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Standing on the Shoulders of Giants Title slide FERMILAB-SLIDES-20-071-E Standing on The Shoulders of Giants Past, Present, and Future of Muon 품 − ퟐ Josh LaBounty, on behalf of the Muon 푔 − 2 Collaboration New Perspectives 2020 07/21/2020 Background: What is 품 − ퟐ? The spin of a muon (or any similarly charged fermion) will precess about an external magnetic field like: 풅풔 품풒 푆Ԧ = 흁 × 푩 = 풔 × 푩 풅풕 ퟐ풎풄 Dirac (in 1928) calculated (for a Spin- ½ charged particle) that 품 = ퟐ 풑ퟐ 풆 푯 = + 푽 풓 + 푩 ⋅ 푳 + ퟐ푺 ퟐ풎 ퟐ풎 By the late 1940’s, there was substantial evidence that this was not exactly true, and so the search was on for the deviation from the 0th order prediction: Inception (2010) 품흁 − ퟐ 풂 ≡ 퐹Ԧ 흁 ퟐ 푔푟푎푣푖푡푦 2 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Initial Calculations Julian Schwinger, in 1948, calculated the first correction to 품 due to the 1- photon loop: 휶 풂퐒퐜퐡퐰퐢퐧퐠퐞퐫 = 흁 ퟐ흅 Since then, over 12,000 QED diagrams have been computed (complete out to 5th order) as well as many other contributions Axis scales will change as we zoom in All 푔 − 2 values scaled 10 × 10 up by a factor of 1010 3 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Present: Theory Whitepaper Released April 2020 (Schwinger term is off the scale) Theory whitepaper just released! Wonderful talk by Prof. Aida El- Khadra given at Fermilab summarizing the results The anomalous magnetic moment of the muon in the Standard Model arXiv:2006.04822 ➢ Uncertainty on the theoretical Why did we need this level × 1010 result is now 풪(ퟑퟎퟎ 풑풑풃) of precision? 4 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: Nevis The Nevis and Liverpool experiments in 1957 showed that 품흁 was consistent with the Dirac prediction: 품흁 = ퟐ ± ퟏퟎ% These experiments both stopped muons in a target and rotated their 푆 = 0 푆Ԧ 푝Ԧ spins with a changing magnetic field. 휇+ ➢ Polarized muons come ‘free’ with 휋+ pion decay ⊢ 푝Ԧ 푆Ԧ 휈휇ҧ ➢ Most importantly, they showed parity violation in the weak decay Ԧ of the muon (decay 풆+/− 푆 푝Ԧ 휇+ 푒+ preferentially emitted in the ⊢ + Neutrinos direction of the spin vector). This Ԧ 푣푠. has formed the basis of every 푆 푝Ԧ + 푒+ measurement of 품 − ퟐ. 휇 ⊢ A refinement of the technique in 1959 showed a result consistent with the 10 Schwinger correction × 10 5 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Phys. Rev. 105, 1415 Past: Nevis The Nevis and Liverpool experiments in 1957 showed that 품흁 was consistent with the Dirac prediction: 품흁 = ퟐ ± ퟏퟎ% These experiments both stopped Phys. Rev. 105, 1415 muons in a target and rotated their spins with a changing magnetic field. ➢ Polarized muons come ‘free’ with pion decay ➢ Most importantly, they showed parity violation in the weak decay of the muon (decay 풆+/− preferentially emitted in the direction of the spin vector). This has formed the basis of every measurement of 품 − ퟐ. A refinement of the technique in 1959 showed a result consistent with the 10 Schwinger correction × 10 6 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: Nevis The Nevis and Liverpool experiments in 1957 showed that 품흁 was consistent with the Dirac prediction: 품흁 = ퟐ ± ퟏퟎ% These experiments both stopped muons in a target and rotated their spins with a changing magnetic field. ➢ Polarized muons come ‘free’ with pion decay ➢ Most importantly, they showed parity violation in the weak decay of the muon (decay 풆+/− preferentially emitted in the direction of the spin vector). This has formed the basis of every measurement of 품 − ퟐ. A refinement of the technique in 1959 showed a result consistent with the 10 Schwinger correction × 10 7 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 푆Ԧ Past: CERN I and II 푝Ԧ Seeing the results from Nevis/Liverpool, groups at CERN 퐵 ⨂ started to show interest in measuring 풂흁 for themselves. ➢ Learning from Nevis: use the relative precession of the spin and cyclotron frequencies → directly proportional to 풂흁 (to first order): 푔푒퐵 푒퐵 휔 = + 1 + 훾 푠 2푚 훾푚 푒퐵 휔 = 푐 훾푚 ↓ 푔 − 2 푒 휔푎 ≡ 휔푠 − 휔푐 = − 퐵 2 푚휇 푒 = −푎휇 퐵 푚휇 × 1010 Measure 휔푎, 퐵 and you have 푎휇 8 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 https://doi.org/10.1016/0370-1573(81)90028-4 Past: CERN I and II Francis Farley and Antonino Zichichi Seeing the results from Nevis/Liverpool, groups at CERN started to show interest in measuring 풂흁 for themselves. ➢ Learning from Nevis: use the relative precession of the spin and https://cerncourier.com/a/a-magnetic-memorial-to-decades-of-experiments/ cyclotron frequencies → directly proportional to 풂흁 (to first order): 푔푒퐵 푒퐵 휔 = + 1 + 훾 푠 2푚 훾푚 푒퐵 휔 = 푐 훾푚 ↓ 푔 − 2 푒 휔푎 ≡ 휔푠 − 휔푐 = − 퐵 2 푚휇 푒 = −푎휇 퐵 푚휇 × 1010 Measure 휔푎, 퐵 and you have 푎휇 9 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 http://cds.cern.ch/record/1758307 https://doi.org/10.1016/0370-1573(81)90028-4 Past: CERN I and II Seeing the results from Nevis/Liverpool, groups at CERN started to show interest in measuring 풂흁 for themselves. ➢ Learning from Nevis: use the relative precession of the spin and cyclotron frequencies → directlyhttp://cdsweb.cern.ch/search?recid=795453 proportional to 풂흁 (to first order): 푔푒퐵 푒퐵 휔 = + 1 + 훾 푠 2푚 훾푚 푒퐵 휔 = 푐 훾푚 ↓ 푔 − 2 푒 휔푎 ≡ 휔푠 − 휔푐 = − 퐵 2 푚휇 푒 = −푎휇 퐵 푚휇 × 1010 Measure 휔푎, 퐵 and you have 푎휇 10 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: CERN III The equations on the previous slide are only valid to first order. A fuller version is: 풆 ퟏ 휷 × 푬 흎 = 풂 푩 + 풂 − + ⋯ 풂 풎 흁 흁 휸ퟐ − ퟏ 풄 Electrostatic focusing → More uniform 푩… at the cost of adding 푬 CERN-III featured a 14.1 푚 diameter storage ring to allow for storing muons at the ‘magic momentum’ (which minimizes the 휷 × 푬 term): ퟏ 푮풆푽 ➢ 휸 = + ퟏ ≈ ퟐퟗ. ퟑ → 풑 = ퟑ. ퟎퟗ 풂흁 풄 흅 injection (rather than a proton target in the ring) helped reduce initial × 1010 splash and increase storage 11 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 https://doi.org/10.1016/0370-1573(81)90028-4 http://cds.cern.ch/record/969031 Past: CERN III The equations on the previous slide are only valid to first order. A fuller version is: 풆 ퟏ 휷 × 푬 흎 = 풂 푩 + 풂 − + ⋯ 풂 풎 흁 흁 휸ퟐ − ퟏ 풄 Electrostatic focusing → More uniform 푩… at the cost of adding 푬 CERN-III featured a 14.1 푚 diameter storage ring to allow for storing Factor of ~35 increase in precision! muons at the ‘magic momentum’ First confirmation of the predicted (which minimizes the 휷 × 푬 term): 60 푝푝푚 contribution to 푎휇 from ퟏ hadronic푮풆푽 vacuum polarization. ➢ 휸 = + ퟏ ≈ ퟐퟗ. ퟑ → 풑 = ퟑ. ퟎퟗ 풂흁 풄 흅 injection (rather than a proton target in the ring) helped reduce initial × 1010 splash and increase storage 12 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: E821 Brookhaven Measurement E821 kept the fundamentals of the CERN-III measurement but improved upon it in pretty much every way. • 20 years of hardware/software advances. • Transition from pion injection to muon injection further reduced the initial splash of particles. • Electromagnetic kicker puts muons onto correct orbits • Transition from 14 separate magnets to a single ring meant that the magnetic field is much more uniform • Magnetic field can be mapped/tracked in situ using trolley / fixed NMR probes About a factor of 14 improvement over CERN-III’s final result. × 1010 13 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: E821 Brookhaven Measurement E821 kept the fundamentals of the CERN-III measurement but improved upon it in pretty much every way. • 20 years of hardware/software advances. • Transition from pion injection to muon injection further reduced the initial splash of particles. • Electromagnetic kicker puts muons onto correct orbits • Transition from 14 separate magnets to a single ring meant that the magnetic field is much more uniform • Magnetic field can be mapped/tracked in situ using trolley / fixed NMR probes About a factor of 14 improvement over CERN-III’s final result. × 1010 14 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 E821 Final Report Past: E821 Brookhaven Measurement E821 Final Report E821 kept the fundamentals of the CERN-III measurement but improved upon it in pretty much every way. • 20 years of hardware/software advances. • Transition from pion injection to muon injection further reduced the initial splash of particles. • Electromagnetic kicker puts muons onto correct orbits • Transition from 14 separate magnets to a single ring meant that the magnetic field is much more uniform • Magnetic field can be mapped/tracked in situ using trolley / fixed NMR probes About a factor of 14 improvement over CERN-III’s final result. × 1010 15 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Present: E989 E989 Muon 품 − ퟐ Experiment Nevis CERN I CERN III G20 ➢ Muons are special: Free ) 훾 polarization and a self- analyzing decay (NOT (NOT ➢ 휔 ∝ 푎 (not 훾!) 휇 푎 휇 푎 Analyzing Decay Analyzing - ➢ Magic momentum cancels Precision ∝ Theoretical Theoretical 푎 퐸 × 퐵 term Free Polarized Muons Polarized Free 휔 and Self and Magic Momentum Magic ➢ Theory can be calculated as precisely as measurements 1959 1961 1979 2020 Image: https://www.drlinkcheck.com/blog/modern-seo 16 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Present: E989 The first run of the Fermilab Muon g-2 experiment is expected to match the final BNL result in precision.
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