In search of scalar gluonium

We discuss a scalar meson coupled strongly to gluons. Radiative decays of the J/ψ are taken as a source of gluons so that our aim is to calculate Γ(J/ψ→σγ), where σ is the presumed scalar gluonium. We use QCD sum rules to find both 〈0|α_sG_μν^aG_μν^a|σ〉 (where G_μν^a is the gluon field strength tensor) and Γ(J/ψ→σγ) in terms of 〈0|α_sG_μν^aG_μν^a|σ〉. The final prediction for the width is expected to be valid within a factor of two and gives $\text{Γ(}\text{J}\text{/ψ→σγ→}\text{two pions in S-wave}\text{+ γ) ? 25}\text{eV for}\text{m}{}_{\mathrm{\sigma }}\text{= 700}\text{MeV}$. Non-perturbative QCD naturally explains the observed asymmetry between scalar and pseudoscalar states in the radiative decays of the J/ψ. Some general remarks on gluonium in QCD are made.     

Masses of lowest lying heavy mesons in QCD

Using QCD sum rules for the polarization operator ∏^J(Q²) induced by all possible currents with J^PC=0^??, 1^??, 0⁺⁺, 1⁺⁺ and 2⁺⁺ we calculate the S- and P-states of charmonium. Power corrections due to the gluon condensate operator G^α_μνG^α_μν are included and shown to be very important. All known lowest lying charmonium states are reproduced extremely well and a firm prediction is made for the ¹P₁ state.     

A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

On investigating the structure of hadrons: Lattice Monte Carlo measurements of colour magnetic and electric fields and the topological charge density inside glueballs

We present some techniques for elucidating hadronic structure via lattice Monte Carlo calculations. Applying these techniques, we measure the fluctuations of colour magnetic and electric fields as well as the topological charge density inside and outside the lowest lying 0⁺ and 2⁺ glueballs in the SU(2) non-abelian lattice gauge theory. This gives us a picture of the glueball structure. We also obtain, as a by-product, an estimate of the gluon condensate ($\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{/π)〈π|F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{F}{}_{\mathrm{\mu \nu }}{}_{\mathrm{a}}\text{|Ω〈}$ and an estimate of the 0^? glueball mass which agrees with our previous estimates.     

Heavy particle content in QCD jets

We calculate the multiplicity of heavy quark pairs in gluon jets in lowest order QCD, along with the non-perturbative correction related to the gluon condensate 〈(α/π)F²〉. The value of the non-perturbative correction is

where M is the mass of the heavy quark, N is the number of colors, and C_F and C_A are the values of the Casimir operators in the fundamental and adjoint representation respectively. α(M) is the running coupling constant at the scale of the heavy quark, and 〈F²〉 is the gluon condensate, usually determined to be 〈α/πF²〉 ∼ 0.012 GeV⁴. The non-perturbative correction is extremely small.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

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.     

Discriminative deep inelastic tests of strong interaction field theories

It is demonstrated that recent measurements of ∫¹₀F₂(x, Q²)dx eliminate already all strong interaction field theories except QCD. A detailed study of scaling violations of F₂(x, Q²) in QCD shows their insensitivity to the gluon content of the hadron at presently measured values of Q².     

Interacting instantons, 1N expansion and the gluon condensate

Based on the dilute gas approximation (DGA) with repulsive and dipole interactions we discuss the N dependence of the vacuum energy density, 〈α_SF_μν^aF_μν^a〉 and of the topological charge correlation function at the crossover point of the instanton driven β function with the strong coupling one.     

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.     

Hidden constants: The θ parameter of QCD and the cosmological constant of N = 8 supergravity

For field theories that include the abelian gauge field A_μν? the field equations allow an arbitrary integration constant, which does not appear in the lagrangian but which does affect the physics. We present two applications: (i) the θ parameter of effective lagrangians for chiral symmetry breaking in QCD, and (ii) the cosmological constant in N = 8 supergravity, which does not require a gauging of the O(8) symmetry, but is rather due to a spontaneous breakdown of supersymmetry.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling $\text{g}\text{(t), t =}\text{ln}\text{[}\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{)}{}^2\text{μ}{}^4\text{]}$. The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F_μν^a = 0, and ferromagnetism, for which (F_μν^a)² = λ², i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.     

General results on glueball masses in QCD

A number of authors have investigated mass inequalities for mesons and baryons in QCD. These provide rigorous non-perturbative constraints on the mass spectrum. Similar inequalities for glueballs are investigated. For nonzero spin J, in the large-N_c approximation, m_J⁻⩾m_J⁺ is found. (For J = 0, the existence of a gluon condensate can modify this statement.) There are also constraints on how fast m_J can grow with J. For example, for m_J = a + bJ^α, 0 ⩽ α ⩽ 1 is found, a result consistent with Regge behaviour.     

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.     

Vacuum condensates in supersymmetric gluodynamics

We analyse the restrictions imposed by supersymmetric Ward identities on the dimension-six condensates in supersymmetric gluodynamics. It is shown that the system of the Ward identities admits a nonzero value for the four-fermion condensate \(\left\langle {\left( {\lambda \sigma _\mu T^a \bar \lambda } \right)^2 } \right\rangle _0 \) while 〈f ^abc F _μν ^a F _νρ ^b F _ρμ ^c 〉₀ must vanish.     

Numerical calculation of the momentum-space gluon propagator in quenched,reduced QCD3

A recently developed method of momentum-space Monte Carlo is applied to compute the momentum-space gluon propagator in quenched, reduced, continuum QCD₃ in axial gauge. There is some evidence that the gluon propagator D_μν(p) is finite as p → 0, which might indicate the existence of a non-perturbative gluon mass.     

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.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.