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Systematic Errors in a New Muon g-2 Experiment

Systematic Errors in a New Muon g-2 Experiment. Jim Miller Boston University BNL, June 13, 2008. We measure the difference frequency between the spin and momentum precession. With an electric quadrupole field for vertical focusing. 0. Precession vector, no EDM.

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Systematic Errors in a New Muon g-2 Experiment

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  1. Systematic Errors in a New Muon g-2 Experiment Jim Miller Boston University BNL, June 13, 2008 James Miller, BNL meeting, June 2008

  2. We measure the difference frequency between the spin and momentum precession With an electric quadrupole field for vertical focusing 0 James Miller, BNL meeting, June 2008

  3. Precession vector, no EDM James Miller, BNL meeting, June 2008

  4. We count high-energy e- as a function of time. James Miller, BNL meeting, June 2008

  5. world average E821 achieved 0.5 ppm and the e+e- based theory is also at the 0.6 ppm level. Both can be improved. All E821 results were obtained with a “blind” analysis. James Miller, BNL meeting, June 2008

  6. The error budget for E969 represents a continuation of improvements already made during E821 • Field improvements:better trolley calibrations, better tracking of the field with time, temperature stability of room, improvements in the hardware • Precession improvementswill involve new scraping scheme, lower thresholds, more complete digitization periods, better energy calibration James Miller, BNL meeting, June 2008

  7. Systematic errors on ωa (ppm) Σ* = 0.11 James Miller, BNL meeting, June 2008

  8. Pileup ‘Pileup’ refers to errors in energy and time measurements, and loss in the number of pulses due to two or more pulses being close together in time • The probability of overlap in time is proportional to the data rate and to the resolving time of the detectors. In a new experiment, it is likely we will have 5-10 times more data per second. It will be very important to spread out intensity over as many pulses as possible to minimize pileup. • Two pulses could not be separated in E821 if they were closer than 3 to 10 ns, depending on the analysis. Intrinsic pulse resolution was about 3 ns; larger dead times were sometimes enforced because of errors in energy or time when pulses are close together in time. James Miller, BNL meeting, June 2008

  9. Method of handling pileup • A pileup spectrum is constructed from raw pulses at random. The pileup spectrum is subtracted from the raw spectrum of electrons versus time. • An event ‘trigger’ is produced when a pulse from a calorimeter is above threshold (typically about 900 MeV). This is a candidate electron. • New pulses which happen to occur within a fixed width time window, and fixed in time after the trigger pulse, are used to construct the pileup spectrum together with the trigger pulse. The number of such pulses is automatically proportional to the rate of pileup at that particular time. • When two pulses are sufficiently close together in time, they cannot be distinguished. Two single pulses are subtracted, one ‘double pulse’=two overlapping single pulses, is added. • The resulting spectrum, with appropriate normalization, is subtracted from the raw data spectrum (number of electron pulses above some threshold versus time) James Miller, BNL meeting, June 2008

  10. There are three categories of systematic errors due to pileup • Uncertainty in pileup amplitude, ~ 8% for E821, 0.038 ppm error on wa.(because its lifetime is half that of the single electron spectrum). This can be decreased with more statistics available to construct the pileup spectrum • Uncertainty in the constructed pileup phase: 0.036 ppm • Also decreases with increased statistics • ‘Unseen’ pileup: due to pileup from pulses too small to be seen, for the purposes of pileup spectrum construction, with the pulse finding algorithm ~0.026 ppm • Reduced backgrounds, with a cleaner beam, will make it easier to pull low energy electrons out of the background, in order to include in pileup spectrum construction. • A more highly segmented detector will reduce this error by about a factor of two-three, and with the same rate/burst we get a similar reduction in pileup. It is critical to increase the number of beam pulses to minimize instantaneous rate and therefore pileup James Miller, BNL meeting, June 2008

  11. Systematic error due to lost muons(~0.04 ppm in E821) • Due almost entirely to the possibility that lost muons have a g-2 oscillation phase which differs from the average phase of detected muons • Muons whose trajectories pass near to the storage aperture are believed to be more likely to be lost, due to slight trajectory instabilities introduced by higher electric and magnetic multipoles in the storage region.. • These may be from muons born at larger angles to the pion momentum, which have a different phase from the average of muons not lost. • Or they could be from muons born near the production target rather in the straight decay section, again with a different phase. • muon losses, by themselves (i.e. with no phase shift) do not cause a shift in wa, just an error in the muon lifetime • How solved • Reduce losses by using ‘scraping’ to reduce the number muons near the beam aperture • Reduce losses by reducing magnitudes of higher electric and magnetic multipoles • Develop a beam line which mixes (or eliminates) muons from different sources; uniform mixing will tend to equalize the phase of lost muons. • Monitor beam phase space- measure its uniformity. e.g.use a tracebacksystem, fiber monitor system,… to monitor the beam phase space James Miller, BNL meeting, June 2008

  12. Coherent betatron oscillations (CBO) • The stored muon beam undergoes focusing and defocusing, and the average radius oscillates, due to betatron oscillations, and this can lead to a systematic error in wa. • The horizontal aperture of the inflector is narrow, so the beam is focused in the horizontal direction at the time of injection. The full-aperture ‘kick’ is not fully efficient, so the average radius is off-center. As a result, the average radial position of the beam, at a fixed location in the ring, oscillates: • The acceptance of electrons depends on radius, therefore an oscillation with frequency near fCBO appears in the electron time spectrum. This leads to an error when the spectrum is fit; the closer to 2fa, the larger the error. • Potential solutions: • RF to reduce CBO amplitude • Add higher multipoles to wash out the CBO more rapidly • Increase width of inflector • Improve uniformity of detector acceptance around the ring; the sum cancels CBO • Improve the efficiency of the full-aperture kick, so that beam does not ‘wobble’ • Adjust the quadrupole E-field to keep fCBO as far away from 2fa as possible. James Miller, BNL meeting, June 2008

  13. Pitch Correction • Vertical betatron oscillation of the stored muon beam causes a small shift in wa. • Last term has a portion proportional to by2 and does not average to zero. • If the distributions of vertical oscillations are known, accurate corrections can be made. • Possible corrective measures • Limit vertical aperture to reduce the amplitude of vertical oscillations- at the expense of ring acceptance. • Improve stored beam monitoring. Traceback, looking for the vertical oscillation frequency, will give this information. Also, at early times, fiber harp monitors. James Miller, BNL meeting, June 2008

  14. E Field Correction • There is a small correction to wa due to the quadrupole electric focusing field. • At the magic momentum, where the Lorentz gmagic~29.3, the focusing electric quadrupole field does not contribute to the spin precession: • However, the stored muons have a range of values, • Possible ways to reduce error: • Reduce horizontal aperture of ring: reduces Dg but also acceptance. • Improve monitoring of stored muon distribution • Fast rotation analysis: improved because of absence of flash • Traceback: chambers work much better in absence of flash • Fiber beam monitors James Miller, BNL meeting, June 2008

  15. Systematic error due to gain shifts in the calorimeters • Systematic error on wa previously ~ 0.13 ppm., goal <0.03 ppm • Gain previously controlled to ~0.25%; shifts partially caused by ‘flash’ and/or PMT gating, or perhaps changes in data rates • Laser calibration system was not sufficiently pulse height stable to give good pulse height calibration, so electron data early-to-late were used. Result was uncertainty on gain shifts and therefore a systematic error on wa • If gain shift does not oscillate at g-2 frequency, it does not correlate very much to wa in N=N0e-lt(1+Acos(wat+p)). • Presence of CBO and other terms in function leads to larger correlation with and contribution of gain shift to wa • Reduce amplitudes of processes which cause departure from 5-par function(e.g.CBO); improve gain monitoring system; eliminate flash and need for PMT gating James Miller, BNL meeting, June 2008

  16. Summary • E821 Achieved a precision of ± 0.5 ppm • There appears to be a discrepancy between experiment and e+e- based theory • E969/New proposes to achieve a precision down to ± 0.25/0.14 ppm • There is lots of work worldwide on the hadronic theory piece, both experimental and theoretical. ! James Miller, BNL meeting, June 2008

  17. James Miller, BNL meeting, June 2008

  18. E821: used a “forward” decay beam Pions @ 3.115 GeV/c Decay muons @ 3.094 GeV/c Near side Far side This baseline limits how early we can fit data Pedestal vs. Time James Miller, BNL meeting, June 2008

  19. Expect for both sides E969: will use a “backward” decay beam new front-end Pions @ 5.32 GeV/c increase of proton beam Decay muons @ 3.094 GeV/c Approximately the same muon flux is realized No hadron-induced prompt flash Then we quadruple the number of quadrupoles in the decay channel x 1 more muons > x 2 James Miller, BNL meeting, June 2008

  20. The incident beam must enter through the magnet yoke and through an inflector magnet James Miller, BNL meeting, June 2008

  21. Upper Pole Piece The mismatch between the inflector exit and the storage aperture + imperfect kick causes coherent beam oscillations James Miller, BNL meeting, June 2008

  22. The E821 inflector magnet had closed ends which lost half the beam. Length = 1.7 m Central field = 1.45 T Open end prototype, built and tested →X2 Increase in Beam James Miller, BNL meeting, June 2008

  23. E821 Electron Detectors were Pb-scintillating fiber calorimeters read-out by 4 PMTs. New experiment needs segmented detectors for pileup reduction. James Miller, BNL meeting, June 2008

  24. We count high-energy e- as a function of time. James Miller, BNL meeting, June 2008

  25. New segmented detectors of tungsten/scintillating- fiber ribbons to deal with pile-up • System fits in available space • Prototype under construction • Again the bases will be gated. James Miller, BNL meeting, June 2008

  26. Calibration to a spherical water sample that ties the field to the Larmor frequency of the free protonwp. So we measure wa and wp The magnetic field is measured and controlled using pulsed NMR and the free-induction decay. James Miller, BNL meeting, June 2008

  27. The ± 1 ppm uniformity in the average field is obtained with special shimming tools. We can shim the dipole, quadrupole sextupole independently 0.5 ppm contours James Miller, BNL meeting, June 2008

  28. E969 (i) (I) (II) (III) (iv) Systematicerrorson ωp(ppm) *higher multipoles, trolley voltage and temperature response, kicker eddy currents, and time-varying stray fields. James Miller, BNL meeting, June 2008

  29. Systematic errors on ωa (ppm) Detector segmentation and lower energy- threshold required for pile-up rejection with higher rates Beam manipulation Backward beam Σ* = 0.11 James Miller, BNL meeting, June 2008

  30. E969 Builds on the apparatus and Experience of E821 • AGS Proton Beam 12 – bunches from the AGS 60 Tp total intensity • 0op Beam • p decay channel • m Beam injected into the ring through a superconducting inflector • Fast Muon Kicker • Precision Magnetic Storage Ring • Electron calorimeters, custom high-rate electronics and wave-form digitizers James Miller, BNL meeting, June 2008

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