Low-energy QED tests (and what we can learn from them) e ( 0 ) 2 ( - PowerPoint PPT Presentation

Low-energy QED tests (and what we can learn from them) e ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ) Indirect Searches for New Physics at the time of LHC Florence, March 2010 Andrzej Czarnecki U. of Alberta & CERN

Outline Gyromagnetic factors and the determination of fundamental constants ( α , m e ) e Polyelectrons and tests of few-body QED ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ) Muonic atoms and new physics searches (lepton flavor violation, new weak-scale forces)

Gyromagnetic factors and the determination of * the electron mass * the fine structure constant e

Free-electron g-factor [ ] ( ) α = 1/137.035999084 51 0.37ppb If you remember three decimal places, 137.036, you get another three free! e

Free-electron g-factor Experimental and theoretical uncertainties: [ ] ( )( ) α = 1/137.035999084 33 39 0.37ppb e

Motion in the Penning trap Motion in the xy plane: e

Bound-electron g-2: measurement From Werth M and m have different origins! e

Bound-electron g-2: theory e e ( ) ( ) 2 4 α α 2 2 ⎡ ⎤ Z Z ( ) ( ) 6 2 = − − + α = + − α 2 1 2 1 g O Z Z ⎢ ⎥ ⎣ ⎦ 3 6 3 Breit 1928 – Dirac theory Note: Breit’s calculation predates Schwinger’s by 20 years e

Bound-electron g-2: theory e e ( ) ( ) 2 4 α α 2 Z Z ( ) 6 = − − + α 2 g O Z 3 6 ⎡ ( ) ⎤ ⎛ ⎞ 2 α α 1 Z ( ) ( ) 4 5 ⎢ ⎥ + + + α ⎜ + ⎟ + α 1 ln Z a a O Z ⎜ ⎟ ( ) π 41 40 2 6 α ⎢ ⎥ Z ⎝ ⎠ ⎣ ⎦ one-loop corrections Pachucki, Jentschura, Yerokhin 2004 e

Bound-electron g-2: theory e e e ( ) ( ) 2 4 α α 2 Z Z ( ) 6 = − − + α 2 g O Z 3 6 ⎡ ( ) ⎤ ⎛ ⎞ 2 α α 1 Z ( ) ( ) 4 5 ⎢ ⎥ + + + α ⎜ + ⎟ + α 1 ln Z a a O Z ⎜ ⎟ ( ) π 41 40 2 6 α ⎢ ⎥ Z ⎝ ⎠ ⎣ ⎦ ⎡ ⎤ ( ) ⎛ ⎞ ⎛ ⎞ 2 2 α α ⎛ ⎞ ⎢ 1 Z ( ) 4 + − ⎜ + ⎟ + α ⎜ + ⎟ + ⎥ 0.65.. 1 ln .. ⎜ ⎟ Z b b ⎜ ⎟ ⎜ ⎟ ( ) 41 40 π 2 ⎝ ⎠ ⎢ 6 α ⎥ Z ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ two-loop corrections e

The two-loop bound-state effect 28 = b 41 9 = − 16.4 b Pachucki, AC, Jentschura, Yerokhin 40 2005 ( + = ) ( ) ( ) 12 5 0.00054857990931 29 1 m C u e exp th Theoretical error: negligible e

2010: new measurement with oxygen, 16 O 7+ Theoretical prediction: ( ) ( ) Z = = th 8 2.00004702032 11 g Measured value: ( ) ( ) Z = = exp 8 2.0000470201 25 g (preliminary) e

The “kinematic” method of finding alpha Rydberg constant is extremely well measured, 2 1 α 2 13.6eV m c ∞ = R � e 2 hc hc We can find alpha if we measure the quotient of the Planck constant and the “ electron ” mass, 2 R h α = 2 ∞ m c In practice e heavier particles 2R m m h = ∞ p Cs are better: c m m m neutrons or atoms. Cs e p e

Fine structure constant: other methods Nature 442 (2006) 516 . Rb ν ν ' ν 2 2 2 h 2 Ry ( ) h ⋅ ν − ν � ' α = h 2 2 m c m c Rb e Δ ν h 2Ry = 2 m m h c = p Rb ν 2 2 m Rb c m m m Rb e e p

α from Paris about 450 Bloch oscillations in each direction : 1800 recoils from F. Nez Statistical uncertainty on α = 4.4×10 -9 α -1 = 137.035 998 78 (91) uncertainty 6.7 × 10 - 9 Cladé et al, PRL 96 , 033001 (2006) Future goal: 1ppb e

Polyelectrons ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

Dipositronium Ps 2 e + e - e - ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ) e + ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

Discovery of dipositronium 2007 Molecule formation kills long-lived positronia. At higher temperature, fewer atoms on the surface, fewer molecules formed. Indeed: at high-T, more long-lived positronia observed. Cassidy & Mills, Nature 2007 ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

Spectrum of the molecule Ps 2 Non-molecular states of e - e - e + e + Molecular states From Suzuki & Usukura, 2000 ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

A direct signal of the molecule: transition line. From Suzuki & Usukura, 2000 Autodissociation forbidden by Bose-Einstein statistics ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

A direct signal of the molecule: transition line. From Suzuki & Usukura, 2000 Observable UV transition ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

with Puchalski, PRL 101, 183001 (2008) Questions about this transition: What is its accurate energy? Δ = − = 0.1815867(8)a.u. E E E P S � 4.9eV Similar to atomic positronium, but softer (dielectric effect?): 3 1 a.u.=0.1875a.u. − = × E E P S 4 4 ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

with Puchalski, PRL 101, 183001 (2008) Questions about this transition: How often does radiative transition appear (before annihilation)? ( ) Γ → P S ( ) ( ) → = dip = BR 0.191 2 P S ( ) ( ) Γ + Γ → P P S annih dip ( 0 γ) 2 γ ( 4 γ) ( 1 γ) 3 γ ( 5 γ)

Muonic atoms

Muonic hydrogen Lamb shift and the proton radius Slides on this topic are not included in this version; please contact Randolf Pohl randolf.pohl@mpq.mpg.de for detailed information about the recent PSI results.

Searches for Lepton Flavor Violation We heard yesterday about MEG: now 10 -11 , goal ~10 -13 Muon-electron conversion: Fermilab proposal Mu2E: 10 -16 New idea: µ - e - → e - e - Koike et al, 1003.1578, in a large-Z atom. Competition with muon capture.

Muon capture Theory and experiment agree, after years of confusion. Average of HBChPT calculations of Λ S further sub percent theory required : = 710.6 s -1 Λ S Theory = 710.6 s -1 Λ S Theory Apply new rad. correction (2.8%): = 725.0 ± 13.7 stat 10.7 sys s -1 Λ S MuCap ± = 725.0 ± 13.7 stat 10.7 sys s -1 Λ S MuCap ± PRL 99 , 032001 (2007)

Summary Continuing progress in determination of α and m e . New opportunities to test QED with three- and four-body bound states. An open problem: organization of the perturbative series; origin of dominant corrections.