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Matter-Antimatter Coexistence Method for Finite Density QCD toward a Solution of the Sign Problem

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Document pages: 8 pages

Abstract: Toward the lattice QCD calculation at finite density, we propose “matter-antimatter coexistence method”, where matter and anti-matter systems are prepared on two parallel R4-sheets in five-dimensional Euclidean space-time. We put a matter system M with a chemical potential μ∈C on a R4-sheet, and also put an anti-matter system withon the other R4-sheet shifted in the fifth direction. Between the gauge variables  in M and in, we introduce a correlation termwith a real parameter λ. In one limit of , a strong constraint is realized, and therefore the total fermionic determinant becomes real and non-negative, due to the cancellation of the phase factors in M and , although this system resembles QCD with an isospin chemical potential. In another limit of , this system goes to two separated ordinary QCD systems with the chemical potential of μ and . For a given finite-volume lattice, if one takes an enough large value of λ, is realized and phase cancellation approximately occurs between two fermionic determinants in M and, which suppresses the sign problem and is expected to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part M. The physical quantities in finite density QCD are expected to be estimated by the calculations with gradually decreasing λ and the extrapolation to λ=0. We also consider more sophisticated improvement of this method using an irrelevant-type correlation.

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