Abstract
We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized ρ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between 0.060 fm and 0.081 fm, different lattice volumes up to mπL = 6.7 and pion masses down to mπ = 150 MeV. Bare lattice results are renormalized non-perturbatively using a variant of the RI′-MOM scheme and converted to the overline{mathrm{MS}} scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants fρT/fρ = 0.629(8) and the values of the second Gegenbauer moments a2‖ = 0.132(27) and a2⊥ = 0.101(22) at the scale μ = 2 GeV for the longitudinally and transversely polarized ρ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of ρ → ππ decay at the smaller pion masses is not taken into account.
Highlights
High energy, eN → eρN, that, besides deeply-virtual Compton scattering (DVCS), allows one to resolve the transverse distribution of partons inside the nucleon
We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized ρ mesons
In this approach the vector mesons are described in terms of lightcone distribution amplitudes (DAs) that specify the distribution of the longitudinal momentum amongst the quark and antiquark in the valence component of the wave function; the transverse degrees of freedom are integrated out
Summary
The ρ meson has two independent leading twist (twist two) DAs, φρ and φρ [16], corresponding to longitudinal and transverse polarization, respectively. Since the anomalous dimensions increase with n, the higher-order contributions in the Gegenbauer expansion are suppressed at large scales so that asymptotically only the leading term survives, usually referred to as the asymptotic DA: φρ, (x, μ → ∞) = φas(x) = 6x(1 − x). Higher Gegenbauer coefficients an mix with the lower ones, ak, k < n [18, 19] This implies, in particular, that Gegenbauer coefficients with higher values of n are generated by the evolution even if they vanish at a low reference scale. This effect is numerically small, so that it is usually reasonable to employ the Gegenbauer expansion to some fixed order
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
