Complex Langevin dynamics and zeroes of the fermion determinant

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity

Initial State Parton Showers Beyond Leading Order

We derive a new method for initial-state collinear showering in Monte-Carlo event generators which is based on the use of unintegrated parton correlation functions. Combined with a previously derived method for final-state showering, the method solves the problem of treating both the hard scattering and the evolution kernels to be used in arbitrarily non-leading order. Although we only treat collinear showering, so that further extensions are needed for QCD, we have discovered several new results: (1) It is better to generate exact parton kinematics in the hard scattering rather than with the subsequent parton showering, and similarly at each step of the showering. (2) Parton showering is then done conditionally on the exact energy-momentum of the initiating parton. (3) We obtain a factorization for structure functions in terms of parton correlation functions so that parton kinematics can be treated exactly from the beginning. (4) We obtain two factorization properties for parton correlation functions, one in terms of ordinary parton densities and one, suitable for event generation, in terms of parton correlation functions themselves.Comment: 45 page