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Register a new userLattice field theory applications in high energy physics
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Steven Gottlieb
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Lattice gauge theory was formulated by Kenneth Wilson in 1974. In the ensuing decades, improvements in actions, algorithms, and computers have enabled tremendous progress in QCD, to the point where lattice calculations can yield sub-percent level precision for some quantities. Beyond QCD, lattice methods are being used to explore possible beyond the standard model (BSM) theories of dynamical symmetry breaking and supersymmetry. We survey progress in extracting information about the parameters of the standard model by confronting lattice calculations with experimental results and searching for evidence of BSM effects.
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This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study (Snowmass). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Lattice calculations using the framework of effective field theory have been applied to a wide range few-body and many-body systems. One of the challenges of these calculations is to remove systematic errors arising from the nonzero lattice spacing. Fortunately, the lattice improvement program pioneered by Symanzik provides a formalism for doing this. While lattice improvement has already been utilized in lattice effective field theory calculations, the effectiveness of the improvement program has not been systematically benchmarked. In this work we use lattice improvement to remove lattice errors for a one-dimensional system of bosons with zero-range interactions. We construct the improved lattice action up to next-to-next-to-leading order and verify that the remaining errors scale as the fourth power of the lattice spacing for observables involving as many as five particles. Our results provide a guide for increasing the accuracy of future calculations in lattice effective field theory with improved lattice actions.
CKM-unitarity, direct and indirect CP-violation and the Delta I=1/2 rule in full lattice QCD are the focus of this talk. To this end I will discuss and compare recent lattice results for leptonic, semi-leptonic and non-leptonic decays of the kaon and neutral kaon mixing and I will motivate current best estimates f_K/f_pi=1.198(10), f_+^{Kpi}(0)=0.964(5) and hat{B}_K=0.720(39). Moreover new theoretical advances that will improve the quality of these computations in the future will be discussed.
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree of freedom on the lattice corresponds to $2^d$ degrees of freedom in the continuum, but all these doublers have (in the case of fermions) the same chirality and can be either identified, thus removing the degeneracy, or, in some theories with extended supersymmetry, identified with different members of the same supermultiplet. 2) The derivative operator, defined on the lattice as a suitable periodic function of the lattice momentum, is an addittive and conserved quantity, thus assuring that the Leibnitz rule is satisfied. This implies that the product of two fields on the lattice is replaced by a non-local star product which is however in general non-associative. Associativity of the star product poses strong restrictions on the form of the lattice derivative operator (which becomes the inverse gudermannian function of the lattice momentum) and has the consequence that the degrees of freedom of the lattice theory and of the continuum theory are in one-to-one correspondence, so that the two theories are eventually equivalent. Regularization of the ultraviolet divergences on the lattice is not associated to the lattice spacing, which does not act as a regulator, but may be obtained by a one parameter deformation of the lattice derivative, thus preserving the lattice structure even in the limit of infinite momentum cutoff. However this regularization breaks gauge invariance and a gauge invariant regularization within the lattice formulation is still lacking.
We review recent lattice QCD activities with emphasis on the impact on nuclear physics. In particular, the progress toward the determination of nuclear and baryonic forces (potentials) using Nambu-Bethe-Salpeter (NBS) wave functions is presented. We discuss major challenges for multi-baryon systems on the lattice: (i) signal to noise issue and (ii) computational cost issue. We argue that the former issue can be avoided by extracting energy-independent (non-local) potentials from time-dependent NBS wave functions without relying on the ground state saturation, and the latter cost is drastically reduced by developing a novel unified contraction algorithm. The lattice QCD results for nuclear forces, hyperon forces and three-nucleon forces are presented, and physical insights are discussed. Comparison to results from the traditional Lueschers method is given, and open issues to be resolved are addressed as well.
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