Effective dilaton lagrangian and gluon condensate in a nucleon medium
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EMENTARY PARTICLES AND FIELDS Theory
Effective Dilaton Lagrangian and Gluon Condensate in a Nucleon Medium N. О. Agasian* Institute of Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya ul 25, Moscow, 117289 Russia Received March 5, 2008
Abstract—The gluon condensate as a function of temperature and baryon density in a nucleon medium is obtained from an effective dilaton Lagrangian. It is shown that, at a normal nuclear density of nucleons, n0 = 0.17 fm−3 , the gluon condensate decreases by about 10%. PACS numbers: 11.10.Wx, 11.15.Ha, 12.38.Gc, 12.38.Mh DOI: 10.1134/S1063778808080115
It is well known that, at temperatures and baryon densities below the phase-transition point, QCD is essentially nonperturbative and is characterized by the phenomena of confinement and spontaneous chiral-symmetry breaking. This is due to the presence of strong gluon fields in the QCD vacuum, which make a finite contribution to the shift of the vacuumenergy density through the anomaly in the trace of the energy–momentum tensor and, thus, through the gluon condensate G2 ≡ (gGaµν )2 . It is highly desirable to study the gluon condensate as a function of the temperature T and the baryon density n. Knowing the dependence of G2 on T and n, one can predict the behavior of physical quantities like the hadron masses and the constant fπ versus medium features (T and n). This may be of paramount importance in studying phenomena in nuclear matter under anomalous conditions—for example, in heavy-ion collisions. The dependence of G2 on T and n was analyzed in a number of studies (see, for example, [1– 13]) on the basis of various physical approaches. In the present study, we employ the low-energy effective dilaton Lagrangian to explore the dependence of G2 on the temperature and baryon density. In contrast to other approaches, the approach based on the effective dilaton Lagrangian makes it possible to take into account the inverse effect of the change in the gluon condensate on particle masses and to find thereby G2 over the entire region of T and n up to the phasetransition point. In this study, we formulate a general approach and find expressions for G2 that are linear in the particle density, this enabling us to compare the results produced by the developed method with other *
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known results for G2 as a function of temperature and baryon density. In gluodynamics, the glueball having the vacuum quantum numbers J P C = 0++ is the lightest hadron, which is therefore stable. A low-energy Lagrangian describing the interaction of the 0++ glueball (dilaton) and realizing scale-invariance Ward identities, in just the same way as the chiral pion Lagrangian realizes chiral Ward identities at the tree level, was constructed in [14, 15]. The effective dilaton Lagrangian has the form 1 (1) L(σ) = (∂µ σ)2 − V (σ), 2 1 σ λ . − V (σ) = σ 4 ln 4 σ0 4 The field σ is related to the trace of the energy– momentum tensor θµµ (x) in gluodynamics by the equation b m40 4 σ (x) = −θµµ (x) = (gGaµν (x))2 . 64|εv | 32
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