Taking the Muon for a Spin Thomas Gadfort Fermilab 47 th FNAL Users - PowerPoint PPT Presentation

Taking the Muon for a Spin Thomas Gadfort Fermilab 47 th FNAL Users Meeting Spin and the Muon Anomalous Magnetic Moment Measuring a µ with Polarized Muons The BNL Result and Goals for Fermilab Muon g-2 Last Summer and This Summer’s Big Move

Spin and Its Observable Effects In the Standard Model (SM), the muon is a point-like spin ½ particle. With spin comes a magnetic dipole moment (MDM) of strength: µ = g q ~ 2 m ~ s Dirac showed that g = 2 for the electron as observed. The 1930‘s and 40’s saw several breakthrough measurements of the g- factor that lead to a new understanding of particles and substructure. Phys. Rev. 72 (1947) g e = 2 . 00229(8) ≈ 2(1 + α / 2 π ) g p ≈ 5 . 6 , g n ≈ − 3 . 8 → QM corrections → nucleon substructure Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 2

Spin and Its Observable Effects In the Standard Model (SM), the muon is a point-like spin ½ particle. With spin comes a magnetic dipole moment (MDM) of strength: µ = g q ~ 2 m ~ s Dirac showed that g = 2 for the electron as observed. The 1930‘s and 40’s saw several breakthrough measurements of the g- factor that lead to a new understanding of particles and substructure. g e = 2(1 + α 2 π ) ≈ 2 . 00232 Phys. Rev. 72 (1947) g e = 2 . 00229(8) ≈ 2(1 + α / 2 π ) � ∗ ` + ` + g p ≈ 5 . 6 , g n ≈ − 3 . 8 → QM corrections → nucleon substructure D. Hanneke, S. Fogwell, and G. Gabrielse g e / 2 = 1 . 001 159 652 180 73(28) PRL 100, 120801 (2008) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 2

Understanding The Muon There is a rich history of muon g-factor measurements starting in the 1950’s at Nevis. g µ = 2(10%) Evidence that the muon is a fundamental particle. Phys. Rev. 105, 1415–1417 (1957) The past 50 years have seen dramatic improvements in precision and experimental techniques. + Hadronic + Weak + Hadronic Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 3

Understanding The Muon There is a rich history of muon g-factor measurements starting in the 1950’s at Nevis. g µ = 2(10%) Evidence that the muon is a fundamental particle. Phys. Rev. 105, 1415–1417 (1957) The past 50 years have seen dramatic improvements in precision and experimental techniques. CERN I + Hadronic + Weak + Hadronic Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 3

Understanding The Muon There is a rich history of muon g-factor measurements starting in the 1950’s at Nevis. g µ = 2(10%) Evidence that the muon is a fundamental particle. Phys. Rev. 105, 1415–1417 (1957) The past 50 years have seen dramatic improvements in precision and experimental techniques. CERN I + Hadronic + Weak + Hadronic CERN II Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 3

Understanding The Muon There is a rich history of muon g-factor measurements starting in the 1950’s at Nevis. g µ = 2(10%) Evidence that the muon is a fundamental particle. Phys. Rev. 105, 1415–1417 (1957) The past 50 years have seen dramatic improvements in precision and experimental techniques. CERN I CERN III + Hadronic + Weak + Hadronic CERN II Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 3

Understanding The Muon There is a rich history of muon g-factor measurements starting in the 1950’s at Nevis. g µ = 2(10%) Evidence that the muon is a fundamental particle. Phys. Rev. 105, 1415–1417 (1957) The past 50 years have seen dramatic improvements in precision and experimental techniques. CERN I CERN III + Hadronic + Weak BNL + Hadronic CERN II Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 3

E821 Brookhaven Muon g-2 Muon injection greatly improved statistics. Continuously wound superconducting (SC) main magnet coils + tunable shimming kit ➝ Reduced multipole field terms. Superconducting coil winding Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 4

E821 Brookhaven Muon g-2 Muon injection greatly improved statistics. Continuously wound superconducting (SC) main magnet coils + tunable shimming kit ➝ Reduced multipole field terms. Dramatic improvement in field uniformity Contours in [ppm]! 10 Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 4

Storage Ring Measurement Technique ( I) In a dipole magnetic field: Muon momentum revolution frequency, ω C ω C = eB mc γ Muon spin revolution frequency, ω S ω S = geB 2 mc γ + (1 − γ ) eB mc γ Muon anomaly revolution frequency, ω a ◆ eB ✓ g − 2 eB ω a ≡ ω S − ω C = mc = a µ mc 2 Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 5

Storage Ring Measurement Technique ( II) Lucky break from parity violation Source of ν µ Polarized Muons γ µ (1 − γ 5 ) π µ Measure Positron Energy Measure Muon Spin Weak decay correlates Highest energy positrons when spin muon spin and electron momentum and momentum are aligned. ν µ ¯ ν e µ e Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 6

Storage Ring Measurement Technique ( II) Lucky break from parity violation Source of ν µ Polarized Muons γ µ (1 − γ 5 ) π µ Measure Positron Energy Measure Muon Spin Weak decay correlates Highest energy positrons when spin muon spin and electron momentum and momentum are aligned. ν µ ¯ ν e µ e E electron Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 6

Storage Ring Measurement Technique ( II) Lucky break from parity violation Source of ν µ Polarized Muons γ µ (1 − γ 5 ) π µ Measure Positron Energy Measure Muon Spin Weak decay correlates Highest energy positrons when spin muon spin and electron momentum and momentum are aligned. ν µ Count N(e) above ¯ ν e µ fixed threshold. Oscillation rate ∝ a µ e E electron Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 6

The Wiggle Plot, ω a , ω p , and a µ Data E821 data ⧳ 5 Param Fit N ( t ) = N 0 e − t γτ [1 + A cos( ω a t + φ )] — Counts per 150 ns 6 10 momentum cut 5 10 4 10 3 10 2 10 0 20 40 60 80 100 3 x10 Counts per 150 ns Counts per 150 ns 3000 120 <A>=0.4 2500 100 2000 80 1500 60 1000 40 500 20 0 0 32 34 36 38 40 692 694 696 698 time ( s) time ( s) µ µ 4 billion muon decays ( ≈ 15% yield >1.8 GeV positrons) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 7

The Wiggle Plot, ω a , ω p , and a µ Data E821 data ⧳ 5 Param Fit N ( t ) = N 0 e − t γτ [1 + A cos( ω a t + φ )] — Counts per 150 ns + 6 10 momentum cut 5 10 4 10 3 ⇒ ω p ( ⟨ B ⟩ ) 10 2 10 0 20 40 60 80 100 3 x10 Counts per 150 ns Counts per 150 ns 3000 120 <A>=0.4 2500 100 2000 80 1500 60 1000 40 500 20 0 0 32 34 36 38 40 692 694 696 698 time ( s) time ( s) µ µ 4 billion muon decays ( ≈ 15% yield >1.8 GeV positrons) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 7

The Wiggle Plot, ω a , ω p , and a µ Data E821 data ⧳ 5 Param Fit N ( t ) = N 0 e − t γτ [1 + A cos( ω a t + φ )] — Counts per 150 ns + 6 10 momentum cut 5 10 4 10 3 ⇒ ω p ( ⟨ B ⟩ ) 10 2 10 0 20 40 60 80 100 3 x10 Counts per 150 ns Counts per 150 ns 3000 120 <A>=0.4 2500 100 Add prior knowledge... 2000 80 1500 60 1000 40 500 20 ω a / ω 0 0 0 32 34 36 38 40 692 694 696 698 p a µ = time ( s) time ( s) µ µ µ µ /µ p − ω a / ω 0 4 billion muon decays p ( ≈ 15% yield >1.8 GeV positrons) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 7

The Wiggle Plot, ω a , ω p , and a µ Data E821 data ⧳ 5 Param Fit N ( t ) = N 0 e − t γτ [1 + A cos( ω a t + φ )] — Counts per 150 ns + 6 10 momentum cut 5 10 4 10 3 ⇒ ω p ( ⟨ B ⟩ ) 10 2 10 0 20 40 60 80 100 3 x10 Counts per 150 ns Counts per 150 ns 3000 120 <A>=0.4 2500 100 Add prior knowledge... 2000 80 a E821 = 0 . 00 116 592 089(63) 1500 60 µ 1000 40 500 20 ω a / ω 0 a SM 0 0 = 0 . 00 116 591 802(49) 32 34 36 38 40 692 694 696 698 p a µ = time ( s) time ( s) µ µ µ µ µ /µ p − ω a / ω 0 4 billion muon decays p ( ≈ 15% yield >1.8 GeV positrons) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 7

The Wiggle Plot, ω a , ω p , and a µ Data E821 data ⧳ 5 Param Fit N ( t ) = N 0 e − t γτ [1 + A cos( ω a t + φ )] — Counts per 150 ns + 6 10 momentum cut 5 10 4 10 3 ⇒ ω p ( ⟨ B ⟩ ) 10 2 10 0 20 40 60 80 100 3 x10 Counts per 150 ns Counts per 150 ns 3000 120 <A>=0.4 2500 100 Add prior knowledge... 2000 80 a E821 = 0 . 00 116 592 089(63) 1500 60 a E821 − a SM = 287 ± 80 µ 1000 40 µ µ 500 20 ω a / ω 0 a SM 0 0 = 0 . 00 116 591 802(49) >3 σ From SM Prediction! 32 34 36 38 40 692 694 696 698 p a µ = time ( s) time ( s) µ µ µ µ µ /µ p − ω a / ω 0 4 billion muon decays p ( ≈ 15% yield >1.8 GeV positrons) Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 7

Explanations Standard Model calculation is incomplete/wrong? a µ = a QED + a EW + a Had µ µ µ Calculated out to 5 loops! T. Aoyama, M. Hayakawa, T. Kinoshita, M. Nio Phys. 287 Rev. Lett. 109 111807 Thomas Gadfort “Taking The Muon For a Spin”, 2014 Users Meeting 8