Precision determination of the pion form-factor and calculation of the muon g-2

May, 2001

28 pages

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Abstract:

We perform a new calculation of the hadronic contributions,

a({\rm Hadronic})

to the anomalous magnetic moment of the muon,

a_\mu

. For the low energy contributions of order

\alpha^2

we carry over an analysis of the pion form factor

F_\pi(t)

using recent data both on

e^+e^-\to\pi^+\pi^-

and

\tau^+\to \bar{\nu}_\tau \pi^+\pi^0

. In this analysis we take into account that the phase of the form factor is equal to that of

\pi\pi

scattering. This allows us to profit fully from analyticity properties so we can use also experimental information on

F_\pi(t)

at spacelike

t

. At higher energy we use QCD to supplement experimental data, including the recent measurements of

e^+e^-\to {\rm hadrons}

both around 1 GeV and near the

\bar{c}c

threshold. This yields a precise determination of the

O(\alpha^2)

and

O(\alpha^2)+O(\alpha^3)

hadronic part of the photon vacuum polarization pieces,

10^{11}\times a^{(2)}({\rm h.v.p.})=6 909\pm64:\quad 10^{11}\times a^{(2+3)}({\rm h.v.p.})=7 002\pm66

As byproducts we also get the masses and widths of the

\rho^0, \rho^+

, and very accurate values for the charge radius and second coefficient of the pion. Adding the remaining order

\alpha^3

hadronic contributions we find

10^{11}\times a^{\rm theory}(\hbox{Hadronic})= 6 993\pm69\quad(e^+e^- + \tau + {\rm spacel.})

The figures given are obtained including

\tau

decay data. This is to be compared with the recent experimental value,

10^{11}\times a^{\rm exp.}(\hbox{Hadronic})=7 174\pm150.

Note:

Plain TeX file. Published version. Correct value for light-by-light included Report-no: FTUAM 01-08

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