Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

Crossing antisymmetric Polyakov blocks + dispersion relation

Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the ‘+ type Polyakov blocks’. These blocks are built from AdSd+1 Witten diagrams. In 1d they encode the ‘+ type’ analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent ‘locality constraints’ in addition to the usual CFT sum rules given by the ‘Polyakov conditions’. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

Assignments of the X 4140 , X 4500 , X 4630 , and X 4685 Based on the QCD Sum Rules

In this article, we take into account our previous calculations based on the QCD sum rules, and tentatively assign the X 4630 as the D s ∗ D ¯ s 1 − D s 1 D ¯ s ∗ tetraquark molecular state or c s P c ¯ s ¯ A + c s A c ¯ s ¯ P tetraquark state with the J P C = 1 − + , and assign the X 3915 and X 4500 as the 1S and 2S c s A c ¯ s ¯ A tetraquark states, respectively, with the J P C = 0 + + . Then, we extend our previous works to investigate the LHCb’s new tetraquark candidate X 4685 as the first radial excited state of the X 4140 with the QCD sum rules and obtain the mass M X = 4.70 ± 0.12 GeV , which is in very good agreement with the experimental value 4684 ± 7 − 16 + 13 MeV . Furthermore, we investigate the two-meson scattering state contributions in details and observe that the two-meson scattering states alone cannot saturate the QCD sum rules, the contributions of the tetraquark states play an unsubstitutable role, and we can saturate the QCD sum rules with or without the two-meson scattering states.

Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

QCD sum rules analysis of weak decays of doubly heavy baryons: the $$b\rightarrow c$$ processes

A comprehensive study of $$b\rightarrow c$$ b → c weak decays of doubly heavy baryons is presented in this paper. The transition form factors as well as the pole residues of the initial and final states are respectively obtained by investigating the three-point and two-point correlation functions in QCD sum rules. Contributions from up to dimension-6 operators are respectively considered for the two-point and three-point correlation functions. The obtained form factors are then applied to a phenomenological analysis of semi-leptonic decays.

Charged and neutral $$ {\overline{B}}_{u,d,s} $$ → γ form factors from light cone sum rules at NLO

We present the first analytic $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s -computation at twist-1,2 of the $$ {\overline{B}}_{u,d,s} $$ B ¯ u , d , s → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ B ¯ u → γ ℓ − v ¯ , contribute to the flavour changing neutral currents $$ {\overline{B}}_{d,s}\to \gamma {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ B ¯ d , s → γ ℓ + ℓ − and serve as inputs to more complicated processes. We provide a fit in terms of a z-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the gBB*γ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms in the supplementary material. We give binned predictions for the $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ B ¯ u → γ ℓ − v ¯ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B-meson distribution amplitude parameter λB = 360(110) MeV. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, χq, compatible with the twist-expansion. The values χq = 3.21(15) GeV−2 and χs = 3.79(17) GeV−2 are obtained.

On the Difference between the Radii of Gluons and Quarks

In this paper, in the scope of a non-extensive statistical model for the nucleon’s structure function, the volume of the gluons in the nucleons and the relations among the temperature, T, the parameter “q” of Tsallis statistics, and the scattering energies, Q2, are studied. A system of equations with the usual sum rules are solved for the valence quarks, the experimental results for the polarized structure function, and the estimated carried moments for gluons and quarks. Each state of T and q leads to a set of chemical potentials and different radii for gluons and quarks. We conclude that gluons must occupy a larger volume than the quarks to fit the fraction of the total momentum. A linear function of the temperature with Q2 is obtained as an approach. The obtained range of temperatures is different from the previous models.