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Journal articles on the topic 'Gluons and lattices'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Steinhauser, Marc, André Sternbeck, Björn Wellegehausen, and Andreas Wipf. "Spectroscopy of four-dimensional N = 1 supersymmetric SU(3) Yang-Mills theory." EPJ Web of Conferences 175 (2018): 08022. http://dx.doi.org/10.1051/epjconf/201817508022.

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Supersymmetric gauge theories are an important building block for extensions of the standard model. As a first step towards Super-QCD we investigate the pure gauge sector with gluons and gluinos on the lattice, in particular the low energy mass spectrum: meson-like gluinoballs, gluino-glueballs and pure glueballs. We report on some first calculations performed with clover improved Wilson fermions on rather small lattices. The supersymmetric continuum limit and particle masses are discussed and compared to predictions from effective field theory.

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2

Stoddart, J. C. "Quarks, Gluons and Lattices: Cambridge Monographs on Mathematical Physics." Physics Bulletin 37, no. 5 (May 1986): 225. http://dx.doi.org/10.1088/0031-9112/37/5/031.

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3

ANTROPOV, S., M. BORDAG, V. DEMCHIK, and V. SKALOZUB. "LONG RANGE CHROMOMAGNETIC FIELDS AT HIGH TEMPERATURE." International Journal of Modern Physics A 26, no. 27n28 (November 10, 2011): 4831–43. http://dx.doi.org/10.1142/s0217751x11054747.

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The magnetic mass of neutral gluons in Abelian chromomagnetic field at high temperature is calculated in SU(2) gluodynamics. It is noted that such fields are spontaneously generated at high temperature. The mass is computed either from the Schwinger–Dyson equation accounting for the one-loop polarization tensor or in Monte Carlo simulations on a lattice. In latter case, an average magnetic flux penetrating a plaquette is measured for a number of lattices. Both calculations are in agreement with each other and result in zero magnetic mass. Some applications of the results obtained are discussed.

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4

CORNWALL, JOHN M. "POSITIVITY VIOLATIONS IN QCD." Modern Physics Letters A 28, no. 38 (December 4, 2013): 1330035. http://dx.doi.org/10.1142/s0217732313300358.

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Both lattice simulations and theoretical studies show that the spectral function of the gluon propagator of QCD (in various gauges, as well as for the gauge-invariant Pinch Technique, or PT, propagator) is not nonnegative everywhere, although it should be if it has a physical interpretation as in QED. Theory says moreover that the non-positive spectral function of the Landau-gauge or of the PT gluon propagator is further constrained to obey a superconvergence relation (the integral of the spectral function vanishes). We review the theoretical and lattice evidence for violation of positivity as well as various interpretations of this violation, and consider methods for checking superconvergence on the lattice (so far undone). The most common interpretation is that positivity violation implies confinement of gluons, so the gluon propagator does not describe processes with physical gluons. Another more direct and gauge-invariant interpretation arises from the PT: Asymptotic freedom alone demands non-positivity and superconvergence.

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5

Costa, Marios, and Haralambos Panagopoulos. "Renormalization of Supersymmetric QCD on the Lattice." EPJ Web of Conferences 175 (2018): 14001. http://dx.doi.org/10.1051/epjconf/201817514001.

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We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green’s functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

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6

JI, XIANGDONG, and YONG ZHAO. "PHYSICS OF GLUON HELICITY." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460028. http://dx.doi.org/10.1142/s2010194514600283.

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The total gluon helicity in a polarized proton is shown to be a matrix element of a gauge-invariant but nonlocal, frame-dependent gluon spin operator [Formula: see text] in the large momentum limit. The operator [Formula: see text] is fit for the calculation of the total gluon helicity in lattice QCD. This calculation also implies that parton physics can be studied through the large momentum limit of frame-dependent, equal-time correlation functions of quarks and gluons.

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7

Fan, Zhouyou, Rui Zhang, and Huey-Wen Lin. "Nucleon gluon distribution function from 2 + 1 + 1-flavor lattice QCD." International Journal of Modern Physics A 36, no. 13 (April 28, 2021): 2150080. http://dx.doi.org/10.1142/s0217751x21500809.

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The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-[Formula: see text] region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that access the [Formula: see text]-dependence of the gluon unpolarized PDF of the nucleon. The lattice calculation is carried out with nucleon momenta up to 2.16 GeV, lattice spacing [Formula: see text] fm, and with valence pion masses of 310 and 690 MeV. We use reduced Ioffe-time distributions to cancel the renormalization and implement a one-loop perturbative pseudo-PDF gluon matching. We neglect mixing of the gluon operator with the quark singlet sector. Our matrix-element results in coordinate space are consistent with those obtained from the global PDF fits of CT18 NNLO and NNPDF3.1 NNLO. Our fitted gluon PDFs at both pion masses are consistent with global fits in the [Formula: see text] region.

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8

CUI, J. Y., and J. M. WU. "THE BOUND STATE EQUATION FOR TWO GLUONS AND ITS SOLUTION." International Journal of Modern Physics A 14, no. 13 (May 20, 1999): 2117–32. http://dx.doi.org/10.1142/s0217751x9900107x.

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We derive the bound state equation for two gluons in relativistic quantum field theory, i.e. the Bethe–Salpeter (BS) equation for two gluons. To solve it, we choose the kernel as the sum of a one-gluon exchange potential, a contact interaction and a linear confining potential. Under instantaneous approximation, this BS equation is solved numerically. The spectrum and the BS wave function of the glueballs are obtained in this framework. The numerical results are in agreement with that of recent lattice calculation.

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9

Villegas, Kristian Hauser, and Jose Perico Esguerra. "Lattice gauge theory and gluon color-confinement in curved spacetime." Modern Physics Letters A 30, no. 05 (February 3, 2015): 1550020. http://dx.doi.org/10.1142/s0217732315500200.

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The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman–Robertson–Walker (FRW) metric. Last, we discussed possible future numerical implementation of lattice QCD in curved spacetime.

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10

NAKAGAWA, Y., A. NAKAMURA, T. SAITO, and H. TOKI. "CONFINING TIME-LIKE GLUON AND CONFINED SPATIAL GLUONS IN COULOMB GAUGE QCD." Modern Physics Letters A 23, no. 27n30 (September 30, 2008): 2352–55. http://dx.doi.org/10.1142/s0217732308029368.

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We investigate the Gribov-Zwanziger scenario in Coulomb gauge QCD using a SU(3) quenched lattice gauge simulation. The ghost propagator diverges in the infrared limit stronger than the free ghost propagator, and the ghost degree of freedom plays a central role in the confinement mechanism in the Coulomb gauge. The infrared divergent ghost dressing function results in the confining color-Coulomb instantaneous interaction. The equal-time transverse gluon propagator is suppressed in the infrared region. Therefore, in the Coulomb gauge, the instantaneous interaction mediated by time-like gluons is responsible for the confining force, and the would-be physical gluons are confined in hadrons.

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11

GONG, M., Y. CHEN, G. MENG, and C. LIU. "LATTICE GLUON PROPAGATOR IN THE LANDAU GAUGE: A STUDY USING ANISOTROPIC LATTICES." Modern Physics Letters A 24, no. 24 (August 10, 2009): 1925–35. http://dx.doi.org/10.1142/s021773230903031x.

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Lattice gluon propagators are studied using tadpole and Symanzik improved gauge action in Landau gauge. The study is performed using anisotropic lattices with asymmetric volumes. The Landau gauge dressing function for the gluon propagator measured on the lattice is fitted according to a leading power behavior: Z(q2) ≃ (q2)2κ with an exponent κ at small momenta. The gluon propagators are also fitted using other models and the results are compared. Our result is compatible with a finite gluon propagator at zero momentum in Landau gauge.

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12

WANG, XIN, JIARONG LI, and JUEPING LIU. "EQUATION OF STATE FOR HOT GLUON PLASMA WITH EFFECTIVE TWO LOOPS." Modern Physics Letters A 16, no. 27 (September 7, 2001): 1751–59. http://dx.doi.org/10.1142/s0217732301005102.

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We present analytical results for the equation of state for hot gluon plasma obtained with an effective perturbation based on hard thermal loops resummation theory. The effective two-loop results depend on Debye screening and finite width of gluons as physical parameters. Considering next-to-leading Debye mass and finite width effects, we find the equation of state to be in good agreement with recent lattice results for T≳2T c .

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13

Shanahan, Phiala. "The gluon structure of hadrons and nuclei from lattice QCD." EPJ Web of Conferences 175 (2018): 01015. http://dx.doi.org/10.1051/epjconf/201817501015.

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I discuss recent lattice QCD studies of the gluon structure of hadrons and light nuclei. After very briefly highlighting new determinations of the gluon contributions to the nucleon’s momentum and spin, presented by several collaborations over the last year, I describe first calculations of gluon generalised form factors. The generalised transversity gluon distributions are of particular interest since they are purely gluonic; they do not mix with quark distributions at leading twist. In light nuclei they moreover provide a clean signature of non-nucleonic gluon degrees of freedom, and I present the first evidence for such effects, based on lattice QCD calculations. The planned Electron-Ion Collider, designed to access gluon structure quantities, will have the capability to test this prediction, and measure a range of gluon observables including generalised gluon distributions and transverse momentum dependent gluon distributions, within the next decade.

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14

GORENSTEIN, M. I., H. G. MILLER, R. A. RITCHIE, and SHIN NAN YANG. "THERMODYNAMICAL FUNCTIONS AND THE HEAVY-QUARK POTENTIAL IN AN SU(2) GLUON PLASMA." Modern Physics Letters A 10, no. 39 (December 21, 1995): 3001–7. http://dx.doi.org/10.1142/s0217732395003136.

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Monte-Carlo lattice data for thermodynamical functions and the heavy-quark potential for an SU(2) gluon plasma are considered in the “cutoff” model with a temperature dependent cutoff parameter. Good agreement with the data in both cases was found. We compare these results with a model of gluons with a thermal mass and find little difference between the two models. The results obtained for the heavy-quark potential are significantly better in both cases than those obtained from pure perturbative calculations.

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15

MA, J. P. "A STUDY OF GLUON PROPAGATOR ON COARSE LATTICE." Modern Physics Letters A 15, no. 04 (February 10, 2000): 229–44. http://dx.doi.org/10.1142/s0217732300000220.

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We study gluon propagator in Landau gauge with lattice QCD, where we use an improved lattice action. The calculation of gluon propagator is performed on lattices with the lattice spacing from 0.40 fm to 0.24 fm and with the lattice volume from (2.40 fm )4 to (4.0 fm )4. We find that the rotation invariance is approximately restored in the q2-range, indicated by the fact that the propagator is a smooth function of the continuum momentum q2. We try to fit our results by two different ways, in the first one we interpret the calculated gluon propagators as a function of the continuum momentum, while in the second we interpret the propagators as a function of the lattice momentum. In both cases we use models which are the same in continuum limit. A qualitative agreement between two fittings is found.

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16

Catterall, Simon, and Aarti Veernala. "Two dimensional super QCD on a lattice." EPJ Web of Conferences 175 (2018): 08005. http://dx.doi.org/10.1051/epjconf/201817508005.

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We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf<Nc.

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17

Machahari, Luxmi, and D. K. Choudhury. "Q2 dependence of the fractional momenta carried by small x quarks and gluons in models of proton structure function." Modern Physics Letters A 34, no. 33 (October 28, 2019): 1950273. http://dx.doi.org/10.1142/s0217732319502730.

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Recently, we suggested two alternative analytical models of proton structure function [Formula: see text] and gluon distribution [Formula: see text] at small [Formula: see text] [L. Machahari and D. K. Choudhury, Eur. Phys. J. A 54, 69 (2018); Commun. Theor. Phys. 71, 56 (2019)] derived from the coupled DGLAP equations for quarks and gluons approximated by Taylor expansion. In this work, we compute the partial momentum fractions carried by quarks and gluons in limited small [Formula: see text] range: [Formula: see text] and compare them with few other models available in the current literature. The analysis leads to understand qualitatively the effects of notions like Froissart saturation and self-similarity in the proton at small [Formula: see text]. We also study if our results conform to the total momentum fractions as predicted in perturbative and lattice QCD.

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18

Hajizadeh, Ouraman, Tamer Boz, Axel Maas, and Jon-Ivar Skullerud. "Gluon and ghost correlation functions of 2-color QCD at finite density." EPJ Web of Conferences 175 (2018): 07012. http://dx.doi.org/10.1051/epjconf/201817507012.

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2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition.

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19

Müller-Preussker, M. "Creutz, M., Quarks, Gluons and Lattices. Cambridge etc. Cambridge University Press 1983. VI, 169 S., £ 7.95, $ 12.95. ISBN 0-521-31535-2. (Cambridge Monogr. on Mathematical Physics)." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 67, no. 1 (1987): 16. http://dx.doi.org/10.1002/zamm.19870670104.

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20

MATHIEU, VINCENT, NIKOLAI KOCHELEV, and VICENTE VENTO. "THE PHYSICS OF GLUEBALLS." International Journal of Modern Physics E 18, no. 01 (January 2009): 1–49. http://dx.doi.org/10.1142/s0218301309012124.

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Glueballs are particles whose valence degrees of freedom are gluons and therefore in their description the gauge field plays a dominant role. We review recent results in the physics of glueballs with the aim set on phenomenology and discuss the possibility of finding them in conventional hadronic experiments and in the Quark Gluon Plasma. In order to describe their properties we resort to a variety of theoretical treatments which include, lattice QCD, constituent models, AdS/QCD methods, and QCD sum rules. The review is supposed to be an informed guide to the literature. Therefore, we do not discuss in detail technical developments but refer the reader to the appropriate references.

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21

Howson, T. L., R. Horsley, W. Kamleh, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, H. Stüben, R. D. Young, and J. M. Zanotti. "Directly calculating the glue component of the nucleon in lattice QCD: QCDSF–UKQCD–CSSM Collaborations." EPJ Web of Conferences 245 (2020): 06031. http://dx.doi.org/10.1051/epjconf/202024506031.

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We are investigating the direct determination and non-perturbative renormalisation of gluon matrix elements. Such quantities are sensitive to ultra– violet fluctuations, and are in general statistically noisy. To obtain statistically significant results, we extend an earlier application of the Feynman–Hellmann theorem to gluonic matrix elements to calculate a renormalisation factor in the RI – MOM scheme, in the quenched case. This work demonstrates that the Feynman–Hellmann method is capable of providing a feasible option for calculating gluon quantities.

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22

Vollmer, G., K. Hepp, F. Haake, R. Sexl, P. Warneck, H. A. Kastrup, and K. Suchy. "Zeh: Die Physik der Zeitrichtung/Pauli: Physik und Erkenntnistheorie/Kümmel: Introduction to Quantum Mechanics/Kanitscheider, Törnebohm, Drieschner: Moderne Naturphilosophie/Fabian: Atmosphäre und Umwelt/Creutz: Quarks, gluons and lattices/Ebeling, Kraeft." Physik Journal 41, no. 2 (February 1985): 53–55. http://dx.doi.org/10.1002/phbl.19850410213.

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23

Harremoës, Peter. "Entropy Inequalities for Lattices." Entropy 20, no. 10 (October 12, 2018): 784. http://dx.doi.org/10.3390/e20100784.

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We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions that exclude the existence of non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group. In order to formulate and prove the results, one has to bridge lattice theory, group theory, the theory of functional dependences and the theory of conditional independence. It is demonstrated that the Shannon inequalities are sufficient for planar modular lattices. The proof applies a gluing technique that uses that if the Shannon inequalities are sufficient for the pieces, then they are also sufficient for the whole lattice. It is conjectured that the Shannon inequalities are sufficient if and only if the lattice does not contain a special lattice as a sub-semilattice.

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24

FEGAN, STUART. "MESON SPECTROSCOPY AT JLAB AT 12 GEV." International Journal of Modern Physics: Conference Series 35 (January 2014): 1460411. http://dx.doi.org/10.1142/s2010194514604116.

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The 12 GeV upgrade to the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab will enable a new generation of experiments in hadronic nuclear physics, seeking to address fundamental questions in our understanding of QCD. The existence of exotic states, suggested by both quark models and lattice calculations, would allow gluonic degrees of freedom to be explored, and may help explain the role played by gluons in the QCD interaction. This article will review the meson spectroscopy program being planned at the lab following the 12 GeV upgrade, utilising real and quasi-real photon beams in two of the lab's four experimental halls, whose distinct capabilities will enable an extensive set of spectroscopy experiments to be performed at the same facility.

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25

Morningstar, Colin. "PWA AND THE LATTICE." International Journal of Modern Physics A 18, no. 03 (January 30, 2003): 377–86. http://dx.doi.org/10.1142/s0217751x03014290.

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26

Nilima, Indrani, and Vineet Kumar Agotiya. "Equation of States and Charmonium Suppression in Heavy-Ion Collisions." Advances in High Energy Physics 2019 (August 6, 2019): 1–13. http://dx.doi.org/10.1155/2019/9574136.

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The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as an equation of state. By employing medium modification to a heavy quark potential thermodynamic observables, viz., pressure, energy density, speed of sound, etc. have been calculated which nicely fit with the lattice equation of state for gluon, massless, and as well massive flavored plasma. For obtaining the thermodynamic observables we employed the debye mass in the quasi particle picture. We extended the quasi-particle model to calculate charmonium suppression in an expanding, dissipative strongly interacting QGP medium (SIQGP). We obtained the suppression pattern for charmonium states with respect to the number of participants at mid-rapidity and compared it with the experimental data (CMS JHEP) and (CMS PAS) at LHC energy (Pb+Pb collisions, sNN = 2.76 TeV).

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27

Kolomoyets, Natalia V., and Vladimir V. Skalozub. "Color structure of gluon field magnetic mass." International Journal of Modern Physics A 34, no. 09 (March 30, 2019): 1950052. http://dx.doi.org/10.1142/s0217751x19500520.

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The color structure of the gluon field magnetic mass is investigated in the lattice SU(2) gluodynamics. To realize that the interaction between a monopole–antimonopole string and external neutral Abelian chromomagnetic field flux is considered. The string is introduced in the way proposed by Srednicki and Susskind. The neutral Abelian field flux is introduced through the twisted boundary conditions. Monte Carlo simulations are performed on 4D lattices at finite temperature. It is shown that the presence of the Abelian field flux weakens the screening of the string field. That means decreasing the gluon magnetic mass for this environment. The contribution of the neutral Abelian field has the form of “enhancing” factor in the fitting functions. This behavior independently confirms the long-range nature of the neutral Abelian field reported already in the literature. The comparison with analytic calculations is given.

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28

Ghiglieri, Jacopo, and Derek Teaney. "Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas." International Journal of Modern Physics E 24, no. 11 (November 2015): 1530013. http://dx.doi.org/10.1142/s0218301315300131.

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We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark–gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include [Formula: see text] scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light-cone. We review recent field-theoretical developments, rooted in the causal properties of these correlators, which simplify the calculation of the appropriate Wilson lines in thermal field theory. With these simplifications lattice measurements of transverse momentum broadening have become possible, and the kinetic equations describing parton transport have been extended to next-to-leading order in the coupling [Formula: see text].

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GOGOHIA, V., H. TOKI, T. SAKAI, and Gy KLUGE. "CHIRAL QCD VACUUM ENERGY DENSITY IN THE ZERO MODES ENHANCEMENT QUANTUM MODEL." International Journal of Modern Physics A 15, no. 01 (January 10, 2000): 45–64. http://dx.doi.org/10.1142/s0217751x00000033.

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Using the effective potential approach for composite operators we have formulated the quantum model of the QCD vacuum. It is based on the existence and importance of the nonperturbative q-4-type dynamical, topologically nontrivial excitations of the gluon field configurations (due to self-interaction of the massless gluons only). The QCD vacuum is found to be stable since the vacuum energy density has no imaginary part. The Yang–Mills (YM) part of the vacuum energy density is always negative and depends on a finite scale at which nonperturbative effects become important. The quark part of the vacuum energy density depends in addition on the constant of integration of the corresponding Schwinger–Dyson equation. The value of the above-mentioned scale is determined from the bounds for the pion decay constant in the chiral limit. Our value for the chiral QCD vacuum energy density is one order of magnitude bigger than the instanton based models can provide while a fair agreement with recent phenomenological and lattice results for the chiral condensate is obtained.

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30

Xu, Xiaoping. "Theta Series of Unimodular Lattices, Combinatorial Identities and Weighted Symmetric Polynomials." Algebra Colloquium 13, no. 01 (March 2006): 67–86. http://dx.doi.org/10.1142/s1005386706000101.

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Hecke proved that the theta series of a positive definite even unimodular lattice is a polynomial of the well-known Essenstein series E4(z) and the Ramanujan series Δ24(z). A natural question is what kind of polynomials in E4(z) and Δ24(z) could be the theta series of positive definite even unimodular lattices. In this paper, we find two combinatorial identities on the theta series of the root lattices of the finite-dimensional simple Lie algebras of type D4n and the cosets in their integral duals, in terms of E4(z) and Δ24(z). Using these two identities, we prove that three families of weighted symmetric polynomials of two fixed families of polynomials of E4(z) and Δ24(z) are the theta series of certain positive definite even unimodular lattices, obtained by gluing finitely many copies of the root lattices of the finite-dimensional simple Lie algebras of type D2n. The results also show that the full permutation groups are the hidden symmetry of the theta series of certain unimodular lattices.

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31

MEI, ZHONG-HAO, and XIANG-QIAN LUO. "EXOTIC MESONS FROM QUANTUM CHROMODYNAMICS WITH IMPROVED GLUON AND QUARK ACTIONS ON THE ANISOTROPIC LATTICE." International Journal of Modern Physics A 18, no. 31 (December 20, 2003): 5713–24. http://dx.doi.org/10.1142/s0217751x03017038.

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Hybrid (exotic) mesons, which are important predictions of quantum chromodynamics (QCD), are states of quarks and antiquarks bound by excited gluons. First principle lattice study of such states would help us understand the role of "dynamical" color in low energy QCD and provide valuable information for experimental search for these new particles. In this paper, we apply both improved gluon and quark actions to the hybrid mesons, which might be much more efficient than the previous works in reducing lattice spacing error and finite volume effect. Quenched simulations were done at β=2.6 and on a ξ=3 anisotropic 123×36 lattice using our PC cluster. We obtain 2013±26±71 MeV for the mass of the 1-+ hybrid meson [Formula: see text] in the light quark sector, and 4369±37±99 MeV in the charm quark sector; the mass splitting between the 1-+ hybrid meson [Formula: see text] in the charm quark sector and the spin averaged S-wave charmonium mass is estimated to be 1302±37±99 MeV. As a byproduct, we obtain 1438±32±57 MeV for the mass of a P-wave 1++[Formula: see text] or [Formula: see text] meson and 1499±28±65 MeV for the mass of a P-wave 1++[Formula: see text] meson, which are comparable to their experimental value 1426 MeV for the f1(1420) meson. The first error is statistical, and the second one is systematical. The mixing of the hybrid meson with a four quark state is also discussed.

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CHEN, YING, BING HE, HE LIN, and JI-MIN WU. "SU(2) GLUON PROPAGATOR ON A COARSE ANISOTROPIC LATTICE." Modern Physics Letters A 15, no. 37 (December 7, 2000): 2245–56. http://dx.doi.org/10.1142/s0217732300002747.

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We calculated the SU(2) gluon propagator in Landau gauge on an anisotropic coarse lattice with the improved action. The standard and improved schemes are used to fix the gauge in this work. Even on the coarse lattice the lattice gluon propagator can be well described by a function of the continuous momentum. The effect of the improved gauge fixing scheme is found not to be apparent. Based on the Marenzoni's model, the mass scale and the anomalous dimension are extracted and can be reasonably extrapolated to the continuum limit with the values α~0.3 and M~600 MeV . We also extract the physical anisotropy ξ from the gluon propagator due to the explicit ξ dependence of the gluon propagator.

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33

SIMJI, P., and VISHNU M. BANNUR. "PHENOMENOLOGICAL MODELS OF GLUON PLASMA IN THE LARGE TEMPERATURE RANGE." International Journal of Modern Physics A 28, no. 25 (October 8, 2013): 1350121. http://dx.doi.org/10.1142/s0217751x13501212.

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Quasiparticle quark–gluon plasma (qQGP) model and strongly coupled quark–gluon plasma (SCQGP) are two different phenomenological models of quark–gluon plasma (QGP) that try to explain the nonideal behavior seen in lattice simulation of QCD and in relativistic heavy ion collisions. These models almost successfully explain the existing lattice data up to 5Tc. Here, we investigate how better these models fit the recent lattice data results of precision SU(3) thermodynamics for a large temperature range (up to 1000Tc) by studying the statistical mechanics and thermodynamics of gluon plasma and hence we have a complete phenomenological description of the equation of state of QGP from the phase transition through the perturbative region up to Stefan–Boltzmann limit. We also study the effect of orders of running coupling constants on the models and used the equation of state obtained using these models in predicting behavior of quantity like velocity of sound in high temperature, which has no lattice QCD results for such high temperatures.

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34

Bietenholz, W., and U. J. Wiese. "Perfect lattice actions for quarks and gluons." Nuclear Physics B 464, no. 1-2 (April 1996): 319–50. http://dx.doi.org/10.1016/0550-3213(95)00678-8.

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35

Cucchieri, Attilio, Tereza Mendes, and Willian M. Serenone. "Lattice Gluon Propagator and One-Gluon-Exchange Potential." Brazilian Journal of Physics 49, no. 4 (April 29, 2019): 548–63. http://dx.doi.org/10.1007/s13538-019-00665-6.

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36

Dzierba, Alex R. "THE SCIENCE OF CONFINEMENT AND THE GLUEX/HALL D PROJECT AT JEFFERSON LAB." International Journal of Modern Physics A 18, no. 03 (January 30, 2003): 397–404. http://dx.doi.org/10.1142/s0217751x03014319.

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One of the outstanding and fundamental questions in physics is the quantitative understanding of the confinement of quarks and gluons in quantum chromodynamics (QCD). Confinement is a unique feature of QCD. Exotic hybrid mesons manifest gluonic degrees of freedom and their spectroscopy will provide the crucial data needed to test assumptions in lattice QCD and phenomenology leading to confinement. Photo-production is expected to be particularly effective in producing exotic hybrids but data using photon probes are sparse. At Jefferson Lab, plans are underway to use the coherent bremsstrahlung technique to produce a linearly polarized photon beam. A solenoid-based hermetic detector will be used to collected data on meson production and decays with statistics that will exceed the current photoproduction data in hand by several orders of magnitude after the first year of running. In order to reach the ideal photon energy of 9 GeV/c for this mapping of the exotic spectra, the energy of the Jefferson Lab electron accelerator, CEBAF, will be doubled from its current maximum of 6 GeV to 12 GeV. The physics and project are described.

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37

IIDA, HIDEAKI, TORU T. TAKAHASHI, and HIDEO SUGANUMA. "PROPERTIES OF SCALAR-QUARK SYSTEMS IN SU(3)c LATTICE QCD." Modern Physics Letters A 23, no. 27n30 (September 30, 2008): 2344–47. http://dx.doi.org/10.1142/s0217732308029344.

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We perform the first study for the bound states of colored scalar particles ϕ (“scalar quarks”) in terms of mass generation with quenched SU (3)c lattice QCD. We investigate the bound states of ϕ, ϕ†ϕ and ϕϕϕ (“scalar-quark hadrons”), as well as the bound states of ϕ and quarks ψ, i.e., ϕ†ψ, ψψϕ and ϕϕψ (“chimera hadrons”). All these new-type hadrons including ϕ have a large mass of several GeV due to large quantum corrections by gluons, even for zero bare scalar-quark mass mϕ = 0 at a−1 ~ 1 GeV . We find a similar mψ-dependence between ϕ†ψ and ϕϕψ, which indicates their similar structure due to the large mass of ϕ. From this study, we conjecture that all colored particles generally acquire a large effective mass due to dressed gluons.

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38

ALKOFER, R., C. S. FISCHER, F. J. LLANES-ESTRADA, and K. SCHWENZER. "WHAT THE INFRARED BEHAVIOR OF QCD VERTEX FUNCTIONS IN LANDAU GAUGE CAN TELL US ABOUT CONFINEMENT." International Journal of Modern Physics E 16, no. 09 (October 2007): 2720–32. http://dx.doi.org/10.1142/s0218301307008367.

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The infrared behavior of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson–Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson–Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.

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39

GANNON, TERRY, and C. S. LAM. "GLUING AND SHIFTING LATTICE CONSTRUCTIONS AND RATIONAL EQUIVALENCE." Reviews in Mathematical Physics 03, no. 03 (September 1991): 331–69. http://dx.doi.org/10.1142/s0129055x91000126.

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This paper deals with the construction and classification of lattices. Two methods of constructing new lattices from old one — gluing and shifting — are discussed. A fairly exhaustive analysis of shifting is carried out, and its close relationships to gluing and to rational equivalence are investigated. This exploration enables rational equivalence to be seen in a more geometric light than has usually been the case. A related classification of lattices, called similarity, is introduced and studied. New geometric proofs of some old theorems are obtained, as well as a number of new results.

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Silva, Paulo J., Orlando Oliveira, David Dudal, and Martin Roelfs. "Finite temperature gluon propagator in Landau gauge: non-zero Matsubara frequencies and spectral densities." EPJ Web of Conferences 175 (2018): 07038. http://dx.doi.org/10.1051/epjconf/201817507038.

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We report on the lattice computation of the Landau gauge gluon propagator at finite temperature, including the non-zero Matsubara frequencies. Moreover, the corresponding Källén-Lehmann spectral density is computed, using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are also discussed.

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CHIKOVANI, Z. E., L. L. JENKOVSZKY, and F. PACCANONI. "DIPOLE GLUON PROPAGATOR AND QUARKONIUM SPECTROSCOPY." Modern Physics Letters A 06, no. 15 (May 20, 1991): 1409–14. http://dx.doi.org/10.1142/s0217732391001500.

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By using a model for the non-perturbative gluon propagator, suggested by analyticity, we determine the heavy quark potential and calculate the mass spectrum of the [Formula: see text] and [Formula: see text] systems. The same model reproduces the results of lattice calculations for the gluon condensate.

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BOINPOLLI, S., P. O. BOWMAN, J. N. HEDDITCH, U. M. HELLER, W. KAMLEH, B. G. LASSCOCK, D. B. LEINWEBER, A. G. WILLIAMS, J. M. ZANOTTI, and J. B. ZHANG. "SOME RECENT LATTICE QCD RESULTS FROM THE CSSM." International Journal of Modern Physics A 22, no. 27 (October 30, 2007): 5053–61. http://dx.doi.org/10.1142/s0217751x07038402.

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Recent CSSM Lattice Collaboration studies of hadron electromagnetic structure and the exotic hadron spectrum are highlighted. The momentum dependence of quark and gluon propagators revealed in lattice simulations of full QCD are also illustrated.

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43

Herrmann, Christian. "Corrigendum: Gluings of Modular Lattices." Order 23, no. 2-3 (November 15, 2006): 169–71. http://dx.doi.org/10.1007/s11083-006-9042-0.

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44

BORNYAKOV, V. G., and V. K. MITRJUSHKIN. "LATTICE QCD GLUON PROPAGATORS NEAR TRANSITION TEMPERATURE." International Journal of Modern Physics A 27, no. 09 (April 10, 2012): 1250050. http://dx.doi.org/10.1142/s0217751x12500509.

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Landau gauge gluon propagators are studied numerically in the SU (3) gluodynamics as well as in the full QCD with the number of flavors nF = 2 using efficient gauge fixing technique. We compare these propagators at temperatures very close to the transition point in two phases: confinement and deconfinement. The electric mass mE has been determined from the momentum space longitudinal gluon propagator. Gribov copy effects are found to be rather strong in the gluodynamics, while in the full QCD case they are weak ("Gribov noise"). Also we analyze finite volume dependence of the transverse and longitudinal propagators.

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45

Carlomagno, Juan Pablo, and Juan Cristóbal Rojas. "Gluon condensate and the Polyakov loop." EPJ Web of Conferences 172 (2018): 02006. http://dx.doi.org/10.1051/epjconf/201817202006.

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The temperature dependence of the gluon condensate is deduced from the Polyakov loop effective potential. It is shown that this approach provides a simple picture for the electric gluon condensate around the deconfinement temperature, showing that it drops to zero in a temperature range which is in good agreement with different pure gauge lattice results.

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46

Lacroix, Gwendolyn, Claude Semay, and Fabien Buisseret. "The SUSY Yang–Mills plasma in a T-matrix approach." International Journal of Modern Physics A 30, no. 24 (August 28, 2015): 1550145. http://dx.doi.org/10.1142/s0217751x15501456.

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In this paper, the thermodynamic properties of [Formula: see text] supersymmetric Yang–Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from noncritical closed superstring theory leads to a prediction for the value of the deconfining temperature [Formula: see text] that agrees with recent lattice data. The deconfined phase is studied by resorting to a [Formula: see text]-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1–5) [Formula: see text], where the interactions are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 [Formula: see text] for any gauge group. The equation of state is then computed numerically for [Formula: see text] and [Formula: see text], and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of nonsupersymmetric Yang–Mills when normalized to the Stefan–Boltzmann pressure and expressed as a function of [Formula: see text].

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47

LIU, WEI, CHE MING KO, and BEN-WEI ZHANG. "JET CONVERSIONS IN QGP AND SUPPRESSION OF IDENTIFIED HADRONS." International Journal of Modern Physics E 16, no. 07n08 (August 2007): 1930–36. http://dx.doi.org/10.1142/s021830130700726x.

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A gluon or quark jet traversing through a quark-gluon plasma can be converted into a quark or gluon jet through scatterings with thermal partons. Their conversion rates due to two-body elastic and inelastic scattering as well as scatterings involving gluon radiation are evaluated in the lowest order in Quantum Chromodynamics (QCD). Including both energy loss and conversions of quark and gluon jets in the expanding quark-gluon plasma produced in relativistic heavy ion collisions, we find a net conversion of quark jets to gluon jets. This reduces the difference between the nuclear modification factors for quark and gluon jets in central heavy ion collisions and thus enhances the p/π+ and [Formula: see text] ratios at high transverse momentum. Using the larger QCD coupling constant from lattice QCD calculations than that given by the perturbative QCD further enhances the net quark to gluon jet conversion rate, leading to a closer similarity between these ratios at high transverse momentum in central Au + Au collisions at [Formula: see text] and in p + p collisions at same energy as observed in experiments.

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48

Blaschke, David, Kirill A. Devyatyarov, and Olaf Kaczmarek. "Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics." Symmetry 13, no. 3 (March 21, 2021): 514. http://dx.doi.org/10.3390/sym13030514.

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In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

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Skullerud, Jonivar, and Ayse Kizilersü. "Quark-gluon vertex from lattice QCD." Journal of High Energy Physics 2002, no. 09 (September 4, 2002): 013. http://dx.doi.org/10.1088/1126-6708/2002/09/013.

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50

MIHARA, ANTONIO, ATTILIO CUCCHIERI, and TEREZA MENDES. "STUDY OF GHOSTS IN MAXIMALLY ABELIAN GAUGE ON THE LATTICE." International Journal of Modern Physics E 16, no. 09 (October 2007): 2935–38. http://dx.doi.org/10.1142/s0218301307008768.

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Abelian dominance is manifested in the (continuum) perturbative regime through the fact that the running coupling constant, obtained from the ghost-gluon vertex in Maximally Abelian Gauge (MAG), depends only on the renormalization factor of the diagonal (or Abelian) gluon propagator, due to cancellation of the other renormalization factors. We investigate such a cancellation nonperturbatively using lattice numerical simulations and present some preliminary results for the running coupling constant.

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