Dilaton chiral perturbation theory and applications

We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu–Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

On boundary corrections of Lüscher-Weisz string

The potential and the density profile of the QCD flux-tube are investigated within the framework of the Luscher-Weisz (LW) string action with two boundary terms. The Numerical simulations involve 4D SU(3) Yang-Mills LGT at finite temperature. In general, we detect signatures of the two boundary terms considered in the LWstring action. Near the end of QCD Plateau, the LW string is yielding a static potential which is in a good agreement with the lattice data for source separations R ≥ 0.3 fm. However, at T/Tc = 0.9, the fit to the potential data improves with a good fit attained at R ≥ 0.7 fm. The mean-square width of the energy profile at T/Tc = 0.9 matches well the width of the LW string over distance scales R ≥ 0.5 fm.

Chiral dynamics with confinement versus the standard chiral theory

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking is predetermined by confinement. It is shown that CCL retains all basic relations of the standard chiral theory but enables one to include quark degrees of freedom in the CCL. The expansion of the CCL provides the Gell–Mann–Oakes–Renner (GMOR) relations and the masses and decay constants of all chiral mesons, including [Formula: see text]. For the latter, one needs to define a nonchiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with the experimental and lattice data.

Light-cone distribution amplitudes of the nucleon and ∆ baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Small-momentum expansion of heavy-quark correlators in the large-β0 limit and αs extractions

We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-β0 limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, αs, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can guide the design of combinations of moments with improved perturbative behaviour.

Bc → J/ψ tensor form factors at large momentum recoil

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

The role of strangeness in chiral and $$U(1)_A$$ restoration

We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ($$\chi _S^\kappa $$ χ S κ , $$\chi _P^K$$ χ P K ) in the isospin 1/2 channel. We show that $$\chi _S^\kappa $$ χ S κ develops a maximum above the QCD chiral transition, after which it degenerates with $$\chi _P^K$$ χ P K . We also obtain $$\chi _S^\kappa $$ χ S κ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $$K_0^*(700)$$ K 0 ∗ ( 700 ) (or $$\kappa $$ κ ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $$\pi K$$ π K scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $$\chi _S^\kappa $$ χ S κ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $$m_l/m_s$$ m l / m s ratio that allows one studying $$K-\kappa $$ K - κ degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for $$O(4)\times U(1)_A$$ O ( 4 ) × U ( 1 ) A restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $$U(1)_A$$ U ( 1 ) A restoration.