Lorentz Invariant Baryon CHPT

Using the example of the elastic $\pi N$-amplitude, we discuss the low energy expansion of QCD amplitudes in the sector with baryon number one. We show that the chiral expansion of these amplitudes breaks down in certain regions of phase space and present a framework which leads to a coherent description throughout the low energy region, while keeping Lorentz and chiral invariance manifest at every stage of the calculation. We explain how to construct a representation of the pion nucleon scattering amplitude in terms of functions of a single variable, which is valid to $O(q^4)$ and properly accounts for the $\pi\pi$- and $\pi N$-cuts required by unitarity.Comment: Latex, 12 pages. Plenary talk given at "Chiral Dynamics 2000: Theory and Experiment", Newport News, USA, 17-22 July 200

Infrared singularities of QCD amplitudes with massive partons

A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for which some general properties are derived. This explains observations recently made by Mitov et al. in terms of symmetry arguments.Comment: 7 pages, 1 figure; v2: minor changes, reference added; v3: note added, correcting some statements regarding F1 and f2 in light of the recent calculations in [45,46], references update

Two-loop QED corrections to Bhabha scattering

We obtain a simple relation between massless and massive scattering amplitudes in gauge theories in the limit where all kinematic invariants are large compared to particle masses. We use this relation to derive the two-loop QED corrections to large-angle Bhabha scattering.Comment: 15 pages; minor changes; version to appear in JHE

Highly Sensitive On-Chip Magnetometer with Saturable Absorbers in Two-Color Microcavities

Interacting resonators can lead to strong non-linearities but the details can be complicated to predict. In this work, we study the non-linearities introduced by two nested microcavities that interact with nitrogen vacancy centers in a diamond waveguide. Each cavity has differently designed resonance; one in the green and one in the infrared. The magnetic-field dependence of the nitrogen vacancy center absorption rates on the green and the recently observed infrared transitions allows us to propose a scalable on-chip magnetometer that combines high magnetic-field sensitivity and micrometer spatial resolution. By investigating the system behaviors over several intrinsic and extrinsic parameters, we explain the main non-linearities induced by the NV centers and enhanced by the cavities. We finally show that the cavities can improve the magnetic-field sensitivity by up to two orders of magnitudes

The self-energy of improved staggered quarks

We calculate the fermion self-energy at O(alpha_s) for the Symanzik improved staggered fermion action used in recent lattice simulations by the MILC collaboration. We demonstrate that the algebraic approach to lattice perturbation theory, suggested by us recently, is a powerful tool also for improved lattice actions.Comment: 6 page

Continuum methods in lattice perturbation theory

We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Using integration-by-parts relations all of these can be expressed in terms of a small number of master integrals. Four master integrals are needed for bosonic one loop integrals, sixteen in QCD with Wilson or staggered fermions.Comment: 5 pages. Talk presented at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, 8-13 Sep 200

On the Normality of Numbers to Different Bases

We prove independence of normality to different bases We show that the set of real numbers that are normal to some base is Sigma^0_4 complete in the Borel hierarchy of subsets of real numbers. This was an open problem, initiated by Alexander Kechris, and conjectured by Ditzen 20 years ago