# ${{\boldsymbol \pi}^{0}}$ ELECTROMAGNETIC FORM FACTOR

The amplitude for the process ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ contains a form factor F($\mathit x$) at the ${{\mathit \pi}^{0}}{{\mathit \gamma}}{{\mathit \gamma}}$ vertex, where $\mathit x$ = [${\mathit m}_{\mathrm { {{\mathit e}^{+}} {{\mathit e}^{-}} }}/{\mathit m}_{{{\mathit \pi}^{0}}}]{}^{2}$. The parameter $\mathit a$ in the linear expansion F($\mathit x$) = 1 + $\mathit a{}\mathit x$ is listed below.
All the measurements except that of BEHREND 1991 are in the time-like region of momentum transfer.

# LINEAR COEFFICIENT OF ${{\boldsymbol \pi}^{0}}$ ELECTROMAGNETIC FORM FACTOR INSPIRE search

VALUE ($10^{-2}$) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 3.35 \pm0.31}$ OUR AVERAGE
$3.68$ $\pm0.51$ $\pm0.25$ 1.1M
 2017
SPEC ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{\pm}}$ ; ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$
$2.6$ $\pm2.4$ $\pm4.8$ 7.5k
 1992
SPEC ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit n}}$ at rest
$2.5$ $\pm1.4$ $\pm2.6$ 54k
 1992 B
SPEC ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit n}}$ at rest
$3.26$ $\pm0.26$ $\pm0.26$ 127 1
 1991
CELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{0}}$
$-11$ $\pm3$ $\pm8$ 32k
 1989
• • • We do not use the following data for averages, fits, limits, etc. • • •
$12$ ${}^{+5}_{-4}$ 2
 1983
THEO FISCHER 1978 data
$10$ $\pm3$ 31k 3
 1978
$1$ $\pm11$ 2.2k
 1969
$-15$ $\pm10$ 7.6k
 1961
$-24$ $\pm16$ 3.0k
 1961
1  BEHREND 1991 estimates that their systematic error is of the same order of magnitude as their statistical error, and so we have included a systematic error of this magnitude. The value of $\mathit a$ is obtained by extrapolation from the region of large space-like momentum transfer assuming vector dominance.
2  TUPPER 1983 is a theoretical analysis of FISCHER 1978 including 2-photon exchange in the corrections.
3  The FISCHER 1978 error is statistical only. The result without radiation corrections is $+0.05$ $\pm0.03$.
References:
 LAZZERONI 2017
PL B768 38 Measurement of the ${{\mathit \pi}^{0}}$ Electromagnetic Transition Form Factor Slope
 FARZANPAY 1992
PL B278 413 Measurement of the Slope of the ${{\mathit \pi}^{0}}$ Electromagnetic Formfactor
 MEIJERDREES 1992B
PR D45 1439 Measurement of the ${{\mathit \pi}^{0}}$ Electromagnetic Transition Formfactor
 BEHREND 1991
ZPHY C49 401 A Measurement of the ${{\mathit \pi}^{0}}$, ${{\mathit \eta}}$ and ${{\mathit \eta}^{\,'}}$ Electromagnetic Form Factors
 FONVIEILLE 1989
PL B233 65 Dalitz Decay. ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \pi}^{0}}$ Electromagnetic Transition Formfactor
 TUPPER 1983
PR D28 2905 Two Photon Exchange Effect in Radiative Corrections to ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{-}}{{\mathit e}^{+}}$
 FISCHER 1978
PL 73B 359 Measurement of the Neutral Pion Electromagnetic Form Factor Slope
 DEVONS 1969
PR 184 1356 Measurement of Neutral- and Charge Pion Form Factor Slopes
 KOBRAK 1961
NC 20 1115 Internal Pairs from ${{\mathit \pi}^{-}}$ Proton Interactions at Rest
 SAMIOS 1961
PR 121 275 Dynamics of Internally Converted Electron Positron Pairs