Journal of High Energy Physics

, 2013:34 | Cite as

The pion vector form factor from lattice QCD and NNLO chiral perturbation theory

  • Bastian B. Brandt
  • Andreas JüttnerEmail author
  • Hartmut Wittig


We present a comprehensive study of the electromagnetic form factor, the decay constant and the mass of the pion computed in lattice QCD with two degenerate O(a)-improved Wilson quarks at three different lattice spacings in the range 0.05 – 0.08 fm and pion masses between 280 and 630 MeV at m π L ≥ 4. Using partially twisted boundary conditions and stochastic estimators, we obtain a dense set of precise data points for the form factor at very small momentum transfers, allowing for a model-independent extraction of the charge radius. Chiral Perturbation Theory (ChPT) augmented by terms which model lattice artefacts is then compared to the data. At next-to-leading order the effective theory fails to produce a consistent description of the full set of pion observables but describes the data well when only the decay constant and mass are considered. By contrast, using the next-to-next-to-leading order expressions to perform global fits result in a consistent description of all data. We obtain \( \left\langle {r_{\pi}^2} \right\rangle =0.481\left( {33} \right)\left( {13} \right) \) fm2 as our final result for the charge radius at the physical point. Our calculation also yields estimates for the pion decay constant in the chiral limit, F π /F = 1.080(16)(6), the quark condensate, \( \sum {\frac{{{1 \left/ {3} \right.}}}{\mathrm{MS}}\left( {2\;\mathrm{GeV}} \right)} =261\left( {13} \right)(1) \) MeV and several low-energy constants of SU(2) ChPT.


Lattice QCD Nonperturbative Effects Chiral Lagrangians 


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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Bastian B. Brandt
    • 1
  • Andreas Jüttner
    • 2
    Email author
  • Hartmut Wittig
    • 3
    • 4
  1. 1.Institut für theoretische PhysikUniversity of RegensburgRegensburgGermany
  2. 2.School of Physics and AstronomyUniversity of SouthamptonSouthamptonUnited Kingdom
  3. 3.PRISMA Cluster of Excellence, Institut für KernphysikUniversity of MainzMainzGermany
  4. 4.Helmholtz Institute MainzUniversity of MainzMainzGermany

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