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arXiv2011

Non-perturbative proton stability

Proton decay is a generic prediction of GUT models and is therefore an important channel to detect the existence of unification or to set limits on GUT models. Current bounds on the proton lifetime are around 10^33 years, which sets stringent limits on the GUT scale. These limits are obtained under `reasonable' assumptions about the size of the hadronic matrix elements. In this paper we present a non-perturbative calculation of the hadronic matrix elements within the chiral bag model of the proton. We argue that there is an exponential suppression of the matrix elements, due to non-perturbative QCD, that stifles proton decay by orders of magnitude -- potentially O(10^-10). This suppression is present for small quark masses and is due to the chiral symmetry breaking of QCD. Such a suppression has clear implications for GUT models and could resuscitate several scenarios.

hep-ph↗
arXiv2012

Scaling properties of Wilson loops pierced by P-vortices

P-vortices, in an SU(N) lattice gauge theory, are excitations on the center-projected Z(N) lattice. We study the ratio of expectation values of SU(2) Wilson loops, on the unprojected lattice, linked to a single P-vortex, to that of Wilson loops which are not linked to any P-vortices. When these ratios are plotted versus loop area in physical units, for a range of lattice couplings, it is found that the points fall approximately on a single curve, consistent with scaling. We also find that the ratios are rather insensitive to the point where the minimal area of the loop is pierced by the P-vortex.

hep-lat↗
arXiv2012

Finite size scaling in minimal walking technicolor

We compare observables to the finite size scaling hypothesis in SU(2) lattice gauge theory with two Dirac fermions in the adjoint representation. The fits that we obtain yield an estimate of the anomalous mass dimension that is consistent with four loop perturbation theory: $γ= 0.51 \pm 0.16$, with the error due to systematic uncertainties in the finite size scaling analysis. The result is somewhat larger than one Schrödinger functional study (by 1.3$σ$) but consistent with another.

hep-lat↗
arXiv2012

The Microscopic Twisted Mass Dirac Spectrum

The microscopic spectral density for lattice QCD with two flavors and maximally twisted mass is computed. The results are given for fixed index of the Dirac operator and include the leading order $a^2$ corrections to the chiral Lagrangian due to the discretization errors. The computation is carried out within the framework of Wilson chiral perturbation theory.

hep-lat↗
arXiv2010

Deconfinement in Yang-Mills theory through toroidal compactification with deformation

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \times S1_L \times S1_β. At large N, fixed-L, and arbitrary β, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of β, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.

hep-th↗
arXiv2012

The $Δ_{mix}$ parameter in the overlap on domain-wall mixed action

A direct calculation of the mixed-action parameter $Δ_{mix}$ with valence overlap fermions on a domain-wall fermion sea is presented. The calculation is performed on four ensembles of the 2+1-flavor domain-wall gauge configurations: $24^3 \times 64$ ($a m_l= 0.005$, $a=0.114\fm$) and $32^3 \times 64$ ($a m_l = 0.004, 0.006, 0.008$, $a=0.085\fm$). For pion masses close to $300\MeV$ we find \hbox{$Δ_{mix}=0.030(6)\GeV^4$} at $a=0.114\fm$ and $Δ_{mix}=0.033(12)\GeV^4$ at $a=0.085\fm$. The results are quite independent of the lattice spacing and they are significantly smaller than the results for valence domain-wall fermions on Asqtad sea or those of valence overlap fermions on clover sea. Combining the results extracted from these two ensembles, we get $Δ_{mix}=0.030(6)(5)\GeV^4$, where the first error is statistical and the second is the systematic error associated with the fitting method.

hep-lat↗
arXiv2012

Renormalization constants of local operators for Wilson type improved fermions

Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level and up to second order in the lattice spacing, is performed for a fermion action, which includes the clover term and the twisted mass parameter yielding results that are applicable for unimproved Wilson fermions, as well as for improved clover and twisted mass fermions. We consider ten variants of the Symanzik improved gauge action corresponding to ten different values of the plaquette coefficients. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations are performed for pion masses in the range of 480 MeV to 260 MeV and at three values of the lattice spacing, a, corresponding to beta=3.9, 4.05, 4.20. For each renormalization factor computed non-perturbatively we subtract its perturbative O(a^2) terms so that we eliminate part of the cut-off artifacts. The renormalization constants are converted to MS-bar at a scale of mu=2 GeV. The perturbative results depend on a large number of parameters and are made easily accessible to the reader by including them in the distribution package of this paper, as a Mathematica input file.

hep-lat↗
arXiv2012

Baryon Number Dirac Spectrum in QCD

The relation between the baryon number in QCD at nonzero chemical potential and the spectral density of the baryon number Dirac operator, $γ_0(D+m)$, is examined. We show that extreme oscillations of the spectral density, caused by the QCD sign problem, are essential for the formation of the average baryon number when $μ>m_π/2$. We compute the oscillating region of the spectral density using chiral perturbation theory. The extreme oscillations have a microscopic period and are resolved using random matrix theory.

hep-lat↗
arXiv2012

Alternate 1/N_c Expansions and SU(3) Breaking from Baryon Lattice Results

A combined expansion in the number of QCD colors 1/N_c and SU(3) flavor breaking parameter epsilon has long been known to provide an excellent accounting for the mass spectrum of the lightest spin-1/2, 3/2 baryons when the quarks are taken to transform under the fundamental SU(N_c) representation, and in the final step N_c \to 3 and epsilon is set to its physical value ~0.3. Subsequent work shows that placing quarks in the two-index antisymmetric SU(N_c) representation leads to quantitatively equally successful mass relations. Recent lattice simulations allow for varying the value of epsilon and confirm the robustness of the original 1/N_c relations. In this paper we show that the same conclusion holds for the antisymmetric quarks, and demonstrate that the mass relations also hold under alternate prescriptions for identifying physical baryons with particular members of the large N_c multiplets.

hep-ph↗
arXiv2012

Multiple-channel generalization of Lellouch-Luscher formula

We generalize the Lellouch-Luscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly-coupled decay channels into two scalar particles. This is a necessary first step on the way to a lattice QCD calculation of weak decay rates for processes such as D -> pi pi and D -> KK. We also present a field theoretic derivation of the generalization of Luscher's finite volume quantization condition to multiple two-particle channels. We give fully explicit results for the case of two channels, including a form of the generalized Lellouch-Luscher formula expressed in terms of derivatives of the energies of finite volume states with respect to the box size. Our results hold for arbitrary total momentum and for degenerate or non-degenerate particles.

hep-lat↗
arXiv2012

Solutions to sign problems in lattice Yukawa models

We prove that sign problems in the traditional approach to some lattice Yukawa models can be completely solved when the fermions are formulated using fermion bags and the bosons are formulated in the worldline representation. We prove this within the context of two examples of three dimensional models, symmetric under $U_L(1) \times U_R(1) \times Z_2 ({Parity})$ transformations, one involving staggered fermions and the other involving Wilson fermions. We argue that these models have interesting quantum phase transitions that can now be studied using Monte Carlo methods.

hep-lat↗
arXiv2012

Chiral symmetry restoration and deconfinement in QCD at finite temperature

The light-quark correlator in the axial-vector channel is used, in conjunction with finite energy QCD sum rules at finite temperature, in order to (a) establish a relation between chiral-symmetry restoration and deconfinement, and (b) determine the temperature behavior of the $a_1(1260)$ width and coupling. Results indicate that deconfinement takes place at a slightly lower temperature than chiral-symmetry restoration, although this difference is not significant given the accuracy of the method. The behaviour of the $a_1(1260)$ parameters is consistent with quark-gluon deconfinement, as the width grows and the coupling decreases with increasing temperature.

hep-ph↗
arXiv2012

Lattice baryons in the 1/N expansion

Results are presented for hadron spectroscopy with gauge groups SU(N) with N=3, 5, 7. Calculations use the quenched approximation. Lattice spacings are matched using the static potential. Meson spectra show independence on N and vacuum-to-hadron matrix elements scale as the square root of N. The baryon spectrum shows the excitation levels of a rigid rotor.

hep-lat↗
arXiv2012

Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model

We calculate the quadratic fluctuations of net baryon number, electric charge and strangeness as well as correlations among these conserved charges in (2+1)-flavor lattice QCD at zero chemical potential. Results are obtained using calculations with tree level improved gauge and the highly improved staggered quark (HISQ) actions with almost physical light and strange quark masses at three different values of the lattice cut-off. Our choice of parameters corresponds to a value of 160 MeV for the lightest pseudo scalar Goldstone mass and a physical value of the kaon mass. The three diagonal charge susceptibilities and the correlations among conserved charges have been extrapolated to the continuum limit in the temperature interval 150 MeV <T < 250 MeV. We compare our results with the hadron resonance gas (HRG) model calculations and find agreement with HRG model results only for temperatures T<= 150 MeV. We observe significant deviations in the temperature range 160 MeV < T < 170 MeV and qualitative differences in the behavior of the three conserved charge sectors. At T < 160 MeV quadratic net baryon number fluctuations in QCD agree with HRG model calculations while, the net electric charge fluctuations in QCD are about 10% smaller and net strangeness fluctuations are about 20% larger. These findings are relevant to the discussion of freeze-out conditions in relativistic heavy ion collisions.

hep-lat↗
arXiv2012

Contact Term, its Holographic Description in QCD and Dark Energy

In this work we study the well known contact term, which is the key element in resolving the so-called $U(1)_A$ problem in QCD. We study this term using the dual Holographic Description. We argue that in the dual picture the contact term is saturated by the D2 branes which can be interpreted as the tunnelling events in Minkowski space-time. We quote a number of direct lattice results supporting this identification. We also argue that the contact term receives a Casimir -like correction $\sim (\Lqcd R)^{-1}$ rather than naively expected $\exp(-\Lqcd R)$ when the Minkowski space-time ${\cal R}_{3,1}$ is replaced by a large but finite manifold with a size $R$. Such a behaviour is consistent with other QFT-based computations when power like corrections are due to nontrivial properties of topological sectors of the theory. In holographic description such a behaviour is due to massless Ramond-Ramond (RR) field living in the bulk of multidimensional space when power like corrections is a natural outcome of massless RR field. In many respects the phenomenon is similar to the Aharonov -Casher effect when the "modular electric field" can penetrate into a superconductor where the electric field is exponentially screened. The role of "modular operator" from Aharonov -Casher effect is played by large gauge transformation operator $\cal{T}$ in 4d QCD, resulting the transparency of the system to topologically nontrivial pure gauge configurations. We discuss some profound consequences of our findings. In particular, we speculate that a slow variation of the contact term in expanding universe might be the main source of the observed Dark Energy.

hep-ph↗
arXiv2012

Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics

We study the interpretation of Lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to tranverse gluon quasiparticles by means of a gas-like effective potential. This study is useful to identify the effective degrees of freedom propagating in the gluon medium above the critical temperature. A main general finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop dynamics, hence the thermodynamics can be described without the need for diverging or exponentially increasing quasiparticle masses as $T \rightarrow T_c$, at variance respect to standard quasiparticle models.

hep-ph↗