CPC(HEP&NP),2009,33(X):1—4 Chinese Physics C Vol.33,No.X, Xxx,2009 * Status of the Fermilab Muon (g−2) Experiment B. Lee Roberts1,2;1) 1(DepartmentofPhysics,BostonUniversity,Boston, MA02215,USA) 0 2(OnbehalfoftheNewMuon(g−2)Collaboration) 1 0 Abstract TheNewMuon(g−2)CollaborationatFermilabhasproposedtomeasuretheanomalousmagnetic 2 momentofthemuon,aµ,afactoroffourbetterthanwasdoneinE821attheBrookhavenAGS,whichobtained n aµ=[116592089(63)]×10−11 ±0.54 ppm. The last digit of aµ is changed from thepublished valueowing toa a new value of the ratio of the muon-to-proton magnetic moment that has become available. At present there J appears to be a difference between the Standard-Model value and the measured value, at the ≃3 standard 0 deviationlevelwhenelectron-positronannihilationdataareusedtodeterminethelowest-orderhadronicpieceof 2 theStandardModelcontribution. Theimprovedexperiment,alongwithfurtheradvancesinthedetermination ] ofthehadroniccontribution,shouldclarifythisdifference. Becauseofitsabilitytoconstraintheinterpretation x of discoveries made at the LHC, the improved measurement will be of significant value, whatever discoveries e - may come from theLHC. p e Key words measurement, muon anomalous magnetic moment h [ PACS 13.40.Em, 12.15.Lk, 14.60.Ef 2 v 1 Introduction mostrecent,E821attheBrookhavenAGS,achieving 8 9 aprecisionofof±0.54partspermillion(ppm) [5,6]: 8 The anomalous magnetic moment (anomaly) of 2 a =[116592089(63)]×10−110.54ppm. (2) the e, µ or τ lepton is defined by µ . 1 The result has been slightly adjusted from the value 0 (g −2) Qe 0 ae,µ,τ= e,µ,2τ ; µ~e,µ,τ =ge,µ,τ 2m ~s, (1) reportedinRef.[5,6]becausethe valueofthefunda- 1 (cid:18) e,µ,τ(cid:19) mentalconstantλ=µ /µ ,themuontoprotonmag- µ p : v where ~µ is the magnetic dipole moment, and the fac- netic moment ratio, (see Eq. (6)), has changed [7]. i tor g is equal to 2 in the Dirac theory. One of the The statistical error in the anomaly is ±0.46 ppm X importantdiscoveriesonthepathtothedevelopment and the systematic error is ±0.28 ppm. The goal of r a ofQED,andthenthe StandardModel,wasthe mea- the new Fermilab experiment [8] is equal statistical surementbyKuschandFoley[1]whichshoweddefini- and systematic errors of ±0.1 ppm, for a combined tively that g >2. Almost simultaneously, Schwinger error of 0.14 ppm. e showedthatthis differencecouldbe explainedbythe Interestingly enough, the measured muon (one-loop in modern language) radiative correction anomaly seems to be slightly larger than the withthe valueα/2π≃0.00116···,independentofthe Standard-Model value of [9] lepton mass. aSM[e+e−]=116591834(49)]×10−11 (3) The Standard-Model value of a arises from loop µ µ contributions containing virtual photons, leptons, which uses e+e− annihilation into hadrons to de- gauge bosons, and hadrons in vacuum polarization termine the hadronic contribution, and the value of loops. Other talksatthis meeting havediscussedthe Pradeset al., [10]for the hadronic light-by-lightcon- Standard-Model contributions in some detail. For a tribution. There is a difference of ∼ 3.2 σ between general review the reader is referred to the review the two. If hadronic τ decays are used to determine article by Miller, et al., [3]. the lowest-orderhadronic contribution (a determina- The muonanomalyhasbeen measuredin a series tionthatreliesonsignificantisospincorrections),the of experiments that began over fifty years ago[4], the difference drops to ∼2σ [11]. Received14January2010 ∗ FERMILAB-CONF-10-012-E:SupportedinpartbytheU.S.NationalScienceFoundationandtheU.S.DepartmentofEnergy 1)E-mail:[email protected] (cid:13)c2009ChinesePhysicalSocietyandtheInstituteofHighEnergyPhysicsoftheChineseAcademyofSciencesandtheInstitute No.X Author1 etal: Instruction fortypesetting manuscripts 2 Non-Standard-Model contributions could come period. Assuming that the muon velocity is trans- from muon substructure, supersymmetry or extra verse to the magnetic field (β~·B~ = 0), the rate at dimensions, to name a few possibilities. Excel- which the spin turns relative to the momentum vec- lent reviews on this topic have been written by tor is given by the difference frequency between the St¨ockinger [12], and Czarnecki and Marciano [13]. spin precession and cyclotron frequencies. With an TheSUSYcontributiondependsontanβandthesign electric field present as well as a magnetic one, the of the µ parameter [12, 13]: difference frequency becomes 100 GeV 2 ~ω = ~ω −~ω aSUSY≃sgnµ130×10−11 tanβ. (4) a S C µ (cid:18) m (cid:19) = − Qe a B~− a − 1 β~×E~ ,(5) Both tanβ and the µ parameter will be difficult m " µ (cid:18) µ γ2−1(cid:19) c # e to determine at LHC.The signofthe deviationofa fromthe StandardModelgivesthe signofµ, andthµe where γ = (1−β2)−21. (The reason for introducing anelectricfieldwillbecomeapparentinthe nextsec- plot below illustrates the sensitivity of LHC and a µ tion.) The experimentallymeasurednumbers arethe to tanβ. It assumes that the SPS1a scenario is real- muonspinfrequencyω andthemagneticfield,which ized at LHC [12]. The difference between the Stan- a ismeasuredwithprotonNMR,calibratedtotheLar- dardModelandtheresultfromE821isassumedtobe ∆ =(255±80)×10−11. Thebandlabeled“Fermilab” mor precession frequency, ωp, of a free proton. The aµ assumesthesame∆ butwithanerrorof±34×10−11 anomaly is related to these two frequencies by aµ The improved error comes from the projected 0.14 ω˜ /ω R ppm experimental error, and improved knowledge of aµ=λ−aω˜ /pω =λ−R, (6) a p the hadronic contribution to a . See Ref. [12, 14] for µ more details. λ=µ /µ =3.183345137(85), and R=ω˜ /ω . The µ p a p tilde over ω means it has been corrected for the a 2255 electric-fieldandpitch(β~·B~ 6=0)corrections[3]. The LHCplus ratioλ is determined experimentally fromthe hyper- amu finestructureofmuonium,theµ+e− atom[7,15]. As 2200 LHC alone mentioned above, the recommended value of λ has changed slightly since the final results of E821 were published[5,6],increasingthevalueofa by9×10−11, 1155 µ FNAL which is reflected in Eq. (2). 2 Χ D 2.1 The Magic-γ Technique 1100 E821 In the 2001 data set, the systematic errorson the magnetic field were reduced to 0.17 ppm. A num- 55 ber of contributions went into this small error, but one which we wish to emphasize here is the aver- age magnetic field experienced by the muon ensem- 00 2 4 6 8 10 12 14 16 18 20 ble. The magnetic field in Eq. (5) is an average that tan Β can be expressed as an integral of the product of the muon distribution times the magnetic field distribu- Fig. 1. A “blueband” plot showing the LHC and muon (g−2) sensitivities to tanβ. The tionoverthestorageregion. Sincethemomentsofthe (Figure courtesy of D.St¨ockinger) muondistributioncoupletotherespectivemultipoles of the magnetic field, either one needs an exceed- ingly uniform magnetic field, or exceptionally good 2 Measuring a µ information on the muon orbits in the storage ring, to determine hBiµ−dist to sub-ppm precision. Thus The measurement of a uses the spin precession traditional magnetic focusing used in storage rings, µ resulting from the torque experienced by the mag- which involves magnetic quadrupole and higher mul- netic moment when placed in a magnetic field. An tipoles, will cause large uncertainties in the knowl- ensembleofpolarizedmuonsisintroducedintoamag- edge ofhBiµ−dist. This problemwasmitigatedin the neticfield,wheretheyarestoredforthemeasurement third CERN experiment[16], and in E821, by using No.X Author1 etal: Instruction fortypesetting manuscripts 3 electrostatic quadrupoles to provide the vertical fo- neededtobewellbelowsaturationandwaschosento cusing,freeingthemagnetic-fielddesigntobeasclose be 1.45 T. The resulting ring had a central orbit ra- to a uniform dipole field as possible. Examination of dius of7.112m, and12detector stationswere placed Eq. (5) shows that for γ = 29.3, called “the magic symmetrically around the inner radius of the stor- γ,” an electric field will not contribute to ω . The age ring. The detector geometry and number were a electric-fieldeffectvanishesforparticleswiththecen- optimized to detect the high-energy decay electrons, tralmomentumequaltop =3.09Gev/c,andisa which carry the largest asymmetry, and thus infor- magic small(sub-ppm)correctionforotherstoredmuons[6]. mation on the muon spin direction at the time of The CERN experiment used a rectangular aper- decay. In this design, many of the lower-energy elec- ture, which at their 7.3 ppm level of precision did trons miss the detectors, reducing background and not cause problems in determining the average field. pileup. The electrostatic quadrupoles [18] cover 43% However, the large moments of a rectangular beam of the ring, leaving significantgaps for the fast muon were not acceptable for the BNL experiment, which kicker[19] and other objects in the ring. aimedatafactor-of-twentyimprovement. Thusacir- While alternate schemes for measuring a have µ cular beam aperture was chosen for E821, which re- been proposed, the magic γ technique has a number sultedinasystematicerroronhBiµ−dist of0.03ppm, of things in its favor. One of the most important is certainly adequate for the experiment now proposed thatsinceE821,itisquitewellunderstoodandoffers at Fermilab. astraightforwardpathtoa0.1ppmmeasurement,or The experiment consists of repeated fills of the perhaps somewhat beyond. Its features are: storage ring, each time introducing an ensemble of • high muon polarization and decay asymmetry; muons into a magnetic storage ring, and then mea- suringthe twofrequencies ω andω . The muonlife- • large storage ring with ample room for detec- a p time is given by γτ =64.4 µs, and the data collec- tors, field mapping, kickers, etc.; µ tion period is typically ∼ 10 muon lifetimes in the • muoninjection, whichhasbeen shownto work; ring. The (g−2) precession period is 4.37 µs, and the cyclotron period is 149 ns. As the µ− (or µ+) • rates in the detectors that are easily handled decay, e− (e+) are emitted in the decay µ−(µ+) → with conventional technology; e−(e+)+ν (ν¯ )+ν¯ (ν ). The high-energy decay elec- µ µ e e • data are fit overmany (g−2) cycles, which is a trons(positrons)carryinformationonthe muonspin powerful tool to unmask systematic errorsthat directionatthedecay. Thusasthespinturnsrelative depend on time; to the momentum, the number of high-energy decay • precision magnetic field techniques which are electronsismodulatedbythefrequencyω ,asshown a well understood; in Fig. 2. • well understood systematic errors. s 9.2n 10 3 The Fermilab Proposal: P989 4 1 er p s 1 nt The Fermilabproposal[8]usesthe magicγ inthe e v E precision storage ring developed for E821, with new n Millio 10-1 detectors, electronics, along with improved magnetic field measurement and control. Central to the new 10-2 proposal is the use of features unique to Fermilab that will provide copious proton bunches of ∼ 1012 10-3 protonsat10to 20ms intervals. This compareswith 0 20 40 60 80 100 ∼4−5×1012 protonsper bunchatBNL,withamax- Time modulo 100m s [m s] imum of 12 bunches per machine cycle time of 2.7 s. Fig. 2. The time spectrum of decay electrons from the2001 E821 runningperiod, when µ− The effective fill rate at BNL was 4.4 Hz, compared with a projected rate of 18 Hz at Fermilab. were stored. (From Ref. [5] ) At BNL, pions 1.7% above the magic momentum The E821 storage ring was constructed as a decayed in an 80 m long FODO line, producing a “super-ferric”magnet[17],meaningthatthe ironde- beamthatcontainedanequalnumberofpions,muons termined the shape of the magnetic field. Thus B and electrons. A large hadronic “flash” accompanied 0 No.X Author1 etal: Instruction fortypesetting manuscripts 4 the injection into the ring causing a significant base- informationfor the interpretationof new phenomena line shift in the detectors near the injection point. that might be discovered at LHC. AtFermilab,theRecyclerRingwillbeusedtore- I wish to thank my many colleagues on E821, and bunch each proton batch from the Booster into four the New (g−2) for useful discussions. Thanks to D. bunches with ∼1012 protons each. These will be ex- Hertzog for comments on this manuscript, and to K. tracted one at a time to a production target at the Ellis for editorial help. My participation in this work location of the present antiproton target. The an- was supported in part by the U.S. National Science tiproton debuncher ring will be used as a 900 m long Foundation. pion decay line. The resulting pion flash will be de- creased by a factor of 20 from the BNL level, and 5 References the muon flux will be significantly increased because of the ability to take zero-degree muons. The stored References muon-per-proton ratio will be increased by a factor of 5 to 10 over BNL. Segmented detectors [20] and 1 P.KuschandH.MFoley,Phys.Rev.73,250(1948). new electronics should easily be able to handle the 2 J.Schwinger,Phys.Rev.73,416L(1948), andPhys.Rev. increased data rates per fill of the ring. 76790(1949).Theformerpapercontainsamisprintinthe The plan is to move the E821 muon storage ring expressionforae thatiscorrectedinthelongerpaper. 3 J.P. Miller, E. de Rafael and B.L. Roberts, to Fermilab, and install it in a new building near hep-ph/0703049, and Rep. Prog. Phys. 70, (2007) 795- the existing AP0 hall. The proposal was well re- 881; ceived by the Fermilab Program Advisory Commit- 4 R.L.Garwin,D.P.Hutchinson,S.PenmanandG.Shapiro, tee, but funding has not yet been secured. An op- Phys.Rev.118,271(1959). 5 G.Bennett,etal.,(Muon(g−2)Collaboration),Phys.Rev. timistic schedule has the ring moved, re-assembled Lett.92,161802(2004). andshimmedby2014. Weestimatethatintwoyears 6 G.Bennett,etal.,(Muon(g−2)Collaboration),Phys.Rev. of running on µ+, we could achieve the goal of the D73,072003(2006), andreferencestherein. ±0.14 ppm error. Most of this running would be 7 PeterJ.Mohr,BarryN.TaylorandDavidB.Newell,Rev. Mod.Phys.80,633(2008). simultaneous with NOVA, using the extra Booster 8 NewMuon(g−2)Collaboration, batches that cannot be used by the Main Injector http://lss.fnal.gov/archive/test-proposal/0000/fermilab-proposal-0989.shtml program. Ifthe MainInjectorprogramisdown,then 9 M. Davier, A. H¨ocker, B. Malaescu, C.Z. Yuan and Z. Zhang,arXiv:0908.4300Aug.2009. (g−2) can use the full Booster beam. With further 10 J. Prades, E. de Rafael and A. Vainshtein, in Lep- running we might be able to approach the 0.1 ppm ton Dipole Moments, Advanced Series on Directions in level. During the ProjectX era,we couldachievea a High Energy Physics -Vol.20, ed. B. Lee Roberts and comparable error for µ−. WilliamJ.Marciano,WorldScientific, p.303, (2010); and arXiv:0901.0306,Jan.2009. 11 M.Davier, A.H¨ocker, G.L´opez Castro, B.Malescu, H.X. 4 Summary and Conclusions Mo,G.ToledoS´anchez,P.Wang,C.Z.YuanandZ.Zhang, arXiv:0906.5443,2009andsubmittedtoEur.Phys.J. 12 DominikSto¨ckinger,inLeptonDipoleMoments,Advanced The muon anomalous magnetic moment has SeriesonDirectionsinHighEnergyPhysics-Vol.20,ed.B. played an important role in the development of the LeeRobertsandWilliamJ.Marciano,WorldScientific,p. Standard Model, and in constraining theories of 393,(2010); andJ.Phys.G 34,R45(2007). physics beyond the Standard Model. E821 at the 13 Andrzej Czarnecki and William J. Marciano, in Lepton Dipole Moments, Advanced Series on Directions in High Brookhaven Lab AGS achieved a factor of 13.5 in EnergyPhysics-Vol.20,ed.B.LeeRobertsandWilliamJ. precision over the famous CERN experiments of the Marciano, World Scientific, p. 11, (2010); and Phys. Rev. 1970s,andreachedarelativeprecisionof±0.54ppm. D 64,013014(2001). The New Muon (g−2) Collaboration has proposed 14 DavidW.Hertzog,etal.,arXiv.0705.4617,May2007. 15 W.Liuetal.,Phys.Rev.Lett.82,711(1999). to improve the error by a factor of four at Fermi- 16 J.Bailey,etal.,Nucl.Phys.B150,1(1979). lab. Given the sensitivity of aµ to a number of pro- 17 G.T.Danby,etal.,Nucl.Inst.andMeth.,A 457,151-174 posedextensionsto the StandardModel, amorepre- (2001). 18 Y.K.Semertzidis,etal.,Nucl.Inst.andMeth.A503,458- cisemeasurement,especiallywhencombinedwithim- 484(2003). provements in the knowledge of the hadronic contri- 19 E.Efstathiatis,etal.,Nucl.Inst.Meth.A496,8(2003). bution that are on the horizon, will provide valuable 20 R.McNabb,etal.,Nucl.Inst.MethA602,396(2009).