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Introduction g -2 ): A particle with spin has a magnetic moment ( - - PowerPoint PPT Presentation

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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

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Electric Field Effects s on the e Muon Anomalous s Precession Frequency in n the Fermilab b Muon n ๐’‰-2 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

FERMILAB-SLIDES-18-043-PPD 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

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Introduction g-2

A particle with spin has a magnetic moment (๐œˆ โƒ—) aligned with its spin (๐‘‡ โƒ‘):

๐œˆ โƒ— = ๐‘• ๐‘Ÿ 2๐‘› ๐‘‡ โƒ—

Dirac, 1928

However, experiments showed that ๐‘• โ‰  2. Anomalous Magnetic Dipole Moment: ๐‘ =

/01 1 .

Dirac Theory predicts that ๐‘• = 2.

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Introduction g-2: Standard Model (SM)

QED: EW: Hadron:

Dirac term Schwinger term Vacuum polarization

๐‘2

34 = ๐‘2 567 + ๐‘2 69 + ๐‘2 :;< = 116591828(50)ร—100FF

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Introduction g-2: New Physics (Beyond the SM)

๐‘2 represents a sum

  • ver all physics, it is

sensitive to a wide range of potential new physics.

SM: 116591828(50)ร—100FF BNL ๐‘•-2: 116592080(63)HIHร—100FF

~3.3๐œ

New Physics proportional to:

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Fermilab Muon g-2 Experiment Big Picture! Spin rotation of a muon in a magnetic field

  • Spin precession frequency
  • Cyclotron rotation frequency

Muon anomalous precession frequency:

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Fermilab Muon g-2 Experiment Big Picture!

Weak focusing muon storage ringโ€” Electrostatic quadrupoles provide vertical focusing

Super conducting coil Super conducting coil Super conducting coil

+27.2 kV +27.2 kV

  • 27.2 kV
  • 27.2 kV
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Fermilab Muon g-2 Experiment Big Picture!

  • Spin precession frequency
  • Cyclotron rotation frequency

Electrostatic focusing

Muon anomalous precession frequency:

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Fermilab Muon g-2 Experiment Big Picture!

  • Assuming ๐›พ

โƒ— M ๐ถ = 0, the second term vanishes.

  • 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œ•; = ๐œ•3 โˆ’ ๐œ•R = ๐‘2 ๐‘Ÿ ๐‘› ๐ถ

  • We measure ๐œ•; by using the decay positron signals and measure ๐ถ

by observing the Larmor frequency of stationary protons (๐œ•S =

12TU โ„ )

with NMR probes.

  • For our final analysis, we can solve for ๐‘2 and rewrite it as (using

๐œˆW = ๐‘•W๐‘“โ„/4๐‘›W): ๐‘2 = ๐œ•; ๐œ•S ๐œˆS ๐œˆW ๐‘›2 ๐‘›W ๐‘•W 2

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shifts in E-field and pitch (๐›พ โƒ— M ๐ถ) corrections if electrostatic quadrupole (ESQ) plates misaligned introduce E-field multipoles closed-orbit distortion muon loss โ€ฆโ€ฆ

ESQ plates

Electric Field Electrostatic Quadrupole System

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Electric Potential at the end of plates (zone map) V=27.2kV, from Downstream theta=0ยฐ

Electric Field OPERA-3D: 3-Dimension Map

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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

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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).

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) (i.e., 50 bins w/width=1.8mm) Time bins (j) (positron count histogram)

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Fast Rotation Analysis Toy MCโ€”Injection Pulse & Signals

Injection Pulse Signals seen by Detector Signals seen by Detector (early time) Signals seen by Detector (late time)

Bunch overlap

Time [ns] Time [ฮผs] Time [ฮผs] Time [ฮผs] counts Counts/[ns] Counts/[ns] Counts/[ns]

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Fit the arrival time of bunches by number of turns to find

  • ut the injection zero time and beam revolution time

Fast Rotation Analysis Toy MCโ€” ๐’–๐Ÿ and ๐‘ผ๐‘ซ

Arrival time of bunch [us] Number of turns

๐‘ข๐‘ž๐‘“๐‘๐‘™ = ๐‘œ๐‘ˆR + ๐‘ขs

Arrival time of bunch by turns

Time [ฮผs] counts/1[ns]

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Fast Rotation Analysis Toy MCโ€”Radial Distribution

Apply the ๐œ“1minimization 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‘ฆW = ๐‘†wW;x โˆ’ ๐‘†s, ๐‘†s is the โ€œmagicโ€ radius; )

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Fast Rotation Analysis Toy MCโ€”Check the Results

Red: Original Data Blue: Fast Rotation Results

Early time Late time

Time [ฮผs] Time [ฮผs] Time [ฮผs] Time [ฮผs] counts counts counts

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Conclusion

(๐‘ฆW = 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!

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Backup

Backup

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Goals: Accuracy: 0.14 ppm Deviation: โ‰ฅ 5๐œ

Backup Measurement of ๐’ƒ๐‚ in History

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Storage Ring Pions with p = 3.11 GeV/c are collected from target and

sent to beamline

Kicker Modules Central Orbit Straw Trackers Calorimeters: *24 around the ring

Backup Big Picture!

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  • For our final analysis, we can solve for ๐‘2 and rewrite it as (using

๐œˆW = ๐‘•W๐‘“โ„/4๐‘›W): ๐‘2 = ๐œ•; ๐œ•S ๐œˆS ๐œˆW ๐‘›2 ๐‘›W ๐‘•W 2 ๐‘2 (140 ppb) Statistical Error (100 ppb) About 1.5ร—10FF decay positron Systematic Error

  • n ๐œ•S (70 ppb)

Systematic Error

  • n ๐œ•; (70 ppb)

Run duration 17 ยฑ 5 months fixed probes, Trolley calibration, trolley measurements of B , etc. Lost Muons CBO E and Pitch (๐›พ โƒ— M ๐ถ โ‰  0) Others 30 ppb < 30 ppb 20 ppb

Backup Big Picture!

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Backup Polarized Muon Beam

Pion decay modes:

  • - http://pdg.lbl.gov/2014/listings/rpp2014-list-pi-plus-minus.pdf

ยง Muon is produced polarized: in-flight decay, both โ€œforwardโ€ and โ€œbackwardโ€ muons are highly polarized

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Quad scan for beam resonance studyโ€”Lost Muons

Lost Muons March 22

Backup Beam Resonances

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BNL gโ€“2 PRD 2006

Backup Decay Positron Signal

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Backup Fast Rotation Analysis

Energy Cut to select the decay positron signal

Decay positron energy histogram Decay positron time histogram (after energy cut)

Real situations: a lot of backgrounds, i.e., muon lifetime, g-2 frequency, CBO, Muon losses โ€ฆ. If we can functionalize the backgrounds, we can remove them in fast rotation analysis, i.e., ๐œ and ๐œ•;

Time [ฮผs] Time [ฮผs] Energy [MeV] counts counts counts

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Backup Fast Rotation Analysis

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Backup Fast Rotation Analysis

Peak at 711.5 cm Example (bunch # 0): Radius distribution