Triply-charmed hexaquark states with the QCD sum rules

In this paper, we construct the charmed-diquark–charmed-diquark–charmed-diquark-type current to study the axial vector triply-charmed hexaquark state with the QCD sum rules in details. In calculations, we take the energy scale formula [Formula: see text] to choose the pertinent energy scale of the QCD spectral density so as to enhance the pole contribution and improve the convergent behavior of the operator product expansion. If the spin-breaking effects are small for the triply-charmed hexaquark states, the ground state hexaquark states with [Formula: see text], [Formula: see text] and [Formula: see text] are estimated to have the masses about 5.8 GeV and narrow widths.

A Diatomic Chain with A Mass Impurity

A classic diatomic chain with one mass impurity is studied using the recurrence relations method. The momentum autocorrelation function of the impurity results from contributions of two pairs of resonant poles and three branch cuts. The pole contribution is given by cosine function(s) and the cut contribution is the acoustic and optical branches. The acoustic and optical branches are given by expansions of even-order Bessel function. The expansion coefficients are integrals of elliptic functions in the real axis in a complex plane for the acoustic branch and along a contour parallel to the imaginary axis for the optical branch, respectively. An integral 22 22 1 2 0 d / ( r sin )( r sin ) 1 1 ϕ θ − θ− θ ∫ (r2 2 >r1 2 >1) is evaluated.

Pseudoscalar pole contribution to the hadronic light-by-light piece of aμ

We have studied the P → γ⋆ γ⋆ form factor in Resonance Chiral Theory, with P = π0; η, η', to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading U(3) chiral symmetry breaking terms, obtaining the most general expression for the form factor of order O(m2P). The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike momentum region of the virtual photon. Chiral symmetry relations among the transition form factors for π0, η and η' allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar π0 data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of aP,HLbLη = (8:47 ± 0:16) · 10-10 for our best fit (neglecting the BaBar π0 data). Also, a preliminary rough estimate of the impact of NLO in 1=NC corrections and higher vector multiplets (asym) enlarges the uncertainty up to aP,HLbLη = (8:47 ± 0:16stat ± 0:09NC +0:5 -0:0asym).

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon g - 2

The well-known discrepancy in the muon g − 2 between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon g − 2 using full QCD.

Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g̅2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor Fπ0γ*γ* (q21; q21) in the spacelike region with photon virtualities up to 1.5 GeV2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ*γ* → hadrons fusion cross sections and then compared with phenomenological models.