1. Marco Incagli - INFN Pisa CERN - 29 apr 2004
g-2 and muon EDM (and maybe deuteron EDM also) at a high intensity storage ring
Marco Incagli - INFN Pisa
CERN - 29 apr 2004

2. The Magnetic Dipole Moment - g
Classically, considering spin s as a rotation around axis, g=1
Quantum physics predicts, for a Dirac particle, g=2 m n W Z0 e p
amQED
amhad,lo
amEW
amlbl
amhad,nlo
Quantum field theory predicts:
g = 2(1+am)
am  a/2p 
am experimentally measured with precision <1ppm

3. SM predictions for am (units 10-10)
amQED =  evaluated up to 5 (!) loops
amhad  700  7 - Hadronic vacuum polarization
amEW = 15.2  Small contribution from Higgs
amlbl = 8  3
BUT recent publication from Melnikov: amlbl = 14  3
dam /am  0.6 ppm
Second largest contribution
Cannot be evaluated in pQCD approach

4. am and hadronic cross section
Dispersion integral relates amhad(vac-pol) to s(e+e-  hadrons)
Im[ ]  | hadrons |2
amhad =
s-1
Hadronic cross section is often written in terms of the pion form factor |Fp|2 :

5. Experimental input in am(had) - I
Standard method : beam energy scan
L= nb-1
 events in  meson region

6. Experimental input in am(had) - II
Alternative approach used by KLOE : radiative return
|Fp|2
— KLOE 40
 CMD2 30
H(s) 20
L= 141 pb-1
Contribution to am due to r resonance:
CMD2 data confirmed by KLOE. 10
1.5 M  events in  meson region
KLOE
(376.5  0.8stat  5.4syst+theo) 10-10
CMD2
(378.6  2.7stat  2.3syst+theo) 10-10
0.5
0.7
0.9

7. Experimental input in am(had) - III
Recently a new method has been proposed which uses t spectral function from t  pp0nt (LEP, CESR data)
Corrections have to be applied due: CVC violation, difference in isospin content, pion mass, effect of r-w interference, possibly different mass and width of r vs r0
The related theoretical error is claimed to be under control
W: I =1 & V,A
CVC: I =1 & V
: I =0,1 & V  e+  
hadrons W e–
hadrons
However, amth(e+e-) – amth(t)  (20±10) (???)

8. Muon-Anomaly: Theory vs. Experiment
Comparison Experimental Value with Theory - Prediction
Preliminary
New cross section data have recently
lowered theory error:
a) CMD-2 (Novosibirsk/VEPP-2M) p+ p-
channel with 0.6% precision < 1 GeV
b) t-Data from ALEPH /OPAL/CLEO
Theoretical values taken from
M. Davier, S. Eidelman, A. Höcker,
Z. Zhang
hep-ex/
THEORY
’20/‘03
e+ e- - Data: 2.7 s - Deviation
t – Data: s - Deviation
Including KLOE result
Experiment BNL-E821
Values for m+(2002) and m-(2004)
in agreement with each other.
Precision: 0.5ppm
Experiment
’20/‘04
am ∙ 10-10

9. Possible new physics contribution…
New physics contribution can affect am through the muon coupling to new particles
In particular SUSY predicts a value that, for neutralino masses of few hundred GeV, is right at the edge of the explored region
t data can be affected differently than e+e- data by this new physics
In particular H- exchange is at the same scale as W- exchange, while m(H0)>>m(r)     W- H-

10. LoI to J-PARC
An experiment with sensitivity of 0.1 ppm proposed at J-PARC
At the moment the project is scheduled for Phase2 (>2011)
Together with the experiment there must be an improvement on:
evaluation of lbl
experimetal data on s(had) to cover m(p)<s<m(r) and 1<s<2 GeV

11. How do we measure am
polarized
Precession of spin and momentum vectors in E, B fields (in the hyp. bB=0) :
Electric field used for focusing (electrostatic quadrupoles) B
(out of plane) E
At g magic = 29.3, corresponding to Em=3.09 GeV, K=0 and precession is directely proportional to am

12. The three miracles
A precision measurement of am is made possible by what Farley called “the three miracles”:
gmagic corresponds to Em~3 GeV , not 300MeV or 30 GeV
It’s very easy to have strongly polarized muons
It’s very easy to measure the polarization of the m by looking at decay electrons

13. BNL E821 beam line

14. SciFi calorimeter module for e detection
The E821 muon storage ring
SciFi calorimeter module for e detection
7.1 m

15. BNL results on 2000 m+ run
4109 events for t>50ms and E>2GeV

16. Magnetic field
Magnetic field is measured with a trolley, which drives through the beam pipe, with array of NMR probes.
366 fixed probes maps the field vs time.

17. Stability of magnetic field
Magnetic field map is known at the 0.1 ppm level
Largest systematics from calibration of trolley probes

18. New proposal - statistics
The new experiment aims to a precision of ppm, which needs a factor of more muons
This can be achieved by increasing the …
… number of primary protons on target  target must be redisigned
… number of bunches
… injection efficiency which, at E821, was 7%
… running time (it was 7months with m- at BNL)
The J-PARC proposal is mostly working on items 2 (go from 12  90 bunches) and 3

19. New proposal - systematics
Systematics for the measurement of wa :
Coherent Betatron Oscillation (CBO) : 0.20 ppm
Pileup : 0.12 ppm
Background from extracted protons : 0.10 ppm
Lost muons : 0.10 ppm
Systematics on magnetic field (really what it’s measured is the proton spin precession frequency wp) :
Calibration of trolley probes : 0.20 ppm
Interpolation with fixed probes : 0.15 ppm
Others (temperature variations, higher multipoles, extra currents from the kicker) : 0.15 ppm
To improve all of this to <0.1 ppm is not an easy job!

20. Electric Dipole Moment (EDM)
The electromagnetic interaction Hamiltonian of a particle with both magnetic and electric dipole moment (EDM) is:
Due to the E, B, s properties under P and T reversal, [HE,P]0 and [HE,T]0
This is not the case for the induced EDM, since dE,ind  E
h=0 , at least at first order (implicitely used in deriving g-2 precession) P T E -E B -B s -s

21. Predictions on EDMs
We know that P and T simmetries are violated so it possible that h0
However, in the frame of Standard Model, where only 1 CP violating phase exists, h is strongly suppressed
This is not the case for supersimmetry, where many CP violating phases exist SM
SUSY

22. Relation between LFV, g-2 and EDM
The magnetic (g-2) and electric (EDM) dipole moments are related to each other as the real and imaginary part of a complex dipole operator
In SUSY, g-2 and EDM probe the diagonal elements of the slepton mixing matrix, while the LFV decay me probes the off-diagonal terms

23. Limits on mEDM from g-2
The presence of h0 perturbates the g-2 precession as follows (bB=bE=0):
At gmagic , with the condition that E<<bB:
EDM
contribution
that is the precession plane is tilted and a vertical oscillation can be observed in the emitted electrons.
dm<2.810-19 e cm

24. Implications of g-2 limit on EDM
Assume that new physics exists in the range of
amNP  amexp-amSM  (1-10)  ppm
then we can write:
D= DSM + DNP = DSM + | DNP |eifCP
New Physics will induce a mEDM :
dmNP  amNP tanfCP e  cm  tanfCP e  cm
Current limit: dm < e  cm
Proposal for a new experiment with sensitivity
dm  e  cm which would probe |tanfCP| > 10-3
unit conversion

25. Limits on fCP according to limit on dm

26. New approach to mEDM Do not use electrostatic but magnetic quadrupoles
Apply, in dipole B field, a radial Er field such that bE // B
Instead of working at gmagic, choose a combination of g,E,B that cancels muon spin (g-2) precession
side
view

27. Muon ring for mEDM measurement
P = 0.5GeV/c
Bz = 0.25 T
Er = 2MV/m
R = 7m
<R> = 11m
B+E = 2.6 m
Intervals = 1.7 m
n. elements = 16
circunference  40m
Stability on B and E fields, in particular in an eventual vertical component of E field, must be kept at the 10-6 level. This has already been achieved (for B field) in g-2 BNL experiment.

28. Statistical error
m = mass, t = muon lifetime, p = momentum, B = magnetic field, A = asimmetry of vertical decays, P = muon beam polarization, Nd = edNm = number of observed decay muons = number of injected muons (Nm) times detection efficiency (ed)
To minimize statistical error:
maximize P2N, B, p
subject to constraint : Er  am B b g2 < 2 MV/m ( Er directed inward )
The number of muons needed to reach sd = ecm , assuming A=0.3 and ed=1 is:
NP2 = 1016

29. Systematics
Basic idea to fight systematics: compare clockwise vs counter-clockwise results
Needs 2 injection points and possibility of changing polarity of dipole magnets (not necessary for quadrupoles)
0 due to choice of b,B,E
cw  ccw
b  -b
B  -B
E  E
Opposite sign
Same sign

30. Summary on muons
Both g-2 and mEDM are sensitive to new physics behind the corner
Unique opportunity of studying phases of mixing matrix for SUSY particles
Historically, limits on dE have been strong tests for new physics models
mEDM would be the first tight limit on dE from a second generation particle
The experiments are hard but, in particular the mEDM, not impossible
A large muon polarized flux of energy 3GeV (g-2) or 0.5GeV (mEDM) is required

31. P.S. - deuteron EDM at storage ring
Er value needed to cancel MDM : Er  am B b g2  BpF

32. Deuteron EDM
Deuterons can be used in the same ring of muons with t  1s  106tm and with the possibility of large fluxes (current flux at AGS is 1011D/s)
Problem: need polarimeters to measure “asimmetry” due to spin precession under EDM torque
The statistical error can be lowered by three orders of magnitude (!) and the nuclear state is easy to interpret
Limit on nuclear EDM much stronger than in standard neutron and Hg experiments

33. Predictions of down squark mass sensitivity for the newly proposed Tl, n and Hg experiments and for the Deuteron experiment, assuming, for the D experiment, a reach of 210-27 e cm
(hep-ph/ )
A proposal for a DEDM experiment will probably be submitted at BNL