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FERMILAB-SLIDES-18-043-PPD Electric Field Effect s s on th e e Muon Anomalou s s Precession n - 2 Frequency i n n the Fermila b b Muo n 2 Experiment Wanwei Wu Department of Physics and Astronomy University of Mississippi (on behalf of the

  1. FERMILAB-SLIDES-18-043-PPD Electric Field Effect s s on th e e Muon Anomalou s s Precession n ๐’‰ - 2 Frequency i n n the Fermila b b Muo n 2 Experiment Wanwei Wu Department of Physics and Astronomy University of Mississippi (on behalf of the Muon ๐‘• -2 Collaboration) APS April Meeting, Columbus, OH Session X08, Tuesday, April 17, 2018 This document was prepared by [Muon g-2 Collaboration] using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359

  2. Introduction g -2 โƒ‘ ): A particle with spin has a magnetic moment ( ๐œˆ โƒ— ) aligned with its spin ( ๐‘‡ โƒ— = ๐‘• ๐‘Ÿ โƒ— ๐œˆ 2๐‘› ๐‘‡ Dirac, 1928 Dirac Theory predicts that ๐‘• = 2. However, experiments showed that ๐‘• โ‰  2. /01 Anomalous Magnetic Dipole Moment: ๐‘ = 1 . Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 2

  3. Introduction g -2: Standard Model (SM) QED : Dirac term Vacuum polarization Schwinger term EW : Hadron : 567 + ๐‘ 2 34 = ๐‘ 2 69 + ๐‘ 2 :;< = 116591828(50)ร—10 0FF ๐‘ 2 Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 3

  4. Introduction g -2: New Physics (Beyond the SM) ๐‘ 2 represents a sum New Physics over all physics, it is proportional to: sensitive to a wide range of potential new physics. SM: 116591828(50)ร—10 0FF ~3.3๐œ BNL ๐‘• -2: 116592080(63) HIH ร—10 0FF Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 4

  5. Fermilab Muon g-2 Experiment Big Picture! Spin rotation of a muon in a magnetic field โ€ข Spin precession frequency โ€ข Cyclotron rotation frequency Muon anomalous precession frequency: Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 5

  6. Fermilab Muon g-2 Experiment Big Picture! Weak focusing muon storage ringโ€” Electrostatic quadrupoles provide vertical focusing Super conducting coil +27.2 kV -27.2 kV -27.2 kV +27.2 kV Super conducting coil Super conducting coil Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 6

  7. Fermilab Muon g-2 Experiment Big Picture! Electrostatic focusing โ€ข Cyclotron rotation frequency โ€ข Spin precession frequency Muon anomalous precession frequency: Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 7

  8. Fermilab Muon g-2 Experiment Big Picture! โƒ— M ๐ถ = 0 , the second term vanishes. Assuming ๐›พ - By choosing ๐›ฟ = 29.3 , the third term vanishes. The corresponding - momentum (3.904 GeV/c)/radius (711.2 cm) is then called โ€œmagicโ€ momentum/radius. ๐‘Ÿ ๐œ• ; = ๐œ• 3 โˆ’ ๐œ• R = ๐‘ 2 ๐‘› ๐ถ We measure ๐œ• ; by using the decay positron signals and measure ๐ถ - 12 T U by observing the Larmor frequency of stationary protons ( ๐œ• S = โ„ ) with NMR probes. For our final analysis, we can solve for ๐‘ 2 and rewrite it as (using - ๐œˆ W = ๐‘• W ๐‘“โ„/4๐‘› W ) : ๐œˆ S ๐‘› 2 ๐‘ 2 = ๐œ• ; ๐‘• W ๐œ• S ๐œˆ W ๐‘› W 2 Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 8

  9. Electric Field Electrostatic Quadrupole System if electrostatic quadrupole (ESQ) plates misaligned ESQ plates introduce E-field multipoles closed-orbit distortion muon loss โƒ— M ๐ถ ) corrections shifts in E-field and pitch ( ๐›พ โ€ฆโ€ฆ Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 9

  10. Electric Field OPERA-3D: 3-Dimension Map Electric Potential at the end of plates (zone map) V=27.2kV, from Downstream theta=0ยฐ Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 10

  11. Electric Field Correction Fast Rotation Analysis - Muons are injected into the storage ring as a bunchโ€”radial distribution - Muons at inner equilibrium radii will go steadily ahead of those at outer equilibrium radii -> debunching - Modulation of decay positron count (fast rotation signals) can be used to study the debunching - Fast rotation analysis: use a model of the time evolution of the bunch structure to obtain the momentum (radial) distribution of decayed muons Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 11

  12. Fast Rotation Analysis ๐›™ ๐Ÿ‘ ๐๐ฃ๐จ๐ฃ๐ง๐ฃ๐ด๐›๐ฎ๐ฃ๐ฉ๐จ ๐๐Ÿ๐ฎ๐ข๐ฉ๐ž Two bin sets: โ€ฆโ€ฆ Radial bins (i) (Lx=90 mm) Time bins (j) (i.e., 50 bins w/width=1.8mm) (positron count histogram) Note: The geometry factors ๐›พ [\ are known functions of ring geometry and the apparent time structure of the injected bunch (injection zero time and beam revolution time). Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 12

  13. Fast Rotation Analysis Toy MCโ€”Injection Pulse & Signals Counts/[ns] counts Time [ns] Time [ฮผs] Signals seen by Detector Injection Pulse Counts/[ns] Counts/[ns] Bunch overlap Time [ฮผs] Time [ฮผs] Signals seen by Detector ( early time ) Signals seen by Detector ( late time ) Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 13

  14. Fast Rotation Analysis Toy MCโ€” ๐’– ๐Ÿ and ๐‘ผ ๐‘ซ Fit the arrival time of bunches by number of turns to find out the injection zero time and beam revolution time ๐‘ข ๐‘ž๐‘“๐‘๐‘™ = ๐‘œ๐‘ˆ R + ๐‘ข s Arrival time of bunch by turns Arrival time of bunch [us] counts/1[ns] Time [ฮผs] Number of turns Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 14

  15. Fast Rotation Analysis Toy MCโ€”Radial Distribution Apply the ๐œ“ 1 minimization analysis and solve for the radial (momentum) bin contents: With this distribution, we are able to evaluate the electric field corrections to g-2. (๐‘ฆ W = ๐‘† wW;x โˆ’ ๐‘† s , ๐‘† s is the โ€œmagicโ€ radius; ) Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 15

  16. Fast Rotation Analysis Toy MCโ€”Check the Results counts Time [ฮผs] Red: Original Data Blue: Fast Rotation Results counts counts Early time Late time Time [ฮผs] Time [ฮผs] Time [ฮผs] Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 16

  17. Conclusion (๐‘ฆ W = ๐‘† wW;x โˆ’ ๐‘† s , ๐‘† s is the โ€œmagicโ€ radius; ) ยง The electric field plays a very important role in the Fermilab Muon g-2 Experiment in many ways, i.e., muon orbits, muon losses, E-field correction. ยง The electric field has a significant effect on the muon anomalous precession frequency: - We need to align the electrostatic quadrupole plates very carefully; - We need to know the 3D electric field map; - We need to know the muon momentum/radius distribution through the so-called fast rotation analysis. ยง The Experiment is running and it will be a great time to study muon anomaly including its electric field corrections. โ€”Thank You! Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 17

  18. Backup Backup Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 18

  19. Measurement of ๐’ƒ ๐‚ in History Backup Goals: Accuracy: 0.14 ppm Deviation: โ‰ฅ 5๐œ Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 19

  20. Backup Big Picture! Straw Trackers Kicker Modules Pions with p = 3.11 GeV/c are collected from target and Central sent to beamline Orbit Storage Ring Calorimeters: *24 around the ring Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 20

  21. Backup Big Picture! For our final analysis, we can solve for ๐‘ 2 and rewrite it as (using - ๐œˆ W = ๐‘• W ๐‘“โ„/4๐‘› W ) : ๐œˆ S ๐‘› 2 ๐‘ 2 = ๐œ• ; ๐‘• W ๐œ• S ๐œˆ W ๐‘› W 2 About 1.5ร—10 FF Statistical Error Run duration 17 ยฑ 5 months (100 ppb) decay positron ๐‘ 2 Systematic Error fixed probes, Trolley calibration, (140 ppb) on ๐œ• S (70 ppb) trolley measurements of B , etc. 20 ppb Lost Muons < 30 ppb CBO Systematic Error on ๐œ• ; (70 ppb) โƒ— M ๐ถ โ‰  0 ) 30 ppb E and Pitch ( ๐›พ Others Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 21

  22. Backup Polarized Muon Beam ยง Muon is produced polarized : in-flight decay, both โ€œforwardโ€ and โ€œbackwardโ€ muons are highly polarized Pion decay modes: -- http://pdg.lbl.gov/2014/listings/rpp2014-list-pi-plus-minus.pdf Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 22

  23. Backup Beam Resonances March 22 Lost Muons Quad scan for beam resonance studyโ€”Lost Muons Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 23

  24. Backup Decay Positron Signal BNL gโ€“2 PRD 2006 Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 24

  25. Backup Fast Rotation Analysis counts Decay positron energy histogram Energy Cut to select the decay positron signal Energy [MeV] counts counts Decay positron time histogram (after energy cut) Time [ฮผs] Time [ฮผs] If we can functionalize the Real situations: a lot of backgrounds, backgrounds, we can remove them in i.e., muon lifetime, g-2 frequency, fast rotation analysis, i.e., ๐œ and ๐œ• ; CBO, Muon losses โ€ฆ. Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 25

  26. Backup Fast Rotation Analysis Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 26

  27. Backup Fast Rotation Analysis Example (bunch # 0): Radius distribution Peak at 711.5 cm Tuesday, 4/17/2018 Wanwei Wu / APS April Meeting 27

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