Soft gluon fields and anomalous magnetic moment of muon

An impact of nonperturbatively treated soft gluon modes on the value of anomalous magnetic moment of muon a_µ is studied within the mean-field approach to QCD vacuum and hadronization. It is shown that radial excitations of vector mesons strongly enhance contribution of hadronic vacuum polarization to a_µ, doubling the contribution of one-meson processes compared to the result for ground state mesons. The mean field also strongly influences the hadronic light-by-light scattering contribution due to the Wilson line in quark propagators.

Different Faces of Confinement

In this review, we provide a short outlook of some of the current most popular pictures and promising approaches to non-perturbative physics and confinement in gauge theories. A qualitative and by no means exhaustive discussion presented here covers such key topics as the phases of QCD matter, the order parameters for confinement, the central vortex and monopole pictures of the QCD vacuum structure, fundamental properties of the string tension, confinement realisations in gauge-Higgs and Yang–Mills theories, magnetic order/disorder phase transition, among others.

An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function G ∣ ϕ ∣ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum η 2 m η 2 F μ ν F μ ν , confining potential V c r , string tension σ , penetration depth λ , superconducting and normal monopole densities ( n s n n ), and the effective masses ( m η 2 and m A 2 ) will be investigated at finite temperature T . We also calculate the strong “running” coupling α s and subsequently the QCD β -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.

Updates on the QCD phase diagram from lattice

Different aspects of the phase diagram of strongly interacting matter described by quantum chromodynamics (QCD), which have emerged from the recent studies using lattice gauge theory techniques, are discussed. A special emphasis is given on understanding the role of the anomalous axial U(1) symmetry in determining the order of the finite temperature chiral phase transition in QCD with two massless quark flavors and tracing its origin to the topological properties of the QCD vacuum.

Operator product expansion of the non-local gluon condensate

We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

Influence of Fermions on Vortices in SU(2)-QCD

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields.

Importance of confinement in instanton induced potential for bottomonium spectroscopy

Mass spectra of bottomonium states are computed using the Instanton Induced potential obtained from Instanton Liquid Model for QCD vacuum and incorporating a stronger confinement term. Spin dependent interactions through confined one gluon exchange potential are incorporated to remove the mass degeneracy. The mass spectra of the $$b\bar{b}$$ b b ¯ states up to 4S states are found to be in good agreement with the values reported by PDG(2020). Mixing of nearby isoparity states are also studied. We found the state $$\varUpsilon (10{,}860)$$ Υ ( 10 , 860 ) as an admixture of $$5^3S_1$$ 5 3 S 1 and $$6^3D_1$$ 6 3 D 1 Upsilon states with mixing angle $$\theta = 39.98^{\circ }$$ θ = 39 . 98 ∘ and the mixed state di-leptonic decay width is found to be 0.25 keV as against the width of $$0.31 \pm 0.07$$ 0.31 ± 0.07 keV reported by PDG. Further the state $$\varUpsilon (11{,}020)$$ Υ ( 11 , 020 ) is also found to be the admixture of $$6^3S_1$$ 6 3 S 1 and $$5^3D_1$$ 5 3 D 1 Upsilon states with the mixing angle $$\theta = 51.69^{\circ }$$ θ = 51 . 69 ∘ and the di-leptonic decay width of the mixed state is obtained as 0.14 keV which is very close to the width of $$0.13 \pm 0.03$$ 0.13 ± 0.03 keV reported by PDG. Present results indicates that addition of confinement to the instanton potential is crucial for the determination of the mass spectroscopy of heavy hadrons.

A gauge invariant order parameter for monopole condensation in QCD vacuum

In this paper we improve the existing order parameter for monopole condensation in gauge theory vacuum, making it gauge-invariant from scratch and free of the spurious infrared problems which plagued the old one. Computing the new parameter on the lattice will unambiguously detect weather dual superconductivity is the mechanism for color confinement.As a byproduct we relate confinement to the existence of a finite correlation length in the gauge-invariant correlator of chromo-electric field strengths.