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Register a new userTowards a Dual Representation of Lattice QCD
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Our knowledge about the QCD phase diagram at finite baryon chemical potential $mu_{B}$ is limited by the well known sign problem. The path integral measure, in the standard determinantal approach, becomes complex at finite $mu_{B}$ so that standard Monte Carlo techniques cannot be directly applied. As the sign problem is representation dependent, by a suitable choice of the fundamental degrees of freedom that parameterize the partition function, it can get mild enough so that reweighting techniques can be used. A successful formulation, capable to tame the sign problem, is known since decades in the limiting case $betato 0$, where performing the gauge integration first, gives rise to a dual formulation in terms of color singlets (MDP formulation). Going beyond the strong coupling limit represents a serious challenge as the gauge integrals involved in the computation are only partially known analytically and become strongly coupled for $beta>0$. We will present explict formulae for all the integral relevant for ${rm SU}(N)$ gauge theories discretised `a la Wilson, and will discuss how they can be used to obtain a positive dual formulation, valid for all $beta$, for pure Yang Mills theory.
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We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling $beta= 2N/g^{2}$. Our method makes use of the recently developed formalism to evaluate the ${rm SU}(N)$ $1-$link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call Decoupling Operator Indices (DOI). The method is not limited to any particular number of dimensions or gauge group ${rm U}(N)$, ${rm SU}(N)$. In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Worm-like algorithms. Higher order $beta$-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.
Progress by the Lattice Hadron Physics Collaboration in determining the baryon and meson resonance spectrum of QCD using Monte Carlo methods with space-time lattices is described. The extraction of excited-state energies necessitates the evaluation of correlation matrices of sets of operators, and the importance of extended three-quark operators to capture both the radial and orbital structures of baryons is emphasized. The use of both quark-field smearing and link-field smearing in the operators is essential for reducing the couplings of the operators to the high-frequency modes and for reducing statistical noise in the correlators. The extraction of nine energy levels in a given symmetry channel is demonstrated, and identifying the continuum spin quantum numbers of the levels is discussed.
We use a variational technique to study heavy glueballs on gauge configurations generated with 2+1 flavours of ASQTAD improved staggered fermions. The variational technique includes glueball scattering states. The measurements were made using 2150 configurations at 0.092 fm with a pion mass of 360 MeV. We report masses for 10 glueball states. We discuss the prospects for unquenched lattice QCD calculations of the oddballs.
An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a $24^3 times 48$ lattice volume with $m_piapprox 900$ MeV by isolating various spectra of the $pipi$ system with isospin-2 including a range of total momenta and irreps. By applying the Luscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $pipi$ scattering with isospin-2 are extracted from the spectra.
We report on the first steps of an ongoing project to add gauge observables and gauge corrections to the well-studied strong coupling limit of staggered lattice QCD, which has been shown earlier to be amenable to numerical simulations by the worm algorithm in the chiral limit and at finite density. Here we show how to evaluate the expectation value of the Polyakov loop in the framework of the strong coupling limit at finite temperature, allowing to study confinement properties along with those of chiral symmetry breaking. We find the Polyakov loop to rise smoothly, thus signalling deconfinement. The non-analytic nature of the chiral phase transition is reflected in the derivative of the Polyakov loop. We also discuss how to construct an effective theory for non-zero lattice coupling, which is valid to $O(beta)$.
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