Asymptotic behavior of meson transition form factors
- PDF / 1,230,320 Bytes
- 34 Pages / 595.276 x 841.89 pts (A4) Page_size
- 58 Downloads / 174 Views
Springer
Received: April 16, Revised: May 1, Accepted: May 9, Published: May 29,
2020 2020 2020 2020
Martin Hoferichtera,b and Peter Stofferc a
Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH–3012 Bern, Switzerland b Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, U.S.A. c Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0319, U.S.A.
E-mail: [email protected], [email protected] Abstract: One of the open issues in evaluations of the contribution from hadronic lightby-light scattering to the anomalous magnetic moment of the muon (g − 2)µ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states. The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors. In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach. Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage. Finally, we compare our results to existing data as well as previous models employed in the literature. Keywords: Chiral Lagrangians, Effective Field Theories, Nonperturbative Effects, Precision QED ArXiv ePrint: 2004.06127
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)159
JHEP05(2020)159
Asymptotic behavior of meson transition form factors
Contents 1
2 Lorentz structure and helicity amplitudes 2.1 Pseudoscalar mesons: J P C = 0−+ 2.2 Scalar mesons: J P C = 0++ 2.3 Axial-vector mesons: J P C = 1++ 2.4 Tensor mesons: J P C = 2++
3 3 4 6 9
3 Brodsky-Lepage limit for the transition form factors 3.1 Pseudoscalar mesons 3.2 Scalar mesons 3.3 Axial-vector mesons 3.4 Tensor mesons 3.5 Summary of Brodsky-Lepage scaling
11 11 13 14 17 18
4 Comparison to data 4.1 Axial-vector mesons 4.2 Scalar and tensor mesons
21 21 23
5 Summary and outlook
27
1
Introduction
The asymptotic behavior of pseudoscalar transition form factors (TFFs)—describing the decay of a pseudoscalar meson into two (virtual) photons P → γ ∗ (q1 )γ ∗ (q2 ) — has been studied in detail in the literature using an expansion along the light cone x2 = 0, with the central result that at leading order the corresponding TFF, e.g. for the pion, can be expressed as [1–3] Fπ0 γ ∗ γ ∗ (q12 , q22 )
2Fπ =− 3
1
Z
du 0
φπ (u) −4 + O q , i uq12 + (1 − u)q22
(1.1)
in terms of the decay constant Fπ = 92.28(19) MeV [4] and the wave function φπ (u). This approach has been widely applied both for kinematic configurations that follow from a strict operator product expansion (OPE), in particular, the symmetric limit [5, 6
Data Loading...
