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

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.

Overall, the goal is to reduce the experimental uncertainty from ퟓퟒퟎ 풑풑풃 → ퟏퟒퟎ 풑풑풃

Like the transition from CERN III → E821, the transition from E821 → E989 is a refinement of the technique • Better detector systems reduce pileup 3.7휎 • Better shimming / mapping of the (central value taken to be the magnetic field same as E821, for illustration) • Fermilab DR allows for a cleaner beam, reduced 휋+ contamination • 20 years of hardware/software 10 improvements × 10

17 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Magnetic Field Uniformity Present: E989 (Preliminary Run 1a − 250 푝푝푏 Contours)

The first run of the Fermilab Muon g-2 experiment is expected to match the final BNL result in precision.

Overall, the goal is to reduce the (‘Q-method’ has reduced experimental uncertainty from statistics) ퟓퟒퟎ 풑풑풃 → ퟏퟒퟎ 풑풑풃

18 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Present: E989 Run 1 The first run of the Fermilab Muon g-2 experiment is expected to match the final BNL result in precision.

Overall, the goal is to reduce the (‘Q-method’ has reduced experimental uncertainty from statistics) ퟓퟒퟎ 풑풑풃 → ퟏퟒퟎ 풑풑풃

19 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Future: Outlook

If the central value from E821 is maintained and we reach our goal of ퟏퟒퟎ 풑풑풃 precision, we will be able to show a ퟓ흈 discrepancy with the standard model calculation.

This has huge implications for many BSM physics models, ruling out some (e.g. MSSM, Dark Photon) and supporting others (Two-Higgs doublet models, Axion, Leptoquarks). 3.7휎

(central value taken to be the same as E821, for illustration) J-PARC Measurement will provide an independent confirmation of 풂흁. > 5휎 (-ish)

× 1010 arXiv:1901.03047

20 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Questions slide

E989: Standing on the shoulders of giants

Muon g-2 Collaboration Meeting − Elba 2019 Thank you!

Questions? transition slide to backups

Bonus Slides! My Contributions Brynn MacCoy, superstar

Detector Operations • Maintaining and improving the detector systems, focusing on the electromagnetic calorimeters • Supported by Fermilab URA Data Processing • Manager of ‘Nearline’ data

analysis system, which can Sept. 2019 process ~30% of the data from the experiment within 2 hours of it Calorimeter 2, ok I suppose. being taken. Provided first look at Run 2+ data. • Web interface for live monitoring • Useful for systematic studies / live optimization of beam parameters

흎풂 Analysis • Systematic studies related to the extraction of 흎풂

23 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 E989 vs. E821 Systematic Errors E989 TDR

24 7/21/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Summary CERN II Nevis 57 CERN I

B. Lee Roberts - Tau2018

FNAL (E989) BNL (E821) CERN III

25 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 What if we’re just wrong?

New Lattice HVP result from BMW (not the car company) gives a value of 풂흁 which is consistent with the standard model.

Currently under scrutiny • New technique • Well-vetted techniques for doing the same calculation differ by > 3 휎

• Fixes 푔휇 anomaly, but causes tension in some well-established electroweak fits • No confirmation by other groups with the same level of uncertainty

Results of this scrutiny will be included in updated theoretical predictions.

26 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Past: Theory Push for E821

A number of mistakes in the QED calculations for 품 − ퟐ were realized during the CERN I-III years and E821 Final Report corrected.

PhysRevLett.23.441

Error on the theoretical result was reduced to be comparable with the × 1010 expected E821 experimental limits

27 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 E821 Final Report 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 B. Roberts • 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

28 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 M. Lancaster Blackboard Interpretations of CERN I

At blackboard (front to rear) : Muller and Farley. Extreme left : J.C. Sens. Extreme right : A. Zichichi. Far background : G. Charpak.

http://cdsweb.cern.ch/search?recid=40058

29 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 “The Big Move”

All for this!

https://muon-g-2.fnal.gov/bigmove/gallery.shtml 30 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Outline • Past

As we go through, we’ll touch on the 4 pillars that make our measurement of 푔 − 2 possible (and viable as a test of the SM) ➢ Muons are special: Free • Present polarization and a self- analyzing decay ➢ 휔푎 ∝ 푎휇 (not 훾!) ➢ Magic momentum cancels 퐸 × 퐵 term ➢ Theory can be calculated as precisely as measurements

• Future Throughout the talk, these bullets will denote the ‘pillars’

31 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 g-2 Throughout The Years

32 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 g-2 Throughout The Years

https://iopscience.iop.org/article/10.1088/0034-4885/70/5/R03

33 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 g-2 Throughout The Years

34 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Future: Outlook

3.7휎

(central value taken to be the same as E821, for illustration)

> 5휎 (-ish)

× 1010

35 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Table of Errors (from E821 Final Report, 2004)

36 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Background

푚휇 ≈ 200 푚푒 ↓ 2 NP휇 ≈ 200 NP푒

37 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Overview

• Goal of the experiment is to measure 푎휇 ≡ (푔 − 2)/2 to 140 ppb • In order to do this, we measure three quantities:

– 휔푎: anomalous spin precession frequency of the muon – 휔푝: free proton precession frequency (∝ 퐵) – Beam Dynamics: the path the muons travel in a magnetic field

• 휔푝 ⊗ 퐵퐷 = 휔෥푝 • We then combine these values with others measured by other experiments 흎풂 휇푝 푚휇 푔푒 푎휇 = 흎෥ 풑 휇푒 푚푒 2 0.3 ppt 22 ppb 3 ppb

38 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Experimental setup

A beam of polarized muons is brought into the storage ring through the inflector magnet, which cancels the field from the main storage ring in a small area. They are placed onto the correct orbit by 3 kicker magnets and then allowed to precess as they orbit in the uniform magnetic field.

39 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 How do we measure 흎풂? 푆Ԧ 푝Ԧ 휇+ 푒+ Conveniently, nature does it 푆Ԧ 푝Ԧ for us. Decay positrons are + 푒+ preferentially emitted in the 휇 direction of the muons spin.

This imprints 휔푎 onto the energy vs. time spectrum of the decay positrons, which we can measure.

퐸/퐸푚푎푥

40 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 How do we measure 흎풂? 푆Ԧ 푝Ԧ 휇+ 푒+ Conveniently, nature does it 푆Ԧ 푝Ԧ for us. Decay positrons are + 푒+ preferentially emitted in the 휇 direction of the muons spin.

This imprints 휔푎 onto the energy vs. time spectrum of the decay positrons, which we can measure.

41 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Experimental setup

After some time, each muon decays into a positron which then spirals inward and strikes a calorimeter. Each of the 24 calorimeters consists of 54 PbFퟒ crystals, which emit Čerenkov light when a decay positron passes through them. The energy of the positron is recorded in the calorimeter as well as the time of impact.

42 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Experimental setup

From each of these positron signals, we construct the right plot of energy vs. time.

43 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Creating the ‘Wiggle Plot’

We can create a plot of the energy vs. time spectrum We fit this plot with a function such as of the decay positrons. Integrating all of the counts −풕/흉흁 푵 풕 = 푵ퟎ 풆 ퟏ + 푨 풄풐풔 흎풂풕 + 흓풂 above a certain energy threshold allows us to + [Higher order terms] capture the ‘wiggle’ which is embedded in this spectrum. In order to extract 흎풂.

44 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Results 푅 = 휔푎 (푝푝푚 from reference value) + [Unknown offset] • A relative (but not absolute) comparison of the 휔푎 analyses has been performed, and all analyzers agree on the result to within statistical + systematic errors. • Final analysis of the first run is nearly complete, and we expect to have a result published in the coming months – The first run is expected to have a total error comparable to the 2003 BNL final result, with 3+ runs to follow. • Run 2 analysis is underway and Run 3 data collection started yesterday(!!!).

45 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Experimental setup

46 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Higher Order Terms

47 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Who’s who.

48 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Calorimeter Crystals

49 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 J-PARC Muon 푔 − 2

http://g-2.kek.jp/portal/index.html

arXiv:1901.03047v2

50 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020 Some References

• Charpak G et al 1961 Phys. Rev. Lett. 6 128 • Bailey et al, Nuclear Physics B150 (1979) • Bailey J et al 1968 Phys. Lett. B 28 287 • Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795-881 • Farley and Semertzidis, Prog. Nucl. Part. Phys. 52 (2004) 1-83. • Bennett et al., Phys. Rev. D 73, 072003 (2006). • B. Lee Roberts - Tau2018 – 27 September 2018 • CERN Courier: A magnetic memorial to decades of experiments • The History of the Muon (g − 2) Experiments --- https://arxiv.org/pdf/1811.06974.pdf • CERN Document Archive: cds.cern.ch

51 7/20/2020 Josh LaBounty | Muon g-2: Past, Present, And Future | New Perspectives 2020