#### ${{\mathit \tau}}$ ELECTRIC DIPOLE MOMENT ($\mathit d_{{{\mathit \tau}} }$)

A nonzero value is forbidden by both $\mathit T$ invariance and $\mathit P$ invariance.
The $\mathit q{}^{2}$ dependence is expected to be small providing no thresholds are nearby.

#### Re($\mathit d_{{{\mathit \tau}} }$)

VALUE ($10^{-16}$ $\mathit e~$cm) CL% DOCUMENT ID TECN  COMMENT
$\bf{-0.22\text{ to }0.45 }$ 95 1
 2003
BELL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 10.6 GeV
• • We do not use the following data for averages, fits, limits, etc. • •
$<2.3$ 90 2
 2009 A
RVUE From ${{\mathit e}}$ EDM limit
$<3.7$ 95 3
 2004 K
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP2
$<11.4$ 95 4
 2004 G
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP2
$<4.6$ 95 5
 2000
ARG ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $10.4$ GeV
$\text{>-3.1 and <3.1}$ 95
 1998 E
L3 1991--1995 LEP runs
$\text{>-3.8 and <3.6}$ 95 6
 1998 N
OPAL 1990--1995 LEP runs
$<0.11$ 95 7, 8
 1997
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<0.5$ 95 9
 1993
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<7$ 90
 1991
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}{{\mathit \gamma}}$ at LEP
$<1.6$ 90
 1990
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 35 GeV
 1 INAMI 2003 use ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ events.
 2 GROZIN 2009A calculate the contribution to the electron electric dipole moment from the ${{\mathit \tau}}$ electric dipole moment appearing in loops, which is $\Delta$d$_{e}$ = $6.9 \times 10^{-12}$ d$_{{{\mathit \tau}} }$. Dividing the REGAN 2002 upper limit $\vert$d$_{e}\vert {}\leq{}1.6 \times 10^{-27}$ e cm at CL=90$\%$ by $6.9 \times 10^{-12}$ gives this limit.
 3 ABDALLAH 2004K limit is derived from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ total cross-section measurements at $\sqrt {s }$ between 183 and 208 GeV and is on the absolute value of ${{\mathit d}_{{\tau}}}$ .
 4 ACHARD 2004G limit is derived from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ total cross-section measurements at $\sqrt {s }$ between 189 and 206 GeV, and is on the absolute value of ${{\mathit d}_{{\tau}}}$ .
 5 ALBRECHT 2000 use ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ events. Limit is on the absolute value of Re($\mathit d_{{{\mathit \tau}} }$).
 6 ACKERSTAFF 1998N use ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}{{\mathit \gamma}}$ events. The limit applies to an average of the form factor for off-shell ${{\mathit \tau}}$ 's having $\mathit p{}^{2}$ ranging from ${{\mathit m}^{2}}_{{{\mathit \tau}}}$ to ($\mathit M_{{{\mathit Z}} }-{\mathit m}_{{{\mathit \tau}}}){}^{2}$.
 7 ESCRIBANO 1997 derive the relationship $\vert \mathit d_{{{\mathit \tau}} }\vert$ = cot$~\theta _{\mathit W}\vert \mathit d{}^{\mathit W}_{{{\mathit \tau}} }\vert$ using effective Lagrangian methods, and use a conference result $\vert \mathit d{}^{\mathit W}_{{{\mathit \tau}} }\vert$ $<5.8 \times 10^{-18}~\mathit e~$cm at 95$\%~$CL (L. Silvestris, ICHEP96) to obtain this result.
 8 ESCRIBANO 1997 use preliminary experimental results.
 9 ESCRIBANO 1993 limit derived from $\Gamma\mathrm {( {{\mathit Z}} \rightarrow {{\mathit \tau}^{+}} {{\mathit \tau}^{-}} )}$, and is on the absolute value of the electric dipole moment.
Conservation Laws:
TIME REVERSAL ($\mathit T$) INVARIANCE
PARITY ($\mathit P$) INVARIANCE
References:
 GROZIN 2009A
PAN 72 1203 Electric Dipole Moments, from ${{\mathit e}}$ to ${{\mathit \tau}}$
 ABDALLAH 2004K
EPJ C35 159 Study of Tau-pair Production in Photon-Photon Collisions at LEP and Limits on the Anomalous Electromagnetic Moments of the Tau Lepton
 ACHARD 2004G
PL B585 53 Muon Pair and ${{\mathit \tau}}$ Pair Production in Two Photon Collisions at LEP
 INAMI 2003
PL B551 16 Search for the Electric Dipole Moment of the ${{\mathit \tau}}$ Lepton
 ALBRECHT 2000
PL B485 37 A Search for the Electric Dipole Moment of the ${{\mathit \tau}}$ Lepton
 ACCIARRI 1998E
PL B434 169 Measurement of the Anomalous Magnetic and Electric Dipole Moments of the ${{\mathit \tau}}$ Lepton
 ACKERSTAFF 1998N
PL B431 188 An Upper Limit on the Anomalous Magnetic Moment of the ${{\mathit \tau}}$ Lepton
 ESCRIBANO 1997
PL B395 369 Improved Bounds on the Electromagnetic Dipole Moments of the ${{\mathit \tau}}$ Lepton
 ESCRIBANO 1993
PL B301 419 New Bounds on the Magnetic and Electric Moments of the ${{\mathit \tau}}$ Lepton
 GRIFOLS 1991
PL B255 611 Electromagnetic Properties of the ${{\mathit \tau}}$ Lepton from ${{\mathit Z}^{0}}$ Decay
 DELAGUILA 1990
PL B252 116 The Electric Dipole Moment of the ${{\mathit \tau}}$