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Register a new userPion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
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Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $delta^pi_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.
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The partonic structure of hadrons plays an important role in a vast array of high-energy and nuclear physics experiments. It also underpins the theoretical understanding of hadron structure. Recent developments in lattice QCD offer new opportunities for reliably studying partonic structure from first principles. Here we report on the use of the Feynman-Hellmann theorem to study the forward Compton amplitude in the unphysical region. We demonstrate how this amplitude provides direct constraint on hadronic inelastic structure functions. The use of external momentum transfer allows us to study the $Q^2$ evolution to explore the onset of asymptotic scaling and reveal higher-twist effects in partonic structure.
We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of Charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited state contributions without assuming quark-hadron duality.
We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_pisim 150 , mathrm {MeV}$. At lattice spacings between $0.06 , mathrm {fm}$ and $0.08 , mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $mu=2 , mathrm {GeV}$ in the $overline{mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.
A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly-coupled intermediate channels are included. These channels can consist of non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al.~[Phys.Rev. D91 114510 (2015)], and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion ($pi gamma^star to [pi pi, K overline K] to pi gamma^star$), kaon ($K gamma^star to [pi K, eta K] to K gamma^star$) and nucleon ($N gamma^star to N pi to N gamma^star$), as well as double-$beta$ decays, and radiative corrections to the single-$beta$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.
We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous dimension is separated from the remaining, continuous, spectrum by a finite gap. The corresponding eigenfunction coincides with the contribution of quark-gluon states to the two-particle DA $phi_-(omega)$ so that the evolution equation for the latter is the same as for the leading-twist DA $phi_+(omega)$ up to a constant shift in the anomalous dimension. Thus, ``genuine three-particle states that belong to the continuous spectrum effectively decouple from $phi_-(omega)$ to the leading-order accuracy. In turn, the scale dependence of the full three-particle DA turns out to be nontrivial so that the contribution with the lowest anomalous dimension does not become leading at any scale. The results are illustrated on a simple model that can be used in studies of $1/m_b$ corrections to heavy-meson decays in the framework of QCD factorization or light-cone sum rules.
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