Complex contour deformations of the path integral have been shown to mitigate sign problems associated with non-zero chemical potential and real-time evolution in lattice field theories. This talk details their application to instead address statistical noise in lattice calculations. Contour deformations allow redefining observables without affecting their expectation value or modifying the Monte Carlo sampling weights; the observable variance can then be optimized to maximize the signal-to-noise ratio. We define families of contour deformations for SU(N) variables and demonstrate exponential improvements in the signal-to-noise ratio of Wilson loops in proof-of-principle applications to U(1) and SU(N) lattice gauge theories.
I will review the status of theoretical predictions for processes such as B->K(*)mumu and B_s->phi mumu. Emphasis will be put on recent progress in the description of so-called non-local contributions to these processes. As part of the review, I will strive to set the stage in a pedagogical way.
We formulate an S-matrix theory in which finite-size localisation effects of the particle interactions involved in a scattering process are consistently taken into account. In the limit of an infinite spread in the localisation of all interactions, the S-matrix assumes its standard form. To better understand the significance of the emerging quantum phenomena in this formalism, we consider a solvable field-theoretic model with spatial Gaussian spreads at the interaction vertices. This solvable model, enables accurate descriptions of detection regions that are either close to or far from the source. In close analogy with light diffraction in classical optics, we call these two regions near-field and far-field zones, or the Fresnel and Fraunhofer regions. We revisit the question whether mixed mediators produce an oscillating pattern if their detection occurs in the Fresnel region. Besides corroborating certain earlier findings of the S-matrix amplitude in the forward Fresnel and Fraunhofer regimes, we observe several novel features with respect to its angular dependence which have not been accounted before in the literature. In particular, we obtain a 'quantum obliquity factor' that suppresses particle propagation in the backwards direction, thereby providing an explicit quantum field-theoretic description for its origin in diffractive optics. Present and future colliders, as well as both short and long baseline neutrino experiments, would greatly benefit from the many predictions that can be offered from such a holistic S-matrix theory.
I will advocate a phase of gauge theories where the long distance scale symmetry is spontaneously broken by the quark condensate. This phase allows for massive hadrons and requires a dilaton, a genuine goldstone boson, which restores the Ward identities. I will discuss this on the example of the gravitational form factors. I will discuss the response of this system to explicit scale breaking of quark masses. At the end I will speculate that QCD itself and the Higgs sector could be of this type.