Dispersive derivation of the pion distribution amplitude

Abstract

We derive the dependence of the leading-twist pion light-cone distribution amplitude (LCDA) on a parton momentum fraction $x$ by directly solving the dispersion relations for the moments with inputs from the operator product expansion (OPE) of the corresponding correlation function. It is noticed that these dispersion relations must be organized into those for the Gegenbauer coefficients first in order to avoid the ill-posed problem appearing in the conversion from the moments to the Gegenbauer coefficients. Given the values of various condensates in the OPE, we find that a solution for the pion LCDA, which is stable in the Gegenbauer expansion, exists. Moreover, the solution from summing contributions up to 18 Gegenbauer polynomials is smooth, and can be well approximated by a function proportional to $x^p(1-x{)}^p$ with $p\approx 0.45$ at the scale $\mu =2$ GeV. Turning off the condensates, we get the asymptotic form, independent of the scale $\mu$, for the pion LCDA as expected. We then solve for the pion LCDA at a different scale $\mu =1.5$ GeV with the condensate inputs at this $\mu$, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from $\mu =2$ GeV to 1.5 GeV. That is, our formalism is compatible with the QCD evolution. The strength of the above approach that goes beyond analyses limited to only the first few moments of a LCDA in conventional QCD sum rules is highlighted. The precision of our results can be improved systematically by including higher-order and higher-power terms in the OPE.

arXiv comment23 pages, 12 figures, journal version, more references included

References in corpus (54)

• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• Higher-Twist Distribution Amplitudes of the K Meson in QCD
• Imaging dynamical chiral symmetry breaking: pion wave function on the light front
• Exclusive processes in position space and the pion distribution amplitude
• QCD Sum Rules for Skeptics
• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• Pion Distribution Amplitude from Lattice QCD
• Twist-3 Distribution Amplitudes of K* and phi Mesons
• QCD-based pion distribution amplitudes confronting experimental data
• Moments of pseudoscalar meson distribution amplitudes from the lattice
• $B\to \pi \ell {\nu }_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules
• Gluon Condensates and m_{c,b} from QCD-Moments and their ratios to Order alpha_s^3 and <G^4>
• Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
• Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders
• Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
• Lattice Results for Low Moments of Light Meson Distribution Amplitudes
• Gluon condensates and c, b quark masses from quarkonia ratios of moments
• Distribution amplitudes and decay constants for $(\pi ,K,\rho ,K^{\ast })$ mesons in light-front quark model
• Direct instantons, topological charge screening and QCD glueball sum rules
• Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD
• Pion and Kaon Distribution Amplitudes in the Continuum Limit
• Pion distribution amplitude from Euclidean correlation functions
• QCD Parameters Correlations from Heavy Quarkonia
• Generalized Parton Distributions and Pseudo-Distributions
• Twist-3 distribution amplitudes of scalar mesons from QCD sum rules
• A Bayesian approach to QCD sum rules
• Distribution Amplitudes of $K^{\ast }$ and $\varphi$ at Physical Pion Mass from Lattice QCD
• Nonperturbative partonic quasidistributions of the pion from chiral quark models
• A Lattice Computation of the First Moment of the Kaon's Distribution Amplitude
• Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules
• $D$ meson mixing as an inverse problem
• An improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude
• Pion Distribution Amplitude and Quasi-Distributions
• The pion light-cone distribution amplitude from the pion electromagnetic form factor
• Second moment of the pion distribution amplitude with the momentum smearing technique
• Exclusive Processes at Intermediate Energy, Quark-Hadron Duality and the Transition to Perturbative QCD
• Tomography of light mesons in light-cone quark model
• Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model
• Pion-photon transition form factor in LCSR and tests of asymptotics
• SVZ sum rules : 30 + 1 years later
• What binds quarks together at different momentum scales? A conceptual scenario
• Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory
• Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the second moment of the pion distribution amplitude
• Dispersive analysis of glueball masses
• QCD sum rules with spectral densities solved in inverse problems
• Pion to photon transition form factors with basis light-front quantization
• Global Analysis of hadronic two-body B decays in the perturbative QCD approach
• Extending the application of the LCSR method to low momenta using QCD renormalization-group summation. Theory and phenomenology
• Second moment of the pion's distribution amplitude
• Vacuum polarization contribution to muon $g-2$ as an inverse problem
• Correlations between the strange quark condensate, strange quark mass, and kaon PCAC relation
• ${\alpha }_s(\mu )$ from $M_{{\chi }_{0c(0b)}}-M_{{\eta }_{c(b)}}$@N2LO
• Stability Analysis of Sum Rules for Compton Scattering
• Pion and Kaon Distribution Amplitudes up to twist-3 in the QCD Instanton Vacuum

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