Transcript g-2 , muon edm and deuteron edm at a high intensity storage ring

g-2 and muon EDM
(and maybe deuteron EDM also)
at a high intensity storage ring
Marco Incagli - INFN Pisa
CERN - 29 apr 2004
The Magnetic Dipole Moment - g
• Classically, considering spin s as a


e 
g
s  g 0 s
2mc
rotation around axis, g=1
• Quantum physics predicts, for a Dirac
particle, g=2
aQED
• Quantum field theory
e
predicts:
ahad,lo
p
g = 2(1+a)
EW
W
a


a  a/2p  0.0012
Z
• a experimentally
albl
measured with precision
<1ppm
ahad,nlo
0
W
n

SM predictions for a (units 10-10)

aQED = 11 658 470.4  0.3

ahad  700  7

aEW = 15.2  0.4  Small contribution from Higgs

albl = 8  3

 evaluated up to 5 (!) loops
 Hadronic vacuum polarization
BUT recent publication from Melnikov: albl = 14  3
 da /a  0.6 ppm
Second largest contribution
Cannot be evaluated in pQCD approach
 

B field

+

+
q


q



hadrons
a and hadronic cross section
Dispersion integral relates ahad(vac-pol) to s(e+e-  hadrons)
a
had =
Im[
]  |
hadrons |2
s-1
Hadronic cross section is often written in terms of the pion form
factor |Fp|2 :
pa 2 3
 
 
2
2
s (e e  p p ) 

|
F
(
M
)
|
p
pp
2
3M pp
Experimental input in a(had) - I
Standard method : beam energy scan
|Fp |2
CMD2@VEPP2M
L= 317.3 nb-1
114000 pp events
in  meson region
2  E, MeV
Experimental input in a(had) - II
Alternative approach used by KLOE : radiative return
|Fp|2
— KLOE
40
 CMD2
30
2
M pp
ds pp
2
dM pp
 s pp ( s)  H(s)
Contribution to a due to  resonance:
KLOE
CMD2
20
L= 141 pb-1
1.5 M pp events
in  meson region
10
(376.5  0.8stat  5.4syst+theo) 10-10
(378.6  2.7stat  2.3syst+theo) 10-10
CMD2 data confirmed by KLOE.
0
0
0.5
0.7
0.9
2
Mpp
(GeV2 )
Experimental input in a(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 w
interference, possibly different mass and width of  vs 0
• The related theoretical error is claimed to be under control
nt
W: I =1 & V,A
: I =0,1 & V
CVC: I =1 & V
e+
t

hadrons
W
hadrons
e–
However, ath(ee) – ath(t)  (20±10)10-10 (???)
Muon-Anomaly: Theory vs. Experiment
Theoretical values taken from
M. Davier, S. Eidelman, A. Höcker,
Z. Zhang
hep-ex/0308213
’20/‘03
THEORY
Comparison Experimental Value with Theory - Prediction
New cross section data have recently
lowered theory error:
a) CMD-2 (Novosibirsk/VEPP-2M) p+pchannel with 0.6% precision < 1 GeV
b) t-Data from ALEPH /OPAL/CLEO
e+ e- - Data: 2.7 s - Deviation
t – Data:
1.4 s - Deviation
Experiment BNL-E821
Values for +(2002) and -(2004)
in agreement with each other.
Precision: 0.5ppm
’20/‘04
Experiment
Including KLOE result
a
- 11 659 000 ∙ 10-10
Possible new physics contribution…




New physics contribution can
affect a 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
t
physics
In particular H- exchange is at
the same scale as W- exchange,
while m(H0)>>m()
nt
W
nt
t
H
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() and
1<s<2 GeV
How do we measure a
polarized
Electric field
used for focusing
(electrostatic
quadrupoles)
B
(out of plane)
E
Precession of spin and momentum
vectors in E, B fields (in the hyp.
B=0) :
 

e
 

wa  ws  wm  mc a B  K  E

 K  a  1

 2 1

• At  magic = 29.3, corresponding to E=3.09 GeV, K=0 and
precession is directely proportional to a
a  wa B
)
The three miracles
•
A precision measurement of a is made possible by what
Farley called “the three miracles”:
1. magic corresponds to E~3 GeV , not 300MeV or 30
GeV
2. It’s very easy to have strongly polarized muons
3. It’s very easy to measure the polarization of the  by
looking at decay electrons
BNL E821 beam line
The E821 muon storage ring
SciFi
calorimeter
module for e
detection
7.1 m
BNL results on 2000 + run
• 4109 events for t>50s and E>2GeV
N (t )  N 0 e
 t / t
1  A coswat   )
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.
Stability of magnetic field
• Magnetic field map is known at the 0.1 ppm level
• Largest systematics from calibration of trolley probes
New proposal - statistics
•
The new experiment aims to a precision of 0.1-0.05 ppm,
which needs a factor of 25-100 more muons
•
This can be achieved by increasing the …
1. … number of primary protons on target  target must
be redisigned
2. … number of bunches
3. … injection efficiency which, at E821, was 7%
4. … running time (it was 7months with  at BNL)
•
The J-PARC proposal is mostly working on items 2 (go
from 12  90 bunches) and 3
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!
Electric Dipole Moment (EDM)
• The electromagnetic interaction Hamiltonian of a particle
with both magnetic and electric dipole moment (EDM) is:

e  g 

d M    g 2mc s  2 0s
   
H     B  d  E where


e   
 dE  d  
s  0s
2mc
2

• Due to the E, B, s properties under P and
T reversal, [HE,P0 and [HE,T0
P
T
• This is not the case for the induced EDM,
since dE,ind  E
E
E
E
 0 , at least at first order (implicitely
used in deriving g-2 precession)
B
B
B
s
s
s
Predictions on EDMs
• We know that P and T simmetries are violated so it
possible that 0
• However, in the frame of Standard Model, where only 1
CP violating phase exists,  is strongly suppressed
• This is not the case for supersimmetry, where many CP
violating phases exist
SM
SUSY
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
1
a 1   5
a 1   5 
LDM   D s
 D * s
Fa

2
2
2 
2m
where : a 
Re D , d   Im D
e
• In SUSY, g-2 and EDM probe the diagonal elements of the
slepton mixing matrix, while the LFV decay e probes
the off-diagonal terms
V~e ~e V~e ~ 


V ~~ V ~~ 
 
 e
Limits on EDM from g-2
• The presence of 0 perturbates the g-2 precession as
follows (B=E=0):
EDM
contribution

e   
1       
 a B   a  2   E  E    B 
w 

mc 
 1 
2



)
• At magic , with the condition that E<<B:
e     
w 
 a B    B 
mc 
2


that is the precession plane is tilted and a vertical oscillation
can be observed in the emitted electrons.
d<2.810-19 e cm
Implications of g-2 limit on EDM

Assume that new physics exists in the range of
aNP  aexpaSM  (1-10) 1010  0.1-1 ppm
then we can write:
D= DSM + DNP = DSM + | DNP |eiCP

New Physics will induce a EDM :
dNP  aNP tanCP 1013 e  cm 

unit conversion
tanCP 1020
e  cm
Current limit: d < 1019 e  cm
 Proposal for a new experiment with sensitivity
d  1024 e  cm which would probe |tanCP| > 103
Limits on fCP according to limit on d
New approach to EDM
• Do not use electrostatic but magnetic quadrupoles
• Apply, in dipole B field, a radial Er field such that E // B
• Instead of working at magic, choose a combination of ,E,B
that cancels muon spin (g-2) precession
 


wa  a B  K  E  a B  KEr )zˆ  0

e    
e
w 
E    B 
Brˆ
mc 2
2mc

side
view
)
Muon ring for EDM 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.
Statistical error
Statistica l error on d  :
sd 
m
2 2tpBAP N d
m = mass, t = muon lifetime, p = momentum, B = magnetic field, A =
asimmetry of vertical decays, P = muon beam polarization, Nd = edN =
number of observed decay muons = number of injected muons (N) times
detection efficiency (ed)
To minimize statistical error:
• maximize P2N, B, p
• subject to constraint : Er  a B  2 < 2 MV/m
( Er directed inward )
The number of muons needed to reach sd = 10-24 ecm , assuming A=0.3 and
ed=1 is:
NP2 = 1016
Systematics
• Basic idea to fight systematics: compare clockwise vs
counter-clockwise results
0 due to choice of ,B,E

e   
1      
 a B   a  2   E  E    B
w 
mc 
 1 
2


Opposite sign
)




cw  ccw
  -
B  -B
EE
Same sign
• Needs 2 injection points and possibility of changing
polarity of dipole magnets (not necessary for quadrupoles)
Summary on muons






Both g-2 and EDM 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
EDM would be the first tight limit on dE from a second
generation particle
The experiments are hard but, in particular the EDM, not
impossible
A large muon polarized flux of energy 3GeV (g-2) or
0.5GeV (EDM) is required
P.S. - deuteron EDM at storage ring
Er value needed to cancel MDM : Er
 a B  2  BpF
Deuteron EDM
Statistica l error on d  :
sd 
m
2 2tpBAP N d
• Deuterons can be used in the same ring of muons with t 
1s  106t 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
• 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/0402023)
• A proposal for a DEDM
experiment will probably be
submitted at BNL