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Home , Charge radius, Lamb shift, Proton radius puzzle

! The Radius Puzzle

Gerald A. Miller, University of Washington Pohl et al 466, 213 (8 July 2010)

Feb. 2014 Pohl, Gilman, Miller, Pachucki H rp =0.84184 (67) fm (ARNPS63, 2013) 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 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)+ 0+ to 0+! (no emission) Electron- resonant elastic scattering Beam dump experiments, muon facilities university of melbourne cssm, university of adelaide The Experimentmuonic experiment Muonic Hydrogen

2P1/2 The 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 μH polar- 205 of 206 meV ization

2S1/2 Dominant in eH electron self- ∞ 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

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 . 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 (<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 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 , 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 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. The ‘prompt’ X-rays are marked in blue (see text and Fig. 1). Inset, plots showing complete is known better than 3 kHz and the whole scanned range is within 70 data; total number of events are shown. FSR of the water line. Other systematic corrections we have considered are Zeeman shift in the 5 T field (,30 MHz), a.c. and d.c. Stark shifts atoms formed. The measurement times varied between 3 and 13 h per (,1 MHz), Doppler shift (,1 MHz) and pressure shift (,2 MHz). laser wavelength. The 75-ns-long laser time window, in which the Molecular effects do not influence our resonance position because 1 30 laser induced Ka events are expected, is indicated in Fig. 4. We have the formed muonic ppm are known to de-excite quickly recorded a rate of 7 events per hour in the laser time window when on and do not contribute to our observed signal. Also, the width of our resonance. The background of about 1 event per hour originates resonance line agrees with the expected width, whereas molecular lines mainly from falsely identified muon-decay and effects would be wider. related to delayed muon transfer to target walls. F~1 F~2 The centroid position of the 2S1=2 {2P3=2 transition is Figure 5 shows the measured 2S–2P resonance curve. It is obtained 49,881.88(76) GHz, where the uncertainty is the quadratic sum of by plotting the number of Ka events recorded in the laser time window, the statistical (0.70 GHz) and the systematic (0.30 GHz) uncertainties. normalized to the number of events in the prompt peak, as a function of This frequency corresponds to an energy of DE˜ 5 206.2949(32) meV. the laser frequency. In total, we have measureduniversity 550 events of melbourne in the res- From equation cssm, university (1), we of deduce adelaide an r.m.s. proton charge radius of onance, where we expect 155 background events. TheThe fit to Experiment the data is a rp 5 0.84184(36)(56) fm, where the first and second uncertainties ori- Lorentzian resonanceThe line on experiment: top of a flat background. Muonic All Hydrogen four para- ginate respectively from the experimental uncertainty of 0.76 GHz and meters (Lorentzian amplitude, position and width, as well as back- the uncertainty in the first term in equation (1). Theory, and here results disagreeground amplitude) with previous were varied freely.measurements A maximum likelihood & world fit mainlyaverage the proton polarizability term, gives the dominant contri- using CERN’s ROOT analysis tool accounted for the statistics at each bution to our total relative uncertainty of 8 3 1024. Our experimental 24 laser wavelength. Our statistical uncertainties are the 1s“Theconfidence 1S-2S transitionprecision in H has been would measured suffice to to deduce rp to 4 3 10 . 34 Hz, that is, 1.4 × 10−14 relative accuracy. intervals. This new value of the proton radius rp 5 0.84184(67) fm is 10 times 2010 Rock Solid! Only an error of about 1,700 times the quoted 3 experimental uncertaintymore could precise, account but for 5.0ours smaller, than the previous world average , 7 CODATA-06 Our value observedwhich discrepancy.” is mainly inferred from H spectroscopy. It is 26 times more accurate, but 3.1s smaller, than the accepted hydrogen-independent 6 e–p scattering value extracted from electron–proton scattering1,2. The origin of this )

–4 large discrepancy is not known. H O calibration 5 2 If we assume some QED contributions in mp (equation (1)) were wrong or missing, an additional term as large as 0.31 meV would be 4 required toJ. Carroll match — Proton our Radius measurement Puzzle — Slide 13 with the CODATA value of rp. We note that 0.31 meV is 64 times the claimed uncertainty of equation 3 (1). The CODATA determination ofrp can be seen in a simplified picture 2 as adjusting the input parameters rp and R‘ (the Rydberg constant) to 8 4–7 Delayed / prompt events (10 Delayed / prompt match the QED calculations to the measured transition frequencies 1 in H: 1S–2S on the one hand, and 2S{n‘ n‘~2P,4,6,8S=D,12D on the other. ðÞ 0 The 1S–2S transition in H has been measured3–5 to 34 Hz, that is, 49.75 49.8 49.85 49.9 49.95 214 Laser frequency (THz) 1.4 3 10 relative accuracy. Only an error of about 1,700 times the quoted experimental uncertainty could account for our observed dis- Figure 5 | Resonance. Filled blue circles, number of events in the laser time crepancy. The 2S{n‘ transitions have been measured to accuracies window7 standard normalized to thedeviation number of ‘prompt’ difference events as a function in of r thep- or between 1/100 (2S–8D) (refs 6, 7) and 1/10,000 (2S1/2–2P1/2 Lamb laser frequency. The fit (red) is a Lorentzian on top of a flat background, and 31 givesvalue a x2/d.f. of of 28.1/28. Rydberg The predictions constant for the line position has using to the be shift ) of the respective line widths. In principle, such an accuracy proton radius from CODATA3 or electron scattering1,2 are indicated (yellow could make these data subject to unknown systematic shifts. We note, data points,shifted- top left). Our(12 result figures) is also shown (‘ouror value’). new All errorphysics! bars are however, that all of the (2S{n‘) measurements (for a list, see, for the 61 s.d. regions. One of the calibration measurements using water example, table XII in ref. 3) suggest a larger proton charge radius. absorption is also shown (black filled circles, green line). Finally, the origin of the discrepancy with the H data could originate 215 ©2010 Macmillan Publishers Limited. All rights reserved The proton radius puzzle In a picture

The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm : 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg.

scatt. JLab

µp 2010 scatt. Mainz

H spectroscopy

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 R. Pohl et al.,Nature466,213(2010). Proton charge radius R [fm] A. Antognini et al., Science 339, 417 (2013). ch Randolf Pohl Mainz, 2nd June 2014 11 QED theory ? • Pohl et al table 32 terms! • Most important -HFS- measured Jan ’13 • QED theory not responsible- electron A new effect on mu-H energy shift muon must vary at least as fast as mass to the fourth power, if short-ranged An effect on electron, but not muon free of this constraint New data- more problems Possible resolutions • QED bound-state calculations not accurate- very unlikely- this includes recoil effects • Electron experiments not so accurate • effect in two photon exchange diagram • soft proton • More e+e- pairs than μ+ μ- pairs in the proton • Muon interacts differently than electron!-new , gravity, non-commutative geometry Electronic Hydrogen -Pohl Need two levels to get Rydberg and Lamb • R L1S shift-haveHydrogen ~ 20 available spectroscopy E(nS) u 1 + n2 n3 2S - 2P 1/2 1/2 CODATA 2S1/2 - 2P1/2

2S1/2 - 2P3/2 reviewed in 2012 1S-2S + 2S- 4S 1/2 changed by 1/2 st. dev 1S-2S + 2S- 4D5/2

1S-2S + 2S- 4P1/2

1S-2S + 2S- 4P3/2

1S-2S + 2S- 6S1/2 1S-2S + 2S- 6D 5/2 Same lab 1S-2S + 2S- 8S1/2

1S-2S + 2S- 8D3/2 maybe not so accurate 1S-2S + 2S- 8D 5/2 Ralston Karshenboim 1S-2S + 2S-12D3/2 µp : 0.84184 +- 0.00067 fm 1S-2S + 2S-12D5/2

1S-2S + 1S - 3S1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm)

Randolf Pohl APS Anaheim, 30 April 2010 p. 20 Deuteron: new experiments • muonic deuteron - CREMA • electronic deuteron isotope shift -two photon spectroscopy

Improved Measurement of the Hydrogen 1S –2S Transition Frequency

Christian G. Parthey,1, ∗ Arthur Matveev,1, ∗ Janis Alnis,1 Birgitta Bernhardt,1 Axel Beyer,1 Ronald Holzwarth,1, † Aliaksei Maistrou,1 Randolf Pohl,1 Katharina Predehl,1 Thomas Udem,1 Tobias Wilken,1 Nikolai Kolachevsky,1, ‡ Michel Abgrall,2 Daniele Rovera,2 Christophe Salomon,3 Philippe Laurent,2 and Theodor W. H¨ansch1, § 1Max-Planck-Institut f¨ur Quantenoptik, 85748 Garching, Germany 2LNE-SYRTE, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France 2 photon3Laboratoire spectroscopy Kastler-Brossel, CNRS, 24 ruePRL Lhomond, 104, 75231 P233001aris, France We have measured the 1S − 2S transition frequency in atomic hydrogen via two photon spec- troscopy on a 5.8 K atomic beam. We obtain f1S−2S =2466061413187035(10)Hzforthehyperfine centroid. This is a fractional frequency uncertainty of 4.2 × 10−15 improving the previous measure- ment by our own group [M. Fischer et al., Phys. Rev. Lett. 92,230802(2004)]byafactorof3.3. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.

PACS numbers: 06.20.Jr, 32.30.Jc, 42.62.Fi

For the last five decades spectroscopy on atomic hydro- 486nm Doppler PMT cryostat with laser - only during nozzle chopper gen along with its calculable atomic structure have been velocity measurement wheel integrating fueling the development and testing of quantum electro- sphere Faraday cage piezo Lyman-α dynamics (QED) and has lead to a precise determination mirror of the Rydberg constant and the proton charge radius [1]. + 243 nm The absolute frequency of the 1S−2S transition has been mirror electrodes 486nm excitation region measured with particularly high precision, so that it now uv photodiode 2S detector quench laser RF discharge serves as a corner stone in the least squares adjustment of H2 the fundamental constants [2]. The resonance has been to cryopump used to set limits on a possible variation of fundamental constants [3] and violation of Lorentz boost invariance [4]. FIG. 1: (color online). Schematic of the beam apparatus. A It further promises a stringent test of the charge conjuga- standing laser wave at 243 nm (between grey mirrors) with 2 tion//time reversal (CPT) theorem by comparison a1/e waist radius of w0 =292µmattheflatcavityfront − with the same transition in antihydrogen [5]. mirror excites the sharp 1S 2S transition in a co-linearly propagating cold thermal beam of atomic hydrogen emerging In this Letter we present a more than three times more − from a cooled copper nozzle. The 2S state is detected af- accurate measurement of the 1S 2S transition as com- ter quenching with a localized electric field which releases a pared to the previous best measurements [3, 6] reaching Lyman-α photon. See text for further details. the 4 × 10−15 regime. The key improvements are the replacement of a dye laser by a diode laser system with improved frequency stability for the two photon spec- troscopy. In addition, a direct measurement of the 2S ve- gen maser which is calibrated using the mobile cesium locity distribution of the thermal atomic hydrogen beam fountain atomic clock FOM [10]. We apply cycle slip allows a more accurate characterization of the second or- detection as described in [9]. der Doppler effect. Finally, a quench laser resetting the The beam apparatus (Fig. 1) follows the design of [11] population to the ground state right after the hydrogen and has been used before [12]. Hydrogen is dissociated nozzle was introduced. This removes possible frequency at a pressure of 1mbar in a radio frequency (rf) dis-

arXiv:1107.3101v1 [physics.atom-ph] 15 Jul 2011 shifts due to the high density of atoms and a possible dc charge running in a sapphire tube. A Teflon capillary Stark shift within the nozzle. controls the flow and Teflon tubing guides the atomic The extended-cavity diode spectroscopy laser system hydrogen to a copper nozzle cooled to 5.8 K by a liquid (ECDL) has been described elsewhere [7]. An ECDL helium flow cryostat. The dissociation fraction at the master oscillator near 972 nm is amplified in a tapered nozzle (2.2 mm diameter) is about 10 %. After 45 min amplifier. The laser radiation is frequency doubled twice of operation the nozzle closes up with frozen molecular within two resonant cavities to obtain 13 mW of the re- hydrogen. We then heat it to 20K for 15min to evapo- quired uv light near 243 nm. Locking the laser to a high rate the hydrogen molecules. The atomic beam is defined finesse cavity made from ultra-low expansion glass leads by a 2.4mm (front) and a 2.1mm (rear) diameter aper- to a line width of less than 1 Hz and a fractional fre- ture which also separate the differentially pumped exci- quency drift of 1.6×10−16 s−1 [8]. A fiber laser frequency tation region (10−5 mbar / 10−8 mbar). This region is comb with a repetition rate of 250 MHz is used to phase- shielded by a grounded Faraday cage from electric stray coherently link the cavity frequency to an active hydro- fields that may build up from laser ionized hydrogen. An Deuteron charge radius electron experiment 2 2 2 H/D isotope shift: rd − rp = 3.82007(65) fm C.G. Parthey, RP et al.,PRL104,233001(2010)

CODATA 2010 rd =2.1424(21)fm uses ep data rp= 0.84087(39) fm from µH givesDeuteronrd =2.1277(2)fm charge radius Lamb shift in muonic rd =2.1282(12)fm PRELIMINARY! µd Borie+Pachucki+Ji+Friar µH and µD are consistent! µd Borie+Ji d Borie+Pachucki (if BSM: no coupling to ) Deuteronµ radii measuredPRELIMINARY by electrons and muons • µd Martynenko WIP: deuteron polarizability (theory) complete? double-counting? µisH the+ iso same, H/D(1S-2S) using the protonWIP: shift radius from QM-interferencemeasured in muonic hydrogen! CODATA-2010 µd Borie+Pachucki+Ji+Friar CODATA D + e-d µd Borie+Ji • Proton radius puzzle reappearsµd inBorie+Pachucki deuterium PRELIMINARY e-d scatt. µd Martynenko It seems is no new effect on Lamb shift • n-p scatt. µH + iso H/D(1S-2S) CODATA-2010 If your2.11 model 2.115 predicts 2.12 neutron 2.125 effect 2.13 on energy 2.135 level 2.14 it 2.145 is ruled out CODATA DDeuteron + e-d charge radius [fm] Randolf Pohl Mainz, 2nd June 2014 26 e-d scatt. n-p scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl Mainz, 2nd June 2014 26 He radius from e-scattering HeHe radius radius from from e-scattering e-scattering

4 Secret results! He

-3 -worlddataofe-scattering.×10 -worlddataofe-scattering.1.2 -worlddataofe-scattering.Theory + Sick ×10-3 -constraintsdensityatlarger: 1.2 -constraintsdensityatlarger:1 Pospelov

Events / Prompt 1

-constraintsdensityatlarger: Events / Prompt -shape:fromp-wavefunction∼Whittaker.Preliminary 0.8 Fit withPreliminary SOG -shape:fromp-wavefunction0.8 ∼Whittaker. Fit with SOG -shape:fromp-wavefunction∼Whittaker. 0.6 Fit with SOG - absolute0.6 density: from p-He scattering + FDR. →R =1.681(4)fm - absolute density: from p-He scattering + FDR. 0.4 →R =1.681(4)fm - absolute density: from p-He scattering + FDR. →R =1.681(4)fm - point0.4 density from potential + GFMC (small r) + FDR0.2 (large(best r). known radius from e-scattering) 0 - point density from potential + GFMC (small r) + FDR (large366 367(best r). 368 known 369 370 radius 371 372 from 373 e-scattering) - point density from potential + GFMC (small r) + FDR (large(best r). known radiusFrequency [THz] from e-scattering) - fold point0.2 density with charge density distributiondn. of p an - fold point density with charge density distributiondn. of p an [Sick, PRC 77, 941392(R) (2008)] - fold0 point density with charge density distributiondn. of p an - include Coulomb366 367 distortions. 368 369 370 371 372 373 [Sick, PRC 77, 941392(R) (2008)] - include Coulomb distortions. Frequency [THz] [Sick, PRC 77, 941392(R) (2008)] - include Coulomb distortions. • The transition has been found at the expectedA. Antognini position MITP workshop, Mainz 02-06 June 2014 – p. 20 A. Antognini MITP workshop, Mainz 02-06 June 2014 – p. 20 i.e., whithin the uncert. given by rHe from e−A.He Antognini scattering. MITP workshop, Mainz 02-06 June 2014 – p. 20 • New physics model of Pospelov excluded • Zavattini value from old µ He+ experiment excluded 4He nuclear charge radius 1.681(4) fm u =2× 10−3 [Sick] Need to summarize all 2S-2P contributions r 1.677(1) fm (VERY preliminary) [µ He+]

A. Antognini MITP workshop, Mainz 02-06 June 2014 – p. 21 No new effect in 4He within 1 st. dev. Several new electron experiments planned • Independent measurement of Rydberg constant. This would change only extracted rp nothing else • 2S-6S UK, 2S-4P Germany,1S-3S France • 2S-2P classic, Canada • Highly charged single electron ions NIST • PRad at Jab - calorimeter extends measurement to very small angles • several others Possible resolutions • QED bound-state calculations not accurate- very unlikely- this includes recoil effects • Electron experiments not so accurate • Strong interaction effect in two photon exchange diagram-my work- soft proton • Muon interacts differently than electron!-new particles, gravity, non-commutative geometry ! Physics Letters B 718 (2013) 1078–1082

Contents lists available at SciVerse ScienceDirect

Physics Letters B Analysiswww.elsevier.com/locate/physletb of Experiment-one example Proton polarizability contribution: Muonic hydrogen Lamb shift and elastic 2 3 scattering Measured =206.2949(32)= 206.0573(45)-5.2262 rp +0.0347 rp meV

Gerald A. Miller computed Department of Physics, Univ. of Washington, Seattle,Explain WA 98195-3560, United puzzle States with radius as in H atom increase 206.0573 meV article info abstractby 0.31 meV-attractive effect on 2S state2 needed Article history: The uncertainty in the contribution to the Lamb shift in muonic hydrogen, !Esubt arising from proton Received 2 October 2012 ′ ℓ − k of momentum q = p − p.as:polarizability effects in the two-photon exchange diagramℓ at large virtual photon momenta is shownℓ large Received in revised form 27 October 2012 enough to account for the proton radius puzzle. This is because !Esubt is determined by an integrand that Accepted 6 November 2012′ µ µ Γµ(p ,p)=γ F (−q2)+Ffalls(−q very2)F slowly(−q2) withO very large virtual(2) photon momenta. We evaluate the necessary integral using a set Available online 8 November 2012N 1 1 a,b,c of chosen form factors and also a dimensional procedure which makes explicit the need for Editor: W. Haxton ′ µ ′ µ (p + p ) ′ (p · γalowenergyconstant.Theconsequencesofourtwo-photonexchangeinteractionforlow-energyelasticN − M) (p · γN − M) Oa = [Λ+(p ) + Λ+(p)] energy shift proportional 2M lepton–protonMOur scattering ideaM are evaluated and could be observable in a planned low energy lepton–proton ′ Oµ =((p2 − M 2)/M 2 +(pscattering2 − M 2) experiment/M 2)γµ planned to run at PSI. 4 b N © 2012 Elsevier B.V. All rights reserved. to lepton mass P P ′ ′ (p · γ − M) (p · γ − M) Oµ = Λ (p )γµ N + N γµ Λ (p), c + N M M N + 1. Introduction FIG. 1: Direct two-photon exchange graph corresponding to where three possible forms are displayed. Other terms of the hitherto neglected term. The dashed line denotes the lepton; the solid line, the ; the wavy lines ; The protonthe radius vertex puzzle function is one of needed the most to satisfy perplexing the physics WT identity do µ⌫ and the ellipse the off-shell nucleon. issues of recentnot times. contribute The extremely significantly precise to extraction theT Lamb of the shift= pro- and are not 2 ton radius [1]shownfrom the explicitly. measured The energy proton difference Dirac between form factor, the F1(−q ) 2P F 2 and 2S F 1 states of muonic hydrogen disagrees with that 2 3/=2 is1/= empirically2 well represented as a dipole F1(−q )=(1− µ⌫ µ µ 2 2 −2 2 Fig.2 1. The box diagram for the (α5m4) corrections. The graph in which the pho- extracted fromq electronic/Λ ) , hydrogen.(Λ = 840 The MeV) extracted for the value values of the of − pro-q ≡ Q > 0 O = tons(g cross is also included. )T1 +(P )(P )T2 ton radius isof smaller up to than about the 1 CODATA GeV2 needed[2] value here. (basedF ( mainly−q2) is an off- interference between one on-shell and one off-shell part on electronic H) by about 4% or 5.0 standard deviations. This im- of the vertex··· function. The change in the invariant ··· am- ··· shell form factor, and Λ+(p)=(p · γN + M)/(2M)tions is an entering in the two-photon exchange term, see Fig. 1,can plies [1] that either the Rydberg constant hasDispersion to be shifted by relation:plitude,ImM [,T due1] to usingW Eq.1 (2)measured along with Oµ,tobe operator that projects on the on-mass-shell protonaccount state. for the 0.31 meV.Off This idea is worthy of consideration be-a 4.9 standard deviations or that present QED calculations for hy- We use Oa unless otherwise stated. cause the computedevaluated effect between is proportional / spinors, to the lepton is given mass in to the rest drogen are insufficient. The Rydberg constantLarge is extremely virtual2 well photon energy ⌫, W ⌫ integral over energy diverges We take the off-shell form factor F (−q ) to vanishthe atfourthframe power, by and so is capable of being relevant1 for muonic measured and the2 QED calculations seem to be very extensive and q = 0. This means that the charge of the off-shell protonatoms, but irrelevant for electronic atoms. ⇠2 highly accurate, so the muonic H finding is a significant puzzle for ¯ will be the same as the chargeSubtraction of a free proton, and function is needed: T1(0,Q ) zero energy the entire physics community. subt demanded by current conservation as expressedF 2 through2. !E and its evaluatione4 d4k F 2(−k2)F (−k2) Pohl et al. show that the energy difference between the 2P 3/=2 1 the Ward-Takahashi identityHill [24, 25]. & We assumePaz- big uncertaintyMOff = 2 4 in 2 dispersion2 (4)approach and 2S F 1 states, !E,isgivenby 2M " (2π) (k + iϵ) 1/=2 The basic idea is that the two-photon exchange term depends 2 2 µ ν ν µ ×(γ (2p + k) + γN (2p + k) ) µν 2 2 2 3−λq /b on the forward virtualN amplitude T (ν, q ) !E 209.9779(49)! 5.2262Fr(−q 0)=.0347r meV, . (1) (3) 2 µ = − p + (1 p− q2/Λ2)1+ξ where q is the square(l · γ − ofk the· γ + fourm) momentum,(l · qγ +ofk · theγ + vir-m) tual photon and× γνµ is its2 time componentγν (+ν γνq p2/M)withp as γµ , where rp is given in units of fm. Using this equation and the exper- # k − 2l · k + iϵ ≡ ·k +2l · k + iϵ $ imentally! measuredThis purely value ! phenomenologicalE 206.2949 meV, form one! can is simple see that and clearlythe proton momentum and M as its mass. One uses symmetries = µν 2 the differencenot between unique. the Pohl The and parameter CODATA valuesb is expected of the proton to be ofto thedecompose T (ν, q ),intoalinearcombinationoftwoterms, 2 2 radius wouldorder be removed of the by an mass,increase because of the first these term longest on the rangeT com-1,2(ν, q ).TheimaginarypartsofT1,2(ν, q ) are related to struc- ! where the lepton momentum is l =(m, 0, 0, 0), the vir- rhs of Eq. (1) byponents 0.31 meV of the3. nucleon1 10 10 areMeV. least bound and more suscep-ture functions F1,2 measured in electron– or muon–proton scat- = × − tual photon momentum is k and the nucleon momentum This protontible radius to puzzle the external has been perturbations attacked from many putting differ- the nucleontering, so that T1,2 can be expressed in terms of F1.2 through p =(M,0, 0, 0). The intermediate proton2 propagator2 ent directionso[3–21]ff its massThe presentshell. At communication large values ofis intended|q2|, F has to thedispersion same relations. However (for fixed values of q ), F1(ν, q ) investigate the hypothesis that the proton polarizability contribu- falls off toois slowly cancelled for large by valuesthe off of-mass-shellν for the dispersion terms of relation Eq. (2). This fall-off as F1, if ξ =0.WetakeΛ = Λ here. to converge.graph Hence, can one be makesthought a subtractionof as involving at ν a contact0, requiring interaction We briefly discuss the expected influence of using 2 = ! that an additionaland the function amplitude of q in(the Eq. subtraction (4) as a function) new proton be in- polariza- E-mail address:[email protected] (2). The ratio, R. ,ofoff-shell effects to on-shell ef- q2 < 2 troduced. Becausetion correction0forlepton–nucleonscattering,oneoften corresponding to a subtraction term in the (p·γN −M) q 2 2 fects, R ∼ λ 2 , (|q | ≪ Λ ) is constrained by 0370-2693/$ – see front matter © 2012M Elsevierb B.V. All rights reserved. dispersion relation for the two-photon exchange diagram http://dx.doi.org/10.1016/j.physletb.2012.11.016a variety of nuclear phenomena such as the EMC effect that is not constrained by the cross section data [34]. (10-15%), uncertainties in quasi-elastic electron-nuclear The resulting virtual-photon-proton Compton scattering scattering [26], and deviations from the Coulomb sum µ ν amplitude, containing the operator γN γN corresponds to rule [27]. For a nucleon experiencing a 50 MeV central the T2 term of conventional notation [35], [36]. Eq. (4) 2 2 potential, (p · γN − M)/M ∼ 0.05, so λq /b is of or- is gauge-invariant; not changed by adding a term of the der 2. The nucleon wave functions of light-front - form kµ kν /k4 to the photon . models [33] contain a propagator depending on M 2. Thus the effect of nucleon virtuality is proportional to Evaluation proceeds in a standard way by taking the the derivative of the propagator with respect to M,orof sum over Dirac indices, performing the integral over k0 the order of the divided by difference be- by contour rotation, k0 →−ik0, and integrating over the tween quark kinetic energy and M. This is about three angular variables. The matrix element M is well approx- times the average momentum of a quark (∼ 200 MeV/c) imated by a constant in momentum space, for momenta divided by the nucleon radius or roughly M/2. Thus typical of a muonic atom, and the corresponding poten- 2 2 r r R ∼ (p · γN − M)2/M , and the natural value of λq /b tial V = iM has the form V ( )=V0δ( ) in coordinate is of order 2. space. This is the “scattering approximation” [3]. Then 2 The lowest order term in which the nucleon is suffi- the relevant matrix elements have the form V0 |Ψ2S(0)| , ciently off-shell in a muonic atom for this correction to where Ψ2S is the muonic hydrogen wave function of the produce a significant effect is the two-photon exchange state relevant to the experiment of Pohl et al. We use 2 3 diagram of Fig. 1 and its crossed partner, including an |Ψ2S(0)| =(αmr) /(8π), with the lepton-proton re- 2 Almost unknown T¯1(0,Q ) Miller PLB 2012 2 2 ↵ 1 dQ 2 Esubt 2 (0) Floop(Q ) ⇠ m S Q2 ··· Z 2 ChooseInfinite Floop(Q ) give 0.31 meV satisfy all constraints Q2 Recast in EFT- parameters seem natural

Soft proton + + e /e and µ /µ scattering on proton So what? MUSE expt

using RF time measurements. Magnet polarities can be reversed to allow the channel to transport A Proposal for the Paul Scherrer Instituteeither positive orπ negativeM1 polarity beam particles. line

Studying the Proton “Radius” Puzzle with µpB.Elastic Detector Overview Scattering

J. Arrington,1 F. Benmokhtar,2 E. Brash,2 K. Deiters,3 C. Djalali,4 L. El Fassi,5 E. Fuchey,6 S. Gilad,7 R. Gilman (Contact person),5 R. Gothe,4 D. Higinbotham,8 Y. Ilieva,4 M. Kohl,9 G. Kumbartzki,5 J. Lichtenstadt,10 N. Liyanage,11 M. Meziane,12 Z.-E. Meziani,6 K. Myers,5 C. Perdrisat,13 E. Piasetzsky (Spokesperson),10 V. Punjabi,14 R. Ransome,5 D. Reggiani,3 A. Richter,15 G. Ron,16 A. Sarty,17 E. Schulte,6 S. Strauch,4 V. Sulkosky,7 A.S. Tadapelli,5 and L. Weinstein18 1 determining the proton radius throughArgonne muon scattering, National with simultaneous Lab, Argonne, electron scattering IL, measurements. USA 2Christopher Newport University, Newport News, Virginia, USA 3 PSI proposal R-12-01.1 FIG. 3. A Geant4 simulation showing part of the MUSE experimental system. Here one sees the beam Paul Scherrer Institut, CH-5232 Villigen,going through Switzerland the GEM chambers and the scattering chamber, along with the spectrometer wire chambers 4 and scintillator hodoscopes. The beam SciFi’s, quartz Cherenkov, and beam monitor scintillators are http://www.physics.rutgers.edu/~rgilman/elasticmup/University of South Carolina, Columbia,missing South from Carolina, this view. USA 5Rutgers University, New Brunswick, New Jersey, USA 6Temple University, Philadelphia, Pennsylvania, USA 2 photon exchange idea isThe testable⇡M1 channel features a momentum dispersed ( 7 cm/%) intermediate focal point (IFP) 7Massachusetts Institute of Technology, Cambridge, Massachusetts, USA ⇡ 8 Jefferson Lab, Newport News, Viginia,and a small beam USA spot (x,y < 1 cm) at the scattering target. The base line design for the MUSE 9 Hampton University, Hampton, Virginia,beam detectors USAhas a collimator and a scintillating fiber detector (SciFi) at the intermediate focus. 10 Tel Aviv University, Tel Aviv,Some of Israel the detectors in the target region are shown in Fig. 3. After the channel and immediately 11University of Virginia, Charlottesville, Virginia, USA before the target there are a SciFi detector, a quartz Cherenkov detector, and a set of GEM 12Duke University, Durham, North Carolina, USA 13College of William & Mary, Williamsburg,chambers. Virginia, A high precision USA beam line monitor scintillator hodoscope is downstream of the target. 14 Norfolk State University, Norfolk, Virginia,The IFP collimator USA serves to cut the ⇡M1 channel acceptance to reduce the beam flux to 15 Technical University of Darmstadt, Darmstadt,manageable levels. Germany The IFP SciFi measures the RF time, for use in determining type, 16Hebrew University of Jerusalem, Jerusalem, Israel and measures beam particle position, to determine the particle momentum and thus the beam 17St. Mary’s University, Halifax, Nova Scotia, Canada 18Old Dominion University, Norfolk,momentum Virginia, spectrum. USA The target SciFi measures the RF time, for use in determining particle type. The quartz About 1.5 years after the radius of muonic hydrogen was found to be 5σ inconsistent with earlier determinations from atomic hydrogen level transitions and ep elastic scattering, no resolution14 to the puzzle has been found. We propose to measure µ±p scattering, which will allow a second de- termination of the consistency of the µp interaction with the ep interaction. If the µp scattering is consistent with muonic hydrogen measurements but inconsistent with ep scattering measurements, the confirmation of consistency between lepton scattering and Lamb shift measurements but differ- ences between electron- and muon-based measurements of ep and µp systems would provide strong evidence for beyond physics. No external programs needed.

muon scattering = (1) + (2) M M M +

R 0.07 (1) (2) 0.06 Re[( )⇤ ] R =2 M M 0.05 (1)] 2 0.04 ~5 % effect|M should| be seen 200 MeV/c 0.03 Normal100 MeV/c LaTeX~10 class. % for ratio +/- 0.02 Easy overlays. 0.01

q 0.5 1.0 1.5 2.0 2.5 3.0 cm Radians Soft proton idea

• explains muon Lamb shift • no change to electron Lamb shift • no hyperfine interaction • no effect on neutron so Deuteron is OK • easily testable in muon-proton scattering • easily testable in heavy muonic atoms Nuclear dependence of short-ranged mu-p effects 7 The first example we consider is the model of Ref. [4]. To make a prediction for the nucleus, one needs to know the contribution of the neutrons. Using the single-quark dominance idea of Sect II gives a specific result obtained by considering the factors of the square of the quark charge that would appear in the calcuation. A proton contains two up and one• downEnergy quark, with shift a resulting is proportional quark charge squared to square factor of 2(2 of/ 3)2e2 + 1(1/3)2e2 = e2 . For a neutron one would have 1(2muon/3)2e2 + wave 2(1/3) 2functione2 =2/3e2. at Thus the the origin neutron contribution would be 2/3 that of the proton. As result, if one considers the Lamb shift in the electron-deuteron atom, the e↵ect would 5/3 as large as for a proton. Such an e↵ect would contradict the existing good agreement between theory and experiment [11]. GAM Suppose you have effect that gives energy More generally,1501.01036 suppose• the contribution of a proton to the Lamb shift is Ep (0.3meV) to resolve the proton radius puzzle) and that of the neutronshifts is E nEp. Then (on for proton) a nucleus with EnA (onnucleons neutron) and Z , we find m 3 m 3 1+ µ 2 1+ µ mp 3 RA mp 3 EA = mµ Z (ZEp + NEn) 1 ( 2 ) mµ Z (ZEp + NEn), (23) 1+ O aµ ⇡ 1+ Amp ! ✓ ◆ Amp ! where aµ is the muon (>100 times larger than nuclearSize radius, ofR Anucleus). The meaning of Eq. (23) is that the contributions of such contact interactions increase very rapidly with atomic number. Nuclear shift 4 In particular, the prediction of Ref. [4](with En =2/3Ep) for He is a Lamb shift that is (1.27) 8 (2)5/3 10 meV, a huge number. The expressionSquare Eq. (23)of wave applies tofun all modelsCounting in which the contribution to the Lamb shift⇡ enters as a delta function (or of very short range) in the lepton-nucleon coordinate, including [9, 10]. In Ref. [9], which 4 concerns polarizabilityMy model: corrections, ~0.3 meV the neutron (8)(2) contribution, =-4.8 meVEn could about vanish, so5 thatst. thedev contribution off for He would 4 be 20 Ep=6 meV. In Ref. [10], which concerns a gravitational e↵ect, En = Ep, so the prediction for He would be 40Ep=12 meV. These various predictions will be tested in an upcoming experiment [12]. It is also worth mentioning the MUon proton Scattering Experiment (MUSE) [13], a simultaneous measurement of µ+ p and e+ p scattering and also a simultaneous measurement of µ p and e p scattering that is particularly sensitive to the presence of contact interactions [9] .

VII. SUMMARY

The work presented here supports the idea of the existence of a non-perturbative lepton-pair content of the proton. Such components are not forbidden by any principle and therefore must appear. However, the presented calculations show that such a content is not a candidate to explain the proton radius puzzle. This is because computation of the necessary loop e↵ects is cannot yield an e↵ective Hamiltonian of the strength and form of Eq. (2). 2 The 1/ml behavior of that equation in Ref. [4] is necessary to obtain the needed magnitude of the separate electron and muon Lamb shifts. Instead, loop calculations are expected to lead to a a dependence of 1/m2,withm the constituent quark mass. This means that the e↵ect of Ref. [4] is expected to be entirely negligible. This is in accord with the estimate: (↵/⇡) times the polarizability correction that is obtained from evaluating the relevant Feynman diagrams. More generally: it can be said that the proton does have Fock -space components containing lepton pairs. However, the simplest and most reliable method of treating such pairs is to compute gauge-invariant sets of Feynman diagrams using QED perturbation theory.

VIII. ACKNOWLEDGEMENTS

This material is based upon work supported by the U.S. Department of Energy Oce of Science, Oce of Basic En- ergy Sciences program under Award Number DE-FG02-97ER-41014. I thank S. Paul, U. Jentschura, S. Karshenboim and M. Eides for useful discussions.

[1] R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, L. M. P. Fernandes, A. Giesen, T. Graf, T. W. H¨ansch, P. Indelicato, L. Julien, C.-Y. Kao, P. Knowles, E.-O. Le Bigot, Y. W. Liu, J. A. M. Lopes, L. Ludhova, C. M. B. Monteiro, F. Mulhauser, T. Nebel, P. Rabinowitz, J. M. F. dos Santos, L. A. Schaller, K. Schuhmann, C. Schwob, D. Taqqu, J. F. C. A. Veloso, and F. Kottmann, Nature (London) 466,213(2010). [2] A. Antognini, F. Nez, K. Schuhmann, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, M. Diepold, L. M. P. Fernandes, A. Giesen, A. L. Gouvea, T. Graf, T. W. H¨ansch, P. Indelicato, L. Julien, C.-Y. Kao, P. Knowles, F. Kottmann, E.-O. Le Bigot, Y.-W. Liu, J. A. M. Lopes, L. Ludhova, C. M. B. Monteiro, F. Mulhauser, T. Soft proton idea is testable- advantage Assume D, He data correct • Deuteron says no neutron effect - • 4He- Effect goes as Z * Z3 =Z4 • This is a 5 st. dev effect NOT seen- RIP for pol idea • Moral- any new short-ranged muon-nucleon interaction ruled out by He data • RIP - enhanced e+e- pairs, short-ranged gravity, .... Possible resolutions • QED bound-state calculations not accurate- very unlikely- this includes recoil effects • Electron experiments not so accurate • Strong interaction effect in two photon exchange diagram-my work- soft proton • More e+e- pairs than μ+ μ- pairs in the proton • Muon interacts differently than electron!-new particles, gravity, non-commutative geometry 20 Sep 2004 16:46 AR AR228-NS54-05.tex AR228-NS54-05.Sgm LaTeX2e(2002/01/18) P1: JRX

116 DAVIER ! MARCIANO 20 Sep 2004 16:46 AR AR228-NS54-05.tex AR228-NS54-05.Sgm LaTeX2e(2002/01/18) P1: JRX

1. INTRODUCTION

One of the great successes of the (1) was its prediction that the magnetic dipole moment, µ,ofaspin116 s DAVIER1/2 particle! MARCIANO such as the electron (or muon) is given by ⃗ |⃗|= e1. INTRODUCTION µl gl s, l e,µ..., 1. ⃗ = 2m ⃗ = l One of the great successes of the Dirac equation (1) was its prediction that the magnetic dipole moment, µ,ofaspin s 1/2 particle such as the electron (or with gyromagnetic ratio gl 2, a value already implied by⃗ early atomic|⃗|= spec- troscopy. Later it was realized= that a relativisticmuon) is given quantum by field theory such as e (QED) can give rise via quantumµ fluctuationsl gl s, to al shifte,µ..., 1. ⃗ = 2ml ⃗ = in gl , with gyromagnetic ratio gl 2, a value already implied by early atomic spec- gtroscopy.l 2 Later it was realized= that a relativistic quantum field theory such as al − , 2. ≡ quantum2 electrodynamics (QED) can give rise via quantum fluctuations to a shift in g , called the magnetic . In a now classicl QED calculation, Schwinger (2) gl 2 found the leading (one-loop) effect (Figure 1), al − , 2. ≡ 2 α al called0.00116 the magnetic anomaly. In a now classic QED calculation, Schwinger (2) = 2π ≃found the leading (one-loop) effect (Figure 1), e2 α α 1/137.036. al 0.001163. ≡ 4π ≃ = 2π ≃ e2 This agreed beautifully with experiment (3), thereby providing strongα confidence1/137.036. 3. ≡ 4π ≃ in the validity of perturbative QED. Today, we continue the tradition of testing QED This agreed beautifully with experiment (3), thereby providing strong confidence and its SU(3)C SU(2)L U(1)Y standard-model (SM) extension (which includes × × in the validity ofexp perturbative QED. Today, we continue the tradition of testing QED strong and electroweak interactions) byand measuring its SU(3)Cal SU(2)forL theU(1) electronY standard-model and muon (SM) extension (which includes × × SM exp ever more precisely and comparing thesestrong measurements and electroweak with interactions)al expectations, by measuring al for the electron and muon SM calculated to muchAnother higher order in perturbationever more muon precisely theory. and Such comparing comparisons opp these measurements testortunity-anomalous with al expectations, moment calculated to much higher order in perturbation theory. Such comparisons test by University of Washington on 01/27/13. For personal use only. by University of Washington on 01/27/13. For personal use only. 3.6 st. dev anomaly now Annu. Rev. Nucl. Part. Sci. 2004.54:115-140. Downloaded from www.annualreviews.org Annu. Rev. Nucl. Part. Sci. 2004.54:115-140. Downloaded from www.annualreviews.org + fix add heavy photon interacts preferentially with H muon Figure 1 The first-order QED correction to g-2 of the Figure 1 The first-order muon. Muon data is g-2 - BNL exp’t, QED correction to g-2 of the Lamb shift ... muon. Hertzog µ p e p Maybe dark Hertzog- Kammel matter, new Flab energy Out particles H H R Essig ’15 APS show up in e

1 µ p 1 muon physics! p

?

? Lepton-universality violating one boson exchange • Tucker-Smith & Yavin PRD83, 101702 new particle scalar or vector coupling • Brax & Burrage scalar particles PRD 83, 035020 &’14 • Batell, McKeen & Pospelov PRL 107, 011803 new kinetically mixing with Fμν plus scalar for muon mag. mom. 1401.6154 W decays enhanced • Carlson Rislow PRD 86, 035013 fine tune scalar pseudoscalar or polar and axial vector couplings • Barger et al PRL106,153001 - new particles ruled out but assumes universal coupling • decays provide constraints New scalar must • give μ-p Lamb shift • almost no hyperfine in μ proton • almost no effect for D, 4He • consistent with g-2 of μ and electron Scalar ok with all constraints using 4 3 g 2.3 10 e, g 1.3 10 e  ⇥ µ  ⇥ 2 2 ge 8 gµ 6 5.3 10 ↵, 1.7 10 ↵ 4⇡  ⇥ 4⇡  ⇥

Tucker-Smith & Yavin (PRD83,101702(R) • be found RAPID COMMUNICATIONS

DAVID TUCKER-SMITH AND ITAY YAVIN D 83, 101702(R) (2011) exp than the corresponding shift in the "-p system [5]. If the a" [14]. For a given mass m0, we can extract the values of force is attractive in both systems, the apparent proton- g" that bring the theoretical and experimental values of radius will always appear smaller in the e-p system, con- g 2 into agreement. In fact, these values are insensi- ð À Þ" trary to observations. An attractive force must therefore tive to m provided m m is satisfied, giving g =e 0 0  " "  couple more strongly to muons than to electrons if it is to 1:6 10 3 for a vector and g =e 1:3 10 3 for a explain the discrepancy in the proton-radius determination.  À "   À scalar. In Fig. 1, we plot the 2S -2P energy-shift, A different possibility is that g is not suppressed rela- 1=2 3=2 e Eq. (2), against the mass of the mediator, m , fixing the tive to g , but the force is repulsive, leading to a larger 0 " coupling to muons in this way. For the purpose of the plot, apparent proton-radius in the e-p system. This possibility we take gp g", but the result for other choices is easily is consistent with the g 2 e constraint discussed in the ¼ next section. However,ð sinceÀ Þ the effects of such a light obtained, as the energy-shift is proportional to gp. As the plot indicates, a new force with a mass MeV force are suppressed at higher momentum transfer, this  possibility seems in tension with the value of the proton- and a coupling to muons that explains the discrepancy in radius extracted from scattering data which generally also the muon anomalous magnetic moment can also give the imply a larger proton-radius [6]. Therefore, for the purpose required energy-shift in muonic hydrogen to reconcile the of this paper, we concentrate on the possibility that it is a proton-radius extracted from this system with the one new attractive force that modifies the "-p system. extracted from hydrogen and electron-proton scattering. The mediator mass that gives the maximum energy-shift is near an MeV because it is essentially determined by the III. CONTRIBUTIONS TO g 2 e; Bohr radius of the "-p system, a 1 0:69 MeV. The ð À Þ "À ¼ The scalar and vector-boson contributions to the elec- choice g g favors m MeV, but a different mass p  " 0  tron and muon anomalous magnetic moments are [7,8], can be accommodated by increasing gp accordingly. For m MeV (m MeV), the required coupling  g" 2 0 0   2 2 Áal $ m0=ml ; (4) becomes large and scales as m (m ). ¼ 2% e ð Þ 0 0À   For m MeV, the coupling to muons necessary to 0  where ml is the mass of the electron or muon, and explain both discrepancies turns out to be close to the 1 1 z 2 1 z muon mass dividedTucker-Smith by the electroweak & scale,Yavinm" =vPRD83, 101702(R) 4 ¼ $ x scalar ð À Þ 2ð þ2 Þ dz (5) 4:3 10 . A Higgs-like coupling proportional to the ð Þ ¼ 0 1 z x z À Z ð À Þ þ mass wouldcouplings resolve any tension with to theµ, constraint p greater from than to e, n 2 1 2z 1 z 0.6 $ x vector ð À2 Þ 2 dz: (6) ð Þ ¼ 0 1 z x z Z ð À Þ þ 0.5 Muonic H Solid is scalar For ml m0 we have the asymptotic behaviors  0.4 dashed is vector $ 3=2 and $ 1. scalar vector meV We! begin with the electron! system. As emphasized in 0.3 H central curve gives

Ref. [9], the g 2 measurement is currently used to E ð À Þe 0.2 define the fine-structure constant . The additional contri- g-2 of muon m r bution to g 2 therefore acts as a shift of the fine- 0.1 6 e ð À Þe V (r)= 1.7 10 ↵ structure constant as Á 2%Áae. Comparing this ¼ 0.0 3 ⇥ r correction to measurements made in Rb and Cs atoms 0.1 1 10 100 [10,11], the shift in  must not exceed 15 ppb, which IV. CONSTRAINTS m MeV constrains the coupling to electrons as [9] 6 2 The most model-independent constraint on an MeV-FIG. 1 (colorL online). The contribution to the energy-shift in ge 9 5 Shift in 4He scale$ m interaction0=ml < between15 10 muonsÀ : and protons(7) comesmuonic from hydrogen, Eq. (2), plotted against the mass of the e ð Þ Â 24  measurements of the 3d5/2-2p3/2 transitions in mediator.Mg In themeV central4 solid-blue curve, we require the coupling H 1 meV shift is OK and 28Si [12]. A weighted-average between theto re- the muon,L g , to be such that the scalar contribution to For m0 MeV, this constraint translates to ge=e & 2:3 "3  sults from 24Mg and 28Si was used to obtain the limit, He 4 4 6 g 2 " equalsm the theoretical deficit. In the upper/lower 10À and ge=e & (4:0exp 10QEDÀ for) /QED scalar=( and0 vector.2 3. media-1) 10 .ð ForÀ Þ H f 2

 ± ⇥ solid-blue2 curve,E the scalar contribution to g 2 is deter- tors, respectively.m The constraintMeV this translates is weakened to a 95% for CL larger limit gpgµ/e < " + d ð À Þ ⇡ 6 mined to be 1s1:d. away from the theoretical deficit. The vectorVertical line- e e threshold 3.1 10 , assuming coupling only to protons. This mea- - values of m0. A similar analysis and limit were recently surement⇥ therefore allows the couplings necessary tocase ex- is similarlyÆ given by the dashed-red curves. The coupling presented in Ref. [12]. 0 plain the muonic hydrogen and (g 2)µ discrepancies.to the proton is fixed0.2 at g 0.5g 1.0. The2.0 solid horizontal5.0 10.0 line More important for the purpose of a direct comparison p ¼ " Mild tension does arise if one assumes that the new forceis the discrepancy between the experimentally measured value of carrier also couples to neutrons since the bound improves mf MeV with the Lamb shift in the "-p system is the constraint the energy and the theoretical prediction assuming the CODATA coming from measurementby a factor of of 2.g However,2 [13 as]. we At now present, discuss, such a coupling to the neutron" is much better constrainedvalue by [2] for the proton-radius, rp 0:8768 fm. The dotted thð À Þ ¼ the theoretical predictionneutron scatteringfor a" seems experiments. to indicate a deficit horizontalFIG. lines 2: The represent contribution the to1s the:d 2S-2P. uncertainty energy splitting about in this 11 muonic helium, Eq. (9), plottedÆ against the mediator’s mass. of 302 88 10À Acompared new force with carrier the with experimental an MeV mass value that couplesvalue. The curve is normalized to EµH = 0.31 meV, which is ð Þ to neutrons produces sizable corrections to the scatter- H L ing cross-section of neutrons on heavy nuclei. This was the discrepancy between the experimentally measured value first realized by Barbieri and Ericson [13] who used the and the theoretical prediction, assuming the CODATA value for the proton-radius, r =0.8768 fm. The dotted curves results of an old experiment [14] on the polarizability p represent the 1 s.d. uncertainty about this value. of the neutron to set a limit on any additional101702-2 force car- ± rier that interferes with the strong interaction amplitude. They showed that such a force will contribute to the an- has searched for a light boson emitted in the scattering gular dependence of the di↵erential cross-section in a dis- of electrons against the nucleus. It sets a strong bound tinct manner as compared with the contribution from the on the coupling to the electron for masses in the range strong interactions. Assuming that the new force couples 1.2

+ ( e e) ! c⌧(m) Assumes largest allowed coupling to electron

m(MeV) ( ) ! c⌧() + c⌧(m) c⌧(e e ) ?

m(MeV) ?

1

1 Physics Letters B 740 (2015) 61–65

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Probing new physics with underground accelerators and radioactive sources a a, a,b Eder Izaguirre , Gordan Krnjaic ∗, Maxim Pospelov a Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada b Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada

Physics Letters B 740 (2015) 61–65 a r t i c l e i n f o a b s t r a c t Contents lists available at ScienceDirect

Physics Letters B Article history: New light, weakly coupled particles can be efficiently produced at existing and future high-intensity Received 3 September 2014 accelerators and radioactive sources in www.elsevier.com/locate/physletbdeep underground laboratories. Once produced, these particles Received in revised form 18 November 2014 can scatter or decay in large detectors (e.g. Super-K and Borexino) housed in the same facilities. Accepted 18 November 2014 We discuss the production of weakly coupled scalars φ via nuclear de-excitation of an excited element Available online 21 November 2014 Probing new physics with underground accelerators 16 into the ground state in two viable concrete reactions: the decay of the 0+ excited state of O populated Editor: M. Trodden and radioactive sources PLB 740, 61 via a (p, α) reaction on fluorine and from radioactive 144Ce decay where the scalar is produced in the Eder Izaguirre144 a, Gordan Krnjaic a, , Maxim Pospelov a,b de-excitation of Nd∗, which occurs∗ along the decay chain. Subsequent scattering on electrons, e(φ, γ )e, a Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada yields a mono-energeticb Department of Physics and Astronomy, signal University of thatVictoria, Victoria, is Britishobservable Columbia, Canada in neutrino detectors. We show that this proposed experimental setupFocus can cover is on new mass territory range for masses 250 keV mφ 2me and couplings to protons and a r t i11 c l e i n f o 7 a b s t r a c t ≤ ≤ electrons, 10− ge gp 10− . This parameter space is motivated by explanations of the “proton charge Article history: ≤ ≤ New light, weakly coupled particles can be efficiently produced at existing and future high-intensity radius puzzle”,Received 3 Septemberthus 2014 this strategy acceleratorsadds aand viable radioactive sourcesnew in physicsdeep underground component laboratories. Once produced,to the these neutrino particles and nuclear Received in revised form 18 November 2014 can scatter or decay in large neutrino detectors (e.g. Super-K and Borexino) housed in the same facilities. astrophysicsAcceptedprograms 18 November 2014at underground facilities. Discusses motivationWe discuss the production ofand weakly coupledexisting scalars φ via nuclear constraints de-excitation of an excited elementBUT Available online 21 November 2014 into the ground state in two viable concrete reactions: the decay of the 0 excited state of 16O populated 2014Editor:The M. TroddenAuthors. Published by Elsevier B.V. This is an open access+ article under the CC BY license © via a (p, α) reaction on fluorine and from radioactive 144Ce decay where the scalar is produced in the 144 3 de-excitation(http://creativecommons.org/licenses/by/3.0/ of Nd∗, which occurs along the decay chain. Subsequent scattering on electrons,). e( φFunded, γ )e, by SCOAP . The region with massyields agreater mono-energetic signal than that is observable 2 electronin neutrino detectors. We masses show that this proposed is NOT experimental setup can cover new territory for masses 250 keV mφ 2me and couplings to protons and ≤ ≤ electrons, 10 11 g g 10 7. This parameter space is motivated by explanations of the “proton charge − ≤ e p ≤ − reallyradius studied puzzle”, thus this anywhere,strategy adds a viable new physicstill component now to the neutrino and nuclear astrophysics programs at underground facilities. © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 1. Introduction • Focus hereIn this on paper detecting we outline electron-positron a novel experimental strategy in which light, “invisible” states φ are produced in underground accelerators 1. Introduction decays of In this paper we outline a novel experimental strategy in which or radioactive materialslight, “invisible” with states Oφ are(MeV produced) inenergy underground release, accelerators and observed In recent years, there has emerged a universal appreciationIn recent years, there for has emerged a universal appreciation for or radioactive materials with O (MeV) energy release, and observed new light, weakly-coupled degrees inof freedom nearby as generic neutrino possi- in nearbydetectors neutrino detectors in thein the samesame facilities facilities as depicted in as depicted in new light, weakly-coupled degrees of freedom as generic possi- Fig. 1: bilities for New Physicsmake (NP) beyond Standard with Model (SM). proton Con- induced reaction or siderable effort• in “intensity frontier”Fig. experiments 1: is now devoted X∗ X φ, production at “LUNA” or “SOX” (1) bilities for New Physics (NP) beyond Standard Modelto NP (SM).searches [1] Con-. In this paper we argue that there is a pow- → + erful new possibility positronfor probing these states-electron by combining large scatteringe φ e γ , detection at “Borexino”. (2) siderable effort in “intensity frontier” experiments isunderground now devoted neutrino-detectors with either high luminosity un- + → + Here X is an excited state of element X, accessed via a nuclear derground accelerators or radioactive Xsources.∗ X φ, production∗ at “LUNA” or “SOX” (1) reaction initiated by an underground accelerator (“LUNA”) or by a to NP searches [1]. In this paper we argue that thereUnderground is a laboratories,pow- typically located→ a few+ km under- radioactive material (“SOX”).1 In the “LUNA”-type setup a proton ground, are shielded from most environmental backgrounds and beam collides against a fixed target, emitting a new light parti- erful new possibility for probing these states by combiningare ideal venues forlarge studying rare processese φsuch as low-ratee γnu-, detection at “Borexino”. (2) cle that travels unimpeded through the rock and scatters inside clear reactions and solar neutrinos. Thus+ far, these→ physics+ goals underground neutrino-detectors with either high luminosity un- a “Borexino”-type detector. Alternatively, in the “SOX” production have been achieved with very different instruments: nuclear re- Here X is an excitedscenario, designedstate to studyof elementneutrino oscillations X ,at accessedshort baselines, via a nuclear actions relevant for astrophysics involve low-energy,∗ high-intensity derground accelerators or radioactive sources. a radioactive material placed near a neutrino detector gives rise to proton or ion beams colliding with fixed targets (such as the LUNA reaction initiated theby reaction an undergroundin Eq. (1) as an intermediate accelerator step of the radioactive (“LUNA”) or by a experiment at Gran Sasso), while solar neutrinos are detected with Underground laboratories, typically located a few km under- material’s decay chain.1 large volume ultra-clean liquid scintillatorradioactive or water Cerenkov material de- We (“SOX”). study one particularlyIn well-motivatedthe “LUNA”-type NP scenario with asetup a proton tectors (SNO, SNO , Borexino, Super-K, etc.). 4 ground, are shielded from most environmental backgrounds and ! MeV scalar particle, very weakly O (10− ) coupled to + beam collides against a fixed target, emitting a new light parti- are ideal venues for studying rare processes such as low-rate nu- * Corresponding author. cle that travels unimpeded1 Our idea is very generic, through not specific to any singlethe experiment rock or location, and which scatters inside clear reactions and solar neutrinos. Thus far, these physicsE-mail address: [email protected] (G. Krnjaic). is why quotation marks are used. a “Borexino”-type detector. Alternatively, in the “SOX” production http://dx.doi.org/10.1016/j.physletb.2014.11.037 have been achieved with very different instruments:0370-2693/ nuclear© 2014 The Authors. re- Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. scenario, designed to study neutrino oscillations at short baselines, actions relevant for astrophysics involve low-energy, high-intensity a radioactive material placed near a neutrino detector gives rise to proton or ion beams colliding with fixed targets (such as the LUNA the reaction in Eq. (1) as an intermediate step of the radioactive experiment at Gran Sasso), while solar neutrinos are detected with material’s decay chain. large volume ultra-clean liquid scintillator or water Cerenkov de- We study one particularly well-motivated NP scenario with a tectors (SNO, SNO , Borexino, Super-K, etc.). 4 + ! MeV scalar particle, very weakly O (10− ) coupled to nucleons

* Corresponding author. 1 Our idea is very generic, not specific to any single experiment or location, which E-mail address: [email protected] (G. Krnjaic). is why quotation marks are used. http://dx.doi.org/10.1016/j.physletb.2014.11.037 0370-2693/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 19 16 p(1.88 MeV) + Fc ↵ + O⇤(6.05) 16 16 ! O⇤(6.05) O(GS)+ Kohler et al PRL 33, 1628! (1974) rules out mass range > 1.03 MeV for coupling const,. 40 times larger than what is needed now • resonance at 1.88 MeV- reaction discovered excited state of 16O (1939) • shielded scintillation detector -detects • decaying to pairs- signal is approximate that of 6.05 gamma ray • 30 hours running 0.04 C on target • need to improve by 1600 Freedman et al. PRL 52, 240 rules out mass >3 MeV p +3 H 4 He(20.1) 4He(GS)+ ! ! 16O(6.05, 0+) 16 O(GS, 0+)+c , No single photon decay ! From electron g-2

+ 2 ⌧(A⇤ A+e e) 3 gee¯ m 2 5/2 ⌧(A! A+ =3.3 10 e2 1 ( 6MeV ) ⇤! ⇥ + 10 ⌧(A⇤ A + e e) : lifetime is 10 s Decay length! (m) nuclear emission of

m(MeV) 1404 H. TSERTOS et aI,.

III. RKSUI.TS AND DISCUSSION c.rn. Energy tkeV) 778 792 806 820 834 Figure 8 displays the counting rate per 5-keV step ob- I I I I 1 tained 25.O' ~ e„b ~ 3I..O' (Fve for Bhabha and Mott scattering [Figs. 8(a) and ~ 25 8(b), respectively] as a function of the beam energy, for X all data taken with the Be target. For each energy step, the sum of the events (-1.6X10 and —8.0X10 for 20 Bhabha and Mott scattering, respectively) were gained @ from the corresponding energy spectra (see an CV Fig. 4) by CD integration of the full-energy peaks using the uniform

+ ~ I I I window: [0.991 ) 1.009]. With a statistical I (ED„/Ep, I I accuracy of 0.25%%uo and 0.11%%uo, respectively, both excita- 0.02 tion functions are smooth, demonstrating the excellent + time stability of the e beam. This implies, furthermore, that the systematic errors occurring in our measurements o.oo e e resonant (?) scattering I must be significantly lower than the statistical ones. The CL + general features of the measured excitation functions are -0.02 + in agreement with the expected beam-energy dependence e Tsertos etof thealscattering PRDprocess 40,according 1397to Eqs. (10) and (11), (c) e respectively. The steeper falloff for Mott scattering is due ~ to the smooth decrease of the detection e%ciency at the ~ ~ ~ g ~ a ~4 r m~ a ~ claim experimentalhigher e+ , assensitivitydiscussed in the previous section. ~ ~ g ~ ~ ~ ~ ~ ~ In accounting for remaining Auctuations in the counting ~ rates, the Bhabha-scattering events were normalized to of 0.5those obtainedb eV/srby Mott scattering for each measuring point. This is shown in Fig. 9(a) as a function of the 2150 2200 2250 2300 2350 e e' Bombarding Energy lkeVl e beam energy (lower scale) and of the c.m. excitation ener- rule out Massgy (upper scale).1.8Since MeVthe corresponding rate for Mott scattering is by a factor of 5 larger, the statistical uncer- FIG. 9. Measured ratio of Bhabha to Mott scattering ob- 2 2 tainties are mainly determined by the counting rate for tained from the sum of our data (Fig. 8) as a function of the g . bombarding energy [(a)]; the corresponding c.m. energy is indi- e 8 2 15 cated in the upper scale. The solid line represents a fit of a sim- Ratio to usual 2 =(5.3 10 ) =2.5 10 ple smooth function to the data. The relative as well as the e c.rn. Energy fkeVl standard deviations from the fitted curve are shown in (b) and ⇥ 77& 792 ⇥806 820 834 (c), respectively.

50 & 340 (FWHM) monoenergetic beam⇣ ⌘on Be 10 — 4~~ We now compare the measured ratio with that expect- ed by Eq. (13) at an incident energy of 2.2 MeV. By an integration of the differential cross section for Bhabha Our parameters and Mott scattering [Eqs. (10) and (11), respectively] we obtain within the full angular O range of observation (Fig. 0) 6): (o~/o ) =0.032. From a calibration the 2 Bhabha Events I of detection efBciencies as a function of the incident energy we esti- mate: [eM(2.2 MeV)/e~(1. 1 MeV)] = 14.3%; this matches 2 V) d 4m 1/2 50— well with calculations showing that the full-energy-peak dE =0.14(1 2 ) 0.14 b eV efficiency of a 2-mm-thick Si(Li) detector only amounts to — ' d⌦ m 40— 15% at this incident energy. With these values and  taking (b,Eslb, E~)= —,', =0.2, (X, /Kk)=4 we get from 30— Eq. (13): (Xii /NM)th =(0.18+0.03). As indicated, the Improve experiment by a factor of 4? 20— calculated ratio is affected by experimental un- R certainties concerning mainly the determination of the Mott Events detection efFiciency at the corresponding Bhabha and Mott energies as well as the effective solid angle for Mott 0 I I I I I I 2150 2200 2250 2300 2350 scattering. The estimated value agrees we11 with the mea- sured ratio of (0. 1972+0. . beam e+ Bombarding Energy [kevl 0005) at this energy. Since our aim, however, was to search for a deviation FIG. 8. Total counting rate per 5-keV incident-energy step from a smooth excitation function we did not apply an for Bhabha and Mott scattering [{a}and {b), respectively] as a efticiency correction to the data. For the same reason, function of the beam energy. The total measuring time per step the contribution of the random coincidences of about amounts to -400 min. 0.05% was not subtracted from the data, since it was Beam dump experiments Dark photons to dark matter

SLAC E137

No one has discovered anything, yet

Phys.Rev.Lett. 113 (2014) 17, 171802 arXiv:1406.2698 Exclusion from e,mu g-2, p Lamb shift, assumes g m g µ = µ = p g m g e ✓ e ◆ e 10-3

10-4 e / g =

10-5

10-6 10-5 10-4 10-3 10-2 0.1 1

m(GeV) Shaded areas excluded white is allowed Exclusion from e,mu g-2, p Lamb shift, and g m 1.5 g beam dump E137 assumes µ = µ = p ge me ge g ✓ ◆ e is much smaller 10-3

10-5 e / g = 10-7

10-9

10-5 10-4 0.001 0.010 0.100

m(GeV) scalar boson survives, but much smaller coupling to electrons, see or not in muon or proton beam dump experiments Summary • If all of the experiments, and their analyses, are correct a new scalar boson of mass ~1 MeV must exist • Direct detection is needed: David McKeen, Yu-Sheng Lu 19 16 p(1.88 MeV) + F ↵ + O⇤(6.05) 16 16 ! O⇤(6.05) O(GS)+ Very difficult: + e e scattering! beam dump constrains e-boson coupling

Need to detect from muon and proton interactions Spares follow Deuteron charge radius

2 2 2 H/D isotope shift: rd − rp = 3.82007(65) fm C.G. Parthey, RP et al.,PRL104,233001(2010)

CODATA 2010 rd =2.1424(21)fm rp= 0.84087(39) fm from µH givesDeuteronrd =2.1277(2)fm charge radius Lamb shift in muonic DEUTERIUM rd =2.1282(12)fm PRELIMINARY! µd Borie+Pachucki+Ji+Friar µH and µD are consistent! µd Borie+Ji µd Borie+Pachucki PRELIMINARY(if BSM: no coupling to neutrons) µd Martynenko WIP: deuteron polarizability (theory) complete? double-counting? µH + iso H/D(1S-2S) WIP: shift from QM-interference CODATA-2010 µd Borie+Pachucki+Ji+Friar CODATA D + e-d µd Borie+Ji µd Borie+Pachucki PRELIMINARY e-d scatt. µd Martynenko n-p scatt. µH + iso H/D(1S-2S) CODATA-2010 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 CODATA DDeuteron + e-d charge radius [fm] Randolf Pohl Mainz, 2nd June 2014 26 e-d scatt. n-p scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl Mainz, 2nd June 2014 26 Deuteron charge radius

2 2 2 H/D isotope shift: rd − rp = 3.82007(65) fm C.G. Parthey, RP et al.,PRL104,233001(2010)

CODATA 2010 rd =2.1424(21)fm

rp= 0.84087(39) fm from µH gives rd =2.1277(2)fm

µH + iso H/D(1S-2S) CODATA-2010

CODATA D + e-d

e-d scatt.

n-p scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl Mainz, 2nd June 2014 26 R Essig talk at APS ‘15

• Dark (heavy) photon is ruled out as explanation of muon g-2 • Complete parameter space has been searched and nothing is found • But other scalar boson not searched completely Yes it really is GE

• Non-relativistic reduction of one-photon exchange leads to the spin independent 2 2 interaction being GE (Q )/Q • All recoil effects properly accounted for:Breit- Pauli Hamiltonian computed for non-zero lepton and proton momentum arXiv:1501.01036v2 [nucl-th] 16 Jan 2015 n hrfr o ato h rtnplrzblt otiuin eew cetti ruetadse odetermine to seek and excited argument this an accept of we Here that contribution. wave is two- polarizability proton state the complete proton to the baryonic the of contribution of intermediate component polarizability part Fock-space the proton not specific therefore the that a and is of e conclude pair time-ordering QED lepton to particular (including the a one if function However, be lead would diagram. might exchange diagram photon 1 this so, Fig If at nucleon. look a (QCD) The particular, chromodynamic quantum a function. figure. non-perturbative with wave the a electron proton in of indicated example the bound is An of a also electron. component of bound lepton-sea blue-antigreen annihilation the the a virtual ( with via indicate annihilates up the interaction lines that The illustrating lepton dashed [4] sea vertical proton. Ref. light The the of inside electromagnetically. diagram (positron) interact Feynman lepton” Typical sea online) “light (color 1: FIG. and in pop one pairs If a muon-anti-muon and or transfer. the momentum electron electron-positron of of see bound source values would the a small one to to e isolation at akin decays is in This seen turn that proton be existence. in a can of which of that out snapshot photon, function a wave virtual Fock-space take a the proton could to of the leads part of sign annihilation also component right The is the that has proton. which positron interaction, the muon-proton of . di 2 versus puzzle cloud the of electron-proton radius presence for the the proton the account in namely the that term review could structure, explain assumption extra the proton’s proton, the to an see the the that magnitude an solutions, of argued and of to is feature possible components leads it non-perturbative of constituent quark, particular, a array as per In vast that fermions radii. is a sea extracted [4] generated light the solutions has of di suggested and this presence novel puzzle, understanding the possible of radius of problem proton The One the hydrogen. [3]. as electronic known ordinary from become obtained has that than smaller 4% about o-etraieLpo e emosi h ulo n h rtnRdu Puzzle Radius Proton the and Nucleon the in Fermions Sea Lepton Non-Perturbative h ai dai htabudeeto a niiaewt oirnta spr ftenon-perturbative the of part is that positron a with annihilate may electron bound a that is idea basic The is that radius proton the of value a obtain 2] [1, hydrogen muonic of studies experimental precision high Recent aua usint s swehro o hsdarmi ato otiuinta sarayicue.In included. already is that contribution a of part is diagram this not or whether is ask to question natural A h ai sgvnas given is ratio The hr etk noacutthat account into take we where nisms n nisncerpoete oara pro- real a to properties nuclear its comparable in and rather mass otherwise its but in neutral would be “proton” course resulting of the proton, the inside quarks o switched we exper- If thought iment: a consider We in protons. nonuniversality with interactions lepton virtual the of in pairs importance electron-positron possible a by inspired structure, proton’s the to contributions nonperturbative as fermions il oqatttvl siae u t rsnei not is presence its but estimate, quantitatively to sible di is QCD, inherently of nature the nonperturbative of because pairs, electron-positron of (probabil- density ity) This 3). Fig. (see alone QED considerations perturbative by pro- for accounted the be cannot inside which ton, pairs conceiv- electron-positron the of for presence room a able is there therefore perturba- and electromagnetic itself, the tion than larger much be can reshaping this highly QCD, of to nature Due nonperturbative nonlinear pairs. electron-positron the and photons contains additionally actual now the which function” and wave reshaping, “proton a to leading previous function” “wave the on backreact would and pairs the photons electron-positron virtual back quarks, include of we interactions if electroweak Now, function.” “wave (QCD) chromodynamic quantum nonperturbative some with ton h ursisd h ulu.Te,teascae mo- is associated scale the mentum Then, nucleus. the inside quarks the Let oaiaiiycnrbto vlae nRf [15]. Ref. in evaluated contribution proton polarizability leading the for order-of-magnitude right the gives cinadtecrepnigeeg cl sotie as obtained is E scale energy corresponding the and action iddprmti siaedsrbdaoe ihone with factor radiative above, described estimate parametric simple- the minded that note to interesting is It puzzle. pro- radius the ton of solution a to contribution significant a make to m e yls hn5.Telaigfiiesz Hamiltonian follows, finite-size as given leading is The 5%. than less by fer etv opiga h cl ftepoo’ momentum proton’s the of di ef- scale the the that at coupling, coupling QED fective the of running the reso- on first based its into proton the the nance, of energy excitation the ↵ e e scnie h osbepeec flgtsea light of presence possible the consider us Let ⇠ R /m r rmtevleof value the from ers / pc e ⇠ h h ⇠ H ⇠ H r p vp 1 fs m I.LGTSAFERMIONS SEA LIGHT III. H eacaatrsi eBolewvlnt of wavelength Broglie de characteristic a be . Any Any effect is small and same for electron and atoms muon i then we electron-positron can show that virtual annihilation processes lead to an extra 32 i arXiv:1401.3666v2 [physics.atom-ph] shift energy UDJ: function. wave proton / in exists lepton-pair Non-perturbative 16 Jan 2014 e eoac t13 e.I ses ocheck, to easy is It MeV. 1232 at resonance fs itnei scnatitrcin r hw ob nraevr ail ihaoi number. atomic with rapidly class the very a on increase of dependence be contributions the to which The shown possibility (for are puzzle. the puzzle interaction) radius out contact radius rule proton as proton diagrams is the the distance loop of of of explanations explanation features potential an general of as and content result lepton-pair large of relatively this that argue endqatte htdpn nti etnpi otn r vlae.Ec sfudt eof be to found is Well- Each evaluated. studied. are is content proton lepton-pair the 10( this of of on order content depend the lepton-pair that non-perturbative quantities the defined from originating puzzle term in the electron-proton versus muon-proton interaction, haswhich the right sign /m ⇠ m ↵ = If we assume an average of roughly ×10−7 0.7 light sea positrons per valence quark, ↵ QED p 1 p p oeta xlnto U .Jnshr,Py.Rv A Rev. Phys. Jentschura, D. [U. explanation potential A rcinlcag numbers, charge the fractional to proportional interactions electromagnetic terquark scmae otepoo,a av onigargu- counting quarks naive valence a with as proton, A shows. the neutron ment proton the to of of compared energy hierarchy the as lowers mass actually among quarks interaction the valence Coulomb of the Namely, inversion neutron. quarks versus an constituent the to the that leads think among would interaction one con- priori, electrostatic the A among [1–4]. interaction quarks stituent electromagnetic di the mass of the There basis explain neutron). to an a attempts into been and have decay atom neutrino beta a hydrogen pair, against (the electron-positron universe unstable the be that of otherwise known would stability the well for is ble di It mass elusive. the somewhat are structure itv nrysitcno xli h asdi mass ra- the explain (QED) cannot electrodynamic shift con- self- energy masses quantum diative all electromagnetic the for the Thus, positive remains that sidered. quarks is the of [1–4] energy e Refs. might bag radiative and in MIT [4] significant reached an structure to peculiar in rise rather give bound a have in- quarks [1] valence further model the wave warrants electromagnetic of and the functions sign, because particular especially vestigation any have to exchange. Coulomb to di due mass and the origin if neu- electromagnetic proton the of the than that lighter suggest is would tron negative, being expression, tews erqie nve ftelre fractional larger the of view in would required self-energy negative be a otherwise where neutron, and proton hra o h eto ihvlnequarks valence with neutron the for whereas QED 2 hc ntr scmesrt with commensurate is turn in which , 2 3 2 ⇠ ⇡↵ /m ⇠ 3 × h lcrmgei set ftepoo n neutron and proton the of aspects electromagnetic The oee,terdaiecreto sntconstrained not is correction radiative the However, 5 m rmtesl-nrylo excluded, loop self-energy the from QED h/r m . m 4 ↵ e 2 ! eateto hsc,Msor nvriyo cec n T and Science of University Missouri Physics, of Department ↵ e 2 ⇥ − e 2 h lcrwa neatosof interactions electroweak the l 2 QED p 10 1 3 m rmanhlto trs.GM Shift GAM: rest. at annihilation from , where m " e 2 4 e 2 tzr oetmtrans- momentum zero at + 1 h ratio The . ih e emosi lcrnPoo n unPoo Inte Muon–Proton and Electron–Proton in Fermions Sea Light m r ↵ r p ff 2 e 2 ASnmes 13.s 61.k 22.s 31.15.-p 12.20.Ds, 36.10.-k, 31.30.js, dis radius numbers: proton the PACS versu explain electron-proton to the v magnitude in that and term show sign extra can right we the an then to quark, lead valence processes per positrons sea light emosa osiun opnnso h rtn fw assu we If proton. the of e components structure, proton’s constituent the as of genu fermions feature conceivable shi any nonperturbative Lamb that e a the conclude with this We to scattering. that contribution double show polarizability to can proton’s we muo the only a However, to present is to which projectiles. opposed quarks, muon valence as two electronic of an exchange into photon electron nonunv scattered a such the to lead to appear could the perturbative processes within interactions lepton-proton in nonuniversality Science p 2 3 2 h rneo rtnadnurni responsi- is neutron and proton of erence c steeoedi therefore is ect r × ⇠ h rtnrdu oudu R Pohl [R. conundrum radius proton The ↵ sPac’ ntof unit Planck’s is p 2 ↵ ⇡ .INTRODUCTION I. uti o impos- not if cult 2 cs n a ru 4 htteitreit tt spr ftepoo aefunction, wave proton the of part is state intermediate the that [4] argue may one ects) 3 ! . ⇠ ( ) 2 − and magnitude to explain the proton radius discrepancy. r T–EPril hsc eerhGop ..o 1 H–4001 51, P.O.Box Group, Research Physics Particle MTA–DE 2 ) ⇥ R (1 ota efidsc etnpi otn xssi h rtn oee,we However, proton. the in exists content lepton-pair a such find we that so , . 3 1 339 10 / stosmall too is " 386) q + e q ¯ 6 ,4 1 7( 2 0 1 3 ) ]h i g h l i g h t st h en e e dt or e v i s i ta n yc o n c e i v a b l e nvriyo ahntn etl A9819-1560 WA Seattle Washington, of University , ! 2 e fprubtv QCD. perturbative of sea ,and − e 2 3 (9) (8) + 1 3 × " ! lu ftepoo.SeFg .Tetr o-etraiehr eest a to refers here non-perturbative term The 1. Fig. See proton. the of cloud × − ~ sntaalbe ycmaio,tefiiencersize nuclear finite the comparison, By available. not is channel annihilation the thus namely, and , pairs lightest electron-positron the from comes to leptons contribution sea dominant the the because vanish to e pected the hydrogen, muonic For proton. the within where iaindarmi h aeo oirnu ed othe to leads e of case the in diagram anni- hilation photon and the exchange units, natural photon In both diagrams. annihilation by given is pro- electron the and between interaction ton the then higher- term, perturbative QED any order in for accounted not are which 3). Fig. and [21–26] Refs. (DICS, see in Scattering confirmed Compton well Inelastic Deep is so-called proton the the signifi- of a content fact, photon In cant experiments. known any by excluded ihntepoo r o oaie,w a replace can we polarized, not are proton pairs the electron-positron within spins the that their Assuming if one. to positron up sea add light the and electron the bound of interaction nonvanishing a gives Hamiltonian This neato fteeeto ihtepoo u othe form to the due of is proton therefore the channel annihilation with electron the of interaction additional the hydrogen, (electronic) atomic For leptons. i leatgengunas sidctdi h figure. the in indicated is also gluon blue-antigreen a via interaction (QCD) chromodynamic quantum exemplary An etn psto)isd h rtn h p( up The proton. the se inside “light a (positron) with lepton” electron bound a of annihilation virtual the illustrati diagram Feynman Typical online.) (Color 3: FIG. h ie ena iga snticue ftepoo is spin-1 proton a the as if perturbatively included treated not is diagram with Feynman given and The contents, quark or sea past and distant al valence the i g its in h proton with ts the future, e of al e state p asymptotic o t formation the o the nt mark h lines dashed a The taelectromagnetically. n n i h i( l a t e sw i t ht h eb o u n de l e c t r o n . 1 3 ! ↵ d − " ff )q u a r k s ,w h i c hc a r r yn o n - i n t e g e rc h a r g en u m b e r s ,i n t e r a c t ftepoo otisteeeeto-oirnpairs, electron-positron these contains proton the If cieitrcin[27] interaction ective + ! cs h conclusion The ects. ↵ 3 1 u u d 2 3 " rn rmtegnrto fpisb vlto nmmnu transfer momentum in evolution by pairs of generation the from erent fe vrgn vrteplrztoso h sea the of polarizations the over averaging after 0 ✏ × p Dtd aur 9 2015) 19, January (Dated: = .INTRODUCTION I. arXiv:1501.01036 esrsteaon feeto-oirnpairs electron-positron of amount the measures ! − − ff H eadA Miller A. Gerald rneo the on erence 3 1 3 1 ff udd = e " H h latter The . uud + rnewere erence + ann ⇡↵ ff e 2 ,wehave rneof erence 3 2 m QED × = u .D Jentschura D. U. a in- has e 2 )anddown( ✏ 2 3 p 3+ (3 tal. et =0 3 ⇡↵ d d 2 m QED ~ e 2 + / ,Nature 2particlewithcharge · ~ hne,wt h ih int xli h unchy- described muonic are the mechanism two explain These to 6]. [5, sign puzzle right drogen the with channel, httepoo aisdpnso h rjcieparti- perturbative of projectile number e the a higher-order that on show can depends one However, radius cle. conceivable lep- is proton it scattered the then or nonuniversal, that is bound proton the the “outside of with inter- the ton interaction with is the proton one the If of world”. if interactions interactions, the electromagnetic proton as “internal” well the as own of its look in structure closer ested a internal for need the the at quarks. highlight 6] down [5, the conundrum dius to compared as up the of charge iepril otn ftepoo.W eeso that show rise Dirac- give here a would We fermions to these proton. of presence the conceivable of the gen- nonperturbative content the a to particle admixture as an uine hadron, fermions the sea of property light physical of presence the of order-of-magnitude e quanti- the the A for shift. estimate Lamb parametric tative the proton’s to the shift contribution to Lamb correction polarizability in radiative absorbed, the is into and calculations, scattering, double to pro- tion or- annihilation e time and this creation possible cesses, particle all virtual of of exchanged care derings because photon take that, a show here into Feynman We inserted quarks. valence is two turn between in vacuum-polarization a which into loop muon) or (electron projectile higher- a e example, for order proton, the of particles constituent of terms correction origin. into physical absorbed known fact in muon-proton are versus interactions electron-proton of nonuniversality a ff 3 e ( c actua ect ) r cnlg,Rla isui O50-60 S and USA MO65409-0640, Missouri, Rolla, echnology, tl,teivsiain 14 swl stepoo ra- proton the as well as [1–4] investigations the Still, h eodpoesi oeseuaieadconjectures and speculative more is process second The the among interactions electromagnetic consider us Let ) e , 3 + tnadMdl uefiily ubrof number a Superficially, Model. Standard ( ff r 88 g,wt h osbepeec flgtsea light of presence possible the with .g., 466 d ) u c sprovided. is ect . urs hc ar o-nee hrenumbers, charge non-integer carry which quarks, ) )anddown ff t qiaett aitv correction radiative a to equivalent ft, ↵ n ouieslt utb connected be must nonuniversality ine 654(03]o h rtnradius proton the of (2013)] 062514 , / sm u o n - p r o t o ni n t e r a c t i o n ,w h i c hh a s c eeae yaculn ftescattered the of coupling a by generated ect c sex- is ect crepancy. NT@UW-14-27 raiy n fteei opigof coupling a is these of One ersality. ,2 1 3( 2 0 1 0 )a n dA .A n t o g n i n i ea vrg fruhy0 roughly of average an me o lcrnpoetlsa poe to opposed as projectiles electron for l spr fterdaiecorrection radiative the of part is lly ruleeto-oirnannihiliation electron-positron irtual i aumplrzto opi the in loop polarization vacuum nic δ u u d 1 (11) (10) ~ ff oeta,i iwo ita annihilation virtual a of view in potential, Phys.Rev. A88 062514 (2013) + ng c culycntttsardaiecorrec- radiative a constitutes actually ect / ff e a 4 f . · cswihcudapa ola osuch to lead to appear could which ects cnttetqakmass) quark (constituent electron not muon Contribution for ercn Hungary Debrecen, ore felectron-muon of sources . 1 ⇥ . ractions 7 × 10 µp tal. et 10 − 7 relative 7 ih e positrons sea light 2 ↵ rnein erence ↵

erence e

e + 2 Almost unknown T 1(0,Q ) Miller PLB 2012

2 2 subt ↵ 2 1 2 h(Q ) 2 Soft proton E = S(0) dQ 2 T 1(0,Q ) m 0 Q 2Z 2 2m 2 M 2 lim h(Q ) , chiral PT : T 1(0,Q )= Q + Q2 ⇠ Q2 ↵ ··· !1 Logarithmic divergence ! Typo bleow T (0,Q2) M Q2F (Q2) Cuts o↵integral 1 ! ↵ loop Birse & McGovern assumedipole : Esubt =0.004 meV very small 2 n 2 Q 1 Miller Floop(Q )= ,n 2,N Nn +3 M 2 (1 + aQ2)N n+3 ✓ 0 ◆ Infinite parameter set gets needed 0.31meV, NO constraint on neutron Choose parameters so shift in proton mass <0.5 MeV (current uncertainty) Recast in EFT- parameters seem natural uate terms up to fourth-order in chiral perturbation theory to find The function h(t) is monotonically falling, approaching 1/⌅t for small values of t, and 2 BM ⇥ Q ⇥ 1 falling as 3/(4t) large2 valuesM 2 of t. The subtraction4 functionM 2 T (0, Q2) is not available T1 (0, Q ) Q 1 2 + (Q ) Q 1 2 , (6) ⇧ ⇤ M O ⌅ ⌅ 2 ⇥ 1 + 2 Q from experimental measurements, except at the real photon point Q 2M=2 0. It comes from ⇥ ⇥ the excitation of the proton, and can be described, at small values of Q2, in terms of the with M⇥ = 460 50 MeV. They also use the most recent evaluation of ⇥M, based on a fit electric (E) and± magnetic (⇥M) polarizabilities. For small values of Q and ⌅ = 0 one to real Compton scattering [29] that finds 2 Q2 sees [23] lim⌅2,Q2 0 T1(0, Q )= ⇥M, where is the fine structure constant. Using this ⇤ 2 4 3 2 simple linear Q -dependence⇥ in Eq.=( (2)3.1 shows0.5) that10 thefm integral, over T1(0, Q ) converges (7) M ± ⇥ at the lower limit, but diverges logarithmically at the upper limit. Thus obtaining a non- where only statistical and Baldin Sum Rule errors are included. Their result is a negligible infinite result depends on including an arbitrary form factor that cuts off the integrand Esubt = 4.1µ eV [20]. The form Eq. (6) achieves the correct 1/Q2 asymptotic behavior for large values of Q2 or some other procedure. 2 of T1(0, Q ) but the coefficient¯ ⇥M2/ is not the same as obtained from the operator prod- We note that limQ2 ⇥ T1(0, Q ) can be obtained from the operator production expan- uct expansion. The coefficient⇤ of Eq. (6) is about twice the asymptotic limit obtained by sion [26, 27]. Using Eq. (2.18) of Ref. [26], neglecting the term proportional to light quark Collins [26]. 2 1 2 masses, and accounting for different conventions yields T¯ (0, Q ) 2.1 fm /Q . This 1 ⇥ Previous2 authors [17, 20] noted the sensitivity of the integrand of Eq. (5)2 to large values 1/Q behavior removes the putative logarithmic divergence of T¯1(0, Q ), but this func- of Q2. Our aim here is to more fully explore the uncertainty in the subtraction term tion is far from determined. 2 that arises from theArbitrary logarithmic divergence. functions We shall use a form of Floop(Q ) that is We follow the previous literature by including a form factor defined as Floop. Then consistent with the constraint on the Q4 term found Birse & McGovern [20]. This is done ⇥ by postulating a term that beginsT (0, atQ order2)=Q6MinQ Eq.2F (4),(Q such2) . as (4) 1 loop n Q2 1 Using Eqs. (2,3,4) one( finds2)= the energy shift to be + Floop Q 2 2 N , n 2, N n 3, (8) ⇤ M0 ⌅ (1 + aQ ) ⇤ ⇤ 2 2 ⇥ 2 subt ⇤ (0) ⇥M 2 1 2 2 4m 2 whereE M0=, a are parameters to2dQ be determined(1 2Q /(4 bym requiring)) 1 + that2 the1 computed+ 1 Floop contribu-(Q ). mT 1(0 ,Q0 ) ⇤ or faster⌦ ,QM ⇥ ⌅ 4 2 tion to the Lamb shift reproduce⇠ the desiredQ 0.31 meV. With Eq. (8)! the low Q behavior ⇧ ⌥ ⌃ (5) ¯ 2 6 4 2 of T1(0, Q ) is of order Q or greater and it falls as 1/Q or greater1 for large values of Q . subt 2 2 n 2 6 4 SoThe far issue as we here know,E is the there arbitrary3 are↵ nom nature constraintsS(0) of the on functionB the(N,n coefficientF)loop, (Q of) the. Pachucki2Q term [24] or the used 1/Q the ⇡ ↵ ! ⌘ M0 a term.dipole However, form, 1/ weQ shall4, often determine used to the characterize subtraction the term’s proton contribution electromagnetic to the form Lamb factors. shift ⇥ 3 parameters: n, N, a (M0 = M) asBut a general the subtraction functionChoose function of parametersn, N. We should note not thatsuch be⇥ M computedthatis anomalously shift fromin proton the small proton duemass formto a< cancellation factors, be- betweencause virtual pion component cloud andelectromagnetic intermediate scattering includes termsuncertainty a [30] term , so in thatwhich of 0.5 one the canMeV photon use a isvalue absorbed ten times and largeremitted than from appears the same in Eq. quark (7) [28]. to set Carlson the overall and Vanderhaeghen scale of the subtraction [17] evaluated term. a Thus loop we di- replaceagram using the term a specific⇥ of Eq. model (4) by and a foundgeneral a form form of factor the same1/Q dimensions2 log Q2, leading⇥: ⇥ to a⇥ larger. M ⇥ M ⌅ contributionThe use of to Eq. the (8) subtraction in Eq. (5) allows term than one previous to state the authors. expression Birse & for McGovern the energy [20] shift eval- in

5 4 2 Almost unknown T 1(0,Q ) Miller PLB 2012

2 2 subt ↵ 2 1 2 h(Q ) 2 Soft proton E = S(0) dQ 2 T 1(0,Q ) m 0 Q 2Z 2 2m 2 M 2 lim h(Q ) , chiral PT : T 1(0,Q )= Q + Q2 ⇠ Q2 ↵ ··· !1 Logarithmic divergence ! Typo bleow T (0,Q2) M Q2F (Q2) Cuts o↵integral 1 ! ↵ loop Birse & McGovern assumedipole : Esubt =0.004 meV very small Q2 n 1 Miller F (Q2)= ,n 2,N N +3 loop M 2 (1 + aQ2)N ✓ 0 ◆ Infinite parameter set gets needed 0.31meV, NO constraint on neutron Choose parameters so shift in proton mass <0.5 MeV (current uncertainty) Recast in EFT- parameters seem natural New 1 MeV scalar boson

• give μ-p Lamb shift • almost no hyperfine in μ proton • consistent with g-2 of μ • almost no effect for D, 4He • evade existing constraints • be found Form factors Unknown asymptotic region Floop 1.0 Miller 0.8

0.6 CPT 0.4

0.2 Birse McGovern Q2 GeV2 0.0 0.2 0.4 0.6 0.8 1.0 If recast into effective field theory strength seems natural I M µ =e 6 !

• Batell, McKeen, Pospelov PRL 107,081802 New force differentiates between lepton species. Models with gauged right-handed muon number, contain new vector and scalar force carriers at the 100 MeV scale or lighter. Such forces would lead to an enhancement by several orders-of-magnitude of the parity-violating asymmetries in the scattering of low-energy muons on nuclei. Related to muon g-2-- • Karshenboim, McKeen Pospelov arXiv:1401.6154 Hyperfine effects in muonium> “completely disfavoring the remainder of the parameter space, !

! No BSM idea solves puzzle at this time, ! but maybe

Three experiments at JLab

R. Essig

Muon data is g-2 - BNL exp’t, Hertzog- Kammel ... Decay modes 2 2 3/2 + ge m 4me ( e e)= 4⇡ 2 1 m2 ,m > 2me ! ⇣ ⌘ c⌧(m)

m(MeV) 2 3 2 ↵ m ( )=ge 3 2 ! 144⇡ me c⌧() + c⌧(m) c⌧(e e ) ?

m(MeV) ?

1

1 Vol 466 | 8 July 2010 | doi:10.1038/nature09250 LETTERS

The size of the proton

Randolf Pohl1, Aldo Antognini1, Franc¸oisNez2, Fernando D. Amaro3, Franc¸oisBiraben2, Joa˜o M. R. Cardoso3, Daniel S. Covita3,4, Andreas Dax5, Satish Dhawan5, Luis M. P. Fernandes3, Adolf Giesen6{, Thomas Graf6, Theodor W. Ha¨nsch1, Paul Indelicato2, Lucile Julien2, Cheng-Yang Kao7, Paul Knowles8, Eric-Olivier Le Bigot2, Yi-Wei Liu7, Jose´ A. M. Lopes3, Livia Ludhova8, Cristina M. B. Monteiro3, Franc¸oiseMulhauser8{, Tobias Nebel1, Paul Rabinowitz9, Joaquim M. F. dos Santos3, Lukas A. Schaller8, Karsten Schuhmann10, Catherine Schwob2, David Taqqu11, Joa˜o F. C. A. Veloso4 & Franz Kottmann12

The proton is the primary building block of the visible Universe, of the trailing digits of the given number). An H-independent but less but many of its properties—such as its charge radius and its anom- precise value of rp 5 0.897(18) fm was obtained in a recent reanalysis alous magnetic moment—are not well understood. The root-mean- of electron-scattering experiments1,2. square charge radius, rp, has been determined with an accuracy of 2 A much better determination of the proton radius is possible by per cent (at best) by electron–proton scattering experiments1,2. The measuring the Lamb shift in muonic hydrogen (mp, an atom formed 2 present most accurate value of rp (with an uncertainty of 1 per cent) by a proton, p, and a negative muon, m ). The muon is about 200 is given by the CODATA compilation of physical constants3. This times heavier than the electron. The atomic Bohr radius is corre- value is based mainly on precision spectroscopy of atomic spondingly about 200 times smaller in mp than in H. Effects of the hydrogen4–7 and calculations of bound-state quantum electrody- finite size of the proton on the muonic S states are thus enhanced. S namics (QED; refs 8, 9). The accuracy of rp as deduced from elec- states are shifted because the muon’s wavefunction at the location of tron–proton scattering limits the testing of bound-state QED in the proton is non-zero. In contrast, P states are not significantly F~1 F~2 ˜ atomic hydrogen as well as the determination of the Rydberg shifted. The total predicted 2S1=2 {2P3=2 energy difference, DE, constant (currently the most accurately measured fundamental in muonic hydrogen is the sum of radiative, recoil, and proton struc- physical constant3). An attractive means to improve the accuracy ture contributions, and the fine and hyperfine splittings for our par- ticular transition, and it is given8,11–15 by 2010in the measurementExperimental of rp is provided by muonic hydrogen summary (a proton orbited by a negative muon); its much smaller Bohr radius com- DEE~~209:9779 49 {5:2262 r2z0:0347 r3 meV 1 pared to ordinary atomic hydrogen causes enhancement of effects ðÞ p p ð Þ related to the finite size of the proton. In particular, the Lamb shift10 2 where rp~ r is given in fm. A detailed derivation of equation (the energy difference between the 2S1/2 and 2P1/2 states) is affected p rffiffiffiffiffiffiffiffiffiffi by as muchPulsed as 2 per cent. laser Here we spectroscopy use pulsed laser spectroscopy to (1) is given inDE Supplementary Information. measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of The first term in equation (1) is dominated by vacuum polariza- 11–15 present calculations of fine and hyperfine splittings and QED tion, which causes the 2S states to be more tightly bound than the 2P “ terms, we find rp 5 0.84184(67) fm, which differs by 5.0 standard states (Fig. 1). The mp fine and hyperfine splittings (due to spin–orbit 3 deviations from the CODATA value of 0.8768(69) fm. Our result and spin–spin interactions) are an order of magnitude smaller than implies that either the Rydberg constant has to be shifted by the Lamb shift (Fig. 1c). The uncertainty of 0.0049 meV in DE˜ is !2110 kHz/c (4.9 standard deviations), or the calculations of the dominatedJan. 2013, by 7 the st. proton dev polarizability term13 of 0.015(4) meV. QED effects in atomic hydrogen or muonic hydrogen atoms are The second and third terms in equation (1) are the finite size con- insufficient. ’’ Antoginitributions. -Sci. They amount339,417 to 1.8% of DE˜, two orders of magnitude ! Bound-state QED was initiated in 1947 when a subtle difference more than for H. between the binding energies of the 2S1/2 and 2P1/2 states of H atoms For more than forty years, a measurement of the mp Lamb shift has was established, denoted as the Lamb shift10. It is dominated by been considered one of the fundamental experiments in atomic spec- Rydbergpurely radiative is known effects8, such to as ‘self12 energy’figures and ‘vacuum polariza- troscopy, but only recent progress in muon beams and laser techno- • tion’. More recently, precision optical spectroscopy of H atoms4–7 logy made such an experiment feasible. We report the first successful and the corresponding calculations8,9 have improved tremendously measurement of the mp Lamb shift. The energy difference between the and reached a point where the proton size (expressed by its root- F~1 F~2 ! 2S1=2 and 2P3=2 states of mp atoms has been determined by means of mean-square charge radius, r ~ r2 ) is the limiting factor when pulsed laser spectroscopy at wavelengths around 6.01 mm. This p p transition was chosen because it gives the largest signal of all six rffiffiffiffiffiffiffiffiffiffi16 ! comparing experiment with theoryDE. allowed optical 2S–2P transitions. All transitions are spectrally well 3 The CODATA value of rp 5 0.8768(69) fm is extracted mainly separated. from H atom spectroscopy and thus relies on bound-state QED (here The experiment was performed at the pE5 beam-line of the proton • Puzzleand elsewhere- why numbers muon in parenthesis H different indicate the 1than s.d. uncertainty e H? accelerator at the (PSI) in Switzerland. We 1Max-Planck-Institut fu¨r Quantenoptik, 85748 Garching, Germany. 2Laboratoire Kastler Brossel, E´cole Normale Supe´rieure, CNRS, and Universite´ P. et M. Curie-Paris 6, 75252 Paris, Cedex 05, France. 3Departamento de Fı´sica, Universidade de Coimbra, 3004-516 Coimbra, Portugal. 4I3N, Departamento de Fı´sica, Universidade de Aveiro, 3810-193 Aveiro, Portugal. 5Physics Department, Yale University, New Haven, Connecticut 06520-8121, USA. 6Institut fu¨r Strahlwerkzeuge, Universita¨t Stuttgart, 70569 Stuttgart, Germany. 7Physics Department, National Tsing Hua University, Hsinchu 300, Taiwan. 8De´partement de Physique, Universite´ de Fribourg, 1700 Fribourg, Switzerland. 9Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009, USA. 10Dausinger & Giesen GmbH, Rotebu¨hlstr. 87, 70178 Stuttgart, Germany. 11Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland. 12Institut fu¨r Teilchenphysik, ETH Zu¨rich, 8093 Zu¨rich, Switzerland. {Present addresses: Deutsches Zentrum fu¨r Luft- und Raumfahrt e.V. in der Helmholtz-Gemeinschaft, 70569 Stuttgart, Germany (A.G.); International Atomic Energy Agency, A-1400 Vienna, Austria (F.M.). 213 ©2010 Macmillan Publishers Limited. All rights reserved !"#$%&'$()*+,-.$/+0$1"#$23&$"/4#$#+0)56#0$1"#$#61/7.-6"8#+1$)9$1"#$$ $$$ !"#$%&'(")*+%,*'-#./"'.&'01,2"%#'-*3).,)''

Purpose: To recognize and encourage outstanding research in theoretical . The prize will consist of $10,000 and a certificate citing the contributions made by the recipient. The prize will be presented biannually or annually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http://www.aps.org/ Look for the support banner and click APS member (membership number needed) and look down the list of causes. $ $ D9$=)*$"/4#$/+=$S*#61-)+6A$?.#/6#$,)+1/,1$R>$%>$TJ#55=U$C-..#5$IVA$W8-..#5X*<>#0*Y>$$ $ $ If annual- number of experimentalists winning Bonner prize goes up by >50%

$ What theorists do

• make up new particles- compute shift • study constraints - • non-observation of new particles that couple mainly to muons

Constraints are obtained from the decay of the Υ resonances; neutron interactions with nuclei; the anomalous magnetic moment of the muon x-ray transitions in 24Mg and 28Mg, Si atoms; J/Ψ decay; neutral pion decay Any time a photon appears can also eta decay have a diagram with heavy photon doi: 10.1038/nature09250 SUPPLEMENTARY INFORMATION Pohl et al. Table of calculations

?  ** # "0"* %(.*5L7  *"9 )"$M 10" /M 10" /M 10" /M 5 !) #" 0 "0"  1% 5I 6 64944<8 6 )"0***  "* D "" E 5L7I 9 445;> 7 )"0*** " 0 1% 9 64946=6 64946=6 Lamb 8 !) K0 "0"  1% 9I 58 594=5 594<> 594=5 9 %0 * * *" * *  02 0*" 5I 6I 9 4594> 4594> 45954 ; !) ( ""K0 "0"  1% 55 44496> < %0 ** *" * *  55I 56 444667 shift:  ( "" 02 0*" D "" E = -( ""K0 1% D0I  "" E 444<; 444<;5 > 3*(2K 00 9I 59I 5; 444547 444547   54 *&(  0*&( "0"  0  ** ; 444579 4M44579 444579 4M44459 vacuum D1* 0 "0 .G " *&E 55 ) **" (  "0"  0 * * 5I 6 444944 4M4454 444; 4M445 4449    * (" 02 0*" 6DE8 56 0"  0 * ("  **" ( 5 444594 Resolution 1-  polarization $  " 6DE8 57 *" "0"   2 0 64 44444< 44444< 8 65L67 58  * 0 * * DE  4454<< 4M4447= 44557 4M4447 4455 4M446 9 66I 67 59  * 0 * * DE  444448< QED calcs not OK 5;  * 0 * * * ("  **" 66I 67 4444459 many, many  6 8 (  DE  5< )"*0  ** 68 449<94 449<9 449<9 5= )"*0 H*" * " 9 445744 4M445 4457 4M445 5> )"*0  "*  1% 9 444854 44485 terms   6I <   64 ) **"  "* $  "  DE  4;;<<4 4;;<< 4;;<== QED calcs    65  2 (*$ 8(  " 9 4445;> 4445;> 9  6I 9L<   66 )"*0  "* $  " DE  4488>< 4489 4488><     67 )"*0 $  " ; 6 444474 44447 68 ) **" "*0  "* $ 5I 6I < 444>;4 444>> 444>; expand in ↵       " DE   69 !0"   "  "* $  " DE9 6I 9I 66I 69 4459 4M448 4456 4M446 4459 4M448 D%  0 * *0*  **E Mostly 67 6; %0 * * "  * "  "* 44445> 9  0" 0 * *0* DE  6< ) **" ( * "  "* 67 444445 9   0" 0 * *0* DE  irrelevant- +2 64;49<7 4M4489 64;4876 4M4467 64;49=9; 4M448;

-0" 5@ 00 .  *K     **  (" 2 (*$ *  $ 2 *" " ( I  theory (" " " "0"" M 3" $00 (" 2"0 " $ * "   < -0" <89    95><8 95><5 6I 6;  6   ) **"  "*  0" H*" * " "" 446<9    446=6 446<7 experiment ; 6 5I 6  6   !0" * "  "* $  " DE    4445687    6  6 -0     ** 966;5>    9669; 96688 9 5I 6  7   !0" * "  "* $  " DE 4478<    447;7 4478<

-0" 6@ 00 "0"  *K     **  22 * " * * " " 0M

7

www.nature.com/nature 3 I. INTRODUCTION

The proton radius puzzle is one of the most perplexing physics issues of recent times. The extremely precise extraction of the proton radius [1] from the measured energy dif- F=2 F=1 ference between the 2P3/2 and 2S1/2 states of muonic hydrogen disagrees with that ex- tracted from electronicwhere hydrogen.nmin is The chosen extracted to be value one order of the higher proton than radius the is power smaller determined than by chiral per- the CODATA [2] valueturbation (based theory. mainly on The electronic free parameters H) by aboutan, cn 4%, M orn could 5.0 standard then be devi- varied to reproduce the ations. This implies [1]desired that either 0.31 meV the Rydberg shift in energy. constant This has means to be shifted that the by application 4.9 standard of chiral perturbation deviations or that presenttheory QED to any calculations finite order for does hydrogen not prevent are insufficient. the choice of The a subtraction Rydberg function that gives constant is extremelythe well necessary measured shift and in the energy. QED calculations seem to be very extensive and highly accurate, soThe the muonic above paragraphs H finding is show a significant that the current puzzle forprocedure the entire used physics to estimate the size of the community. subtraction term is rather arbitrary. This arises because the chiral EFT is being applied F=2 F=1 Pohl et al. show thatto the the virtual-photon energy difference nucleon between scattering the 2P3/2 amplitude.and 2S1/2 Anotherstates, effectiveDE is field theory tech- given by nique would be to develop an procedure to determine the short-distancee lepton-nucleon amplitude implied by the subtraction term. This is the direction we pursue now. DE = 209.9779(49) 5.2262r2 + 0.0347r3 meV, (1) p p where r is given ine units of fm. Using this equation, one can see that the difference p III. FOR THE µp INTERACTION between the Pohl and CODATA values of the proton radius would be removed by an increase of the first termThe on previous the rhs of considerations Eq. (1) by 0.31 show meV=3.1 the sensitivity10 10 MeV. to assumptions regarding the behav- ⇥ 2 2 This proton radiusior puzzle of T1(0, hasQ been) for attackedlarge values fromQ manyabout different which little directions or nothing [3]-[21] is known. This results

The present communicationform the is logarithmic intended to divergence investigate in the the hypothesis integral of that Eq. the (5) proton for the po- case Floop = 1, and is a larizability contributions,symptom that that enter an in inefficient the two-photon technique exchange has been term, used see [27]. Fig. A more1, can efficient way to pro- Caswell Lepage ’86 account for the 0.31 meV.ceed would This idea be us is worthyEFT to use an of of effective considerationµp interaction field theory because (EFT) the computed for the lepton-proton ef- interaction. fect is proportionalIn to EFT the lepton logarithmic• massCompute divergences to the fourth Feynman identified power, diagram, and through so is dimensional capableremove of log being regularization are renor- relevant for muonicmalized atoms, but away irrelevant by includingdivergence for electronic a lepton-proton using atoms. dimensional contact interaction regularization in the Lagrangian. We may handle• include the divergence counter using term standard in Lagrangian dimensional regularization (DR) tech- niques by evaluating the scattering amplitude of Fig. 1. The term of interest is obtained by includingq only T (0, Q2) of Eq. (3)q with F = 1. We evaluate the integral in d = 4 e 1 loop dimensions and obtain the result: relevant data is the 0.31 meV needed to account for the proton radius puzzle. Thus we 3 b 2 µ2 5 DR = i a2m M + log + g + log 4p u u U U , (13) FIG. 1: Thewrite box the diagram resulting for the scattering(a5m2 4 amplitude) corrections. as The graph in2 which theE photons crossf isi f i O M 2 a e m 6 also included. b ⇥ ⇤ where lower caseDR spinors= i a2m representM (l + 5/4 leptons) u u ofU massU m, and upper case proton(14) of mass M, M2 a f i f i q is momentum transferred to the proton, and g is Euler’s constant, 0.577216 . E ··· where l is determinedThe resultChoose by fittingEq. (13) to2 corresponds the Lambto get shift. to 0.31 The an infiniteµ dependence meV contribution shift of the to counter the Lamb term shift in the is chosen solimit that that the resulte goes is to independent zero. In EFT of oneµ. Eq. removes (14) corresponds the divergent to piece using by the addingMS a contact scheme because the term log(4p) g is absorbed into l. interaction to the Lagrangian E that removes the divergence, replacing it by an unknown The correspondingfinite part. contribution The finite part to the is obtained Lamb shift by fitting is given to by a relevant piece of data. Here the only b DEDR = a2m M f2(0)(l + 5/4). (15) a 6

Setting DEDR to 0.31 meV in the above equation requires that l = 769 which seems like a large number. However bM is extraordinarily small. The natural units of polarizability are bM 4p/L3 , [28] where L 4p f ,(f is the pion decay constant). Then Eq. (14) a ⇠ c c ⌘ p p becomes

DR 2 4p 2 = i 3.84 a m 3 u f uiU f Ui. (16) M Lc

The coefficient 3.84 is of natural size. Thus standard EFT techniques result in an effective lepton-proton interaction of natural size that is proportional to the lepton mass. The present results, Eq. (11) and Eq. (15) represent an assumption that there is a lepton- proton interaction of standard-model origin, caused by the high-momentum behavior of the virtual scattering amplitude, that is sufficiently large to account for the proton radius puzzle. Fortunately, our hypothesis can be tested in an upcoming low-energy µ± p, e± p scattering experiment [22] planned to occur at PSI.

IV. LEPTON PROTON SCATTERING AT LOW ENERGIES

Our aim is to provide a prediction for the PSI experiment. It is well-known that two- photon exchange effects in electron-proton scattering are small at low energies. Our con- tact interaction is proportional to the lepton mass, so it could provide a measurable effect for muon-proton scattering but be ignorable for electron-proton scattering. We shall in- vestigate the two consequences of using form factors (FF) and EFT.

7 contact interaction to the Lagrangian that removes the divergence, replacing it by an unknown finite part. The finite part is obtained by fitting to a relevant piece of data. Here the only relevant data is the 0.31 meV needed to account for the proton radius puzzle. The low energy term contributes

DR(LET)=iC(µ), (14) M2 where C(µ) is chosen such that the sum of the terms of Eq. (13) and Eq. (14), DR, is ⌘ M2 finite and independent of the value of µ. Thus we write the resulting scattering amplitude as

b DR = i a2m M (l + 5/4) u u U U (15) M2 a f i f i where l is determined by fitting to the Lamb shift. Eq. (15) corresponds to using the MS scheme because the term log(4p) g is absorbed into l. E The corresponding contributionsubt to the Lamb shift2 is givenM by2 E (DR)=↵ m S(0)( +5/4) b DEDR = a2m M f2(0)(l + 5/4↵). (16) Esubt(DR)=0a .31 meV = 769 Setting DEDR to 0.31 meV in the above equation requires that!l = 769 which seems like a large number. However, bM is extraordinarily small due to a4 cancellation3 between M (magnetic polarizability) = 3.1 10 fm very small paramagnetic effects of an intermediate D and diamagnetic effects⇥ of the pion cloud [30]. 3 Natural units MbM/↵ 4⇡/3(4⇡f⇡) Butler & Savage 092 The natural units of polarizability are ⇠4p/L , [31] where Lc 4p fp,(fp is the a ⇠ c ⌘ pion decay constant). Then Eq. (15) becomes

DR 2 4p 2 = i 3.95 a m 3 u f uiU f Ui. (17) M Lc

The coefficient 3.95 is of natural size.3.95 Thus =natural standard EFT techniques result in an effective lepton-proton interaction of natural size that is proportional to the lepton mass. The present results, Eq. (11) and Eq. (16) represent an assumption that there is a lepton- proton interaction of standard-model origin, caused by the high-momentum behavior of the virtual scattering amplitude, that is sufficiently large to account for the proton radius puzzle. Fortunately, our hypothesis can be tested in an upcoming low-energy µ± p, e± p scattering experiment [23] planned to occur at PSI.

7 Summary of D

• If there is no new Lamb shift effect on the neutron, muon hydrogen and muon deuterium are consistent • Moreover, an electronic experiment is consistent with muonic experiments. • If there is an effect on the neutron, a puzzle remains