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

Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context