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The Proton Radius Puzzle ! The Proton Radius Puzzle Gerald A. Miller, University of Washington Pohl et al Nature 466, 213 (8 July 2010) Feb. 2014 Pohl, Gilman, Miller, Pachucki muon H rp =0.84184 (67) fm (ARNPS63, 2013) electron H rp =0.8768 (69)fm 2 2 dGE(Q ) electron-p scattering rp =0.875 (10)fm rp 6 ⌘ dQ2 Q2=0 2 PRad at JLab- lower Q 4 % Difference 4 % in radius: why care? • Can’t be calculated to that accuracy • 1/2 cm in radius of a basketball Is the muon-proton interaction the same as the electron-proton interaction? - many possible ramifications Does 4% matter? YES Summary/Outline • If all of the experiments, and their analyses, are correct a new scalar boson of mass ~1 MeV must exist • Direct detection is needed.: detection seems to be difficult: David McKeen, Yu-Sheng Lu 19 16 p(1.88 MeV) + F ↵ + O⇤(6.05) 16 16 ! O⇤(6.05) O(GS)+φ 0+ to 0+! (no photon emission) Electron-positron resonant elastic scattering Beam dump experiments, muon facilities university of melbourne cssm, university of adelaide The Experimentmuonic hydrogen experiment Muonic Hydrogen 2P1/2 The Lamb shift is the splitting of the degenerate 2S1/2 and 2P1/2 eigenstates The Lamb shift is the splitting ∆ 2S−2P ELamb of the degenerate 2S1/2 and 2P1/2 eigenstates,Dominant due to in vacuum μH polar- vacuum polarization 205 of 206 meV ization 2S1/2 Dominant in eH electron self-energy ∞ 2 Zα α d(q ) −meqr 4 2 VVP(r)=− 2 e 1 − 2 1+ 2 r 3π 4 q q q Proton radius in! " # $ ? Lamb shift J. Carroll — Proton Radius Puzzle — Slide 8 pt 2 2 ∆E = V V = ⇡↵ (0) ( 6G0 (0)) h S| C − C | Si 3 | S | − E • Muon/electron mass ratio 205! 8 million times larger for muon Recoil effects included: interaction computed for moving fermions 1 RESEARCH ARTICLES Figure 3 shows the two measured mp res- The uncertainties result from quadratically This rE value is compatible with our pre- onances. Details of the data analysis are given adding the statistical and systematic uncertain- vious mp result (6), but 1.7 times more precise, in (12). The laser frequency was changed every ties of ns and nt. and is now independent of the theoretical pre- few hours, and we accumulated data for up to The charge radius. The theory (14, 16–22) diction of the 2S-HFS. Although an order of 13 hours per laser frequency. The laser frequen- relating the Lamb shift to rE yields (13): magnitude more precise, the mp-derived proton cy was calibrated [supplement in (6)] by using radius is at 7s variance with the CODATA-2010 th 2 well-known water absorption lines. The reso- DE 206:0336(15 − 5:2275(10 r DETPE (7)valueofr =0.8775(51)fmbasedonHspec- L ¼ Þ Þ E þ E nance positions corrected for laser intensity ef- 7 troscopy and electron-proton scattering. fects using the line shape model (12)are ð Þ Magnetic and Zemach radii. The theoretical stat sys where E is in meV and rE is the root mean prediction (17, 18, 27–29)ofthe2S-HFSis(13) ns 54611:16(1:00) (30) GHz 2 ¼ ð Þ square (RMS) charge radius given in fm and 2 3 2 th pol stat sys defined as rE = ∫d rr rE(r) with rE being the DE 22:9763(15 − 0:1621(10)rZ DE nt 49881:35(57) (30) GHz 3 HFS ¼ Þ þ HFS ¼ ð Þ normalized proton charge distribution. The first 9 where “stat” and “sys” indicate statistical and sys- term on the right side of Eq. 7 accounts for ð Þ tematic uncertainties, giving total experimental un- radiative, relativistic, and recoil effects. Fine and where E is in meV and rZ is in fm. The first term is certainties of 1.05 and 0.65 GHz, respectively. hyperfine corrections are absent here as a con- the Fermi energy arising from the interaction Although extracted from the same data, the fre- sequence of Eqs. 4. The other terms arise from between the muon and the proton magnetic mo- quency value of the triplet resonance, nt,isslightly the proton structure. The leading finite size effect ments, corrected for radiative and recoil con- 2 more accurate than in (6)owingtoseveralimprove- −5.2275(10)rE meV is approximately given by tributions, and includes a small dependence of 2 ments in the data analysis. The fitted line widths Eq. 1 with corrections given in (13, 17, 18). −0.0022rE meV = −0.0016 meV on the charge are 20.0(3.6) and 15.9(2.4) GHz, respectively, com- Two-photon exchange (TPE) effects, including the radius (13). patible with the expected 19.0 GHz resulting from proton polarizability, are covered by the term The leading proton structure term depends the laser bandwidth (1.75 GHz at full width at half DETPE =0.0332(20)meV(19, 24–26). Issues on rZ,definedas maximum) and the Doppler broadening (1 GHz) related with TPE are discussed in (12, 13). th exp of the 18.6-GHz natural line width. The comparison of DEL (Eq. 7) with DEL 3 3 ′ ′ ′ rZ d r d r r r (r)r (r − r ) 10 The systematic uncertainty of each measure- (Eq. 5) yields ¼ ∫ ∫ E M ð Þ ment is 300 MHz, given by the frequency cal- exp th ibration uncertainty arising from pulse-to-pulse rE 0:84087(26) (29) fm with rM being the normalized proton mag- fluctuations in the laser and from broadening ¼ 0:84087(39) fm 8 netic moment distribution. The HFS polariz- effects occurring in the Raman process. Other ¼ ð Þ systematic corrections we have considered are Muonic Hydrogen Experiment the Zeeman shift in the 5-T field (<60 MHz), AC and DC Stark shifts (<1 MHz), Doppler shift (<1 MHz), pressure shift (<2 MHz), and black-body radiation shift (<<1 MHz). All these typically important atomic spectroscopy system- atics are small because of the small size of mp. The Lamb shift and the hyperfine splitting. From these two transition measurements, we can independently deduce both the Lamb shift (DEL = DE2P1/2−2S1/2) and the 2S-HFS splitting (DEHFS) by the linear combinations (13) 1 3 hns hnt DEL 8:8123 2 meV 4 þ 4 ¼ þ ð Þ hns − hnt DEHFS − 3:2480 2 meV 4 ¼ ð Þ ð Þ Finite size effects are included in DEL and DEHFS. The numerical terms include the cal- From 2013 culated values of the 2P fine structure, the 2P3/2 hyperfine splitting, and the mixing of the 2P states (14–18). The finite proton size effects on Science paper the 2P fine and hyperfine structure are smaller than 1 × 10−4 meV because of the small overlap between the 2P wave functions and the nu- cleus. Thus, their uncertainties arising from the proton structure are negligible. By using the measured transition frequencies ns and nt in Eqs. 4, we obtain (1 meV corresponds to 241.79893 GHz) Fig. 1. (A)Formationofmpinhighlyexcitedstatesandsubsequentcascadewithemissionof“prompt” DEexp 202:3706(23) meV 5 L ¼ ð Þ Ka, b, g.(B)Laserexcitationofthe2S-2Ptransitionwith subsequent decay to the ground state with Ka emission. (C)2Sand2Penergylevels.Themeasuredtransitionsns and nt are indicated together with DEexp 22:8089(51) meV 6 HFS ¼ ð Þ the Lamb shift, 2S-HFS, and 2P-fine and hyperfine splitting. EMBARGOED UNTIL 2PM U.S. EASTERN TIME ON THE THURSDAY BEFORE THIS DATE: 418 25 JANUARY 2013 VOL 339 SCIENCE www.sciencemag.org NATURE | Vol 466 | 8 July 2010 LETTERS a 105 We obtain a centroid position of 49,881.88(70) GHz, and a width of 200 1.32 × 106 events 104 18.0(2.2) GHz, where the given uncertainties are the 1 s.d. statistical 103 150 uncertainties. The width compares well with the value of 20(1) GHz 102 expected from the laser bandwidth and Doppler- and power-broad- 10 100 1 ening of the natural line width of 18.6 GHz. The resulting background 01234 amplitude agrees with the one obtained by a fit to data recorded 50 without laser (not shown). We obtain a value of x2 5 28.1 for 28 0 degrees of freedom (d.f.). A fit of a flat line, assuming no resonance, 5 2 b 10 6 200 1.02 × 10 events gives x 5 283 for 31 d.f., making this resonance line 16s significant. 104 Events in 25 ns The systematic uncertainty of our measurement is 300 MHz. It 103 150 102 originates exclusively from our laser wavelength calibration proced- 10 ure. We have calibrated our line position in 21 measurements of 5 100 1 different water vapour absorption lines in the rangel 5 5.49–6.01 mm. 01234 28 50 The positions of these water lines are known to an absolute precision of 1 MHz and are tabulated in the HITRAN database29. The measured 0 –0.5 0 0.5 1 1.5 2 2.5 3 relative spacing between the 5 lines agrees with the published ones. One Time (μs) such measurement of a water vapour absorption line is shown in Fig. 5. Our quoted uncertainty of 300 MHz comes from pulse to pulse fluc- Figure 4 | Summed X-ray time spectra. Spectra were recorded on resonance tuations and a broadening effect occurring in the Raman process. The (a) and off resonance (b). The laser light illuminates the muonic atoms in the FSR of the reference Fabry–Perot cavity does not contribute, as the FSR laser time window t g [0.887, 0.962] ms indicated in red.
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