Pion distribution amplitude extracted from the experimental data with the local duality sum rule

Guo, Zhongyu; Liu, Jueping

doi:10.1103/physrevd.78.076006

Cited by 6 publications

(6 citation statements)

References 76 publications

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“…For the calculation of the next-to-next-to-leading-order correction to the pion transition form factor in the collinear factorization, refer to [18]. The BaBar data are consistent with those of CELLO [19] and CLEO [20] below Q 2 ≈ 9 GeV 2 , from which an endpoint suppressed shape of the pion DA has been extracted [21,22]. Taking into account high-power corrections, the asymptotic pion DA can also explain the CLEO data [23].…”

supporting

confidence: 56%

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Pion transition form factor in k_T factorization

Li,

Mishima

2009

Preprint

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It has been pointed out that the recent BaBar data on the πγ * → γ transition form factor Fπγ (Q 2 ) at low (high) momentum transfer squared Q 2 indicate an asymptotic (flat) pion distribution amplitude. These seemingly contradictory observations can be reconciled in the kT factorization theorem: the increase of the measured Q 2 Fπγ (Q 2 ) for Q 2 > 10 GeV 2 is explained by convoluting a kT dependent hard kernel with a flat pion distribution amplitude, kT being a parton transverse momentum. The low Q 2 data are accommodated by including the resummation of αs ln 2 x, x being a parton momentum fraction, which provides a stronger suppression at the endpoints of x. The next-to-leading-order correction to the pion transition form factor is found to be less than 20% in the considered range of Q 2 .

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supporting

confidence: 56%

“…That is, it is difficult to explain the continuous growth of Q 2 F πγ (Q 2 ) above Q 2 ≈ 10 GeV 2 using the asymptotic model. The overshoot in the low Q 2 region is expected, since this portion of data favors an endpoint suppressed shape [21,22]. Note that the overshoot can be resolved within the theoretical uncertainty from…”

mentioning

confidence: 73%

Pion transition form factor in k_T factorization

Li,

Mishima

2009

Preprint

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“…To be consistent with the previous estimation in a wider kinematical region, we chose the same scale for R as in [25], R = 9 GeV 2 , to avoid influence from the resonances in the J/ψ region and keep R large enough. The values of N 1 and N 2 are determined by minimizing the amount of the magnitude of the fit and asymptotic errors.…”

Section: Numerical Simulationmentioning

confidence: 97%

“…Note that the different models for the twist-two pion DA, such as the asymptotic form (namely all a n = 0 in equation ( 25)) and the Chernyak-Zhitnitsky (CZ) one [32] (a 2 = 2/3, a n>2 = 0 at the factorization scale μ F = 500 MeV in equation ( 25)), differ only in the values of a n of equation (25). The experimental data for the pion transition form factor F γ π (Q 2 ) multiplied by Q 2 from the BABAR Collaboration [13] show significant growth between 8 and 40 GeV 2 and the effective Q 2 dependence of the form factor (∼1/Q 3/2 ) differs significantly from the leading-order pQCD prediction (∼1/Q 2 ).…”

Section: The γmentioning

confidence: 99%

“…Comparing the theoretical results with the experimental data, useful constraints on the shape of the pion DA in terms of confidential regions for the Gegenbauer coefficients a 2 and a 4 can be obtained. Recently a quite different sum rule, namely the light-cone sum rule based on the analytic continuation by duality (ACD) [5,24,25], has been used to analyze the γ γ * → π 0 transition form factor. It is found that the ACD sum rule provides a reliable way to extract the form factor F γ π from F γ * π (Q 2 , q 2 ), and the rescaled form factor is consistent with the experimental results at least for Q 2 less than 10 GeV 2 [24].…”

Section: Introductionmentioning

confidence: 99%

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The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π⁰

Li¹,

Guo²,

Liu³

2013

J. Phys. G: Nucl. Part. Phys.

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The pion transition form factor F γ * π (q 2 1 , q 22 ) at the photon mass-shell of q 2 1 = q 2 2 = 0 is fixed by the axial anomaly, which may serve as a criterion in checking the consistency of the underlying quantum chromodynamics (QCD). We choose to work in the symmetric kinematical region where two photons have the same virtualities and hope to reproduce the experimental value of F γ * π (q 2 1 = 0, q 2 2 = 0) from light-cone QCD sum rules instead of direct extrapolation of the QCD expression to such a low-energy scale. The form factor of the transition γ * γ * → π 0 is investigated in the framework of the zero-and finite-width light-cone local duality QCD sum rules. The expression of the pion transition form factor F γ * π QCD (q 2 1 = t, q 2 2 = t ) at large t is independent of the twist-two and twist-three pion distribution amplitudes; therefore a more accurate conclusion may be reached. The influence of the light quark mass and the ωρπ coupling constant to our sum rules is also considered. The consistency between the axial anomaly, the intermediate hadronic structure and the QCD perturbative dynamics is tested to be true within a reasonable region of input parameters.

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Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

2009

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The transition pion-photon form factor is studied within the framework of Light-Cone QCD Sum Rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the β-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor F γ * γπ (Q 2 ) has been analyzed, making use of the BLM scalesetting procedure. In addition, predictions for the form factor F γ * ρπ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-Q 2 BaBar data on F γ * γπ arguing that the significant growth of the form factor between 10 and 40 GeV 2 cannot be explained in terms of higher-order perturbative corrections at the NNLO.

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Pion distribution amplitude extracted from the experimental data with the local duality sum rule

Cited by 6 publications

References 76 publications

Pion transition form factor in k_T factorization

Pion transition form factor in k_T factorization

The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π⁰

Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

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Pion distribution amplitude extracted from the experimental data with the local duality sum rule

Cited by 6 publications

References 76 publications

Pion transition form factor in k_T factorization

Pion transition form factor in k_T factorization

The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π0

Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

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Product

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The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π⁰