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: τ r r = 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, σ μ μ this aμ(had1) can be related to σ + − → = (e e hadrons) R + − μ+ − (e e → μ ) + e ντ measured in e+e- collisions. τ γ or τ decay. h W μ h α 2 e- ⎛ mμ ⎞ ∞ ds a (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, σ μ μ this aμ(had1) can be related to σ + − → = (e e hadrons) R + − μ+ − (e e → μ ) + e ντ measured in e+e- collisions τ γ or τ decay (assuming CVC). h W μ h α 2 e- ⎛ mμ ⎞ ∞ ds a (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 ω m ω •Bω ω = g eB s 2 m

− = − = 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 ω = τ []+ ()+ 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~ μ γ γ

2 − ⎛100GeV ⎞ asusy ≅ sgn()×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. Plot by K. Olive

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Prospects and Summary for g-2

• Total experimental error (statistics dominated): 0.5ppm; probing physics beyond the S.M.

•More data (×10) from the theory front are being analyzed: Novosibirsk, KLOE, BaBar, Belle.

• The g-2 collaboration is working towards reducing the experimental error to 0.2ppm. The proposal at BNL received scientific approval (E969) in 2004 and in Spring 2006 it is going to P5 (a US national committee); funding approval is pending from DOE.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt A Permanent EDM Violates both T & P Symmetries:

+ T - + - P - +

dsr v r r = μr × B + d × E dt A Permanent EDM Violates both T & P Symmetries: σ r T r r H = −dσr ⋅ E H = −d()− r ⋅ E = dσr ⋅ E σ r P r r H = −dσr ⋅ E H = −d r ⋅ ()− E = dσr ⋅ E

dsr v r r = μr × B + d × E dt How about Induced EDMs? r r d ∝ dE r r T H = −dE ⋅ E OK r r P H = −dE ⋅ E OK

r H = −dσr ⋅ E 1st order Stark effect. T, P Violation! r r H = −dE ⋅ E 2nd order Stark effect. Allowed! dsr v r r = μr × B + d × E dt MDMs are Allowed…

r T r r H =−μσr ⋅B H =−−⋅−=−⋅μσ()r μσ()BBr

r P r r H =−μσr ⋅B H =−μσ() μσr ⋅()BB =−r ⋅

dsr v r r = μr × B + d × E dt CPT T-Violation CP-Violation ≈ −9 Andrei Sakharov 1967: nB / nγ 10 CP-Violation is one of three conditions to enable a universe containing initially equal amounts of matter and antimatter to evolve into a matter-dominated universe, which we see today…. dsr v r r = μr × B + d × E dt EDM Searches are Excellent Probes of Physics Beyond the SM:

Most models beyond the SM predict values within the sensitivity of current or planned EDM experiments:

•SUSY • Multi-Higgs • Left-Right Symmetric …

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt EDM in an Electric Field… r r ds r r d + =×dE - dt r E + -

dsr v r r = μr × B + d × E dt Precession of a Top in a Gravitational Field

mgl r r ω = , L = I S L

dsr v r r = μr × B + d × E dt Usual Experimental Method dsr v r r = μr × B + d × E dt Ε Small Signal Compare the Zeeman Frequencies When E-field is Flipped: + ()ω − ω = - hσ 1 2 4dE 1 1 d ∝

E τ dsr v r r N T = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Schiff Theorem: A Charged Particle at Equilibrium Feels no Force… …An Electron in a Neutral Atom Feels no Force Either: r = r + r = ETot Eext Eint 0

…Otherwise it Would be Accelerated… dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Neutron EDM Vs Year Neutron EDM Limits

1000000

100000

10000

1000

100

10^-25 e-cm 10

0.1 50 60 70 80 90 Year “…at 6 x 10-26 e cm, it is analogous to the Earth's surface being smooth dsr v r r and symmetric to less than 1 µm” (John Ellis). = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Schiff Theorem: A Charged Particle at Equilibrium Feels no Force… …An Electron in a Neutral Atom Feels no Force Either. However:

rrr=++ = FTot qE ext qEint Other Forces 0

…the net E-field is not zero! dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Current Atomic EDM Limits

• Paramagnetic Atoms, 205Tl: electron × -27 |de| < 1.6 10 e·cm (90%CL) PRL 88, 071805 (2002)

• Diamagnetic Atoms, 199Hg Nucleus: |d(199Hg)| < 2.1×10-28e·cm (95%CL) PRL 86, 2505 (2001)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt EDM Status

Particle System Limit [e⋅cm]

Electron 205Tl (~10-24 e⋅cm) 1.5×10-27

Mercury 199Hg atom 2×10-28

Neutron Ultra-Cold n 5×10-26

Proton 199Hg atom 5×10-24

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Future Prospects on electron EDM:

• Electron: YbF Ultra-cold molecules. Goal ~1000, B.E. Sauer et al.

• Electron: PbO*, goal ~1000, D. DeMille et al.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Prospects of neutron EDM:

• UCN at PSI: Ramsey’s method of separated oscillatory fields. First goal 1×10-27e⋅cm, begin data taking ~2008.

• UCN at ILL (Sussex, RAL,…): Ramsey’s method of separated oscillatory fields. Goal 2×10-28e⋅cm/year, begin data taking 2009.

• Ultra-Cold Neutrons (UCN), at SNS (LANL,…): Polarized 3He stored together in a superfluid 4He. Goal 1×10-28 e⋅cm, begin data taking ~2011.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Hadronic EDMs α L = θ s GG CP 8 π Order of magnitude estimation of the neutron EDM: e m − mm dm()θθ~ θ* ~⋅×() 6 1017 e ⋅ cm, = ud n * + mmnn m u m d M. Pospelov, A. Ritz, Ann. Phys. 318 (2005) 119. ()θθ−×⋅() θ−16 →≤×θ −10 ddnp3.6 10 e cm 210 Why so small? Axions? CAST, ADMX,…

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt θ …In the vicinity of the deconfinement phase transition QCD might not be small: P & T-violating bubbles are possible at H.I. collisions. D. Kharzeev, R. Pisarski, M. Tytgat, PRL81, (1998) 512; D. K., R. P., PRD 61 (2000) 111901; D. K., hep-ph/0406125.

r r p1 L r p2

pr r Interaction plane 3 p4 of H.I. collisions

Where p1 and p2 are the momenta of the positive pions and p3 and p4 those of the negative pions. dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt prediction

)

t CP-violation

m at RHIC!!

m (preliminary)

y s Nucl-ex/0510069

(

(Centrality of Collisions)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Comments

• If it survives the systematics checks it will be a phenomenal discovery

• The bubbles can evaporate by emitting axions…!

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt UCN experiment at ILL: Expect a factor of ~100 improvement in sensitivity due to • Neutrons in 0.5 K He bath

•~50× more neutrons

• E-field: 4-6× at cryo temp.

• Longer coherence times

They are expecting to announce a factor of 2 improvement in the neutron EDM limit, shortly dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Neutron EDM at SNS. Aiming at 1×10-28e⋅cm, begin construction 2007, begin data taking 2011

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Q=CV

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt 3

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Deuteron EDM

=++π NN ddddDnpD()

()ϑϑ−⋅−16 dD  10 e cm − i.e. @ 10-29e⋅cm: ϑ≤10 13

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt θ -13 A value of QCD =10 would create an EDM of

System EDM value Proton ≈3×10-29e⋅cm Neutron ≈-3×10-29e⋅cm Deuteron ≈1×10-29e⋅cm Tl atom ≈5×10-31e⋅cm Hg atom ≈1×10-32e⋅cm

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Quark EM and Color EDMs

i μν μν =−()σσ μν μν + c γ LCP∑ qd q F d q G5 q 2 q ()ccccc()+−()() −− + dddDqq,0.55.60.2 d u d d edd u d edd u d

()ccc()−+() + dddnqq, 0.7 d d 0.25 d u 0.55 ed d 0.5 d u i.e. Deuterons and neutrons are sensitive to different linear combination of quarks and chromo-EDMs… cc ddq

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Sensitivity to SUSY models d EDM at ~10-29e⋅cm n EDM at ~10-28e⋅cm

Relative strength of various EDM limits as a function of left handed down squark mass (O. Lebedev, K. Olive, M. Pospelov and A. Ritz, PRD 70, 016003 (2004) hep-ph/0402023)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Sensitivity to right-handed ντ mass

“…

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 …”Yannis Semertzidis, BNL dt CEDMs for the down quark vs MN3

Neutron sensitivity at 10-28 e⋅cm

Deuteron sensitivity at 10-29 e⋅cm

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Deuteron vs. neutron sensitivity …it depends on the source

cc≈× Color EDM: ddDq()10 dd nq ()

1 θ : dd()θθ≈× () QCD Dn3

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Experimental Principle of EDM

• Polarize (e.g. deuteron polarized source, ~100%)

• Interact in an E-field

• Analyze as a function of time (e.g. deuteron polarimeter, analyzing power up to 100%)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Experimental Methods of Storage Ring Electric Dipole Moments

•Parasitic to g-2

•Frozen spin

•Resonance

dsr v r r = μr × B + d × E dt Electric Dipole Moments in Storage Rings dsr r r = d × ur × B dt

e.g. 1T corresponds to 300 MV/m for relativistic particles

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Indirect Muon EDM limit from the g-2 Experiment z B r r ωa ω θ r e r η r ω = {}aB + () ur × B m 2c ωr edm y s ωr ωr + ωr = a edm β x ω tanθ = edm ω a

−19 Ron McNabb’s Thesis 2003:< 2.7 ×10 e ⋅cm 95% C.L.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt The Vertical Spin Component Oscillates due to EDM

c g-2 period

μ μ dsr v r r 0 s Time 8 s = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Effect of Radial Electric Field

Spin vector • Low energy particle Momentum vector • …just right

• High energy particle

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Use a Radial Electric Field and a

Spin vector • Low energy particle Momentum vector

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 Spin Precession in EDM Ring (Top View) Momentum μ vector Spin vector

ωr = a 0

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt (U-D)/(U+D) Signal vs. Time Side view

)

(

)

(

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Muon EDM Letter of Intent to J-PARC/Japan, 2003

†

# †Spokesperson

dsr v r r # Resident Spokesperson = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt SUSY: EDM, MDM and Transition Moments are in Same Matrix

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Expectedαβ Muon EDM Value from a μσ μ αβ 1 ⎡ 1γ+ αβ 1− ⎤ L = D 5 + D* 5 F , DM ⎢ α ⎥ σ2 ⎣ β 2 μσ 2 ⎦ γ αβ 1 γ μ whereμ = [],γ and 2 μe a = ℜD, 2mμ d = ℑD, Probe this phase to 1% μ φ DSUSY = DSUSY ei CP aSUSY d = 2 × 10−22 e⋅cm μ tan(φ ) 25 × 10−10 CP

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt z

B ωr ωr a e r η r ωr = {}aB + () ur × B θ m 2c ωr edm y s ωr ωr + ωr = a edm β ω x tanθ = edm ω a

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Vertical Spin Component without Velocity Modulation (deuterons)

dsr v r r Time = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Vertical Spin Component with ω Velocity Modulation at a

dsr v r r Time = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Vertical Spin Component with Velocity Modulation (longer Time)

μ dsr v r r μ Time 75 s = μr × B + d × E Axion Training, 1 December,0 s 2005 Yannis Semertzidis, BNL dt Velocity (top) and g-2 oscillations A new idea by Yuri Orlov! Particle velocity δβ oscillations

Time

L Particle SL S oscillations (i.e. g-2 oscillations)

Time dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Nuclear Scattering as Deuteron EDM polarimeter Ed Stephenson’s IDEA: - make thick target defining aperture detector - scatter into it with thin target system Alternative way: resonant slow extraction “defining aperture” U primary target “extraction” L R target -ribbon

D R Δ D Target could be Hole is large Detector is far enough Ar gas (higher Z). compared to away that doughnut beam. Every- illumination is not an Target “extracts” by thing that goes acceptance issue: Coulomb scattering through hole Δ < R. deuterons onto thick stays in the main target. There’s ring. not enough good events here to warrant detectors.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt × 2 Figure of merit = effiency 〈 iT11 〉

Absorptive spin-orbit Absorptive inclusive spin-orbit

? Experimental Work at KVI by G. Onderwater, Coulomb E. Stephenson (IUCF), rainbow et al. to explore this parameter space.

momentum (GeV/c) Nuclear rainbow Extrapolation of nuclear rainbow effect is not known.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Deuteron Coherence Time • B-fields stability

• Multipoles of B-fields

• Vertical (Pitch) and Horizontal Oscillations

• Finite Momentum Acceptance ΔP/P I.B. Vasserman et al., Phys. Lett. B198, 302 (1987); A.P. Lysenko, A.A. Polunin, and Yu.M. Shatunov, Particle Accelerators 18, 215 (1986). dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Deuteron Statistical Error:

σ ≈ 16h d cBAPNf T βτ δβ 0 cpTot τ p : 1000s Polarization Lifetime (Coherence Time) A : 0.6 The left/right asymmetry observed by the polarimeter P : 0.95 The beam polarization × 11 Nc : 4 10 d/cycle The total number of stored particles per cycle TTot: 5000h/yr. Total running time per year f : 0.05 Useful event rate fraction δβ 0 : 0.01 Velocity modulation : 1T The average magnetic field around the ring σ ≈×310ecm−29 ⋅ / year d dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Resonance spin-flip z s θ = z S cos B ss()+1 μ θ BB= sin ()ω t d Ra0

BR or ER rr=×==γγγω()r ()ω = γω ERavB vBBv0 sin t , aca

• ER works on the EDM (signal)

• BR works on the magnetic moment (background)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Yuri Orlov’s new lattice 5m P≈1GeV/c

B≈2T

D=0 D≠0 10m RF

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Systematic errors due to AC forces ω • AC forces, due to modulating v at a.

Examples: 1) Radial B-field or skew quadrupole where D≠0, 2) RF-cavity (vertical offset or misalignment), …

• Remedy: They depend on the vertical tune… They all do! dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt AC Backgrounds are vertical tune dependent; EDM signal is not!

ds 1 v ∝ 1 22 − D dt Q Q 0 vs P 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 S_v/S (10^-3)

-1

-2 Q_v

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Storage Ring Electric Dipole Moments

•D @ 10-29e·cm would be the best EDM sensitivity θ over present or planned experiments for QCD, quark, and quark-chromo (T-odd Nuclear Forces) EDMs.

•P, D, 3He, etc., i.e. a facility to pin down the CP- violation source.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Deuteron EDM Timeline

• ~end of this year/January 2006 Letter of Intent

• We need to develop the final ring lattice and tolerances on parameters

• Goal for a proposal by the end of next year

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Neutron/deuteron EDM Timeline

Exp begin sens. Exp goal 2005 data taking

2007 UCN-PSI 10-27e⋅cm

2009 UCN-ILL 2×10-28e⋅cm/yr Deuteron in Storage 2010 10-29e⋅cm Ring 2011 UCN-LANL/SNS 1×10-28e⋅cm

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Summary • Neutron, and deuteron EDM experiments are sensitive probes of physics beyond the SM and of CP-violation in particular. Unique sensitivity to θ • QCD •Quark EDM • Quark-color EDM with the deuteron at 10-29e·cm holding the best EDM sensitivity over present or planned experiments. Together n (p) and deuteron EDM exp: pinpoint EDM source, promising a very exciting decade…! dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Extra Slides

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt List of things to do… α α ≠ 1. Compaction factor: p=1 or p 1 Graziano Venanzoni, and Yuri Orlov 2. Low beta (=0.6) Super-Conducting Cavities with ω ω one mode having =3 RF Alberto Facco, … 3. Space Charge, Impedance, etc. Mikhail Zobov 4. RFQ 5. Polarimetry M.C. Anna Ferrari, Ed Stephenson 6. Slow Extraction together with polarimetry 7. Spin Coherence Time Yuri Orlov 8. Sextupoles, Decapoles, how many needed? Y.O. dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt RF-fields and oscillation phases

E-field in RF-cavity E-field [V/m] Time [ns]

BR-field in RF-cavity B-field [T] Time [ns] Particle velocity δβ oscillations

Time [ns]

Particle SL L S oscillations (g-2)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL Time [ns] dt Other Issues

• Spin coherence time. I.B. Vasserman et al., Phys. Lett. B198, 302 (1987); A.P. Lysenko, A.A. Polunin, and Yu.M. Shatunov, Particle Accelerators 18, 215 (1986).

• RF-system: frequency, shape, strength, normal/SC. Is partial linearization needed? C. Ohmori, et al., 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, Nov. 2003; M. Yamamoto et al., PAC99.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Two half beam technique

This tune makes the Deuteron spin more Sensitive to background

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Resonance EDM Systematic Errors

• Two classes of systematic errors: DC, or frequency dependent (AC)

• Vertically offset RF-cavity

• Misaligned in angle RF-cavity

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt S. Lamoreaux at “Lepton Moments”

E=5MV/m, T=108s

R&D

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Last generation of detectors at VEPP-2M CMD-2 SND

1-vacuum chamber; 2- drift chamber; 3 – Z-chamber; 4-main solenoid; 5-compensating solenoid; 1-vacuum chamber; 2 – drift chambers; 3 – internal 6-BGO calorimeter; 7-CsI calorimeter; scintillating counter; 6-NaI crystals; 7-vacuum phototri- 8-muon range system; 9-yoke; r odes; 8-absorber; 9-strimer tubes; 11- scintillatords r v pla-r r 10-quadrupoles = μ × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis,tes; BNL dt 5-parameter Function Not Quite Adequate. Fourier Spectrum of the Residuals:

fg-2 ≈229 KHz fcbo≈466 KHz

Data of 2000, n = 0.137

≈ (− − ) fcbo fC 1 1 n dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt φ Modulation of N0, A, a with fcbo: − t ω = ()τ []+ ()()+φ () dN / dt N0 t e 1 A t cos at a t

− t π ⎡ τ ⎤ = + cbo ()+φ N0 (t) N0 ⎢1 AN e cos 2 fcbot N ⎥ ⎣⎢ ⎦⎥ φ − t π ⎡ τ ⎤ φ cbo A(t) = A⎢1+ A e τ cos()2 f t +φ ⎥ φA cbo A ⎣⎢ ⎦⎥ − t π = + cbo ()+φ a (t) a A e cos 2 fcbot φ

Amplitudes of AN, AA, Aφ, Consistent with Values -2 -3 -3 from MC Simulations (10 , 10 , 10 respectively)dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt 2001 Run with Negative Muons

• In 2001 we have collected 3.7 Billion electrons with E>1.8GeV from a run with negative muons (μ-). Run at n=0.122 and n=0.142.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Vertical vs. Horizontal Tune

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Systematic/Statistical Uncertainties for the ωa Analysis.

Size [ppm] Systematic Uncertainties 2001 2000 Coherent Betatron Oscillations (CBO) 0.07 0.21 Pileup (Overlapping Signals) 0.08 0.13 Gain Changes 0.12 0.12 Lost Muons 0.09 0.10 Others 0.11 0.08 Total Systematics 0.21 0.31 Statistical Uncertainty 0.66 0.62

Total Uncertainty: 0.7 0.7

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Magnetic Field measurement

B- [ppm] θ=0o 150 100 50 0 -50 -100

=270 o =90

o θ

θ=180 o The B field azimuthal variation at the center of the storage The B field averaged region. ≈1.45 T over azimuth. dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Magnetic Field Measurement

Systematic Uncertainties for the ωp Analysis. Size [ppm] Source of Errors 2001 2000 Absolute Calibration of Standard Probe 0.05 0.05 Calibration of Trolley Probe 0.09 0.15 Trolley Measurements of B-field 0.05 0.10 Interpolation with Fixed Probes 0.07 0.10 Uncertainty from Muon Distribution 0.03 0.03 Others 0.10 0.10 Total 0.17 0.24

dsr v r r = μr × B + d × E dt Computation of a : μ μ μ ω μω /ω a = a = a ωp e / − /ω μ B μ p a p m

• Analyses of ωa and ωp are Separate and Independent (“Blind Analysis”). When Ready, only then, Offsets

are Removed and aμ is Computed.

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt μ ω ω Computationω of a : μ μμ μ μ μ ω R − a a / p a − = = ω = e − / − / λ − R − B p a p μ m −

≡ ω ω = Rμ − a / p 0.003 707 208 3 (26)

λ = μ μ = W.L. et al., PRL 82, 711 (1999) μ / p 3.183 345 39 (10)

Data of 2001: -10 aμ(exp)=11 659 214(8)(3)×10 (0.7 ppm)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Average of aμ:

CPT? Δ = μ − = ± × −9 R R − Rμ + (3.5 3.4) 10

Exp. World Average: -10 aμ(exp)=11 659 208(6)×10 (0.5 ppm)

-10 + - aμ(exp)- aμ(SM) = 27 (10)×10 , 2.7σ, based on e e data

-10 τ aμ(exp)- aμ(SM) = 12 (9) ×10 , 1.4σ, based on -data

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Ramsey’s method

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Systematic errors due to ~0Hz forces • DC, or almost DC forces (other than magnetic) r = rr+×=r FFvext0(DC)v0⇒ qBR ω i.e. modulating v at a modulates BR at the same frequency.

• Examples: 1) Gravity, 2) Charging up the beam pipe…

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Remedy

• Clock-Wise (CW) injection and Counter-Clock- Wise (CCW) injection (Imitates T→-T): B → -B v → -v v×B → v×B

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Developments in Theory

× -10 • aµ(had, LBL) = +8.6(3.5) 10 Large N QCD+Chiral × -10 • aµ(had, LBL) = +13.6(2.5) 10 Melnikov + Vainshtein × -10 • aµ(had, LBL) = +11.1(1.7) 10 Dubnicka et al × -10 • aµ(had, LBL) = +9.2(3.0) 10 T+Ynd. × -10 • aµ(had, LBL) = +11.0(2.0) 10 W. Marciano, prelim.

• Use +12.0(3.5)×10-10 WM

× -10 • aµ(QED) = 11 658 472.07(0.04)(0.1) 10 Recent Kinoshita Update

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Developments in had1 -10 • aµ(had,1) = 696.3(6.2)(3.6)×10 DEHZ -10 • aµ(had,1) = 696.2(5.7)(2.4)×10 HMNT -10 • aµ(had,1) = 694.8 (8.6) ×10 GJ -10 • aµ(had,1) = 692.4(5.9)(2.4)×10 HMNT inclusive -10 • aµ(had,1) = 693.5(5.0)(1.0)×10 TY

• Use = 694.4 (6.2)(3.6)×10-10 WM

-10 • aµ(SM) = 11 659 184.1 (7.2)VP (3.5)LBL (0.3)EW,QED ×10 -10 • aµ(Exp) = 11 659 208.0 (5.8)×10

Δ -10 σ • aµ= aµ(Exp) - aµ(SM) = 23.9 (9.9)×10 or 2.4 deviationdsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Hadronic contribution to muon (g-2)

Hadronic contribution to the muon (g-2) is calculated via dispersion integral: μ α 2 ∞ ⎛⎞mμ Ks() alohad (. .)= dsRs ( ) ⎜⎟∫ 2 3 2 s ⎝⎠π 4mπ

Contribution to the integral from different modes e+e-→hadrons:

2π 2π

> 5 GeV > 5 GeV 25− GeV 25− GeV < 2 GeV < 2 GeV ω,ϕ ω,ϕ e+e- → 2π gives dominant contribution both to the value and

to the uncertainty of the hadronic contribution dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt R, the current status

VEPP-2M energy region

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Implication to aμ (very unofficial) Michel Davier, Bill Marciano-2004:

−10 ∆aμ = (23.9 ± 7.2had,LO ±3.5other ±5.8exp)·10

•0.6<√s<1.0 GeV CMD-2 (95): 378.6 ± 2.7 ± 2.3 (3.6) CMD-2 (98): 382.3 ± 1.9 ± 3.1 (3.6) SND: 385.6 ±5.2 KLOE: 375.6(?) ± 0.8 ± 4.9 (5.0) •0.4<√s<1.0 GeV CMD-2 (95,96,98): 482.1 ± 3.1 ± 3.2 (4.4) SND: 488.7 ± 2.6 ± 6.6 (7.1) •0.4<√s<1.4 GeV

CMD-2 (all): 495.23 ± 3.07 ± 3.38 (4.57) aμ(had;0.6<√s<1.0 GeV)

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Recent KLOE Results

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt Comparison of CMD2 data with KLOE

2 ΔF F(exp) Plotted is =π -1 F F2 (CMD-2 fit) π 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

Upper Limits on SUSY Mass Scales are set by Muon g-2

dsr v r r = μr × B + d × E Axion Training, 1 December, 2005 Yannis Semertzidis, BNL dt