Article

Screening masses in SU(2) pure gauge theory

Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Physics Letters B (Impact Factor: 6.13). 01/2000; 471(4):382-387. DOI: 10.1016/S0370-2693(99)01404-5
Source: arXiv

ABSTRACT

We perform a systematic scaling study of screening masses in pure gauge SU(2) theory at temperatures above the phase transition temperature. Finite volume effects are strongly connected with spatial Wilson lines and hence related to spatial deconfinement. We extract the screening masses in the infinite volume and zero lattice spacing limit. We find that these physical results can be deduced from runs on rather coarse lattices. Dimensional reduction is clearly seen in the spectrum.

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    ABSTRACT: When ordinary nuclear matter is heated to a high temperature of ~ 10^12 K, it undergoes a deconfinement transition to a new phase, strongly interacting quark-gluon plasma. While the color charged fundamental constituents of the nuclei, the quarks and gluons, are at low temperatures permanently confined inside color neutral hadrons, in the plasma the color degrees of freedom become dominant over nuclear, rather than merely nucleonic, volumes. Quantum Chromodynamics (QCD) is the accepted theory of the strong interactions, and confines quarks and gluons inside hadrons. The theory was formulated in early seventies, but deriving first principles predictions from it still remains a challenge, and novel methods of studying it are needed. One such method is dimensional reduction, in which the high temperature dynamics of static observables of the full four-dimensional theory are described using a simpler three-dimensional effective theory, having only the static modes of the various fields as its degrees of freedom. A perturbatively constructed effective theory is known to provide a good description of the plasma at high temperatures, where asymptotic freedom makes the gauge coupling small. In addition to this, numerical lattice simulations have, however, shown that the perturbatively constructed theory gives a surprisingly good description of the plasma all the way down to temperatures a few times the transition temperature. Near the critical temperature, the effective theory, however, ceases to give a valid description of the physics, since it fails to respect the approximate center symmetry of the full theory. The symmetry plays a key role in the dynamics near the phase transition, and thus one expects that the regime of validity of the dimensionally reduced theories can be significantly extended towards the deconfinement transition by incorporating the center symmetry in them. In the introductory part of the thesis, the status of dimensionally reduced effective theories of high temperature QCD is reviewed, placing emphasis on the phase structure of the theories. In the first research paper included in the thesis, the non-perturbative input required in computing the g^6 term in the weak coupling expansion of the pressure of QCD is computed in the effective theory framework at an arbitrary number of colors. The two last papers on the other hand focus on the construction of the center-symmetric effective theories, and subsequently the first non-perturbative studies of these theories are presented. Non-perturbative lattice simulations of a center-symmetric effective theory for SU(2) Yang-Mills theory show --- in sharp contrast to the perturbative setup --- that the effective theory accommodates a phase transition in the correct universality class of the full theory. This transition is seen to take place at a value of the effective theory coupling constant that is consistent with the full theory coupling at the critical temperature. Kun protoneista ja neutroneista koostuvaa ydinainetta kuumennetaan hyvin korkeaan lämpötilaan ~ 10^12 K, se läpikäy olomuodon muutoksen vahvasti vuorovaikuttavaksi kvarkkigluoniplasmaksi. Matalassa lämpötilassa vahva ydinvoima sitoo ydinhiukkasten rakennusosaset kvarkit ja gluonit tiukasti ydinhiukkasten sisälle, mutta olomuodon muutoksessa ydinhiukkasten rakenne sulaa ja kvarkit sekä gluonit vapautuvat vankeudestaan. Vahvan ydinvoiman teoria kvanttikromodynamiikka on tunnettu jo yli kolme vuosikymmentä, mutta silti teorian monimutkaisuuden takia tarkkojen ennusteiden tekeminen teoriasta on hyvin haastavaa ja uusia teoreettiesia tutkimusmenetelmiä tarvitaan. Eräs tällainen menetelmä on ulottuvuuksien supistaminen, jossa joitakin alkuperäisen neliulotteisen teorian tiettyjä tarkkaan rajattuja ominaisuuksia voidaan tutkia paljon helpommin yksinkertaisemmassa kolmiulotteisessa teoriassa. Asymptoottisen korkeassa lämpötilassa kvarkkien ja gluonien vuorovaikutuksen voimakkuus heikkenee, ja kolmiulotteinen teoria voidaan rakentaa käsittelemällä vain pieniä häiriöitä vapaan teorian ympärillä. Numeerisilla simulaatioilla on kuitenkin havaittu, että tämä efektiivinen teoria kuvaa tarkasti alkuperäistä teoriaa vielä yllättävänkin matalissa lämpötiloissa. 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Jälkimmäiset julkaisut keskittyvät keskussymmetrian säilyttävien efektiivisten teorioiden rakentamiseen ja näiden ensimmäisiin numeerisiin analyyseihin. Numeeriset hilasimulaatiot osoittivat että, toisin kuin keskussymmetrian rikkovalla teorialla, SU(2)-mittaryhmän tapauksessa keskussymmetrian säilyttävällä efektiivisellä teorialla on faasitransitio, joka kuuluu samaan universaalisuusluokkaan alkuperäisen teorian kanssa.
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    ABSTRACT: We compute the mass spectrum of the SU(2) adjoint Higgs model in 2+1 dimensions at several points located in the (metastable) confinement region of its phase diagram. We find a dense spectrum consisting of an almost unaltered repetition of the glueball spectrum of the pure gauge theory, and additional bound states of adjoint scalars. For the parameters chosen, the model represents the effective finite temperature theory for pure SU(2) gauge theory in four dimensions, obtained after perturbative dimensional reduction. Comparing with the spectrum of screening masses obtained in recent simulations of four-dimensional pure gauge theory at finite temperature, for the low-lying states we find quantitative agreement between the full and the effective theory for temperatures as low as T=2Tc. This establishes the model under study as the correct effective theory, and dimensional reduction as a viable tool for the description of thermodynamic properties. We furthermore compare the perturbative contribution ∼gT with the non-perturbative contributions ∼g2T and ∼g3T to the Debye mass. The latter turns out to be dominated by the scale g2T, whereas higher order contributions are small corrections.
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