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II.3. Anomales magnetisches Moment (g-2) µ

g. coupling to virtual fields. e. . II.3. Anomales magnetisches Moment (g-2) µ. Das gyromagnetische Verhältnis g verknüpft Spin und magnetisches Moment Dirac Theorie für punktförmige Spin-1/2 Teilchen: g = 2 but ... Proton Hyperonen Elektron Myon

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II.3. Anomales magnetisches Moment (g-2) µ

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  1. g coupling to virtual fields e  II.3. Anomales magnetisches Moment (g-2)µ • Das gyromagnetische Verhältnis gverknüpft Spin und magnetisches Moment • Dirac Theorie für punktförmige Spin-1/2 Teilchen: g = 2 but ... • Proton • Hyperonen • Elektron • Myon • Das anomale magnetische Moment des Myons ist g  2 g almost equal to 2

  2. Coupling to X goes asmm2/mX2factor of 40,000 compared to e Muon anomalous magnetic moment am(SM) = am(QED) + am(weak) +am(had) x 10-10 am(QED) = 11658471.935 (.143) BNL E821 data

  3. zo m µ µ W W µ µ B field Coupling to X goes asmm2/mX2factor of 40,000 compared to e Muon anomalous magnetic moment am(SM) = am(QED) + am(weak) +am(had) x 10-10 am(QED) = 11658471.935 (.143) + am(weak) = 15.4__ (.2) +3.89 BNL E821 data -1.94(Higgs < 0.01)

  4. Coupling to X goes asmm2/mX2factor of 40,000 compared to e Muon anomalous magnetic moment am(SM) = am(QED) + am(weak) +am(had) x 10-10 am(QED) = 11658471.935 (.143) + am(weak) = 15.4__ (.2) + am(had1sto) = 696.3__ (7.2) + am(had h.o.) = -10.0__ (.6) BNL E821 data Requires Data

  5. Coupling to X goes asmm2/mX2factor of 40,000 compared to e Muon anomalous magnetic moment am(SM) = am(QED) + am(weak) +am(had) x 10-10 am(QED) = 11658471.935 (.143) + am(weak) = 15.4__ (.2) + am(had1sto) = 696.3__ (7.2) + am(had h.o.) = -10.0__ (.6) + am(hadl-by-l) = + 13.6__ (2.5) BNL E821 data

  6. D am= any new physics Coupling to X goes asmm2/mX2factor of 40,000 compared to e Muon anomalous magnetic moment am(SM) = am(QED) + am(weak) +am(had) x 10-10 am(QED) = 11658471.935 (.143) + am(weak) = 15.4__ (.2) + am(had1sto) = 696.3__ (7.2) + am(had h.o.) = -10.0__ (.6) + am(hadl-by-l) = + 13.6__ (2.5) BNL E821 data

  7. p p g m Z m p p B Weak Had LbL Had VP Had VP QED 2006 plot KEY REGION

  8. How to Measure a Magnetic Moment Brookhaven provides the pions from protons on nickel tgt Forward-going daughter muons are polarized 0 m- p- nm

  9. How to Measure a Magnetic Moment wc (Tc = 149 ns) wa = ws- wc (precesses ~120 per cycle) ws = 1+g (g-2) eB and wc = eB 2 mg mg wa = ws - wc = (g-2) eB 2 m (am- ) b x E e m 1 g2 -1 Quadrupole E field gives additional term in wa : + Which vanishes at the “magic momentum” of 3.094 GeV/c

  10. WEAK-FOCUSSING MUON STORAGE RING B = 1.45 T Pm= 3.094 GeV/c Rring = 7.112 m Rstor = 4.5 cm Kicker Quad Quad Inflector 24 SciFi Calorimetersrecord time and energy of decay e+ (or e-) nmne m-e- Quad Calorimeters select high energy e’s These e’s are preferentially emitted in the direction of the m spin Quad

  11. 2001 data set: 4 billion e+ (E > 1.8 GeV, t > 32 ms after injection) Cyclotron Frequency at early times g-2 Precession Frequency after debunching Fit for g,m radial distribution, bxE correction: (0.47 + 0.05) ppm Million evts per 149.2 ns Fit for wa: No e-t/gt (1 + A cos (wat +j)) is no longer good enough.

  12. m e Energy Spectrum late time(no pileup) early + late early + late(corrected) Main Disturbances • Pileup of real pulses <5 ns apart1% at earliest times: model and subtract • Muon Lossesbump beam and scrape (first 11 ms) scintillator paddles measure triples • Rate dependent calorimeter responsechanges the effective Ethrin situ laser calibration system • Bunched beamrandomize time spectrum in bins of Tcyclotron • Coherent Betatron Oscillations image of the inflector exit moves around the ring as a beat frequency of wc and wb fiber harp and traceback chamber measure stored muon profile vs time

  13. Measuring the Magnetic Field 0.5 ppm contours are 750 nT over an average field of 1.45 Tesla. muon sees the field averaged over azimuth vertical distance (cm) -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 17 calibrated NMR probes inside the trolley measure the field every cm horizontal distance (cm)

  14. Blind Analysis Decay positrons NMR wa = am e B mp B = h wp m am = Rl - R where R = wa / wp is measured by E821 and l = mm / mpfrom muonium hyperfine structure • Offline Team (5 analyses) Magnet Team (2 analyses) • wa wp • Both w’s and all analyses have computer-generated secret offsets. • Study stability of R under all conditions • Finish all studies and assign all uncertainties BEFORE revealing offset.

  15. Finally, remove offsets to double-blind analysis Magnetic Field Secret Offsets Secret Offsets UIUC UIUC Data Production Yale am = 116 592 08(6)  10-10(0.5 ppm) PHYSICAL REVIEW D 73, 072003 (2006) Final average

  16. Finally, remove offsets to double-blind analysis Magnetic Field Secret Offsets Secret Offsets UIUC UIUC Data Production Yale am = 116 592 08(6)  10-10(0.5 ppm) PHYSICAL REVIEW D 73, 072003 (2006) Final average

  17. Evolution of the Experimental Uncertainties Data Set: 1997 1998 1999 2000 2001 p-injection kicker installed 1st long run new inflector reverse polarity field stabilized 12 M e+ 84 M e+ 1 B e+ 4 B e+ 4 B e-Statistics (Ne above Ethr)12.5 ppm 4.9 ppm 1.25 ppm 0.6 ppm 0.7 ppm Systematics2.9 ppm 1 ppm 0.5 ppm 0.4 ppm 0.3 ppm dwa 2.6 ppm 0.7 ppm 0.3 ppm 0.3 ppm 0.21 ppm Dominated byWFD threshold pileup pileup coherent betatron gain stability pion flash AGS mistune AGS mistune m loss, pileup m loss dwp1.3 ppm 0.5 ppm 0.4 ppm 0.24 ppm 0.17 ppm Dominated bythermal fluctuations trolley position trolley position trolley position trolley position no active feedback inflector inflector Still statistics dominated!

  18. Theory + Exp. E821 Experimental Results TIME James P Miller, Eduardo de Rafael, B Lee Roberts Rep.Prog.Phys. 70, 795 (2007). K. Hagiwara, A.D. Martin, Daisuke Nomura, T. Teubner

  19. Mögliche SUSY Beiträge zu (g-2)µ • 1-Loop Beiträge • Für ähnliche Massen ~ MSUSY in der Schleife:mit tanb:=v2/v1 und Higgsino Massenparameter µ

  20. D.Stöckinger hep-ph/0609168 • µ>0, wenn Daµ durch SUSY verursacht • Kleines mSUSY oder großes tanb:=v2/v1 nötig

  21. 2-loop Beiträge ergeben ~ 2% Korrektur

  22. J.Ellis, K.Olive et al hep-ph/0303043 • Übersicht mehrerer Randbedingungen (LEP,WMAP, (g-2)µ, Dunkle Materie etc )

  23. III. Dunkle Materie • Nur 4-5 % des Universums ist “normale” Materie des SM • Ca. 23% ist “Dunkle Materie”(weakly interacting massive particles WIMPS) • X-ray measurements (Chandra) • [weak] gravitational lensing • Primordial Nucleosythesis • Rotation Curves • Bullet Cluster • WMAP et al. Clowe et al. (2006) NASA/WMAP Science Team

  24. im Kontrast zu ... Rotationsgeschwind.der Sterne um dasGalaxienzentrum Rotationsgeschwindigkeit der Planeten um die Sonne Gravitationslinsen:Lichtablenkung durch Materie Gravitative Hinweise auf “dunkle” Materie

  25. Neutrinos influence several cosmological epochs Dark Matter and Cosmology

  26. Premordiale Nukleosythese • Aus gemessenem Baryon/PhotonVerhältnis, mit bekanntem ngaus CMB:hB = nB / ng= 2,7 x 10-8 WB h2 • erhält man WBh2 ~ 0,02 << WMh2 hB / 10-10

  27. Beispiele zur Vermessung der Hintergrundstrahlung 1999BOOMERanG

  28. Nach Abzug unserer Milchstraße • Winzige Temperaturschwankungen: T=2,73 K +- 0,00002 K • “heiße” und “kalte” Flecken = “dichte” und “dünne” Gebiete • genau wie bei Schall  Klang des Universums

  29. Die Obertöne des Kosmischen Klangs • Das Ohr hört an Obertönen: • Art des Instruments • geübtes Ohr: Bauweise • Astrophysiker erkennen an den Obertönen: • „Form“ des Universums • Zusammensetzung

  30. Vergleich der Akustischen Wellen Luft Universum Verhält. Wechselwirkung Druck d. Strahlung+ Gravitation (!) Druck d. Stöße Dichte 3x1025 Moleküle / m3 3x108 Protonen / m3(bei 380.000 Jahren) 10-17 Zustandsgleichung pVk= const. p ~ rk p = ⅓c2r Geschwindigkeit v= Ökp/r = 340 m/s v= c/Ö 3 =1,7x108m/s 500.000 Wellenlänge 20 mm – 20 m 20.000 – 400.000 Lj 1020 - 1022 Frequenz 17.000 – 17 Hz 10-12 – 0,4x10-13 Hz 10-14-10-16 • Akustik bis zu Frequenzen von 0,04 pHz !

  31. CMB DATA: INCREASING PRECISION Map of CMBR temperature Fluctuations Multipole Expansion Angular Power Spectrum

  32. Zusammensetzung des Universums • Beiträge zur Gesamtenergie W • atomare Materie (p,n,e):WBSterne, Planeten, Gaswolken, Schwarze Löcher,…-- dämpft den ersten „Oberton“-- verstärkt den zweiten „Oberton“ • nichtatomare „dunkle“ Materie (n, …): WDMUngebundene Elementarteilchen, schwach wechselwirkend -- verstärkten den zweiten „Oberton“ • „dunkle“ Energie:WV„kosmologische Konstante“ „Vakuumenergie“ unverdünnbar W = WB+ WDM + WV= 1

  33. Zeitliche Dichteoszillationen halbe WellenlängeÛDoppelte Frequenz

  34. Der Effekt von Gravitation (~Materiedichte) Veränderung der Amplitudenverhältnisse

  35. Ergebnis • 5% atomare Materie(WB =0,05) • 22% nichtatom. Materie(WDM =0,22) • Summe: W=1,00  • 73% „dunkle Energie“(WV=0,73) ! Selber probieren: http://map.gsfc.nasa.gov/resources/camb_tool/

  36. Galaxy Surveys 2dFGRS SDSS

  37. 2dFGRS Galaxy Survey ~ 1300 Mpc

  38. Field of density Fluctuations CMB experiments SDSS Galaxy Surveys Matter power spectrum is the Fourier transform of the two-point correlation function Power Spectrum of density fluctuations

  39. MPI für Astrophysik München, MIllenium Simulation (Colloq Dresden 22.6.10!)http://www.mpa-garching.mpg.de/galform/virgo/millennium/ Strukturbildung im Universum t = 4,7 Mrd. Jahre150 Mio Lichtjahre t = 0,2 Mrd. Jahre20 Mio Lichtjahre “erste Sterne” t = heute300 Mio Lichtjahre t = 1,0 Mrd. Jahre50 Mio Lichtjahre “erste Galaxien”

  40. leichtestes SUSY Teilchen (LSP): Oft Neutralino • Neutralinos sind ein exzellenter Dark Matter Kandidat! • Das Leichteste könnte ein stabiles “WIMP” with h2  DMh2 sein Eigenschaften des LSP Neutralinos abhängig von Zusammensetzung! Siehe ausführliche Diskussion in späteren Vorlesungen und S.Martin, Kap 9.3

  41. Next transparencies: Laura Baudis: Dark Matter SearchesGraduate School Rathen 2009, http://bnd-graduateschool.org/2009/

  42. WIMP Relic Density 1. Annahme: WIMPS waren im thermischen Gleichgewicht • Löse die Boltzmann Gleichung um heutige Dichte n zu finden.

  43. WIMP search results :Uwe Oberlack: http://iopscience.iop.org/1742-6596/110/6/062020 (2008)

  44. J.Ellis, K.Olive et al hep-ph/0303043 • Übersicht mehrerer Randbedingungen (LEP,WMAP, (g-2)µ, Dunkle Materie etc )

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