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The Proton Radius Puzzle =================================================== The proton radius puzzle Measure the 2S − 2P splitting in µp ↓ determine the proton rms radius rp (10× better ) But large discrepancy observed: • 4σ from H spectroscopy value • 6σ from e-proton scattering value A. Antognini MPQ, Garching, Germany ETH, Zurich, Switzerland A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.1 ================ The good, the bad and the ugly Who is the bad? - Muonic hydrogen - Hydrogen ? - Scattering Discrepancy → active discussion: • H and µp energy levels - bound-state QED theory - effective field theories - spectroscopy measurements, R∞ • Scattering measurements and analysis • Proton structure • New physics A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.2 Aim of the µp Lamb shift experiment (before we dit it!) 8.4 meV • Measure the 2S − 2P energy difference (Lamb shift) in µp F=2 2P3/2 F=1 2 3 2P1/2 F=1 ∆E(2S − 2P ) = 209.9779(49) − 5.2262 rp + 0.0347 rp meV F=0 with 30 ppm precision. 206 meV 50 THz µ 2 −3 6 m • Extract rp ≡ rp with ur ≈ 10 (rel. accuracy) → bound-stateq QED test in hydrogen −7 to a level of ur ≈ 3 × 10 (10× better) 1 ∞ 2 2 → improve Rydberg constant (cR = 2 α mec /h) −12 to a level of ur ≈ 1 × 10 (6× better) fin. size: 3.8 meV → benchmark for lattice QCD calculations F=1 2S1/2 23 meV → confront with electron scattering results F=0 A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.3 Finite size effect (in leading order) −ieγµ F (q2) gµν 1 2 → 2 −i 2 q q Potential q rp −ieF (q2)γν 2 3 2 rp ≡ d r ρ(r)r R 2 2 3 −iq·r q 2 R (fm) F (q )= d r ρ(r)e ≃ Z(1 − 6 rp + ··· ) Maxwell equation: R ∇E = 4πρ Zα ∆V (r)= V (r) − − r Zα r 2 − 3 − ( ) (r < rp) 4πZα “ ” 2π(Zα) 2rp rp q q 2 V = ∆V ( )= q2 (1 − F ( )) ≃ 3 rp 8 Zα “ ” − r (r > rp) < 2π(Zα) 2 ∆V (r)= 3 rp δ(r) : Ze2 r 2rp − 3 − ( )2 − 2π(Zα) 2rp rp r FS 2 2 ∆V = ∆E = 3 rp |Ψn(0)| 8 0 “ ” 4 < 2(Zα) 3 2 FS = 3 mr rp δl0 ∆E := hΨ¯ |∆V |Ψi 3n A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.4 Principle of µp(2S-2P) experiment − • special low-energy µ beam-line at PSI (unpulsed!) 8.4 meV 2P F=2 − 3/2 F=1 2P1/2 F=1 • µ detected in-flight → trigger of laser system F=0 − • µ p atoms formed in 1 mbar H2 gas 206 meV • laser pulse excites the 2S-2P transition (λ ≈ 6 µm) 50 THz • delayed 2P-1S X-ray detected: signature 6 µm “prompt” (t ∼ 0) “delayed” (t ∼ 1 µs) n~14 2 P 2S-vac.pol. Laser 1 % 99 % = -206meV 2 S proton 2 P fin. size: 3.8 meV 2 S γ F=1 2 keV γ 2 keV 2S1/2 23 meV F=0 linewidth = Γ =18.6GHz 1 S 2P 1 S → 6 transitions separated ! 1% with τ2S = 1 µs normalize delayed/prompt [R. Pohl ..., PRL 97,193402 (2006)] A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.5 The resonance: discrepancy, sys., stat. Discrepancy: −3 5.0 σ ↔∼ 75 GHz ↔ δν/ν = 1.5 × 10 Waterline known with 1 MHz accuracy ] -4 7 CODATA-06 our value 6 e-p scattering H2O 5 calib. Fitted position: 700 MHz unc. 4 → rp delayed / prompt events [10 3 Fitted width 2 as predicted 1 0 49.75 49.8 49.85 49.9 49.95 laser frequency [THz] Systematics: 300 MHz Laser frequency known with 300 MHz uncertainty Statistics: 700 MHz A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.6 Proton radius from µp Lamb shift F =1 F =2 Measured µp resonance: ν(2S1/2 − 2P3/2 ) = 49881.88(76) GHz (15 ppm!) • Comparing measurement with theoretical prediction −→ r.m.s. proton radius: ∆Eexp. = 206.2949(32) meV ⇒ rp = 0.84184(67) fm ∆Eth. = 209.9779(49) − 5.2262 r2 + 0.0347 r3 meV ) p p exp −4 ur = 4.3 × 10 R. Pohl et al., Nature 466, 213 (2010) th −4 ur = 6.7 × 10 A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.7 Proton radius from µp Lamb shift F =1 F =2 Measured µp resonance: ν(2S1/2 − 2P3/2 ) = 49881.88(76) GHz (15 ppm!) • Comparing measurement with theoretical prediction −→ r.m.s. proton radius: ∆Eexp. = 206.2949(32) meV ⇒ rp = 0.84184(67) fm ∆Eth. = 209.9779(49) − 5.2262 r2 + 0.0347 r3 meV ) p p exp −4 ur = 4.3 × 10 R. Pohl et al., Nature 466, 213 (2010) th −4 ur = 6.7 × 10 . • But big discrepancy (75 GHz = 0.31 meV in ∆E): µp: rp = 0.842 ± 0.001 fm Discrepancy of rp(µp): H-spectroscopy: rp = 0.876 ± 0.008 fm • 4.3 σ from H from e-p scatt. e-p scattering: rp = 0.897 ± 0.018 fm [Sick 2005] • 3.1 σ CODATA-2006: rp = 0.877 ± 0.007 fm • 5.0 σ from CODATA • rp 4% smaller A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.7 Proton radius from µp Lamb shift F =1 F =2 Measured µp resonance: ν(2S1/2 − 2P3/2 ) = 49881.88(76) GHz (15 ppm!) • Comparing measurement with theoretical prediction −→ r.m.s. proton radius: ∆Eexp. = 206.2949(32) meV ⇒ rp = 0.84184(67) fm ∆Eth. = 209.9779(49) − 5.2262 r2 + 0.0347 r3 meV ) p p exp −4 ur = 4.3 × 10 R. Pohl et al., Nature 466, 213 (2010) th −4 ur = 6.7 × 10 . • But big discrepancy (75 GHz = 0.31 meV in ∆E): µp: rp = 0.842 ± 0.001 fm Discrepancy of rp(µp): H-spectroscopy: rp = 0.876 ± 0.008 fm • 4.3 σ from H from e-p scatt. e-p scattering: rp = 0.897 ± 0.018 fm [Sick 2005] • 3.1 σ CODATA-2006: rp = 0.877 ± 0.007 fm • 5.0 σ from CODATA new: • rp 4% smaller e-p, Mainz 2010: r = 0.879 ± 0.008 fm p • 6.5 σ from e-p scatt. e-p, JLab 2011: rp = 0.875 ± 0.010 fm A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.7 Proton radius puzzle: What may be wrong? 75 GHz Discrepancy: ∆Eth.(rCODATA) − ∆Eexp. = 0.31 meV µp p µp 0.15 % (1) µp exp. wrong ? but • good statistics (σ = 0.76 GHz ≪ discrepancy) • linewidth ∼ 19 GHz ≪ discrepancy (2) µp theory wrong? but • several methods for frequency calibration • mainly pure QED (vac.pol., etc.) • another µp(2S-2P) measured! • ’huge’ relative discrepancy • hadronic terms small (3) H spectroscopy wrong ? but • pol.term = 0.015(4)meV • 2S-8S, 2S-8D, 2S-12S, etc. all consistent ... • weak interactions very small (4) H theory wrong? but • uncertainties at leat 25× smaller than discrepancy ... (5) e-p scattering wrong? but • new Mainz and JLab results ... A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.8 rp puzzle (1): Is the µp experiment wrong ? th exp ∆E-discrepancy = 75 GHz ↔ ur = 1.5% ↔ 4Γ and Γ =Γ • Laser frequency calibration Two consistent ways (→ σ =0.3 GHz): (i) at 6 µm with H2O lines (20 measurements of 5 different lines) (ii) at 708 nm with λ-meter, wavemeter, and FP (calibrated to I2, Rb, Cs lines) Statistical uncertainty= 700 MHz, Systematic uncertainty= 300 MHz. • Systematic uncertainties: -laserfrequencycalibration 0.300GHz - Zeeman effect (B = 5 Tesla) 0.030 GHz Systematics ∼ 1/m - AC-Stark, DC-Stark shift < 0.001 GHz -Dopplershift <0.001GHz Finite size ∼ m3 - pressure shift (1 mbar) 0.001 GHz - molecules, ions (ppµ)∗, (µp)e− < 0.001 GHz (τppµ ∼ps → no population left for laser experiment!) No broadening observed! A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.9 rp puzzle (1): Is the µp experiment wrong ? th exp ∆E-discrepancy = 75 GHz ↔ ur = 1.5% ↔ 4Γ and Γ =Γ • Pressure shift ? - pressure shift of H(1S-2S) in H2 gas: ∼10 MHz/mbar - µp is me/mµ smaller (stronger E-fields): - less disturbed by external fields - smaller mixing of states Detailed calculations give a pressure shift of ∼1 MHz at 1 mbar ∗ − • Spectroscopy of (ppµ) -molecules, or (µp2S)e -ions, instead of µp ? + ∗ ∗ (a) µp(2S) + H2 → {[(ppµ) ] pee} → µp(1S)+ ... [PRL 97, 193402 (2006)] + ∗ ∗ [(ppµ) ] pee} is formed but τppµ . 1 ps [PRA 70, 042506 (2004)] ∗ (b) µp + H2 → (µp2S)e + ··· − The e in (µp2S)e leads to ∆E ∼ 0.4 meV if re = a0 [EJPD 61, 7 (2011)] Loosly bound system: “each” collision ionizes it. Internal and external Auger No population left for laser experiment! No broadening or double-line observed! A. Antognini, PANIC11, MIT, Cambridge, USA 25.07.2011 – p.9 rp puzzle (2): Is µp(2S-2P) theory wrong ? # Contribution Value Unc. 3 Relativistic one loop VP 205.0282 Vac.pol. + 4 NR two-loop electron VP 1.5081 e− e 5 Polarization insertion in two Coulomb lines 0.1509 6 NR three-loop electron VP 0.00529 7 Polarisation insertion in two and three Coulomb lines (corrected) 0.00223 8 Three-loop VP (total, uncorrected) 9 Wichmann-Kroll −0.00103 10 Light by light electron loop ((Virtual Delbrück) 0.00135 0.00135 11 Radiative photon and electron polarization in the Coulomb line α2(Zα)4 −0.00500 0.0010 12 Electron loop in the radiative photon of order α2(Zα)4 −0.00150 13 Mixed electron and muon loops 0.00007 4 14 Hadronic polarization α(Zα) mr 0.01077 0.00038 5 Hadron 15 Hadronic polarization α(Zα) mr 0.000047 2 4 16 Hadronic polarization in the radiative photon α (Zα) mr −0.000015 17 Recoil contribution 0.05750 18 Recoil finite size Recoil 0.01300 0.001 19 Recoil correction to VP −0.00410 n k 20 Radiative corrections of order α (Zα) mr −0.66770 µ+ µ− 21 Muon Lamb shift 4th order −0.00169 5 m − 22 Recoil corrections of order α(Zα) M mr 0.04497 6 23 Recoil of order α 0.00030 − + µ+ µ e e − n m e + e − Hadrons − + − 24 Radiative recoil corrections of order α(Zα) mr 0.00960 e e + − M e e 25 Nuclear structure correction of order (Zα)5 (Proton polarizability) 0.015 0.004 5 26 Polarization operator induced correction to nuclear polarizability α(Zα) mr 0.00019 e+ 5 e − 27 Radiative photon induced correction to nuclear polarizability α(Zα) mr −0.00001 + e e − Sum 206.0573 0.0045 A.
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