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Low-energy Experiments and their Impact in Particle Physics

This lecture discusses the importance of low-energy experiments in particle physics and their impact on the field. It focuses on select relevant subjects such as lepton magnetic moments and atomic physics experiments. The lecture also explores the potential of "table-top" experiments to compete with the Large Hadron Collider (LHC) and provides insights into the advancements and perspectives in ae measurements.

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Low-energy Experiments and their Impact in Particle Physics

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  1. “Small may be beautiful” (part A) Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay CERN Academic Training 13-15 June 2005    hadrons davier@lal.in2p3.fr

  2. Foreword • lectures sollicited by D. Treille who proposed the title • discuss low-energy experiments and their impact in particle physics • precision as an approach to frontier high-energy physics • select only a few particularly relevant subjects • lepton magnetic moments interplay and progress experiment / theory • atomic physics experiments: weak-EM interference through P violation search for electric dipole moments • (M. Davier) • physics with ultra-cold neutrons • (T. Soldner) Can ‘table-top’ experiments compete with the LHC ?

  3. Part I : Lepton Magnetic Moments Michel Davier Laboratoire de l’Accélérateur Linéaire, Orsay CERN Academic Training 13-15 June 2005    hadrons davier@lal.in2p3.fr

  4. Magnetic Moment of a Charged Spin-1/2 Particle Dirac’s triumph: relativistic equation describing spin-1/2 particle charge e  magnetic dipole moment   = g B s with B = e  2m and g = 2 (k) (k’) e u(k’) u(k) = e u(k’) [ (k+k’)+ i(k’-k)] u(k)  2m cf. spin-0 charge currentmagnetic current (B ) Non-point-like particles have g much different from 2 (internal structure) Yet, the electron shows small deviation from g=2 (Rabi 1947) later explained by quantum fluctuations (virtual processes in QED) First-order correction (1-loop order)  shift in g Schwinger 1948

  5. Measurements of ae • electron bunch (U. Michigan 1953-1972) • ge ae (gain 3 orders of magnitude) • single e in a cold Penning trap • (U. Washington 1977-1990, H. Dehmelt et al) • principle: • cyclotron motion (B) • spin precession • frequency difference B =5.5 T c  s  150 GHz a  170 MHz

  6. ae results from U.Washington experiments • (1987) • B field = 6 T cavity cooled to 4.2 K • electron ae- = 11 596 521 884 (43) 10-133.7 ppb • positron ae+ = 11 596 521 879 (43) 10-133.7 ppb • CPT test • to be compared to SM prediction • results unchallenged for nearly 20 years

  7. Theory of ae • until recently the experimental accuracy reached in ae did not require • non-QED contributions in the theoretical calculation •  ae pure test of QED at high orders • rapidly increasing calculational difficulties  ae = Cn ()n n • n #diagrams analytic numerical Cn • 1 + 0.5 Schwinger 1948 • 7 + -0.328… Sommerfield, Petermann 1957 • 72 + 1.181… Laporta-Remiddi 1996 • 891 + -1.71… Kinoshita-Nio 2004 • 12672 estimate only Need precise value of (0) (where from ?) • non-QED non e-loop vacuum polarization • muon loop VP ae = 27.21 10-13 • hadronic VP aehad = 16.42 (27) 10-13

  8. Perpectives for improvement in ae measurement • UW technique under improvement at Harvard for the last 20 years (Gabrielse) • main point: cool cavity at sub-K temperature (dilution refrigerator) • many other improvements (better geometry, bigger cavity) • single very cold electron: cyclotron transitions only when excited by applied RF cyclotron quantum jumps and quiet ground state observed (Peil-Gabrielse 1999) non-destructive observation of Fock states of single-electron oscillator

  9. A new preliminary result • Harvard experiment starting to produce results • anomaly and cyclotron frequency broadening 10x less as in UW • true quantum spectroscopy between n=0  n=1 cyclotron and • n=0   n=0  spin-flip transitions • only preliminary result available • B. Odom thesis (Harvard Oct 2004) • ae- = 11 596 521 808.6 (5.7) 10-13 • 0.5 ppb (8x more precise as UW) • uncertainty limited by systematics from • cavity frequency shifts

  10. Sensitivity of ae to beyond QED revisited • new preliminary result from Harvard sensitive to interactions beyond (e,) QED • at the level of precision reached, should take into account muon and hadronic • vacuum polarization • unfortunately, the accuracy of the exp. result cannot be fully exploited to • compare to theory because  is not known precisely enough • argument can be turned • around Odom thesis 2004

  11. The value of (0)  can be deduced from ae measurement and QED prediction + small non-QED corrections and compared to standard determinations • Quantum Hall effect   • Other involve several measurements • ex. h mCs from Cs recoil expts • h mCs = h me (me mp) (mp mCs) • = 2 c 2R (me mp) (mp mCs) QED tested at 10-8 level 0 on the right scale corresponds to CODATA 1998 value using ae (UW) and QED with an error in 4 term (6 ppb) (!) Odom thesis 2004

  12. 1958-1979: Pioneering CERN work on a • inspired from the 1957 historical exptsGarwin-Lederman-Weinrich • g  2 (10%)Friedman-Telegdi • first expt at SC  1960Lederman + Garwin-Charpak-Sens-Zichichi • precision on a 0.4% • second expt 1962-1968muon storage ringFarley-Picasso-…. • relativistic muons  longer storage time • precision 270 ppm 2 above QED (missing LBL contributions!) • third expt 1969-1976E focussing and magic momentum • precision 10 ppm for both  • hadronic vacuum polarization established at 5 (see OPAL hep-ex/0505072) a(exp) = 11 659 240(85)  10–10 a(exp) – a(SM) = 30(120)  10–10

  13. B Principle of (g-2) measurement E821 at BNL muons stored on a circular orbit (B field) spin precesses (1)Precession frequency (2) Muon distribution (3) Magnetic field map ratio of 2 frequencies [D.W. Hertzog] hep-ex/0501053

  14. What is needed ? n p+ m+ • Polarized muons Parity violation in  decay [D.W. Hertzog] hep-ex/0501053

  15. Muons are created from in-flight p decay and enter ring in a bunch [D.W. Hertzog] hep-ex/0501053

  16. What is needed ? n p+ m+ • Polarized muons Parity violation in  decay • Precession proportional to (g-2) µ [D.W. Hertzog] hep-ex/0501053

  17. e Momentum Spin The muon spin precesses faster than the cyclotron frequency: amis proportional to the frequency difference between precession and rotation identical to nonrelativistic equation

  18. What is needed ? n p+ m+ • Polarized muons Parity violation in  decay • Precession proportional to (g-2) • Pm ‘magic’ momentum E field doesn’t affect muon spin when g = 29.3 µ Bargmann-Michel-Telegdi [D.W. Hertzog] hep-ex/0501053

  19. incoming muons Quads BNL Storage Ring Only a few percent get stored!

  20. What is needed ? n p+ m+ • Polarized muons Parity violation in  decay • Precession proportional to (g-2) • Pm ‘magic’ momentum E field doesn’t affect muon spin when g = 29.3 • Parity violation in  decay µ [D.W. Hertzog] hep-ex/0501053

  21. 2001 1 ppm contours 0.05 0.09 0.05 0.07 0.10 0.17 Magnetic Field Measured in situ using an NMR trolley Continuously monitored using 150 fixed probes mounted above and below the storage region

  22. Fit to Simple 5-Parameter Function N(t) = N0e-t/t[1+Acos(wat + f)] Few billion events

  23. fg-2 ≈229 KHz fCBO≈466 KHz In 2001, the ring index was adjusted to avoid frequency overlap Coherent Betatron Oscillations Fourier Spectrum of Fit Residuals

  24. 2001: The First Round of BNL Results on a The E821 (g –2) experiment at BNL published early 2001 a value 3 more precise than the previous CERN and BNL exps. combined: a(exp) = 11 659 202(16)  10–10 SM BNL compared with Standard Model prediction: a(SM) = 11 659 159.6(6.7)  10–10 Averaging E821 with previous experiments gave: a(exp) – a(SM) = 43(16)  10–10 [2.7 ] BUT: In November 2001, Knecht & Nyffeler corrected a sign error in the dominant (-pole) contribution from hadronic light-by-light (LBL) scattering, reducing the above discrepancy to LBLS  had 25(16) 10–10 [1.6 ]  Knecht-Nyffeler,hep-ph/0111058; result approved by: Hayakawa-Kinoshita, hep-ph/0112102; Bijnens-Pallante-Prades, hep-ph/0112255 

  25. 2002: The Second Round of BNL Results on a The new analysis, first presented at ICHEP’02, achieved 2 times better precision (using 4 more statistics) than the 2001 result: a(exp) = 11 659 203(7)(5)  10–10 • Error dominated by statistics; systematics are: • 3.6  10–10 from precession frequency • 2.8  10–10 from magnetic field BNL compares WA with SM prediction (using DH’98 for hadronic vac. pol.): a(exp) – a(SM) = 25(10)  10–10 Experimental and theoretical uncertainties now of similar order ! But new calculations of hadronic vacuum polarization show a problem when using either ee or  data (see later)

  26. 2004: The Final E821 Results on a Analysis of  data of comparable accuracy (CPT test) a(exp) = 11 659 203(7)(5)  10–10  a(exp) = 11 659 214(8)(3)  10–10 average a (exp) = 11 659 208.0(5.8)  10–10 (ppm) Latest comparison with SM prediction (ee) (DEHZ presented by A. Höcker at ICHEP04): a(exp) – a(SM) = 25.2(9.2)  10–10 Experiment is now more precise than Theory ! combined 0.5 More work and, in particular, better data needed to achieve a more precise prediction of the hadronic contribution

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