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

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  0.0012 am experimentally measured with precision <1ppm

SM predictions for am (units 10-10) amQED = 11 658 470.4  0.3 - evaluated up to 5 (!) loops amhad  700  7 - Hadronic vacuum polarization amEW = 15.2  0.4 - 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

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 :

Experimental input in am(had) - I Standard method : beam energy scan CMD2@VEPP2M L= 317.3 nb-1 114000  events in  meson region

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

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)10-10 (???)

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/0308213 THEORY ’20/‘03 e+ e- - Data: 2.7 s - Deviation t – Data: 1.4 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 - 11 659 000 ∙ 10-10

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-

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

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

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

BNL E821 beam line

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

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

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 … … 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

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: 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

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

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

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

Implications of g-2 limit on EDM Assume that new physics exists in the range of amNP  amexp-amSM  (1-10) 10-10  0.1-1 ppm then we can write: D= DSM + DNP = DSM + | DNP |eifCP New Physics will induce a mEDM : dmNP  amNP tanfCP 10-13 e  cm  tanfCP 10-20 e  cm Current limit: dm < 10-19 e  cm Proposal for a new experiment with sensitivity dm  10-24 e  cm which would probe |tanfCP| > 10-3 unit conversion

Limits on fCP according to limit on dm

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

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.

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 = 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 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

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

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

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

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