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Register a new userQCD in the delta-Regime
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The delta-regime of QCD is characterised by light quarks in a small spatial box, but a large extent in (Euclidean) time. In this setting a specific variant of chiral perturbation theory - the delta-expansion - applies, based on a quantum mechanical treatment of the quasi one-dimensional system. In particular, for vanishing quark masses one obtains a residual pion mass M_pi^R, which has been computed to the third order in the delta-expansion. A comparison with numerical measurements of this residual mass allows for a new determination of some Low Energy Constants, which appear in the chiral Lagrangian. We first review the attempts to simulate 2-flavour QCD directly in the delta-regime. This is very tedious, but results compatible with the predictions for M_pi^R have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the delta-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constant bar l_3.
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We summarize the results recently reported in Ref.[1] [A. Deuzeman, M.P. Lombardo, T. Nunes da Silva and E. Pallante,The bulk transition of QCD with twelve flavors and the role of improvement] for the SU(3) gauge theory with Nf=12 fundamental flavors, and we add some numerical evidence and theoretical discussion. In particular, we study the nature of the bulk transition that separates a chirally broken phase at strong coupling from a chirally restored phase at weak coupling. When a non-improved action is used, a rapid crossover is observed at small bare quark masses. Our results confirm a first order nature for this transition, in agreement with previous results we obtained using an improved action. As shown in Ref.[1], when improvement of the action is used, the transition is preceded by a second rapid crossover at weaker coupling and an exotic phase emerges, where chiral symmetry is not yet broken. This can be explained [1] by the non hermiticity of the improved lattice Transfer matrix, arising from the competition of nearest-neighbor and non-nearest neighbor interactions, the latter introduced by improvement and becoming increasingly relevant at strong coupling and coarse lattices. We further comment on how improvement may generally affect any lattice system at strong coupling, be it graphene or non abelian gauge theories inside or slightly below the conformal window.
Combining strong coupling and hopping expansion one can derive a dimensionally reduced effective theory of lattice QCD. This theory has a reduced sign problem, is amenable to analytic evaluation and was successfully used to study the cold and dense regime of QCD for sufficiently heavy quarks. We show results from the evaluation of the effective theory for arbitrary $N_c$ up to $kappa^4$. The inclusion of gauge corrections is also investigated. We find that the onset transition to finite baryon number density steepens with growing $N_c$ even for $T eq 0$. This suggests that in the large $N_c$ limit the onset transition is first order up to the deconfinement transition. Beyond the onset, the pressure is shown to scale as $p sim N_c$ through three orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature.
After combined character and hopping expansions and integration over the spatial gauge links, lattice QCD reduces to a three-dimensional $SU(3)$ Polyakov loop model with complicated interactions. A simple truncation of the effective theory is valid for heavy quarks on reasonably fine lattices and can be solved by linked cluster expansion in its effective couplings. This was used ealier to demonstrate the onset transition to baryon matter in the cold and dense regime. Repeating these studies for general $N_c$, one finds that for large $N_c$ the onset transition becomes first-order, and the pressure scales as $psim N_c$ through three consecutive orders in the hoppoing expansion. These features are consistent with the formal definition of quarkyonic matter given in the literature. We discuss the implications for $N_c=3$ and physical QCD.
We compute the isospin susceptibility in an effective O($n$) scalar field theory (in $d=4$ dimensions), to third order in chiral perturbation theory ($chi$PT) in the delta--regime using the quantum mechanical rotator picture. This is done in the presence of an additional coupling, involving a parameter $eta$, describing the effect of a small explicit symmetry breaking term (quark mass). For the chiral limit $eta=0$ we demonstrate consistency with our previous $chi$PT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using $chi$PT with dimensional regularization, we determine the $chi$PT expansion for $eta$ to third order. The behavior of the shape coefficients for long tube geometry obtained here might be of broader interest. The susceptibility calculated from the rotator approximation differs from the $chi$PT result in terms vanishing like $1/ell$ for $ell=L_t/L_stoinfty$. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant.
We present the first calculation on the $Delta$ axial-vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to $Delta$ axial transition coupling constant and $Delta$ axial charge.
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