${{\mathit \tau}}$ MAGNETIC MOMENT ANOMALY

The $\mathit q{}^{2}$ dependence is expected to be small providing no thresholds are nearby.

${{\mathit \mu}_{{{\tau}}}}/({{\mathit e}}\hbar{}/2{{\mathit m}_{{{\tau}}}})−$1 = (${{\mathit g}_{{{\tau}}}}−$2)/2 INSPIRE search

For a theoretical calculation [(${\mathit g}_{{{\mathit \tau}}}−$2)/2 = 117$~721(5){\times }10^{-8}$], see EIDELMAN 2007.
S035MM
VALUE CL% DOCUMENT ID TECN  COMMENT
$\bf{-0.0024\text{ to }0.0047 }$ 95 1
AAD
2025BB
ATLS 140 fb${}^{-1}$, ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-0.041$ ${}^{+0.012}_{-0.009}$ 2, 3
AAD
2023BM
ATLS ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$, ${}^{}\mathrm {Pb}−{}^{}\mathrm {Pb}$
$-0.057\text{ to }0.024 $ 95 2
AAD
2023BM
ATLS ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$, ${}^{}\mathrm {Pb}−{}^{}\mathrm {Pb}$
$0.001$ ${}^{+0.055}_{-0.089}$ 4, 3
TUMASYAN
2023AS
CMS ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$, ${}^{}\mathrm {Pb}-{}^{}\mathrm {Pb}$
$-0.018$ $\pm0.017$ 5, 3
ABDALLAH
2004K
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$
$<0.107$ 95 6
ACHARD
2004G
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$
$-0.007\text{ to }0.005 $ 95 7
GONZALEZ-SPRI..
2000
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ and ${{\mathit W}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \nu}_{{{\tau}}}}$
$-0.052\text{ to }0.058 $ 95 8
ACCIARRI
1998E
L3 1991--1995 LEP runs
$-0.068\text{ to }0.065 $ 95 9
ACKERSTAFF
1998N
OPAL 1990--1995 LEP runs
$-0.004\text{ to }0.006 $ 95 10
ESCRIBANO
1997
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<0.01$ 95 11
ESCRIBANO
1993
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at LEP
$<0.12$ 90
GRIFOLS
1991
RVUE ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}{{\mathit \gamma}}$ at LEP
$<0.023$ 95 12
SILVERMAN
1983
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ at PETRA
1  AAD 2025BB limits are obtained by comparing the inclusive ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ fiducial cross-section in ${{\mathit p}}{{\mathit p}}$ collisions as a function of visible invariant mass at large masses to the Standard Model prediction.
2  AAD 2023BM measurement is derived from ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ total cross-section TeV. Authors report both the measured value and the corresponding 95$\%$ CL limit. from 1.44 nb${}^{-1}$ LHC ${}^{}\mathrm {Pb}−{}^{}\mathrm {Pb}$ collisions at $\sqrt {{{\mathit S}_{{{NN}}}} }$ = 5.02
3  Measurement ill-suited for a standard average because its likelihood appears to be remarkably non-Gaussian and asymmetric according to the model-dependent extraction procedure and the reported 95$\%$ CL limits.
4  TUMASYAN 2023AS measurement is derived from ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ total cross-section from 404 ${{\mathit \mu}}$b${}^{-1}$ LHC ${}^{}\mathrm {Pb}-{}^{}\mathrm {Pb}$ collisions at $\sqrt {{{\mathit S}_{{{NN}}}} }$ = 5.02 TeV.
5  ABDALLAH 2004K measurement 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. In addition to the measurement, the authors also quote 95$\%$ CL limits of $>$ -0.052 and $<$ 0.013.
6  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 the magnetic moment anomaly.
7  GONZALEZ-SPRINBERG 2000 use data on tau lepton production at LEP1, SLC, and LEP2, and data from colliders and LEP2 to determine limits. Assume imaginary component is zero.
8  ACCIARRI 1998E use ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}{{\mathit \gamma}}$ events. In addition to the limits, the authors also quote a value of $0.004$ $\pm0.027$ $\pm0.023$.
9  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 ($\mathit M_{{{\mathit Z}}}-{\mathit m}_{{{\mathit \tau}}}){}^{2}$.
10  ESCRIBANO 1997 use preliminary experimental results.
11  ESCRIBANO 1993 limit derived from $\Gamma\mathrm {( {{\mathit Z}} \rightarrow {{\mathit \tau}^{+}} {{\mathit \tau}^{-}})}$, and is on the absolute value of the magnetic moment anomaly.
12  SILVERMAN 1983 limit is derived from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ total cross-section measurements for $\mathit q{}^{2}$ up to (37 GeV)${}^{2}$.
  References:
AAD 2025BB
JHEP 2510 054 A measurement of the high-mass $?\bar?$ production cross-section at $\sqrt{s}=13$ TeV with the ATLAS detector and constraints on new particles and couplings
AAD 2023BM
PRL 131 151802 Observation of the $\gamma\gamma\to\tau\tau$ process in Pb+Pb collisions and constraints on the $\tau$-lepton anomalous magnetic moment with the ATLAS detector
TUMASYAN 2023AS
PRL 131 151803 Observation of $\tau$ lepton pair production in ultraperipheral lead-lead collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV
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
GONZALEZ-SPRINBERG 2000
NP B582 3 Model Independent Bounds on the ${{\mathit \tau}}$ Lepton Electromagnetic and Weak Magnetic Moments
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
SILVERMAN 1983
PR D27 1196 Limits on the Composite Structure of the ${{\mathit \tau}}$ Lepton and Quarks from Anomalous Magnetic Moment Measurements in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation