g-2 and muon EDM (and maybe deuteron EDM also)

at a high intensity storage ring

Marco Incagli - INFN PisaCERN - 29 apr 2004

The Magnetic Dipole Moment - g

sgsmceg

02 • Classically, considering spin s as a

rotation around axis, g=1• Quantum physics predicts, for a Dirac particle, g=2

aQED

ahad,lo

aEW

albl

ahad,nlo

• Quantum field theory predicts:

g = 2(1+a)a

0.0012• a experimentally measured with precision <1ppm

W W

Z0

e

SM predictions for a (units 10-10)

hadrons

+ +

B field

q

q

Cannot be evaluated in pQCD approach

aQED = 11 658 470.4 evaluated up to 5 (!)

loops a

had 700 7 Hadronic vacuum polarization a

EW = 15.2 0.4 Small contribution from Higgs a

lbl = 8 3 BUT recent publication from Melnikov: a

lbl = 14 3

aa 0.6 ppmSecond largest contribution

a and hadronic cross section

Dispersion integral relates ahad(vac-pol) to (e+e- hadrons)

Im[ ] | hadrons |2

ahad =

s-1

2232

2

|)(|3

)(

MFM

ee

Hadronic cross section is often written in terms of the pion form factor |F|2 :

Experimental input in a(had) - I

2|F |

2 E, MeV

L= 317.3 nb-1

114000 events in meson region

CMD2@VEPP2M

Standard method : beam energy scan

Contribution to a due to resonance:

CMD2 data confirmed by KLOE.

Experimental input in a(had) - II

Alternative approach used by KLOE : radiative return

)(22 s

dMd

M

H(s)

|F|2

CMD2

— KLOE

0.5 0.7 0.90

20

40

10

30

0M GeV

2 2( )

(376.5 0.8stat 5.4syst+theo) 10-10(378.6 2.7stat 2.3syst+theo) 10-10

KLOECMD2

L= 141 pb-1

1.5 M events in meson region

Experimental input in a(had) - III

• Recently a new method has been proposed which uses spectral function from (LEP, CESR data)

• Corrections have to be applied due: CVC violation, difference in isospin content, pion mass, effect of interference, possibly different mass and width of vs

• The related theoretical error is claimed to be under control

However, ath(ee – a

th() (20±10)10-10 (???)

hadrons

W hadrons

e+

e–

CVC: I =1 & V W: I =1 & V,A : I =0,1 & V

Muon-Anomaly: Theory vs. Experiment

Comparison Experimental Value with Theory - Prediction

a 11 659 000 ∙ 1010

TH

EO

RY

’20/

‘03

e+ e - Data: 2.7 - Deviation – Data: 1.4 - Deviation

Exp

erim

ent

’20/

‘04 Experiment BNL-E821

Values for +(2002) and -(2004)in agreement with each other.Precision: 0.5ppm

New cross section data have recently lowered theory error:

a) CMD-2 (Novosibirsk/VEPP-2M) channel with 0.6% precision < 1 GeVb) -Data from ALEPH /OPAL/CLEO

Theoretical values taken fromM. Davier, S. Eidelman, A. Höcker,

Z. Zhanghep-ex/0308213

Including KLOE result

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

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()

W

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 (had) to cover m()<s<m( and 1<s<2 GeV

How do we measure a

• At magic = 29.3, corresponding to E=3.09 GeV, K=0 and

precession is directely proportional to a

B (out of plane)

11

2

aK

EKBamce

msa

Precession of spin and momentum vectors in E, B fields (in the hyp. B=0) :Electric field

used for focusing (electrostatic quadrupoles)

E

Ba a

polarized

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

• 4109 events for t>50s and E>2GeV

tAeNtN at cos1)( /

0

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 a :– 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 p) :– 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:

0

0

22

22 wheres

mcedd

gsmcegd

EdBHE

M

P T

E E E

B B B

• Due to the E, B, properties under P and T reversal, [HE,Pand [HE,T

• This is not the case for the induced EDM, since dE,ind E

, at least at first order (implicitely used in deriving g-2 precession)

Predictions on EDMs

• We know that P and T simmetries are violated so it possible that

• 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

• 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

DdDem

a

FDDLDM

Im , Re2

: where

21*

21

21 55

~~~~

~~~~

VVVV

e

eee

Limits on EDM from g-2• The presence of perturbates the g-2 precession as

follows (B=E=0):

• At magic , with the condition that E<<B:

BEEaBamce

211

2

BBa

mce

2

that is the precession plane is tilted and a vertical oscillation can be observed in the emitted electrons.

d<2.810-19 e cm

EDMcontribution

Implications of g-2 limit on EDM Assume that new physics exists in the range of

aNP a

expaSM (1-10) 11 0.1-1 ppm

then we can write:

D= DSM + DNP = DSM + | DNP |eiCP

New Physics will induce a DM :

dNP a

NP tanCP 11e cm tanCP 1e cm

Current limit: d11e cm

Proposal for a new experiment with sensitivity

d1e cm which would probe |tanCP| 1

unit conversion

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

rB

mceBE

mce

zEKBaEKBa ra

ˆ22

0ˆ

sideview

Muon ring for EDM measurement

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.

P = 0.5GeV/cBz = 0.25 TEr = 2MV/mR = 7m<R> = 11mB+E = 2.6 mIntervals = 1.7 mn. elements = 16circunference 40m

Statistical error

dd NpBAP

md

22 : on error lStatistica

m = mass, = muon lifetime, p = momentum, B = magnetic field, A = asimmetry of vertical decays, P = muon beam polarization, Nd = dN = number of observed decay muons = number of injected muons (N) times detection efficiency (d)

To minimize statistical error:• maximize P2N, B, p• subject to constraint : Er a B < 2 MV/m ( Er directed inward )

The number of muons needed to reach d = 10-24 ecm , assuming A=0.3 and d=1 is:

NP2 = 1016

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)

cw ccw -B -BE E

BEEaBamce

211

2

Opposite sign Same sign

0 due to choice of ,B,E

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 BpF

Deuteron EDM

• Deuterons can be used in the same ring of muons with 1s 106 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

dd NpBAP

md

22 : on error lStatistica

• 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 210-27 e cm (hep-ph/0402023)

• A proposal for a DEDM experiment will probably be submitted at BNL