Gluon Condensate Research Articles

Bootstrapping gauge theories

We consider asymptotically free gauge theories with gauge group SU(Nc) and Nf quarks with mass mq≪ΛQCD that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S matrix of the pseudo-Goldstone bosons (pions) that dominate the low-energy physics. For the important case of Nc=3, Nf=2, a numerical implementation of the method gives the phase shifts of the S0, P1 and S2 waves in good agreement with experimental results. The method incorporates gauge theory information (Nc, Nf, mq, ΛQCD) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the Shifman-Vainshtein-Zakharov (SVZ) sum rules. At low energy we impose constraints from chiral symmetry breaking. The only low-energy numerical inputs are the pion mass mπ and the quark and gluon condensates. Published by the American Physical Society 2024

Explaining Muon Excess in Cosmic Rays Using the Gluon Condensation Model

Ultrahigh-energy cosmic rays are often characterized indirectly by analyzing the properties of secondary cosmic ray particles produced in the collisions with air nuclei. The particle number N μ of muon and the depth of shower maximum X max after air shower cascade are mostly studied to infer the energy and mass of the incident cosmic rays. Research has shown that there is a significant excess in the observed number of muons arriving at the ground from extensive air showers compared to the simulations using the existing cosmic ray hadronic interaction model. To explain this muon excess phenomenon, a new theoretical model, the gluon condensation model, is introduced in this paper and simulated by using the AIRES engine. We assume that the gluon condensation (GC) effect appears mainly in the first collision of the cascade, leading to a significant increase in the strangeness production, consequently, the production rate of kaons is increased, and n K /n π is greater than the value of the usual hadronic interaction process. In the calculation, the model assumes that only pions and kaons are produced in the GC state. The increase of strange particle yield would mean that the energy transferred from the hadronic cascade to the electromagnetic cascade through π 0 → 2γ decay is reduced. This would in turn increase the number of muons at the ground level due to meson decays. Our model provides a new theoretical possibility to explain the muon excess puzzle.

Chromoelectric flux tubes within non-Abelian Proca theory

Flux tube solutions within non-Abelian SU(3) Proca theory with external sources are obtained. It is shown that such tubes have a longitudinal chromoelectric field possessing two components (nonlinear and gradient), as well as a transverse chromomagnetic field whose force lines create concentric circles with the center on the axis of the tube. The scenario of a possible relationship between non-Abelian Proca theory and quantum chromodynamics is considered. In such scenario: (a) the components of color fields have different behavior: those which are almost classical, and those which are purely quantum; (b) the second components create a gluon condensate that is a source of the field for the almost classical components of the Proca field; (c) Proca masses may appear as a result of an approximate description of the gluon condensate; (d) the question of gauge invariance is considered. It is shown that the results obtained are in good agreement with the results of lattice calculations. We make an assumption that an approximate description of a flux tube in quantum chromodynamics can be carried out using classical Proca equations but with a mandatory account of a gluon condensate.

Responses of quark-antiquark interactions and heavy quark dynamics to magnetic fields

We investigate the impact of the magnetic field generated by colliding nuclei on heavy quark-antiquark interactions and heavy quark dynamics in the quark-gluon plasma (QGP). By means of the hard-thermal-loop resummation technique combined with dimension-two gluon condensates, the static heavy quark potential and heavy quark momentum diffusion coefficient, which incorporate both perturbative and nonperturbative interactions between heavy quarks and the QGP medium, are computed beyond the lowest Landau level approximation. We find that the imaginary part of the heavy quark potential in the magnetic field exhibits significant anisotropy. Specifically, the absolute value of the imaginary part is larger when the quark-antiquark separation is aligned perpendicular to the magnetic field direction, compared to when it is aligned parallel to the magnetic field direction. The heavy quark momentum diffusion coefficient in the magnetized QGP medium also becomes anisotropic. As the temperature rises, the influence of higher Landau levels becomes increasingly significant, resulting in a decrease in the anisotropy ratio of the heavy quark momentum diffusion coefficient to values even below 1. At sufficiently high temperatures, this ratio ultimately approaches 1. The nonperturbative interactions are indispensable for understanding heavy quark dynamics in the low-temperature region. We also study the response of viscous quark matter to the magnetic field and explore its implications for heavy quark potential, thermal decay widths of quarkonium states, as well as heavy quark momentum diffusion coefficient. Published by the American Physical Society 2024

Power corrections to the modified QCD perturbative series based on conformal mapping of the Borel plane

Modifications of the QCD perturbative expansions by the subtraction of the dominant infrared renormalon have been proposed recently as attempts to solve the longstanding discrepancy between fixed-order and contour-improved perturbation theory for the hadronic τ decays. In this approach, the modified perturbative series is supplemented by a modified gluon condensate in the operator product expansion of the Adler function. Motivated by these works, we revisited recently a formulation of the QCD perturbation theory, proposed some time ago, which takes into account the renormalons by means of the conformal mapping of the Borel plane. One expects that the modified perturbative series obtained in this framework should be accompanied by modified power-suppressed nonperturbative corrections. However, in the previous studies the focus was on the perturbative series and the question of the possible power corrections has not been considered. In the present paper, we investigate for the first time this problem. Using techniques from the mathematical resurgence theory, we derive the expression of the dominant power correction to the perturbative series obtained by conformal mapping of the Borel plane, and discuss its implications for phenomenological applications. Published by the American Physical Society 2024

Negative moment of inertia and rotational instability of gluon plasma

Using first-principle numerical simulations of the lattice SU(3) gauge theory, we calculate the isothermal moment of inertia of the rigidly rotating gluon plasma. We find that the moment of inertia unexpectedly takes a negative value below the “supervortical temperature” Ts=1.50(10)Tc, vanishes at T=Ts, and becomes a positive quantity at higher temperatures. The negative moment of inertia indicates a thermodynamic instability of rigid rotation. We derive the condition of thermodynamic stability of the vortical plasma and show how it relates to the scale anomaly and the magnetic gluon condensate. The rotational instability of gluon plasma shares a striking similarity with the rotational instabilities of spinning Kerr and Myers-Perry black holes.

2++ Tensor di-gluonium from Laplace sum rules at NLO

We evaluate the next-to-leading (NLO) corrections to the perturbative (PT) and 〈αsG2〉 condensate and the LO constant term of the 〈G3〉 contributions to the 2++ tensor di-gluonium two-point correlator. Using these results into the inverse Laplace transform sum rules (LSR) moments and their ratio, we estimate the mass and coupling of the lowest ground state. We obtain: MT=3028(429) MeV and the renormalization group invariant (RGI) coupling fˆT=167(40) MeV within a vacuum saturation estimate of the D=8 dimension gluon condensates (kG=1). We study the effect of kG on the result and find: MT=3188(405) MeV and fˆT=164(28) MeV for kG=(3±2). Absolute upper bounds for the mass and coupling from the positivity of the spectral function are also derived. Our result does not favour the pure gluonia/glueball nature of the observed f2(2010,2300,2340) states.

Gluon condensation: From nucleon to Galactic Center

Gluon condensation: From nucleon to Galactic Center

Open charm mesons and charmonium states in magnetized strange hadronic medium at finite temperature

In this paper, we investigate the masses of the pseudoscalar ([Formula: see text]([Formula: see text], [Formula: see text]), [Formula: see text]([Formula: see text], [Formula: see text]) and vector open charm mesons ([Formula: see text]([Formula: see text], [Formula: see text]), [Formula: see text]([Formula: see text], [Formula: see text]) as well as the pseudoscalar ([Formula: see text], [Formula: see text]) and the vector charmonium states ([Formula: see text], [Formula: see text], [Formula: see text]) in the asymmetric hot strange hadronic medium in the presence of strong magnetic fields. In the magnetized medium, the mass modification of open charm mesons due to their interactions with baryons and the scalar fields ([Formula: see text], [Formula: see text], and [Formula: see text]) is investigated in a chiral effective model. Moreover, the charged pseudoscalar meson ([Formula: see text]), as well as the longitudinal component of charged vector meson ([Formula: see text]), experience additional positive mass modifications in the magnetic field due to Landau quantization. The effect of the modification of gluon condensates simulated by the medium change of dilaton field [Formula: see text] on the masses of the charmonia is also calculated in the chiral effective model. The contribution of masses of light quarks is also considered in the modification of gluon condensates. At high temperatures, the magnetically induced modifications of scalar fields significantly reduce the in-medium masses of mesons. The effects of magnetically induced spin mixing between the pseudoscalar and the corresponding vector mesons are incorporated in our study through a phenomenological effective Lagrangian interaction. The spin mixing result in a positive mass shift for the longitudinal component of the vector mesons and a negative mass shift for the pseudoscalar mesons in the presence of the magnetic field. From the obtained in-medium masses of charmonia and open charm mesons, we have also calculated the partial decay widths of [Formula: see text] to [Formula: see text], using a light quark pair creation model, namely, the [Formula: see text] model.

Deconfinement transition in the revolving bag model

Based on the bag model, we revisit the deconfinement phase transition under rotation. On top of the usual rotational energy for noninteracting particles, we perturbatively analyze the revolution effect of the hadron bag, i.e., of the potential confining quarks. The revolution effect can be phenomenologically translated into the rotational correction to the QCD vacuum energy or the gluon condensate. We demonstrate that if the revolution effect is (is not) taken into account, the transition temperature increases (decreases) as the angular velocity increased. The ‘revolving bag model’ provides a feasible explanation of the recent lattice simulations showing, contrary to effective models, that rotation favors the confined phase.

Research on electron and positron spectrum in the high-energy region based on the gluon condensation model

Electron (positron), proton and nuclei can be accelerated to very high energy by local supernova remnants (SNR). The famous excesses of electron and proton (nuclei) potentially come from such kind of local sources. Recently, the DAMPE experiment measured the electron spectrum (including both electrons and positrons) of cosmic rays with high-accuracy. It provides an opportunity to further explore the excess of electrons. According to the gluon condensation (GC) theory, once GC occurs, huge number of gluons condense at a critical momentum, and the production spectra of electron and proton showing typical GC characteristics. There are exact correlations between the electron and proton spectrum from a same GC process. It is possible to interpret the power-law break of cosmic rays in view of GC phenomenon, and predict one from another based on the relations between electron and proton spectrum. In this work, we point out the potential existence of a second excess in the electron spectrum, the characteristics of this excess is derived from experimental data of proton. We hope that the future DAMPE experiments will confirm the existence of this second excess and support the result of GC model.

Stability of Yang Mills vacuum state

We examine the phenomena of the chromomagnetic gluon condensation in the Yang-Mills theory and the problem of stability of the chromomagnetic vacuum fields. The apparent instability of the chromomagnetic vacuum fields is a result of quadratic approximation. The stability is restored when the nonlinear interaction of negative/unstable modes is taken into account in the case of chromomagnetic vacuum fields and the interaction of the zero modes in the case of (anti)self-dual covariantly-constant vacuum fields. All these vacuum fields are stable and indicate that the Yang-Mills vacuum is highly degenerate quantum state.

Hadron spectra and pion form factor in dynamical holographic QCD model with anomalous 5D mass of scalar field* *Supported in part by the National Natural Science Foundation of China (NSFC) (12235016, 12221005, 11725523, 11735007, 12275108), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030000, XDPB15), the start-up funding from University of Chinese Academy of Sciences (UCAS), and the

The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized. The light-flavor hadron spectra and the pion form factor were investigated, but it was difficult to reconcile the light-flavor hadron spectra and pion form factor. By considering the anomalous 5-dimension mass correction of the scalar field from QCD running coupling, it is found that the light flavor hadron spectra and pion form factor can be described well simultaneously. In particular, the ground state and lower excitation states of the scalar, pseudo scalar, and axial vector meson spectra are improved. However, the vector meson spectra are not sensitive to the anomalous 5-dimension mass correction of the scalar field.

Gluon condensation signature in the GeV gamma-ray spectra of pulsars

The accumulation of gluons inside nucleons, i.e., the gluon condensation, may lead to a characteristic broken power-law gamma-ray spectrum in high-energy nucleon collisions. Here we show that the observed spectra of at least 25 sources in the second Fermi Large Area Telescope Catalog of Gamma-ray Pulsars can be well fitted by such a broken power-law function that has only four free parameters. It strongly indicates that the gamma-ray emission from these pulsars is of hadronic origin, but with gluon condensation inside hadrons. It is well known that the quark-gluon distribution in a free nucleon is different from that in a bound nucleon. This work exposes the nuclear $A$ dependence of the gluon condensation effect, where $A$ refers to the baryon number. Our study reveals the gluon condensation under the condition of $A\ensuremath{\rightarrow}\ensuremath{\infty}$, which may open a new window for eavesdropping on the structure of compact stars on the subnuclear level.

Holographic imaginary potential of a quark antiquark pair in the presence of gluon condensation

For a moving heavy quark antiquark (QQ) in a quark gluon plasma (QGP), we use gauge/gravity duality to study both real and imaginary parts of the potential ( operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} respectively) in a gluon condensate (GC) theory. The complex potential is derived from the Wilson loop by considering the thermal fluctuations of the worldsheet of the Nambu-Goto holographic string. We calculate operatorname{Re}{V}_{Qoverline{Q}} and operatorname{Im}{V}_{Qoverline{Q}} in both cases where the axis of the moving Qoverline{Q} pair is transverse and parallel with respect to its direction of movement in the plasma. Using the renormalization scheme for the operatorname{Re}{V}_{Qoverline{Q}} , we find that the inclusion of GC increases the dissociation length while rapidity has the opposite effect. While for the operatorname{Im}{V}_{Qoverline{Q}} , we observe that by considering the effect of GC, the operatorname{Im}{V}_{Qoverline{Q}} is generated for larger distance thus decreasing quarkonium dissociation, while rapidity has opposite effect. In particular, as the value of GC decreases in the deconfined phase, the operatorname{Im}{V}_{Qoverline{Q}} is generated for smaller distance thus enhancing quarkonium dissociation, and at high temperatures it is nearly not modified by GC, consistent with previous findings of the entropic force.

Hadronic light-by-light contribution to the muon g−2 from holographic QCD with solved U(1)A problem

We employ the comparatively minimal extension of hard-wall AdS/QCD due to Katz and Schwartz which takes into account the U(1)$_A$ anomaly for computing hadronic light-by-light scattering contributions of pseudoscalar and axial vector mesons to the anomalous magnetic moment of the muon $a_\mu$. By including a gluon condensate as one extra tunable parameter besides those fixed by $f_\pi$ and the pion, kaon, and rho masses, we obtain remarkably accurate fits for $\eta$ and $\eta'$ masses and their decay rates to photons, leading to $a_\mu$ contributions in complete agreement with the Standard Model result by the Muon $g-2$ Theory Initiative. Turning to the less well understood axial vector contributions, we update our previous predictions obtained in flavor-symmetric hard-wall AdS/QCD models without U(1)$_A$ breaking.

QCD spectral sum rules 2022

We present a compact review of the status of QCD spectral sum rules until 2022. We emphasize the recent progresses for determining the QCD input parameters (αs, running quark masses, quark and gluon condensates) where their correlations have been taken into account. Some selected phenomenological uses of the sum rules in different channels (light and heavy quarks, gluonia/glueballs, hybrids and four-quark states) are briefly reviewed and commented. The estimate of the 1−+ light hybrid mass is revised which confirms the hybrid nature of the π1(1600) but not the π1(2050).

Infrared renormalons in supersymmetric theories

I argue that in large-$N$ supersymmetric QCD infrared renormalons are absent in the conformal window, there is no need in conspiracy, and vacuum expectation values of at least some gluon operators vanish. Basing on this conclusion I conjecture that in supersymmetric gluodynamics (supersymmetric Yang-Mills theory without matter) at least the leading renormalon ambiguity disappears which would be consistent with the fact that the gluon condensate vanishes in this theory, $\langle G_{\mu\nu}^a G^{\mu\nu\,a}\rangle =0$.

QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis

In-medium masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in the magnetized asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. Masses are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, $\ensuremath{\chi}$ introduced in the model through a scale-invariance breaking logarithmic potential. Contribution of the Dirac sea is incorporated through the nucleonic tadpole diagrams. Treating the scalar fields as classical, the dilaton field, $\ensuremath{\chi}$, the isoscalar nonstrange $\ensuremath{\sigma}(\ensuremath{\sim}(⟨\overline{u}u⟩+⟨\overline{d}d⟩))$, strange $\ensuremath{\zeta}(\ensuremath{\sim}⟨\overline{s}s⟩)$ and isovector $\ensuremath{\delta}(\ensuremath{\sim}(⟨\overline{u}u⟩\ensuremath{-}⟨\overline{d}d⟩))$ fields, are obtained by solving their coupled equations of motion as derived from the chiral model Lagrangian. The effects of magnetic field are incorporated through the Dirac sea as well as the Landau energy levels of the protons, and the anomalous magnetic moments of the nucleons. The scalar fields modify appreciably with magnetic field due to the Dirac sea contribution. In-medium masses of the charmonium and bottomonium ground states are observed to have significant modifications with magnetic field due to the effects of (inverse) magnetic catalysis. In presence of an external magnetic field, there is mixing between the longitudinal component of the vector and the pseudoscalar mesons (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of $J/{\ensuremath{\psi}}^{||}({\ensuremath{\eta}}_{c})$ and ${\mathrm{\ensuremath{\Upsilon}}}^{||}(1S)({\ensuremath{\eta}}_{b})$ states. These might show in the experimental observables, e.g., the dilepton spectra in the noncentral, ultrarelativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.

Background effective action with nonlinear massive gauge fixing

We combine a recent construction of a Becchi-Rouet-Stora-Tyutin (BRST)-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.