The Measurement of the Muon's Anomalous Magnetic Moment Isn't

2 Pages·0.14 MB·English

by  Jonathan L. Feng

UCI-TR-2002-29, UFIFT-HEP-02-26, CERN-TH/2002-187
The Measurement of the Muon’s Anomalous Magnetic Moment Isn’t
Jonathan L. Feng,1 Konstantin T. Matchev,2,3 and Yael Shadmi4,∗
1Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
2Department of Physics, University of Florida, Gainesville, FL 32611, USA
3Theory Division, CERN, CH-1211 Geneva, Switzerland
4Department of Physics, Technion, Haifa 32000, Israel
Recentresultsannouncedasmeasurementsofthemuon’sanomalousmagneticmomentareinfact
measurementsofthemuon’sanomalousspinprecessionfrequency. Thisprecessionfrequencyreceives
contributions from both the muon’s anomalous magnetic and electric dipole moments. We note
thatallexistingdatacannotresolvethisambiguity,andthecurrentdeviationfromstandardmodel
predictions may equally well be interpreted as evidence for new physics in the muon’s anomalous
magnetic moment, new physicsin themuon’s electric dipole moment, or both.
3
PACSnumbers: PACS:13.40.Em,14.60.Ef
0
0
2
Recently the Muon(g−2)Collaborationannounceda

n
newmeasurementofthemuon’sanomalousmagneticmo-
a
ment [1]. More precisely, however, what has been mea-
J
suredisthemuon’sanomalousspinprecessionfrequency.
0
2 Thisreceivescontributionsfromboththemuon’sanoma-
lousmagneticandelectricdipolemoments,andwepoint

2 out that the reported data and all existing constraints
v
cannot distinguish between the two.
6
The recent result is the latest tour de force from the
0
1 Muon(g−2) Experiment[2]. This experimentmeasures
8 the anomalousspinprecessionfrequency ofmuons circu-
0 latinginaperpendicularanduniformmagneticfield. For
2
fermions with gyromagnetic ratio g = 2, the cyclotron
0
and spin precession frequencies are identical. Measure-
/
h ments of the anomalous spin precession frequency have
p therefore been reported as measurements of the anoma- FIG.1: Regionsofthe(dµ,aµ)planeconsistentwiththemea-
p- lous magnetic dipole moment (MDM) aµ =(gµ−2)/2. sured |ωa| at 1σ (dark) and 2σ (light). The most recent SM
e The spin precession frequency is also sensitive to the aµ predictions [5, 6, 7] are also shown, with horizontal off-
h sets to the SM prediction of dµ ≈0 inserted for clarity. The
muon’s electric dipole moment (EDM), however [3, 4].
: vertical linesare thecentral valueand ±1σ direct boundson
v For a muon traveling with velocity β perpendicular to dµ [3].
i both a magnetic field B and an electric field E, the
X
anomalous spin precession vector is
r
a Assuming anegligible d , the measurementshowstenta-
e 2c µ
ω =−a B−d β×B tiveevidencefornewphysicsina withuncertainsignif-
a µm µ ¯h µ
µ icance, given the spread in theoreticalpredictions. How-
e 1 2
− −a β×E−d E , (1) ever, the |ω | result could just as well be taken as evi-
m c γ2−1 µ µ¯h a
µ (cid:16) (cid:17) dence for new physics in d . The best direct bound on
µ
d [3] is also shown. Clearly it does not resolve this am-
where m and d are the muon’s mass and EDM. In µ
µ µ
recentexperiments,theβ×E termofEq.(1)isremoved biguity; if anything, it favors the EDM interpretation.
In fact, even taking the lowest SM prediction for a , a
by running at the ‘magic’ γ ≈ 29.3, and the last term µ
is negligible. For highly relativistic muons with |β| ≈ 1, striking and unambiguous conclusion is that, barring a
fine-tunedcancelation,theMuon(g−2)Experimenthas
then, the anomalous spin precession frequency is
now set the most stringent upper bound on the muon’s
e 2 2c 2 1/2 electric dipole moment with |dµ|<3.2×10−19 e cm.
|ω |≈|B| a2 + d2 , (2)
a (cid:20)(cid:16)mµ(cid:17) µ (cid:16)¯h (cid:17) µ(cid:21) The MDM/EDM ambiguity may be resolved by ap-
pealing to theoretical prejudice that d is small. In su-
µ
and it constrains only a combination of d and a . persymmetry, for example, the maximal value of a is
µ µ µ
InFig.1weshowregionsofthe(d ,a )planethatare amax ∼ 10−7, assuming only flavor conservation [8]. By
µ µ µ
consistent with the new |ω | measurement. Also shown a phase rotation of the relevant operator, this implies
a
are the latest standard model (SM) predictions [5, 6, 7]. a maximal EDM of roughly dmax ∼ (e¯h/2m c)amax ∼
µ µ µ
2
10−20 e cm. This conclusion is far from universal, how- [1] G. W. Bennett [Muon g-2 Collaboration], Phys. Rev.
ever. For example, large muon EDMs are possible in Lett. 89, 101804 (2002) [hep-ex/0208001].
modelswhereEDMsscaleapproximatelyasd ∝m3 [9]. [2] For previous results, see R. M. Carey et al., Phys.
f f Rev. Lett. 82, 1632 (1999); H. N. Brown et al.
Given our current profound ignorance of the origins of
[Muon (g-2) Collaboration], Phys. Rev. D 62, 091101
electroweak symmetry breaking, flavor, and CP viola-
(2000) [hep-ex/0009029]; H. N. Brown et al. [Muon
tion, no definitive statement can be made. g-2 Collaboration], Phys. Rev. Lett. 86, 2227 (2001)
The effects of dµ and aµ are, of course, distinguish- [hep-ex/0102017].
able[3]: aµ causesprecessionaroundthemagneticfield’s [3] J. Bailey et al.[CERN-Mainz-Daresbury Collaboration],
axis,but d leadsto oscillationofthe muon’s spinabove Nucl. Phys. B150, 1 (1979).
µ
and below the plane of motion. A search for up-down [4] J. L. Feng, K. T. Matchev and Y. Shadmi, Nucl. Phys.
B 613, 366 (2001) [hep-ph/0107182].
asymmetry in the current data is in progress [10]. A
[5] F. Jegerlehner, talk given at the Workshop Centre de
dedicated EDM experiment [11] would provide a conclu-
PhysiqueTh´eoriqueMarseille,France,14-16March2002.
siveresolutionbyeithermeasuringanon-vanishingd or
µ [6] K. Hagiwara, A. D. Martin, D. Nomura and T. Teub-
constrainingthecontributionofdµ to|ωa|tobeinsignif- ner,talkgivenbyT.TeubneratICHEP’02,Amsterdam,
icant. Netherlands, 24-31 July 2002.
For now, however, the reported data is not a model- [7] M. Davier, S. Eidelman, A. Hocker and Z. Zhang,
independentmeasurementofthemuon’sanomalousmag- hep-ph/0208177.
[8] J.L.FengandK.T.Matchev,Phys.Rev.Lett.86,3480
netic moment. If measurements of precession frequency
(2001) [hep-ph/0102146].
are interpreted as measurements of a , the assumption
µ [9] See, e.g., K. S. Babu, S. M. Barr and I. Dorsner, Phys.
of a negligible muon EDM is best made explicit. Al- Rev. D 64, 053009 (2001) [hep-ph/0012303].
ternatively, the experimental status may be summarized [10] J. Miller, private communication.
without theoretical assumptions as in Fig. 1. [11] Y. K. Semertzidis et al., hep-ph/0012087; J. L. Feng,
K. T. Matchev and Y. Shadmi, in Proc. of the
APS/DPF/DPBSummerStudyontheFutureofParticle
Physics(Snowmass2001) ed.R.DavidsonandC.Quigg,
hep-ph/0110157.
∗
Incumbent of a Technion Management Career Develop-
ment Chair.