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Magnetic & Electric Dipole Moments Axion Academic Training CERN, 1 December 2005 Magnetic & Electric Dipole Moments. Yannis K. Semertzidis Brookhaven National Lab •Muon g-2 experiment d c •EDMs: What do they probe? q •Physics of Hadronic EDMs θ •Probing QCD directly (RHIC), & indirectly (Hadronic EDM) •Experimental Techniques dsr v r r = μr × B + d × E dt Building blocks of matter Force carriers Muons decay to an electron and two neutrinos with a lifetime of 2.2μs (at rest). dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Quantum Mechanical Fluctuations •The electron particle is surrounded by a cloud of virtual particles, a …soup of particles… •The muon, which is ~200 times heavier than the electron, is surrounded by a heavier soup of particles… dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt A circulating particle with r charge e and mass m: μr, L r • Angular momentum e, m L = mvr e r • Magnetic dipole μr = L moment 2m μ = IA dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt For particles with intrinsic angular momentum (spin S): e r μr = g S 2m The anomalous magnetic moment a: g − 2 a = 2 dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt In a magnetic field (B), there is a torque: r τr = μr × B Which causes the spin to precess in the horizontal plane: dsr r =×μr B dt r ds v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Definition of g-Factor magnetic moment g ≡ eh / 2mc angular momentum h From Dirac equation g-2=0 for point-like, spin ½ particles. Exp.: g-2 measures the difference between the charge and mass distribution. g-2=0 when they are the same all the time… dsr v r r = μr × B + d × E dt g-factors: • Proton (gp=+5.586) and the neutron (gn=-3.826) are composite particles. • The ratio gp/gn=-1.46 close to the predicted –3/2 was the first success of the constituent quark model. • The experimental sensitivity of ge-2 sensitive to quantum field fluctuations involving only QED. •The gμ-2 is sensitive to heavier particles more than 2 the ge-2 by (mμ/me) ~40,000. dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt g - 2 for the muon μμ γ α 1 Largest contribution : aμ = ≈ 2π 800 γ Other standard model contributions : μμe, μ μμ μμν μμ μ Z h w w γ γ γ γ QED hadronic weak dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Theory of aµ • aµ(theo) = aµ(QED)+aµ(had)+aµ(weak) + aµ(new physics) -10 • aµ(QED) = 11 658 470.6 (0.3) ×10 -10 + - • aµ(had) = 694.9 (8.) ×10 (based on e e ) -10 τ • aµ(had) = 709.6 (7.) ×10 (based on ) -10 • aµ(weak) = 15.4 (0.3) ×10 -10 + - • aµ(SM) = 11 659 181(8)×10 (based on e e ) -10 τ • aµ(SM) = 11 659 196(7)×10 (based on ) dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Hadronic contribution (had1) Cannot be calculated from pQCD alone γ because it involves low energy scales. h However, by dispersion theory, μ μ this aμ(had1) can be related to σ(e+e− → hadrons) R = σ(e+e− → μ+μ− ) + e ντ measured in e+e- collisions. τ γ or τ decay. h W h 2 e- ⎛ αmμ ⎞ ∞ ds aμ (had,1) = ⎜ ⎟ K(s)R(s) ⎜ ⎟ ∫4m2 2 ⎝ 3π ⎠ π s dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Hadronic contribution (had1) Cannot be calculated from pQCD alone γ because it involves low energy scales. h However, by dispersion theory, μ μ this aμ(had1) can be related to σ(e+e− → hadrons) R = σ(e+e− → μ+μ− ) + e ντ measured in e+e- collisions τ γ or τ decay (assuming CVC). h W h 2 e- ⎛ αmμ ⎞ ∞ ds aμ (had,1) = ⎜ ⎟ K(s)R(s) ⎜ ⎟ ∫4m2 2 ⎝ 3π ⎠ π s dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt VEPP-2M collider • VEPP-2M collider: 0.36-1.4 GeV in c.m., L≈1030 1/cm2s at 1 GeV • Detectors CMD-2 and SND: 50 pb-1 collected in 1993-2000 dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt CMD-2 Result Gounaris-Sakurai formula Systematic error dsr v r r 0.7% 0.6 / 0.8% 1.2-4.2% = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Theory and Experiment vs. Year 11659350 ] -10 Yellow Band: World Average Experiment 11659300 Black Squares: Experiment Blue Circles: Theory 11659250 11659200 tau ee 11659150 Muon Anomalous MagneticMuon Anomalous [10 Moment 11659100 1998 1999 2000 2001 2002 2003 2004 Publication Year dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Experimental Principle: −− • Polarize: Parity Violating Decay π →+μ ν μ • Interact: Precess in a Uniform B-Field μ −−→++νν •Analyze: Parity Violating Decay e e μ dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt The Principle of g-2 Spin vector Non-relativistic case Momentum vector ω = eB c m •B ω = g eB s 2 m − ω = ω −ω = g eB − eB = ⎛ g 2 ⎞ eB ω = eB a s c ⎜ ⎟ ⇒ a a 2 m m ⎝ 2 ⎠ m m dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Spin Precession in g-2 Ring (Top View) Momentum μ vector Spin vector e r ωr = a B a m dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Effect of Radial Electric Field Spin vector • Low energy particle • …just right • High energy particle dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Effect of Radial Electric Field Spin vector • …just right, γ≈29.3 for muons (~3GeV/c) dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Beamline: Polarized Muon Beam Production 80m dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt • The Muon Storage Ring: B ≈ 1.45T, Pμ ≈ 3 GeV/c •High Proton Intensity from AGS dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Detectors and vacuum chamber dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Energy Spectrum of Detected Positrons 35 Counts Momentum vector 30 Spin vector 25 20 Momentum 15 vector 10 Spin vector 5 Software Energy Threshold 0 dsr v r r 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis,Energy BNL (GeV) dt 4 Billion e+ with E>2GeV − t = τ []+ ()ω + φ dN / dt N 0 e 1 A cos a t a dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt G.B. et al., Phys.Rev.Lett.92:161802,2004, hep-ex/0401008 Error: 0.5ppm, Statistics dominated dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt EDM: Particles with Spin… + - r r d = 0 dd∝ σˆ dsr v r r = μr × B + d × E dt Current Status and Future Prospects 11659350 ] -10 Yellow Band: World Average Experiment 11659300 Black Squares: Experiment Blue Circles: Theory 11659250 11659200 tau ee 11659150 Muon Anomalous MagneticMuon Anomalous [10 Moment 11659100 1998 1999 2000 2001 2002 2003 2004 Publication Year dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt New g-2 Proposal at BNL • Increase Beamline acceptance (×4) • Open up the two Inflector ends (×1.7) • Use Backward Muons (i.e. π @ 5.3GeV/c, μ @ 3.1GeV/c). Provides great π-Rejection. ω • Reduce systematics both in a and in B dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Future measurements at VEPP-2000 • Factor >10 in luminosity •measure 2π mode to 0.2-0.3% • Up to 2 GeV c.m. energy •measure 4π mode to 1-2% • CMD-3: major upgrade of CMD-2 • overall improvement in R (new drift chamber, LXe calorimeter) precision by factor 2-3 Under construction. Data taking is expected to start is 2007-2008.dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Beyond standard model, e.g. SUSY μμν~ μμχ~0 ~~ χχ μ~ μ~ γ γ 2 − ⎛100GeV ⎞ asusy ≅ sgn()μ ×13×10 10 ⎜ ⎟ tan β μ ⎜ ⎟ ⎝ msusy ⎠ W. Marciano, J. Phys. G29 (2003) 225 dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt SUSY Dark Matter Following Ellis, Olive, Santoso, Spanos. Plot by K. Olive scalar mass gaugino mass dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt SUSY Dark Matter Following Ellis, Olive, Santoso, Spanos.
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