative sensitivity, to the top quark and Higgs masses, of the two definitions, when extracted from semi-leptonic neutrino scattering experiments is considered.     

Regeneration of arbitrary coherent neutral kaon states: A new method for measuring theK^0 - \bar K^0 forward scattering amplitudeforward scattering amplitude

We propose a new method for measuring the difference $\Delta f = f(0) - \bar f(0)$ of the forward scattering amplitudes for K⁰ and $\bar K^0 $ by use of decay rates of initially pure strangeness states after passage through a regenerator. The phenomenology of coherent kaon regeneration is presented for arbitrary mixtures of K⁰ and $\bar K^0 $ .     

Forward {{\bar p} d} Elastic Scattering and Total Spin-Dependent pd Cross Sections

Glauber theory is applied to ${{\bar p} d}$ scattering at beam energies 20?C300?MeV using the ${{\bar N} N}$ amplitudes of the Jülich models. The available data for unpolarized differential and total cross section are well described within this approach. The polarized total ${{\bar p} d}$ cross sections are calculated within the single-scattering approximation using the optical theorem.     

The Kaon-Few-Nucleon Levels and Lifetimes Calculated by a Variational Method

The search for nuclear states of ${\overline{\rm K}}$ mesons is presented and the main uncertainties: off-shell extrapolation of meson-nucleon scattering amplitudes, behavior of hadronic resonances in nuclei and extrapolation to high density nuclear regions are discussed. A two step method to perform variational calculations in the ${\overline{\rm K}}$ -few-nucleon systems is suggested.     

Extreme-ultraviolet metrology at SURF III

Inelastic X-ray scattering (IXS) is a general experimental technique for studying lattice and electronic excitations, which has undergone rapid development following the advent of the third generation synchrotron radiation facilities. X-ray Raman scattering (XRS) is inelastic scattering of X-rays due to the excitation associated with bound electrons in an atom. Its very small scattering cross-section is compensated for by a high-flux beam generated from a strong photon source. Instrumentation for IXS is now highly sophisticated, and has been applied to study a broad range of condensed matter systems [1 Schülke, e.g., W., ed. 2007. “We would like to limit our discussion to electronic excitations. For a comprehensive survey in the field, see”. In Electron Dynamics by Inelastic X-ray Scattering, New York: Oxford University Press.  [Google Scholar]].     

The isosinglet and isovector ππ scattering lengths

The ππ scattering lengthsa ₀ ⁰ ,a ₂ ⁰ anda ₁ ¹ are determined from πN elastic scattering data using interior dispersion relations. The importance of the Born-Term contribution, via unitarity, to the imaginary part of all amplitudes is discussed. Proper consideration of these contributions and the analytic properties of the amplitudes near threshold allows us to obtain from the recent πN partial wave analysis of Pietarinen the following scattering lengths $$\begin{gathered} \mu a_0^0 = 0.27 \pm 0.03,\mu ^3 a_1^1 = 0.032 \pm 0.005, \hfill \\ \mu ^5 a_2^0 = 0.002 \pm 0.001. \hfill \\ \end{gathered} $$      

Thepp —p \bar p difference and the behaviour of phases at high energies

Predictions based on axiomatic field theory are obtained from the assumption that the difference between thepp and thep \(\bar p\) elastic scattering observed at the CERN ISR is caused by an “odderon-like” term in the scattering amplitude. A wide class of amplitudes violating the Pomeranchuk relation is considered. Contrary to common opinion, severe restrictions on the high-energy behaviour of the phase of the crossing-odd amplitude are shown to follow for the whole class. Less pronounced but still visible consequences follow for the phases of thepp andp \(\bar p\) amplitudes separately. We derive the corresponding high-energy bounds and correlations using the general frame of analyticity, crossing symmetry and unitarity. As a special case, the maximal odderon amplitude is discussed.     

Test of 600 and 750 MeV NN matrix on elastic scattering Glauber model calculations

The 600 and 750 MeV proton nucleus elastic scattering cross section and polarization calculations have been performed in the framework of the Glauber model to test the pp and pn scattering amplitudes deduced from a phase shift analysis by Bystricky, Lechanoine and Lehar. It is well known that up to now we do not possess a non-phenomenological NN scattering matrix at intermediate energies. However proton-nucleus scattering analyses are used to extract information about short range correlations¹), Δ resonance²) or pion condensation presences)... etc. Most scattering calculations made at these energies have been done with phenomenological NN amplitudes having a gaussian q-dependence $$A(q) = \frac{{k\sigma }}{{4\pi }}(\alpha + i) e^{ - \beta ^2 q^2 /2} $$ and $$C(q) = \frac{{k\sigma }}{{4\pi }}iq(\alpha + i) D_e - \beta ^2 q^2 /2$$ K andσ being respectively the projectile momentum and the total pN total cross section. The parameters α, β and D are badly known and are adjusted by fitting some specific reactions as p+⁴He elastic scattering⁴). Even when these amplitudes provide good fits to the data, our understanding of the dynamics of the scattering remains obscure.     

Global study of electron–quark unparticle interactions

We perform a global fit on parity-conserving electron–quark interactions via spin-1 unparticle exchange. Besides the peculiar features of unparticle exchange due to non-integral values for the scaling dimension \(d_{\mathcal {U}}\) and a non-trivial phase factor \(\exp (-id_{\mathcal {U}}\pi)\) associated with a time-like unparticle propagator, the energy dependence of the unparticle contributions in the scattering amplitudes are also taken into account. The high energy data sets taken into consideration in our analysis are from (1) deep inelastic scattering at high Q ² from ZEUS and H1, (2) Drell–Yan production at Run II of CDF and DØ, and (3) e ⁺ e ^?→ hadrons at LEPII. The hadronic data at LEPII by itself indicated a 3–4 sigma preference of new physics over the Standard Model. However, when all data sets are combined, no preference for unparticle effects can be given. We thus deduce an improved 95% confidence level limit on the unparticle energy scale \(\varLambda_{\mathcal {U}}\).     

Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on \({\mathbb{R}^n}\), with magnetic and potential terms. In particular, for each classical path γ connecting points q ₀ and q ₁ in time t, we define a formal power series V _γ (t, q ₀, q ₁) in \({\hbar}\), given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V _γ ) satisfies Schrödinger’s equation, and explain in what sense the \({t \to 0}\) limit approaches the δ distribution. As such, our construction gives explicitly the full \({\hbar\to 0}\) asymptotics of the fundamental solution to Schrödinger’s equation in terms of solutions to the corresponding classical system. These results justify the heuristic expansion of Feynman’s path integral in diagrams.     

Harmonic Oscillator Trap and the Phase-Shift Approximation

The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts \(\delta \) of the particles by a formula first published by Busch et al. It is here used to find an expression for the shift of the energy levels, caused by the interaction, rather than the perturbed spectrum itself. In the limit of high energy (large quantum number \(n\) of the H.O.) this shift (in H.O. units) is shown to be given by \(\Delta =-2\frac{\delta }{\pi }\) , also exact in the limit of infinite scattering length ( \(\delta =\pm \frac{\pi }{2}\) ) in which case \(\Delta =\mp 1\) . Numerical investigation shows that this expression otherwise differs from the exact result of Busch et al., by less than \(\frac{1}{2}\,\%\) except for \(n=0\) when it can be as large as \(\approx \) 2.5 %. This result for the energy-shift is well known from another exactly solvable model, namely that of two particles interacting in a spherical infinite square-well trap (or box) of radius \(R\) in the limit \(R\rightarrow \infty \) , and/or in the limit of large energy. It is in solid state physics referred to as Fumi’s theorem. It can be (and has been) used in (infinite) nuclear matter calculations to calculate the two-body effective interaction in situations where in-medium effects can be neglected. It is in this context referred to as the phase-shift approximation a term also used throughout this report.     

Scattering amplitudes with massive fermions using BCFW recursion

We study the QCD scattering amplitudes for and where q is a massive fermion. Using a particular choice of massive fermion spinor we derive compact expressions for the partial spin amplitudes for the 2→2 process. We then investigate the corresponding 2→3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we present new expressions, but we were unable to treat the helicity-flip amplitudes recursively, except for the case where all the gluon helicities are the same. We therefore evaluate the remaining partial amplitudes using standard Feynman diagram techniques.     

Three applications of a bonus relation for gravity amplitudes

Arkani-Hamed et al. have recently shown that all tree-level scattering amplitudes in maximal supergravity exhibit exceptionally soft behavior when two supermomenta are taken to infinity in a particular complex direction, and that this behavior implies new non-trivial relations amongst amplitudes in addition to the well-known on-shell recursion relations. We consider the application of these new ‘bonus relations’ to MHV amplitudes, showing that they can be used quite generally to relate (n−2)!$(n-2)!$-term formulas typically obtained from recursion relations to (n−3)!$(n-3)!$-term formulas related to the original BGK conjecture. Specifically we provide (1) a direct proof of a formula presented by Elvang and Freedman, (2) a new formula based on one due to Bedford et al., and (3) an alternate proof of a formula recently obtained by Mason and Skinner. Our results also provide the first direct proof that the conjectured BGK formula, only very recently proven via completely different methods, satisfies the on-shell recursion.     

Dependence of electroweak parameters on the definition of the top-quark mass

The QCD corrections to electroweak parameters depend on the renormalization scheme and scales used to define the top-quark mass. We analyze these dependences for theW-boson mass predicted via Δr to ${\mathcal{O}}(\alpha \alpha _s )$ and ${\mathcal{O}}(\alpha \alpha _s^2 )$ in the on-shell and $\overline {MS} $ schemes. These variations provide us with a hint on the magnitude of the unknown higher-order QCD effects and contribute to the theoretical error of the prediction.     

Pomerons and BCFW recursion relations for strings on D-branes

We derive pomeron vertex operators for bosonic strings and superstrings in the presence of D-branes. We demonstrate how they can be used in order to compute the Regge behavior of string amplitudes on D-branes and the amplitude of ultrarelativistic D-brane scattering. After a lightning review of the BCFW method, we proceed in a classification of the various BCFW shifts possible in a field/string theory in the presence of defects/D-branes. The BCFW shifts present several novel features, such as the possibility of performing single particle momentum shifts, due to the breaking of momentum conservation in the directions normal to the defect. Using the pomeron vertices we show that superstring amplitudes on the disc involving both open and closed strings should obey BCFW recursion relations. As a particular example, we analyze explicitly the case of 1→1$1\to 1$ scattering of level one closed string states off a D-brane. Finally, we investigate whether the eikonal Regge regime conjecture holds in the presence of D-branes.