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Register a new userPion electromagnetic form factor from full lattice QCD
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We present the first calculation of the pion electromagnetic form factor at physical light quark masses. This form factor parameterises the deviations from the behaviour of a point-like particle when a photon hits the pion. These deviations result from the internal structure of the pion and can thus be calculated in QCD. We use three sets (different lattice spacings) of $n_f = 2+1+1$ lattice configurations generated by the MILC collaboration. The Highly Improved Staggered Quark formalism (HISQ) is used for all of the sea and valence quarks. Using lattice configurations with $u$/$d$ quark masses very close to the physical value is a big advantage, as we avoid the chiral extrapolation. We study the shape of the vector ($f_+$) form factor in the $q^2$ range from $0$ to $-0.15$~GeV$^2$ and extract the mean square radius, $langle r^2_vrangle$. The shape of the vector form factor and the resulting radius is compared with experiment. We also discuss the scalar form factor and radius extracted from that, which is not directly accessible to experiment. We have also calculated the contributions from the disconnected diagrams to the scalar form factor at small $q^2$ and discuss their impact on the scalar radius $langle r^2_srangle$.
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We compute the electromagnetic form factor of a pion with mass m_pi=330MeV at low values of Q^2equiv -q^2, where q is the momentum transfer. The computations are performed in a lattice simulation using an ensemble of the RBC/UKQCD collaborations gauge configurations with Domain Wall Fermions and the Iwasaki gauge action with an inverse lattice spacing of 1.73(3)GeV. In order to be able to reach low momentum transfers we use partially twisted boundary conditions using the techniques we have developed and tested earlier. For the pion of mass 330MeV we find a charge radius given by <r_pi^2>_{330MeV}=0.354(31)fm^2 which, using NLO SU(2) chiral perturbation theory, extrapolates to a value of <r_pi^2>=0.418(31)fm^2 for a physical pion, in agreement with the experimentally determined result. We confirm that there is a significant reduction in computational cost when using propagators computed from a single time-slice stochastic source compared to using those with a point source; for m_pi=330MeV and volume (2.74fm)^3 we find the reduction is approximately a factor of 12.
We present an investigation of the electromagnetic pion form factor, $F_pi(Q^2)$, at small values of the four-momentum transfer $Q^2$ ($lesssim 0.25$ GeV$^2$), based on the gauge configurations generated by European Twisted Mass Collaboration with $N_f = 2$ twisted-mass quarks at maximal twist including a clover term. Momentum is injected using non-periodic boundary conditions and the calculations are carried out at a fixed lattice spacing ($a simeq 0.09$ fm) and with pion masses equal to its physical value, 240 MeV and 340 MeV. Our data are successfully analyzed using Chiral Perturbation Theory at next-to-leading order in the light-quark mass. For each pion mass two different lattice volumes are used to take care of finite size effects. Our final result for the squared charge radius is $langle r^2 rangle_pi = 0.443~(29)$ fm$^2$, where the error includes several sources of systematic errors except the uncertainty related to discretization effects. The corresponding value of the SU(2) chiral low-energy constant $overline{ell}_6$ is equal to $overline{ell}_6 = 16.2 ~ (1.0)$.
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 0.05-0.08fm and pion masses between 280 and 630MeV at m_pi 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 <r^2_pi>=0.481(33)(13)fm^2 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_pi/F=1.080(16)(6), the quark condensate, Sigma^{1/3}_MSbar(2GeV)=261(13)(1)MeV and several low-energy constants of SU(2) ChPT.
We present lattice QCD calculations of nucleon electromagnetic form factors using pion masses $m_pi$ = 149, 202, and 254 MeV and an action with clover-improved Wilson quarks coupled to smeared gauge fields, as used by the Budapest-Marseille-Wuppertal collaboration. Particular attention is given to removal of the effects of excited state contamination by calculation at three source-sink separations and use of the summation and generalized pencil-of-function methods. The combination of calculation at the nearly physical mass $m_pi$ = 149 MeV in a large spatial volume ($m_pi L_s$ = 4.2) and removal of excited state effects yields agreement with experiment for the electric and magnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ up to $Q^2$ = 0.5 GeV$^2$.
Lattice QCD can provide a direct determination of meson electromagnetic form factors, making predictions for upcoming experiments at Jefferson Lab. The form factors are a reflection of the bound-state nature of the meson and so these calculations give information about how confinement by QCD affects meson internal structure. The region of high squared (space-like) momentum-transfer, $Q^2$, is of particular interest because perturbative QCD predictions take a simple form in that limit that depends on the meson decay constant. We previously showed incite{jonnaff} that, up to $Q^2$ of 6 $mathrm{GeV}^2$, the form factor for a `pseudo-pion made of strange quarks was significantly larger than the asymptotic perturbative QCD result and showed no sign of heading towards that value at higher $Q^2$. Here we give predictions for real mesons, the $K^+$ and $K^0$, in anticipation of JLAB results for the $K^+$ in the next few years. We also give results for a heavier meson, the $eta_c$, up to $Q^2$ of 25 $mathrm{GeV}^2$ for a comparison to perturbative QCD in a higher $Q^2$ regime.
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