${{\mathit \pi}^{0}}$ 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 ${{\mathit \pi}^{0}}$ ELECTROMAGNETIC FORM FACTOR INSPIRE search

S009A

VALUE ($ 10^{-2} $)

EVTS

DOCUMENT ID

TECN

COMMENT

$\bf{ 0.0318 \pm0.0028}$

OUR AVERAGE

$0.0315$ $\pm0.0026$ $\pm0.0010$

2.4M

PRAKHOV

2026

SPEC

${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit p}}$, ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$

$3.0$ $\pm1.0$

0.4M

ADLARSON

2017

SPEC

${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit p}}$, ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$

$3.68$ $\pm0.51$ $\pm0.25$

1.1M

LAZZERONI

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

FARZANPAY

1992

SPEC

${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit n}}$ at rest

$2.5$ $\pm1.4$ $\pm2.6$

54k

MEIJERDREES

1992

SPEC

${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit n}}$ at rest

$3.26$ $\pm0.26$ $\pm0.26$

127

BEHREND

1991

CELL

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{0}}$

$-11$ $\pm3$ $\pm8$

32k

FONVIEILLE

1989

SPEC

Radiation corr.

• • • We do not use the following data for averages, fits, limits, etc. • • •

$12$ ${}^{+5}_{-4}$

⁴

TUPPER

1983

THEO

FISCHER 1978 data

$10$ $\pm3$

31k

⁵

FISCHER

1978

SPEC

Radiation corr.

$1$ $\pm11$

2.2k

DEVONS

1969

OSPK

No radiation corr.

$-15$ $\pm10$

7.6k

KOBRAK

1961

HBC

No radiation corr.

$-24$ $\pm16$

3.0k

SAMIOS

1961

HBC

No radiation corr.

¹ PRAKHOV 2026 is a continuation of ADLARSON 2017A, and also measure ${{\mathit \pi}^{0}}$ Dalitz decays at MAMI.

² ADLARSON 2017A use the A2 tagged photon facility at the Mainz Microtron, MAMI to measure ${{\mathit \pi}^{0}}$ Dalitz decay. The error is the total estimated experimental uncertainty .

³ 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.

⁴ TUPPER 1983 is a theoretical analysis of FISCHER 1978 including 2-photon exchange in the corrections.

⁵ The FISCHER 1978 error is statistical only. The result without radiation corrections is $+0.05$ $\pm0.03$.

References:

PRAKHOV

2026

PR C113 065202

New high-statistics measurement of the $?^0 \to e^+e^-?$ Dalitz decay at the Mainz Microtron

ADLARSON

2017A

PR C95 025202

Measurement of the ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ Dalitz decay at the Mainz Microtron

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