Results and prospects for the measurement of muon (g − 2)

PROCEEDINGS SUPPLEMENTS FJ~,S~ER

Results

Nuclear Physics B (Proc. Suppl.) 131 (2004) 157-161

and prospects

for the measurement

of muon

www.elsevierphysics.com

(g - 2) *

B. Lee Roberts (On behalf of the Muon (g - 2) Collaboration[i]) Department of Physics Boston University 590 Commonwealth Avenue Boston, MA 02215, USA The status of the Brookhaven-based muon (g - 2) experiment, E821 is presented, along with possibilities for future improvements. Four of the five data sets are now published, which have produced a value for a,+ with a relative precision of -4-0.7 parts per million. The final data collected using # - is being analyzed, and the result is expected early in 2004.

1. I N T R O D U C T I O N

through the g-factor as defined by

The muon ( g 2) experiment at the Brookhaven National Laboratory AGS has been underway since the mid 1980s. The original motivation was to observe the electroweak contribution from virtual W and Z ° bosons. The precision goal for the experiment was set at ±0.35 parts per million (ppm), which was about one fifth of the lowest-order electroweak contribution. Because the muon anomalous moment arises from virtual radiative corrections, there was also the possibility of observing contributions from physics beyond the standard model such as supersymmetry in the few-hundred GeV range, as well as a sensitivity to muon substructure at the few TeV scale.J2] The principle of the experiment is to measure the difference frequency between the spin precession and momentum precession for muons in a storage ring, and results with precisions of 13 ppm, 5 ppm, 1.3 ppm and 0.7 ppm have been published.J3-6] The apparatus is now mostly documented in the literature,J7-13]

e _, fis=gs(-~m)S,

2. D I P O L E M O M E N T S The magnetic dipole moment associated with a charged spin-one-half particle is related to the anomalous magnetic moment a (anomaly) *This work sponsored in part by the US National Science Foundation and the US Department of Energy. 0920-5632/$ - see front matter © 2004 Published by Elsevier B.V.. doi: 10.1016/j.nuclphysbps.2004.02.021

eh #=(l+a)--2m,

a--

g- 2 2 .(1)

We understand that the large anomalies of the proton and neutron are a result of their internal structure, whereas the leptons e, p and ~- have anomalies which are expected to only arise from radiative corrections. This has been discussed in some detail by other speakers. The lowestorder radiative correction (Schwinger term) gives an anomaly of a/27r, which is 0.0011614 .... and dominates the anomaly of the leptons. While a magnetic dipole moment (MDM) is allowed, an electric dipole moment (EDM) is forbidden by both parity and time reversal symmetries, which can be seen from the transformation properties of the Hamiltonian

= - ~ . ~ - d. £

(2)

under the three symmetries C, P and T. Thus while the magnetic anomaly has a substantial standard model value, the expectation for the EDM is orders of magnitude below what is experimentally accessible. Any discrepancy between the measured and expected MDM or EDM would signify the presence of new physics. A popular example of new physics is SUSY, which connects the EDM, MDM and the leptonnumber violating conversion process # -+ e in the field of a nucleus, which is shown pictorially below

158

B.L. Roberts~Nuclear Physics B (Proc. Suppl.) 131 (2004) 157-161

in Fig. 1. My colleague Yannis Semertzidis will discuss EDMs in his talk at this conference.

li--~ e ~

, .

1...=..~_~ 1 ~ ~ " 3 ~ 1

~

MDM EDM

.__~_..__~_

Figure 1. The supersymmetric contributions to the anomaly, and to It -+ e conversion, showing the relevant slepton mixing matrix elements. The MDM and EDM give the real and imaginary parts of the matrix element, respectively. (The × indicates a chirality flip)

One of the main reasons why we are here at this workshop is to discuss the strong-interaction contribution to the muon anomaly, which is related to the data from electron-positron annihilation to hadrons through a dispersion relation. It is clear that for the interpretation of the present experiment, E821, as well as for the interpretation of any improved experiment at Brookhaven or at J-PARC, further improvement on the strong interaction contribution is essential.

to ±1 ppm uniformity when averaged over azimuth. A contour map from one of the field maps is shown in Fig. 2. The B which appears in Eq. 3 is the field averaged over the muon distribution in the ring. With such a uniform field, only modest information is needed on the muon distribution, and in our data set from 2000 the systematic error from our knowledge of the muon distribution was ±0.03 ppm.[6] To monitor the magnetic field during data collection, 366 fixed NMR probes were placed around the ring and continuous readings from about 150 probes were used to track the field in time. About twice per week a trolley with 17 NMR probes was used to map the field in the storage ring. During muon data collection, the trolley is stored in a garage inside the vacuum chamber. The trolley probes were calibrated with a special spherical water probe, which provides a calibration to the free proton precession frequency wp.

Multipoles [ppm] :

J

il.

=

i-io. ....

-u.........i...-- - ,;.......i.....,--i}..-.

-4

The difference frequency, which is the difference between the spin and momentum precession in the storage ring, wa -- ws - w e , is given by a,

.........

.o~.i~..L.

3. T H E E X P E R I M E N T

race a , B -

i

72 2_1

'

where the electric field does not contribute to the spin motion for " / = 29.3. The storage ring is a weak focusing ring, and we ran with field indices of 0.142, 0.137 and 0.122 during our three main periods of data collection. As can be seen from Eq. 3, both wa and the magnetic field B must be known to extract a value of a , from the experiment. The field is measured with NMR techniques, and has been shimmed

-3

-2

-1

0

normal

skew

Quad 0.24

0.29

Sext -0.53

-1.06

Octu -0.10

-0.15

Decu 0.82

0.54

~-........! ,..... ~..........~

, ~iio i'U-!-I i......~.~:ti : .........ii ...........

C~a-

i

1 2 3 4 radial distance[cm]

Figure 2. A contour plot of the magnetic field from the Y2000 run.

Positrons (electrons) from the parity violating decay #+(-) -+ e +(-) + Ve(Pe) + Pt~(v~) are detected in lead-scintillating-fiber calorimeters[13] where the energy and arrival time is measured. The highest energy positrons (electrons) carry the spin information, and the number of high-energy positrons (electrons) as a function of time is given

B.L. Roberts~Nuclear Physics B (Proc. Suppl.) 131 (2004) 157-161 by N ( t ) = N o ( E ) e ~ [1 + A ( E ) sin(w~t + ¢~(E))] ,(4) where the energy threshold E is chosen to optimize the quantity N A ~. In the analysis of the data, many small effects such as coherent beam motion in the storage ring must be included.[5,6] The data from the Y2000 run are shown below in Fig. 3, and one can see qualitatively that Eq. 4 gives a good description of the data.

4 Billion Positrons with E > 2 G e V

~ I0 7 H

A ^ ^ _

~

, v V V VV'-~/\..~..AAAAA 10 ~

./~AAAAAAA

A

,

v I

v

~ v

v v VV'71~2oo~s

v vVVVvI/~AAA~,~^^^_ - v v VVVVw~AAA~^/

,, v

i

A_

J v

l0 s V V V U ~t ~-i~-'~,. A A A r~A

V V

V l 2eO'300~s

300-400~ls

10 ~A ~~

J

" ""

-=3]V\/:AAAA

400-S00 ~a

~ ^

A[~ '~ A -

~.

,

,

v V V VV'

v ~ V V ', ". , I i [ ' . , A . ~

I mmvvW 0

v "

v ,' V V V V V b ~ / ' ~ A A A ~

10

20

30

40

50

S00-600~s

r. A ~,

7O0-80O~s 800-8[0 ~s

60

70

80

90 1~ T i m e ~ts

Figure 3. The time spectrum of decay positrons from the Y2000 data set.J6] The muon lifetime in the ring is 64.4 #s, and each line of wiggles is for a 100 #s time period, as labeled on the right-hand side. The data points are shown in red, the error bars are shown in blue.

4. A N A L Y S I S F O R a~ Two numbers are needed to determine au, w~ and Wp. The magnetic field (Wp) is averaged over time according to the number of muons stored during each time interval, and the relation ~Ma / b d p

a -

A _ ~a/~p,

(5)

159

is used, where A = ~# p is a constant known from experiment and theory.J14] The time spectrum is fit to determine Wa and then the value of a~ is determined.

4.1. The Blind Analysis To avoid the possibility that data selection, cuts and other analysis choices might be made in a way which biases the result towards one or another answer, the analysis in E821 has been carried out in a fashion that prevents (%) being determined until after the analysis is completed. The analysis splits into two pieces, wa and Wp, and two separate and independent groups within the collaboration carry out these analyses. Initially, each person analyzing one or the other frequency places an arbitrary offset on the resulting frequency, so that only relative comparisons can be made, even among those analyzing the same frequency. Once there seems to be relative agreement, the relative offsets within a subgroup are set to a common offset, to see if the separate analyses agree. Since there are two independent offsets, one per analysis subgroup, which are known only to those directly involved in the analysis, and since the collaboration has agreed that no single person shall have access to both offsets, it is impossible for anyone to determine the result in advance. Typically we have had two independent analyses of Wp and four to five of Wa. Only after all questions are answered, and there is complete internal consistency in the largely independents analyses of both Wa and Wp, are the relative offsets removed and the final result obtalned. The decision to remove the offsets is made by the entire collaboration and requires a unanimous vote. While the arithmetic is checked by all who wish to do so, we have agreed that no further analysis is permitted once the offsets are removed. This plan permits an unbiased analysis of the data, and prevents analysis cuts from moving the result in one or another way which might be desirable to a particular analyzer. 4.2. Blind Analysis of R(s)? The usefulness of independent measurements of a quantity is obvious. The E821 analysis is

160

B.L. Roberts~Nuclear Physics B (Proc. Suppl.) 131 (2004) 157-161

done completely blind, and is thus unaffected either by our previous measurements or by agreement/disagreement with theory. The interpretation of our ( g - 2) result depends critically on the measurements of the cross section for e+e annihilation to hadrons, since they determine the hadronic piece of the standard model value. At present, only the new results from Novosibirsk have been published,J15] and as we know from this conference, K L O E and BaBar are poised to make important contributions to this field. Because of the discrepancy between the e+e - and T-decay data, J16] the Novosibirsk group found a normalization problem in their cross-section measurements,[17] which moved the e+e - results closer to those from T-decay, but discrepancies remain.[18] The theoretical path from e+e - data to a hadronic contribution to a , is fairly straightforward. However, as discussed in ref. [18] and at this meeting by Jagerlehner, Davier and others, the path from hadronic w-decay data to a(Had; 1) seems to have some unresolved issues. In order to have confidence in the standard model value, we must have confidence that the e+e - data which go into the dispersion relation are correct. Thus it is important the the measurements done at K L O E and BaBar are quite independent from the Novosibirsk results, and check each other in an independent way. I strongly encourage those involved in the R measurements to devise a way to keep their analysis blind, so that the different measurements are truly independent. 5. M U O N

( g - 2) R E S U L T S T H U S F A R

E821 has obtained four data sets for a~+ ,[3-6] which are shown graphically in Fig. 4 along with the earlier CERN measurements.J19] Also shown is the standard model value obtained by Davier et al.[18] using e+e - data, since the use of T-data still has open questions. The analysis of e+e data presented by Teubner at this meeting obtained an even lower value for a(Had; 1), which increases the difference between theory and experiment. One additional data set for it- is available, and we expect the uncertainly to be between ±0.7 to

(10 ppm) (13 ppm)

""====41.

- -

(5 ppm)

(9.4 ppm) "

I

-I I

,,~-

(1.3ppm) (0.7 ppm)

CERN ~÷ CERN ,LL-

E821 (97) Ix+ E821 (98) Ix+ E821 (99) ~+

I

,,I.,,-

E821 (O0)

il+

I

,Illll

o+ =,

0 0 0

=,~

03 L{3

IIII

illl

lJll

0 0 0 ~ ~ Lt3

0 0 0 ~ ~ L¢3

0 0 0 ~ ~ ~

I

~

~

~

X

0 T--

121

Figure 4. Results for a , from CERN and from E821. The line marked DEHZ03 is the standard model value using e+e - data as reported by Davier, et. al.[18]

0.8 ppm. I hope that this final result will be reported in early 2004. 6. F U T U R E

POSSIBILITIES

The technique developed at CERN and substantially improved in E821 at BNL could be improved further, and we are actively exploring possibilities to upgrade the experiment. At BNL we believe that a precision on the order of 0.2 - 0.1 ppm could be reached with suitable upgrades. To go beyond that precision, one would need to go to J-PARC, and we have submitted a letter of intent with the goal of 0.06 ppm.[20] Both of these possibilities need further study, and after our final result from E821 is available, we will begin to study these options in detail. 7. C O N C L U S I O N S Enormous progress has been made since 1984, when efforts began in earnest to mount a new experiment at Brookhaven to measure the muon anomaly. The resulting measurements will reach

B.L. Roberts~NuclearPhysicsB (Proc. Suppl.) 131 (2004) 157-161

a precision of ,,0 0.5 parts per million. Data collection was terminated before we reached our goal of 0.35 ppm, and the measurement is still limited by statistical errors rather than systematic ones. The final run, which would have permitted us to reach our design, goal was denied. Now that many people have left the collaboration, the only possibility is gather a new collaboration to substantially upgrade the experiment to reach an improved precision. Some of us are strongly committed to this endeavor, and we hope that E821 is a beginning, rather than an end. Acknowledgments: I wish to thank my colleagues on E821/or many discussions on aspects of the experiment. I wish to thank Dave Hertzog, Jim Miller and Ernst Sichtermann for reading this manuscript and making helpful suggestions. REFERENCES

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2. An overview of non-standard model physics is given by T. Kinoshita and W.J. Marciano in Quantum Electrodynamics (Directions in High Energy Physics, Vol. 7), ed. T. Kinoshita, (World Scientific, Singapore, 1990), p. 419. 3. R.M. Carey et al., Phys. Rev. Lett. 82, 1632 (1999) 4. H.N. Brown et al., (Muon (g - 2) Collaboration), Phys. Rev. D62 (2000) 091101. 5. H.N. Brown, et al., (Muon (g - 2) Collaboration), Phys. Rev. Lett. 86 (2001) 2227. 6. G.W. Bennett, et al., (Muon (g - 2) Collaboration), Phys. Rev. Lett. 89 (2002) 101804. 7. A. Yamamoto, et al., Nucl. Instrum. and Methods Phys. Res. A491 (2002) 23-40. 8. G.T. Danby, et al., Nucl. Instr. and Methods Phys. Res. A 457 (2001) 151-174. 9. Efstratios Efstathiadis, et al., Nucl. Inst. and Methods Phys. Res. A496 (2002) 8-25. 10. Y.K. Semertzidis, Nucl. Instrum. Methods Phys. Res. A503 (2003) 458-484. 11. S.I. Redin, et al., Nucl. Instrum. Methods Phys. Res. A473 (2001) 260-268. 12. R. Prigl, et al., Nucl. Inst. Methods Phys. Res. A374 (1996) 118, and X. Fei, V. Hughes and R. Prigl, Nucl. Inst. Methods Phys. Res. A394 (1997) 349. 13. S.A. Sedykh et al., Nucl. Inst. Methods Phys. Res. A455 (2000) 346. 14. D.E. Groom et al., (Particle Data Group) Eur. Phys. J. C15 (2000) 1, and W. Liu, et al, Phys. Rev. Lett.82 711 (1999). 15. R.R. Akhmetshin et al., CMD-2 Collaboration), Phys. Lett. B 52'/(2002) 161. 16. M. Davier, S. Eidelman, A. Hocker, Z. Zhang, Eur. Phys. J. C 27 (2003) 497. 17. R.R. Akhmetshin et al., CMD-2 Collaboration), Aug 2003. e-Print Archive: hepex/0308008, submitted to Physics Letters 18. M. Davier, S. Eidelman, A. Hocker, Z. Zhang, Aug 2003, Submitted to Eur. Phys. J. and ePrint Archive: hep-ph/0308213 19. J. Bailey, et. al, Nucl. Phys. B150, 1 (1979). 20. J-PARC Letter of Intent L17, B.L. Roberts contact person.