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

INSPIRE   PDGID:
S035EDM
VALUE ($ 10^{-16} $ $\mathit e~$cm) CL% DOCUMENT ID TECN  COMMENT
$\bf{-0.185\text{ to }0.061 }$ 95 1
INAMI
2022
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
GROZIN
2009A
 RVUE From ${{\mathit e}}$ EDM limit
$<3.7$ 95 3
ABDALLAH
2004K
 DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP2
$<11.4$ 95 4
ACHARD
2004G
 L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP2
$-0.22\text{ to }0.45 $ 95 5
INAMI
2003
BELL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 10.6 GeV
$<4.6$ 95 6
ALBRECHT
2000
ARG ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $10.4$ GeV
$\text{>-3.1 and <3.1}$ 95
ACCIARRI
1998E
 L3 1991--1995 LEP runs
$\text{>-3.8 and <3.6}$ 95 7
ACKERSTAFF
1998N
 OPAL 1990--1995 LEP runs
$<0.11$ 95 8, 9
ESCRIBANO
1997
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<0.5$ 95 10
ESCRIBANO
1993
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<7$ 90
GRIFOLS
1991
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}{{\mathit \gamma}}$ at LEP
$<1.6$ 90
DELAGUILA
1990
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 35 GeV
1  INAMI 2022 use ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ events from 833 fb${}^{-1}$ of data. Also report a measurement of Re(d$_{\tau }$) = ($-0.62$ $\pm0.63$) $ \times 10^{-17}{{\mathit e}}$cm.
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  INAMI 2003 use ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ events.
6  ALBRECHT 2000 use ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ events. Limit is on the absolute value of Re($\mathit d_{{{\mathit \tau}}}$).
7  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 ($\mathit M_{{{\mathit Z}}}-{\mathit m}_{{{\mathit \tau}}}){}^{2}$.
8  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.
9  ESCRIBANO 1997 use preliminary experimental results.
10  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:
INAMI 2022
JHEP 2204 110 An improved search for the electric dipole moment of the $\tau$ lepton
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 ${{\mathit \tau}}$