Non-relativistic physics is often associated with atomic physics and low-energy phenomena of the strong interactions between nuclei and quarks. In this review we cover three topics in contemporary high-energy physics at or close to the TeV scale, whe
re non-relativistic dynamics plays an important if not defining role. We first discuss in detail the third-order corrections to top-quark pair production in electron-positron collisions in the threshold region, which plays a major role at a future high-energy e+ e- collider. Threshold effects are also relevant in the production of heavy particles in hadronic collisions, where in addition to the Coulomb force soft gluon radiation contributes to enhanced quantum corrections. We review the joint resummation of non-relativistic and soft gluon effects for pair production of top quarks and supersymmetric particles to next-to-next-to-leading logarithmic accuracy. The third topic deals with pair annihilation of dark matter particles within the framework of the Minimal Supersymmetric Standard Model. Here the electroweak Yukawa force generated by the exchange of gauge and Higgs bosons can cause large Sommerfeld enhancements of the annihilation cross section in some parameter regions.
The combination of collinear factorization with effective field theory originally developed for soft interactions of heavy quarks provides the foundations of the theory of exclusive and semi-inclusive B decays. In this article I summarize some of the
later conceptual developments of the so-called QCD factorization approach that make use of soft-collinear effective theory. Then I discuss the status and results of the calculation of the hard-scattering functions at the next order, and review very briefly some of the phenomenology, covering aspects of charmless, electroweak penguin and radiative (semi-leptonic) decays.
Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective field theory
for unstable particles, based on the hierarchy of scales between the mass, M, and the width,Gamma, of the unstable particle that allows resonant processes to be systematically expanded in powers of the coupling alpha and Gamma/M, thereby providing gauge-invariant approximations at every order. I illustrate the method with the next-to-leading order line-shape of a scalar resonance in an abelian gauge-Yukawa model, and results on NLO and dominant NNLO corrections to (resonant and non-resonant) pair production of W-bosons and top quarks.
We describe the computation of the one-loop muon anomalous magnetic moment and radiative penguin transitions in the minimal and custodially protected Randall-Sundrum model. A fully five-dimensional (5D) framework is employed to match the 5D theory on
to the Standard Model extended by dimension-six operators. The additional contribution to the anomalous magnetic moment from the gauge-boson exchange contributions is Delta a_mu approx 8.8 (27.2) x 10^(-11) x (1 TeV/T)^2, where the first (second) number refers to the minimal (custodially-protected) model. Here $1/T$ denotes the location of the TeV brane in conformal coordinates, and is related to the mass of the lowest gauge-boson KK excitation by M_KK approx 2.35 T. We also determine the Higgs-exchange contribution, which depends on the 5D Yukawa structure and the precise interpretation of the localisation of the Higgs field near or at the TeV brane.
Pair production of massive coloured particles in hadron collisions is accompanied by potentially large radiative corrections related to the suppression of soft gluon emission and enhanced Coulomb exchange near the production threshold. We recently de
veloped a framework to sum both series of corrections for the partonic cross section using soft-collinear and non-relativistic effective theory. If it can be argued that the resummed cross section approximates the complete result over a significant kinematic range, an improvement of the hadronic cross section results, even when the production is not kinematically constrained to the threshold. This is discussed here for the case of top quark production.
We consider tan(beta)-enhanced quantum effects in the minimal supersymmetric standard model (MSSM) including those from the Higgs sector. To this end, we match the MSSM to an effective two-Higgs doublet model (2HDM), assuming that all SUSY particles
are heavy, and calculate the coefficients of the operators that vanish or are suppressed in the MSSM at tree-level. Our result clarifies the dependence of the large-tan(beta) resummation on the renormalization convention for tan(beta), and provides analytic expressions for the Yukawa and trilinear Higgs interactions. The numerical effect is analyzed by means of a parameter scan, and we find that the Higgs-sector effects, where present, are typically larger than those from the wrong-Higgs Yukawa couplings in the 2HDM.
We demonstrate that exclusive B decays to P-wave charmonium factorize in the non-relativistic limit provided that colour-octet contributions are taken into account, and estimate the branching fractions. Although there are very large uncertainties, we
find reasonable parameter choices, where the main features of the data -- large corrections to (naive) factorization and suppression of the chi_{c2} and h_c final states -- are reproduced though the suppression of chi_{c2} is not as strong as seen in the data. Our results also provide an example, where an endpoint divergence in hard spectator-scattering factorizes and is absorbed into colour-octet operator matrix elements.
We calculate the parametrically dominant next-to-next-to-leading order corrections to four-fermion production e^- e^+ -> mu^- nubar_mu u dbar + X at centre-of-mass energies near the W-pair production threshold employing the method of unstable-particl
e effective theory. In total the correction is small, leading to a shift of 3 MeV in the W-mass measurement. We also discuss the implementation of realistic cuts and provide a result for the interference of single-Coulomb and soft radiative corrections that can easily be extended to include an arbitrary number of Coulomb photons.
We compute the third-order correction to the heavy-quark current correlation function due to the emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QCD sum rules.
We compute the third-order correction to the S-wave quarkonium wave functions |psi_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultras
oft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.
