Dynamical interactions of dark energy and dark matter:Yang-Mills condensate and QCD axions

We analyze a model of cold axion dark matter weakly coupled with a dark gluon condensate,reproducing dark energy.We first review how to recover the dark energy behavior using the functional renormalization group approach,and ground our study in the properties of the effective Lagrangian,to be determined non-perturbatively.Then,within the context of G_(SM)×SU(2)_D×U(1)_(P Q),we consider Yang-Mills condensate(YMC)interactions with QCD axions.We predict a transfer of dark energy density into dark matter density,that can be tested in the next generation of experiments dedicated to dark energy measurements.We obtain new bounds on the interactions between the Yang-Mills condensate and axion dark matter from Planck data:the new physics interaction scale related to the axion/gluon condensate mixing is constrained to be higher than the 10~6GeV energy scale.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

Gluon condensates at finite baryon densities and temperature

We derive here the equation of state for quark matter with a nontrivial vacuum structure in QCD at finite temperature and baryon density. Using thermofield dynamics, the parameters of thermal vacuum and the gluon condensate function are determined through minimisation of the thermodynamic potential, along with a self-consistent determination of the effective gluon and quark masses. The scale parameter for the gluon condensates is related to the SVZ parameter in the context of QCD sum rules at zero temperature. With inclusion of quarks in the thermal vacuum the critical temperature at which the gluon condensate vanishes decreases as compared to that containing only gluons. At zero temperature, we similarly obtain the critical baryon density for the same to be about 0.36 fm^?3.     

Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering

In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure as has been used to calculate gluon production in a heavy ion collision. In particular the discretization of the longitudinal coordinate has a large numerical effect on the relation between the color charge density parameter g²μ and the saturation scale Q_s. Our result for this relation is Q_s≈0.6g²μ, which results in the classical Yang–Mills value for the “gluon liberation coefficient” c≈1.1. PACS  24.85.+p; 25.75.-q; 13.60.Hb     

Determination of QCD condensates frome + e − annihilation: anL ∞ norm approach

Results of a new determination of QCD condensates frome ⁺ e ^?→Isospin 1 hadrons data are given. Using a new method to analyse these data, we show that the range of values for the gluon condensate <α/πGG> and for the four quarks condensates, compatible with these data, is even larger than what could be expected from the already large dispersion of previous determinations. The ‘standard’ value 0.01 GeV⁴ are not completely excluded for the gluon condensate. Its value is however strongly correlated with the value of the four quarks condensates. We also find evidences that the dimension 8 condensates should be rather large.     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

Jet quenching parameter $\hat{q}$ in the stochastic QCD vacuum with Landau damping

We argue that the radiative energy loss of a parton traversing the quark–gluon plasma is determined by Landau damping of soft modes in the plasma. Using this idea, we calculate the jet quenching parameter of a gluon. The calculation is done in SU(3) quenched QCD within the stochastic vacuum model. At the LHC-relevant temperatures, the result depends on the gluon condensate, the vacuum correlation length, and the gluon Debye mass. Numerically, when the temperature varies from T=T_c to T = 900 MeV, the jet quenching parameter rises from to approximately 1.8 GeV²/fm. We compare our results with the predictions of perturbative QCD and other calculations.     

A comment on octet enhancement in the ΔI=1/2 rule

We apply vacuum background fields method to correct the coefficient functions of theO ₊ andO _? operators in ΔS=1 effective weak Hamiltonian responsible forK→2π decays. The additional relative octet enhancement factor of 2–3 is obtained by accounting for the gluon condensate corrections if the scale parameterπ ²x is set below 1 GeV₂.     

The ratios among condensates from e+e− (I=1) data

We calculate the ratios among condensates from the ρ channel (I=1) e⁺e⁻ data in a systematic way. We use quotients of SVZ sum rules for different moments of the correlation functions. The results turn out to be very accurate. A factor of 1.6 for the ratio of the four quark condensate over the gluon condensate compared with the standard value is predicted.     

Charmonium states in quark-gluon plasma

We discuss how the spectral changes of quarkonia at T _c can reflect the ‘critical’ behaviour of QCD phase transition. Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the scalar and spin-2 gluon condensates near T _c. We also parametrize these changes into the electric and magnetic condensate near T _c. While the magnetic condensate hardly changes across T _c, we find that the electric condensate increases abruptly above T _c. Similar abrupt change is also seen in the scalar condensate. Using the QCD second-order Stark effect and QCD sum rules, we show that these sudden changes induce equally abrupt changes in the mass and width of J/ψ, both of which are larger than 100 MeV at slightly above T _c.      

Vacuum polarization due to a non-Abelian spherically symmetric chromodynamic field at a finite temperature

The model for gluon condensate of the form A _i ^a = _i ^a , A ₀ ^a =0, = const is considered at finite temperatures. The thermodynamic potential is computed in the one-loop approximation. Unlike the zero temperature case, it has a minimum at a nonvanishing condensate field.M. V. Lomonosov State University, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 65–71, November, 1992.     

Analysis of the logarithmic slope of <Emphasis Type="Italic">F</Emphasis><Subscript>2</Subscript> from the Regge gluon density behavior at small <Emphasis Type="Italic">x</Emphasis>

We study the accuracy of the Regge behavior of the gluon distribution function for an approximate relation that is frequently used to extract the logarithmic slopes of the structure function from the gluon distribution at small x. We show that the Regge behavior analysis results are comparable with HERA data and are also better than other methods that expand the gluon density at distinct points of expansion. We also show that for Q ² = 22.4 GeV², the x dependence of the data is well described by gluon shadowing corrections to the GLR-MQ equation. The resulting analytic expression allows us to predict the logarithmic derivative ∂F ₂(x, Q ²)/∂lnQ ² and to compare the results with the H1 data and a QCD analysis fit with the MRST parameterization input.     

Deconfinement in dense two-color QCD

We study SU(2) lattice gauge theory with two flavors of Wilson fermion at non-zero chemical potential μ and low temperature on a 8³×16 system. We identify three régimes along the μ-axis. For μ≲m_π/2 the system remains in the vacuum phase and all physical observables considered remain essentially unchanged. The intermediate régime is characterised by a non-zero diquark condensate and an associated increase in the baryon density, consistent with what is expected for Bose–Einstein condensation of tightly bound diquarks. We also observe screening of the static quark potential here. In the high-density deconfined régime we find a non-zero Polyakov loop and a strong modification of the gluon propagator, including significant screening in the magnetic sector in the static limit, which must have a non-perturbative origin. The behaviour of thermodynamic observables and the superfluid order parameter are consistent with a Fermi surface disrupted by a BCS diquark condensate. The energy per baryon as a function of μ exhibits a minimum in the deconfined régime, implying that macroscopic objects such as stars formed in this theory are largely composed of quark matter.     

Space-time dependence of the gluon condensate correlation function and quarkonium spectra

We consider the influence of the gluon condensate in QCD on the energy levels of quarkonia, taking into account the x-dependence of 〈ω|:G_μv^a(x) G^aμv(0):|ω〉. The modification compared to earlier approaches which approxim ated the above vacuum expectation value by a constant is quite sizeable; for the b?b system we find that the effect can be essentially described in terms of a local potential.     

Photon-gluon fusion at HERA: measurement of the fractional momentum of the gluon in lowQ 2 events

We have performed a Monte Carlo study of photon-gluon interactions at theep collider HERA. We show that it is possible to determine the fractional momentum carried by the gluon (x _g) from hadronic informations alone. In particular, in the photoproduction region, where thex andQ ² are badly measured, this could be the only global physical variable of interest, together with the hadronic invariant mass. The study of these quantities would allow a direct measurement of the gluon density of the proton in the rangex _g=2.5×10^?3∶5×10^?1.     

Use and misuse of QCD sum rules,factorization and related topics

The purpose of this paper is twofold. First, we are prompted by some recent publications to reply to the criticism of the QCD sum-rules approach contained therein. Hopefully, some of the discussion is of wider interest. In particular, we point out that the multi-gluon operators unlike the multi-quark ones, relevant to the sum rules, do not factorize at large N_c. This implies that the masterfield, even if it is found, will be of no immediate help in evaluating the quarkonium spectrum. Second, we derive new sum rules for light quarks which are sensitive to the mean intensity of the gluon field in the vacuum (the so-called gluon condensate, or 〈vac|G²|vac〉). New sum rules confirm the standard value of 〈vac|G²|vac〉. Some casual remarks on the π⁰ transitions into two virtual photons, π⁰ → γ^*γ^*, are also presented. Finally, we enumerate (in sect. 7) basic points of the sum-rule approach and discuss, im brief, the unsolved problems.     

Non-perturbative QCD vacuum frome +e−→I=1 hadron data

We estimate the gluon vacuum condensate α _s 〈F ²〉 from thee ⁺e^?→I=1 hadron cross-section known below 2 GeV using moment sum rules ratios. We obtain α _s 〈F ²〉= (3.9±1.0)10^?2GeV⁴. We also re-evaluate the contribution of the dimension-six vacuum condensates to the above sum rule and test the factorization hypothesis of the four-quark operator. Useful rules for the evaluation of the dimension-six vacuum condensates contributions are given.     

Scaling violations and the gluon distribution of the nucleon

Using recent data on deep inelastic lepton-nucleon scattering an attempt is made to extract the gluon distributionG(x, Q ²=4 GeV²) from the observed scaling violations of structure functions. The accuracy of the data allows only for a rough determination of the gluon distribution. In particular it is found that a hard gluon distributionis consistent with present measurements. Implications of the hard gluon distribution for charm production in the gluon fusion model and for the perturbative contributions to σ _L /σ _T are further discussed. Finally, analytic parametrizations of the QCDx- andQ ²-dependence of quark and gluon distributions are presented facilitating further possible applications.     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.