# ${{\boldsymbol W}}$ ANOMALOUS MAGNETIC MOMENT INSPIRE search

The full magnetic moment is given by ${\mathit \mu}_{{{\mathit W}}}$ = $\mathit e(1+\kappa +\lambda )/2{\mathit m}_{{{\mathit W}}}$. In the Standard Model, at tree level, $\kappa ~=~$1 and $\lambda ~=~$0. Some papers have defined $\Delta \kappa$ =$~1−\kappa$ and assume that $\lambda ~=~$0. Note that the electric quadrupole moment is given by $−\mathit e(\kappa −\lambda )/{{\mathit m}^{2}}_{{{\mathit W}}}$. A description of the parameterization of these moments and additional references can be found in HAGIWARA 1987 and BAUR 1988 . The parameter$~\Lambda$ appearing in the theoretical limits below is a regularization cutoff which roughly corresponds to the energy scale where the structure of the ${{\mathit W}}$ boson becomes manifest.
VALUE (${{\mathit e}}/2{\mathit m}_{{{\mathit W}}}$) EVTS DOCUMENT ID TECN  COMMENT
$2.22$ ${}^{+0.20}_{-0.19}$ 2298 1
 2001 I
DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 183+189 GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
2
 1995 G
CDF
3
 1992 C
UA2
4
 1992
THEO
5
 1991
THEO
6
 1988
THEO
7
 1987
THEO
8
 1987
THEO
9
 1985
THEO
10
 1985
THEO
11
 1984
THEO
1  ABREU 2001I combine results from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ interactions at 189 GeV leading to ${{\mathit W}^{+}}{{\mathit W}^{-}}$ , ${{\mathit W}}{{\mathit e}}{{\mathit \nu}_{{e}}}$ , and ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ final states with results from ABREU 1999L at 183 GeV to determine $\Delta \mathit g{}^{{{\mathit Z}}}_{1}$, $\Delta \kappa _{{{\mathit \gamma}}}$, and $\lambda _{{{\mathit \gamma}}}$. $\Delta \kappa _{{{\mathit \gamma}}}$ and $\lambda _{{{\mathit \gamma}}}$ are simultaneously floated in the fit to determine $\mu _{{{\mathit W}}}$.
2  ABE 1995G report $-1.3<\kappa <3.2$ for $\lambda$=0 and $-0.7<\lambda <0.7$ for $\kappa$=1 in ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}_{{e}}}{{\mathit \gamma}}$ X and ${{\mathit \mu}}{{\mathit \nu}_{{\mu}}}{{\mathit \gamma}}$ X at $\sqrt {\mathit s }$ = $1.8$ TeV.
3  ALITTI 1992C measure $\kappa$ = $1$ ${}^{+2.6}_{-2.2}$ and $\lambda$ = $0$ ${}^{+1.7}_{-1.8}$ in ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit \gamma}}$ + X at $\sqrt {\mathit s }$ = 630 GeV. At 95$\%$CL they report $-3.5<\kappa <5.9$ and $-3.6<\lambda <3.5$.
4  SAMUEL 1992 use preliminary CDF and UA2 data and find $-2.4<\kappa <3.7$ at 96$\%$CL and $-3.1<\kappa <4.2$ at 95$\%$CL respectively. They use data for ${{\mathit W}}{{\mathit \gamma}}$ production and radiative ${{\mathit W}}$ decay.
5  SAMUEL 1991 use preliminary CDF data for ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit W}}{{\mathit \gamma}}$ X to obtain $-11.3$ ${}\leq{}$ $\Delta \kappa$ ${}\leq{}$ $10.9$. Note that their $\kappa$ = 1$−\Delta \kappa$.
6  GRIFOLS 1988 uses deviation from $\rho$ parameter to set limit $\Delta \kappa$ ${ {}\lesssim{} }$ 65 ($\mathit M{}^{2}_{\mathit W}/\Lambda {}^{2}$).
7  GROTCH 1987 finds the limit $-37$ $<$ $\Delta \kappa$ $<$ 73.5 (90$\%$ CL) from the experimental limits on ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ assuming three neutrino generations and $-19.5$ $<$ $\Delta \kappa$ $<$ 56 for four generations. Note their $\Delta \kappa$ has the opposite sign as our definition.
8  VANDERBIJ 1987 uses existing limits to the photon structure to obtain $\vert \Delta \kappa \vert$ $<$ 33 (${\mathit m}_{{{\mathit W}}}/\Lambda$). In addition VANDERBIJ 1987 discusses problems with using the $\rho$ parameter of the Standard Model to determine $\Delta \kappa$.
9  GRAU 1985 uses the muon anomaly to derive a coupled limit on the anomalous magnetic dipole and electric quadrupole ($\lambda$) moments 1.05 $>\Delta \kappa$ ln($\Lambda /{\mathit m}_{{{\mathit W}}}$) $+$ $\lambda$/2 $>-2.77$. In the Standard Model $\lambda$ = 0.
10  SUZUKI 1985 uses partial-wave unitarity at high energies to obtain $\vert \Delta \kappa \vert$ ${ {}\lesssim{} }$ 190 (${\mathit m}_{{{\mathit W}}}/\Lambda ){}^{2}$. From the anomalous magnetic moment of the muon, SUZUKI 1985 obtains $\vert \Delta \kappa \vert$ ${ {}\lesssim{} }$ 2.2/ln($\Lambda /{\mathit m}_{{{\mathit W}}}$). Finally SUZUKI 1985 uses deviations from the $\rho$ parameter and obtains a very qualitative, order-of-magnitude limit $\vert \Delta \kappa \vert$ ${ {}\lesssim{} }$ 150 (${\mathit m}_{{{\mathit W}}}/\Lambda ){}^{4}$ if $\vert \Delta \kappa \vert$ ${}\ll$1.
11  HERZOG 1984 consider the contribution of ${{\mathit W}}$-boson to muon magnetic moment including anomalous coupling of ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ . Obtain a limit $-1$ $<$ $\Delta \kappa$ $<$ 3 for $\Lambda$ ${ {}\gtrsim{} }$ 1 TeV.
References:
 ABREU 2001I
PL B502 9 Measurement of Trilinear Gauge Boson Couplings $\mathit WWV$, ($\mathit V$ ${}\equiv$ ${{\mathit Z}}$, ${{\mathit \gamma}}$) in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at 189 GeV
 ABE 1995G
PRL 74 1936 Measurement of ${{\mathit W}}$ Photon Couplings with CDF in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.8 TeV
 ALITTI 1992C
PL B277 194 Direct Measurement of the ${{\mathit W}}$ $−$ ${{\mathit \gamma}}$ Coupling at the CERN ${{\overline{\mathit p}}}{{\mathit p}}$ Collider
 SAMUEL 1992
PL B280 124 The Magnetic Moment of the ${{\mathit W}}$ Boson
 SAMUEL 1991
PRL 67 9 Bounds on the Magnetic Moment of the ${{\mathit W}}$ Boson
 GRIFOLS 1988
IJMP A3 225 Electroweak Boson Selfcouplings and the Scale of Compositeness
 GROTCH 1987
PR D36 2153 New Limits from Single Photon Searches at ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Colliders
 VANDERBIJ 1987
PR D35 1088 New Bound on the Anomalous Magnetic Moment of the ${{\mathit W}}$ Boson
 GRAU 1985
PL 154B 283 Effects of Anomalous Magnetic Dipole and Electric Quadrupole Moments of the Charged Weak Boson on ($\mathit g-2)_{{{\mathit \mu}}}$
 SUZUKI 1985
PL 153B 289 Magnetic Moment of ${{\mathit W}}$ and Scale of Composite Weak Bosons
 HERZOG 1984
PL 148B 355 Constraints on the Anomalous Magnetic Moment of the ${{\mathit W}}$ Boson from the Magnetic Moment of the Muon
 ABREU 1999L
PL B459 382 Measurements of the Trilinear Gauge Boson Couplings $\mathit WWV$ ($\mathit V$ ${}\equiv$ ${{\mathit \gamma}}$, ${{\mathit Z}}$) in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at 183 GeV
 HAGIWARA 1987
NP B282 253 Probing the Weak Boson Sector in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$
 BAUR 1988
NP B308 127 Probing the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ Vertex at Future Hadron Colliders