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by: Justine Nitzsche


Justine Nitzsche
GPA 3.82


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Class Notes
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This 4 page Class Notes was uploaded by Justine Nitzsche on Monday October 19, 2015. The Class Notes belongs to PHYS 4100 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 38 views. For similar materials see /class/224886/phys-4100-rensselaer-polytechnic-institute in Physics 2 at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15
PHYSICAL REVIEW D VOLUME 62 091 101R Improved measurement of the positive muon anomalous magnetic moment H N Brown2 G Bunce2 R M Carey1 P Cushman10 G T Danby2 P T Debevec7 H Deng12 W Deninger7 S K Dhawan12 V P Druzhinin3 L Duong10 W Earle1 E Efstathiadis1 G V Fedotovich3 E J M Farley12 S Giron10 F Gray7 M GrosseiPerdekamp12 A Grossmann6 U Haeberlen8 M F Hare1 E S Hazen1 D W Hertzog7 V W Hughes12 M Iwasaki11 K Jungmann6 D Kawall12 M Kawarnura11 B I Khazin3 J Kindem10 F Krienen1 I Kronkvist10 R Larsen2 Y Y Lee2 ILogashenko1393 R McNabb W Meng2 J Mi2 J P Miller1 W M Morse2 C J G Onderwater7 Y Orlov4 C Ozben2 C Polly7 C Pai2 J M Paley1 J Pretz12 R Prigl2 G zu Putlitz6 S I Redin12 O Rind1 B L Roberts1 N Ryskulov3 S Sedykh7 Y K Semertzidis2 Yu M Shatunov3 E Solodov3 M Sossong7 A Steinmetz12 L R Sulak1 C Timmermans10 A Tro mov1 D Ugner7 P von Walter6 D Warbur ton2 D Winn A Yamamoto9 and D Zimmerman 1 Muon g 7 2 Collaboration 1Department of Physics Boston University Boston Massachusetts 02215 2Brookhaven National Laboratory Upton New York 11973 3Budker Institute of Nuclear Physics Novosibirsk Russia 4Newman laboratory Cornell University Ithaca New York 14853 SFairj ield University Fair eld Connecticut 06430 6Physikalisches Institut der Universitat Heidelberg 69120 Heidelberg Germany 7Department ofPhysics University ofIllinois at UrbanaiCharnpaign Illinois 61801 8MPIfiir Med Forschung 69120 Heidelberg Germany QKEK High Energy Accelerator Research Organization Tsulmba Ibaraki 3050801 Japan 1ODepartment ofPhysics Univers39ny ofMinnesota Minneapolis 1Iinnesota 55455 11Tokyo Institute of Technology Tokyo Japan 12Department of Physics Yale University New Haven Connecticut 06511 Received 27 June 2000 published 28 September 2000 A new measurement of the positive muon39s anomalous magnetic moment has been made at the Brookhaven Alternating Gradient Synchrotron using the direct injection of polarized muons into the superferric storage ring The angular frequency difference run between the angular spin precession frequency us and the angular orbital frequency we is measured as well as the free proton NMR frequency w These determine R P ma wP3707 20119gtlt10 3 With a ap3l83 3453910 this gives aw 11 659 l9l59gtlt 10710 5 ppm in good agreement with the previous CERN and BNL measurements for a and a7 and with the standard model prediction PACS numbers I4 60 Ef In this Rapid Communication we present a new measure ment of the anomalous givalue a g 722 of the positive muon from the Brookhaven Alternating Gradient Synchroi tron AGS experiment E821 We previously reported a re sult based on data collected during 1997 1 In that work as in the CERN measurements 23 pions were injected into the storage ring and approximately 25 parts per million ppm of the daughter muons from pion decay were stored In August 1998 a fast muon kicker was commissioned which permitted the direct injection of muons into the stor7 age ring Except for the use of muon injection many of the experi7 mental aspects are the same as described in Ref 1 How ever important improvements were implemented These in cluded better stability and homogeneity of the storage ring magnetic eld improved stability of the positron detection system and extended capacity of the data acquisition system For the 1998 run e AGS contained six proton bunches each with a maximum intensity of about 7 X1012 with one bunch extracted every 33 ms The 31 GeVc positive muon beam was formed from decays of a secondary pion beam which was 17 higher in momentum thus providing a 05567282l2000629091101 415 00 62 09110171 muon polarization of about 95 The pion decay channel consists of a 72 m long straight section of the secondary beamline The muons were selected at a momentum slit Where the higher energy pions were directed into a beam dump The beam composition entering the storage ring was measured with a threshold Cerenkov counter lled with isobutane By stepping the pressure from zero to 12 atm the threshold for Cerenkov light from e then 2 and nally 7r was crossed The beam was found to consist of equal parts of positrons muons and pions consistent with Monte Carlo predictions While this measurement was not sensitive to the proton content of the beam calculations predict it to be approximately one third of the pion ux The ux incident on the storage ring was typically 2gtlt106 for each proton bunch The 10 mrad kick needed to put the muon beam onto a stable orbit was achieved with a peak current of 4100 A and a half period of 400 ns Three pulseiforming networks pow ered three identical 17 m long oneiloop kicker sections con sisting of 95 mm high parallel plates on either side of the beam The current pulse was formed by an underidamped LCR circuit The kicker plate geometry and composition were chosen to minimize eddy currents The residual eddy 2000 The American Physical Society H N BROWN 61 al current effect on the total eld seen by the muons was less than 01 ppm 20 us after injection The time varying mag netic eld from the eddy currents was calculated with the program OPERA 4 and was measured in a full size straight prototype vacuum chamber with the use of the Faraday effect 5 Since the muons circulate in 149 ns they were kicked several times before the kicker pulse died out About 104 muons were stored in the ring per proton bunch With muon injection the number of detected posi trons per hour was increased by an order of magnitude over the pion injection method employed previously Further more the injection related background ash in the positron detectors was reduced by a factor of about 50 since most of the pions were removed from the beam before entering the storage ring For polarized muons moving in a uniform magnetic eld E perpendicular to the muon spin direction and to the plane of the orbit and with an electric quadrupole eld E which is used for vertical focusing 215 the angular frequency dif ference wa between the spin precession frequency us and the cyclotron frequency we is given by e w 7 m 1 aMBaM 7271 8gtltE The dependence of mg on the electric eld is eliminated by storing muons with the magic 71293 which corre sponds to a muon momentum p309 GeVc Hence mea surements of can and of B determine a At the magic gamma the muon lifetime is 71739 644 us and the gi2 precession period is 437 us With a eld of 145 T in our storage ring the central orbit radius is 711 m The magnetic eld in Eq 1 is the average over the muon distribution We obtained the equilibrium radius distribution by determining the distribution of rotation frequencies in the ring from the time spectra of decay positrons The distri bution reproduced with a tracking code was found to be 3 mm toward the outside of the central storage region This offset was caused by the mode of operating the kicker The calculated and measured radial distributions are shown in Fig 1 The magnetic eld seen by the muon distribution was calculated by tracking a sample of muons in software through the eld map measured by NlVIR and by averaging the eld values The resulting average corresponds within 002 ppm to the eld value taken at the beam center and averaged over azimuth We used the latter to account for variations with time and to obtain the present result Positrons from the in ight decay u gte 1 V817 were de tected with 24 Pb scintillating ber calorimeters 7 placed symmetrically around the inside of the storage ring Twenty one of these detectors were used in the present analysis The observed positron time spectrum shown in Fig 2 was ad equately represented by 23 N0Ee 771 AEcoswaz E 2 The normalization constant N 0 depends on the energy thresh old E placed upon the positrons The integral asymmetry RAPID COMlVIUNICATIONS PHYSICAL REVIEW D 62 091101R A B E g 318 0 Data 3 Simulation O L 16 D 1 8 t 14 D D E 312 C 1 08 06 04 r 02 i u 39 O La immdc i1ii1iuliiiiProwl 707 708 709 710 711 712 713 714 715 Rodiol Distribution cm FIG 1 The equilibrium radius distribution calculated using the tracking code histogram and obtained from an analysis of the beam debunching at early times points A depends on E and on the beam polarization The fractional statistical error on mg is proportional to A TIN U2 where N8 is the number of decay positrons detected above threshold For an energy threshold of 18 GeV where NeA2 is maxi mum A was found to be 034 on average As in Ref the photomultiplier tubes were gated off before injection With the reduced ash associated with muon injection it was possible to begin counting as soon as 5 us after injection in the region of the ring 270 around from the injection point and 35 us in the injection region Positrons1492115 0 100 100 200 quot 11 quot 200300 4 12 angina2 v HE E A I k v P quotquotHquot quot V i Mquot J1391 fV 39i i 11w r qli f1 y i i 39139 i i V i H WAVNVA m 139 I l mwmw w 10 20 30 40 50 60 70 80 90 1 me ms j n c 300400 400500 500550 5 FIG 2 The positron time spectrum obtained with muon injec tion for E gt 18 GeV These data represent 84 million positrons 091101 2 IMPROVED MEASUREMENT OF THE POSITIVE MUON August 22 1998 field map V cm M 00 h 01 l 2ppm 2 ppm X cm FIG 3 A magnetic eld pro le averaged over azimuth The circle encloses the muon storage region of 45 cm radius The con tours represent 2 ppm changes in the eld Data from the detectors gated on at 5 us were used in the rotation frequency analysis mentioned above The t to Eq 2 was begun after scraping 1 was completed and when the photomultiplier outputs from the 21 detectors used in this analysis were stable 25 40 us after injection Time histo grams were formed for each detector These data were ana lyzed separately and the resulting values for ma were in good agreement X2 1 17220 Values for ma and up the free proton NIVIR angular fre quency in the storage ring magnetic eld were determined separately and independently Thereafter the frequency ratio R paup was determined A correction of 09 ppm was added to R to account for the effects 3 of the electric eld and the muon vertical betatron oscillations on ma We obtain R 3707 20119gtlt10 3 where the 5 ppm error includes a 1 ppm systematic error discussed below Since the 1997 run a substantial reduction in the overall systematic error has been achieved As regards up the sta bility of the magnetic eld has been improved by thermal insulation of the magnet and by NIVIR feedback control to the main magnet power supply The eld homogeneity has been improved by additional shimming with iron shims near the intersections of pole pieces and the surface coils around the ring on the pole faces have been used to compensate on average for the higher multipoles in the magnet Additional shimming was also done using the iron wedges placed in the air gap separating the high quality low carbon pole piece steel from the yoke steel This shimming produced a eld which when averaged over the azimuth was uniform to within i4 ppm as is shown in Fig 3 The knowledge of the muon distribution in the ring obtained as indicated above allows us to determine the average eld B seen by the muons The uncertainty in B is i 05 ppm The other systematic errors are associated with the deter RAPID COMIVIUNICATIONS PHYSICAL REVIEW D 62 091101R II CERN w 94 ppm 9 CERN ll39 9 10ppm E821 97 e 13 ppm E821 98 if e 5 ppm II New Average e ii 4 ppm IllllIllllIlllllllilillllllllllll y Theor o T O gtlt 11659500 11659400 9 11659300 116592 00 11659100 11659000 395 FIG 4 The four precise measurements of the muon anomalous magnetic moment and their weighted average The 1039 region al lowed by the standard model see text is indicated by the dashed lines mination of can from the positron data These arise princi pally from pile up and from AGS ashlets A pile up error occurs when two pulses overlap within the time reso lution of about 5 ns and are incorrectly identi ed as one which then gives incorrect times and energies for the posi trons Pile up is estimated to produce an effect on mg of less than 06 ppm which we conservatively take as an error es timate Occasionally under unstable conditions the AGS was observed to extract beam during our data collection period of 600 us which caused a background in our calorimeters ashlets We conservatively estimate that this effect on can in the 1998 data sample is less than 05 ppm Smaller errors arise from the details of the tting procedure rate dependent timing shifts gain changes in the photomultipli ers uncertainties about the radial electric eld and the verti cal betatron motion and from muon losses Altogether the systematic errors on mg and up added in quadrature are less than 1 ppm The anomalous magnetic moment is obtained from the frequency ratio R by aw 1165919159gtlt10710 3 in which A uMup3183 345 3910 89 This new re sult is in good agreement with the mean of the CERN mea surements for aM and a 38 and our previous measure ment of aw Assuming CPT symmetry the weighted mean of the four measurements gives a new world average of a 1165920546gtlt10 10 i4 ppm 4 X2 v273 The theoretical value of a in the standard model SM has its dominant contribution from quantum electrodynamics 091101 3 H N BROWN et al but the strong and weak interactions contribute as well The standard model value is aMSM116591638gtlt10 10 i07 ppm where the error is dominated by the uncere tainty in the lowest order hadronic vacuum polarization 10 In Fig 4 the four precise measurements of an and their average are shown along with the standard model predice tion The weighted mean of the experimental results agrees with the standard model with aMExpt7aMTheory4247gtlt10 10 5 or equivalently 36i40 ppm This agreement of theory and experiment further constrains new physics beyond the standard model 1112 Data collected in early 1999 should give a statistical error of about 1 ppm with a systematic error below 1 ppm There is substantial activity at the ee colliders of Novosibirsk PHYSICAL REVIEW D 62 09llOlR 13 and Beijing 14 to measure aee ahadrons and these new data will further improve our knowledge of the hadronic contribution and thereby the standard model value of a M We thank T B W Kirk D I Lowenstein P Pile and the staff of the BNL AGS for the strong support they have given this experiment We also thank C Coulsey G De Santi and J Sinacore for their contributions to the preparation and running of the experiment This work was supported in part by the US Department of Energy the US National Science Foundation the German Bundesminister fiir Bildung und Forschung The Russian Ministry of Science and the US Japan Agreement in High Energy Physics A Steinmetz ace knowledges support by the Alexander von Humboldt Foune ation l gi2 Collaboration RM Carey et al Phys Rev Lett 82 1632 1999 2 J Bailey et al Nucl Phys 13150 1 1979 3 F J M Farley and E Picasso in Quantum Electrodynamics edited by T Kinoshita World Scienti c Singapore 1990 p 479 4 Vector Fields Limited 24 Bankside Kidlington Oxford OX5 lJE England 5 Muon gi2 note 286 E Efstathiadis et al The gi2 Muon Kicker Design and Status 1997 Efstathiadis et al The Muon gi2 Muon Kicker in preparation 6 GD Danby et al Nucl Instrum Methods to be published 7 S Sedykh et al Nucl Instrum Methods to be published 8 Particle Data Group C Caso et al Eur Phys J C 3 l 1998 9 W Liu et al Phys Rev Lett 82 711 1999 10 VW Hughes and T Kinoshita Rev Mod Phys 71 S133 1999 l l T Kinoshita and WJ Marciano in Quaan Electrodynamics Directions in High Energy Physics Vol 7 edited by T Kie noshita World Scienti c Singapore 1990 p 419 12 A Czarnecki and W Marciano Nucl Phys B Proc Suppl 76 245 1999 and references therein 13 CMD2 Collaboration RR Akhmetshin et al Phys Lett B 475 190 2000 and references therein 14 Zhengguo Zhao Proceedings for LeptonePhoton 99 hepeex0002025 v2 BES Collaboration JZ Bai et al Phys Rev Lett 84 594 2000 15 YK Semertzidis et al The Brookhaven Muon ge2 Storage Ring High Voltage Quadruples in preparation 09110174


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