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g-2 and muon EDM (and maybe deuteron EDM also) 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. e. p. W. W. m. m. n. Z 0. Classically, considering spin s as a rotation around axis, g=1

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g-2 and muon EDM (and maybe deuteron EDM also) at a high intensity storage ring

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  1. 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 e p W W m m n Z0 • Classically, considering spin s as a rotation around axis, g=1 • Quantum physics predicts, for a Dirac particle, g=2 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

  3. 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

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

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

  6. Experimental input in am(had) - II H(s) Alternative approach used by KLOE : radiative return |Fp|2 — KLOE 40  CMD2 30 20 L= 141 pb-1 10 Contribution to am due to r resonance: CMD2 data confirmed by KLOE. 1.5 M events in  meson region (376.5  0.8stat  5.4syst+theo) 10-10 KLOE (378.6  2.7stat  2.3syst+theo) 10-10 0 CMD2 0 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)10-10 (???)

  8. Muon-Anomaly: Theory vs. Experiment ComparisonExperimental ValuewithTheory - 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: 2.7s - Deviation t – Data: 1.4s - 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

  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 • At gmagic= 29.3, corresponding to Em=3.09 GeV, K=0 and precession is directely proportional to am 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

  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. 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 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

  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 andelectric dipole moment (EDM)is: • Due to the E, B, s properties under P and T reversal,[HE,P]0and[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)

  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 SUSY SM

  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) 10-10 0.1-1 ppm then we can write: D= DSM + DNP = DSM + | DNP |eifCP • New Physics will induce a mEDM : dmNP amNP tanfCP10-13e  cm tanfCP10-20e  cm • Current limit: dm < 10-19e  cm • Proposal for a new experiment with sensitivity dm  10-24e  cmwhich 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 acombination 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 bg2 < 2 MV/m ( Er directed inward ) • The number of muons needed to reachsd = 10-24 ecm , assumingA=0.3anded=1is: • 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 bg2  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/0402023) • A proposal for a DEDM experiment will probably be submitted at BNL

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