Proton radius puzzle

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1 Proton radius puzzle Krzysztof Pachucki Universiy of Warsaw Frascati, December 21, 2016

2 Measurements of atomic spectra Measurement of transition frequencies can be very accurate [Garching, 2013] ν(1s 2S) H = (10) Hz sensitive to the nuclear size and the nuclear polarizability from ν(1s 2S) H D : rd 2 r P 2 = (65) fm2 determination of fundamental constants Another example: electron mass from the g-factor measurement in hydrogen-like C, [Sturm, et al, Nature 2014] m e = (14)(9)(2) au

3 Proton charge radius puzzle global fit to H and D spectrum: r p = (77) fm (CODATA 2010) e p scattering: r p = (79) (Bernauer, 2010) from muonic hydrogen: r p = (39) fm (PSI, 2010, 2012) If all these measurements and Lamb shift calculations are correct, this discrepancy does not find explanation within the known description of electroweak and strong interactions Potential to discover new physics...

4 The proton radius puzzle The proton rms charge radius measured with electrons: muons: ± fm ± fm 6.7 σ CODATA-2010 µ p 2013 electron avg. scatt. JLab µp 2010 scatt. Mainz H spectroscopy Proton charge radius R [fm] ch RP, Gilman, Miller, Pachucki, Annu. Rev. Nucl. Part. Sci. 63, 175 (2013). Randolf Pohl HC2NP, Tenerife, 30 Sept

5 Proton charge radius puzzle δ fs E = 2 π α 3 φ 2 (0) r 2 ch this formula is universal for all light atoms the energy shift is proportional to the mean square charge radius r 2 ch two-photon exchange O(Z α r ch / λ), pretty small nuclear polarizability effects are in general quite small, significant only for muonic atoms how come r p from (electronic) H differs by 4% from that of µh?

6 Proton charge radius puzzle The only solution which does not violate SM is the assumption that the hydrogen spectroscopy and e-p scattering measurements, although in agreements, are both incorrect How it can be verified? muon-proton scattering: MUSE project (PSI) low Q 2 e-proton scattering: PRad (Jefferson lab) µhe: CREMA collaboration (rhe 2 from e-α scattering) rhe 2 from spectroscopy of He: 23 S 2 3 P (Warsaw) H-spectroscopy: 2S-4P (Garching), 2S-3S (Paris) He + (1S 2S) (Amsterdam, Garching) Let us say few words about µh theory, why is it so reliable.

7 energy levels of µh in comparison to H

8 energy levels of µh

9 µh energy levels µh is essentially a nonrelativistic atomic system muon and proton are treated on the same footing m µ /m e = β = m e /(µ α) = the ratio of the Bohr radius to the electron Compton wavelength the electron vacuum polarization dominates the Lamb shift in muonic hydrogen

10 Theory of µh energy levels nonrelativistic Hamiltonian H 0 = p2 2 m µ + p2 2 m p α r mr α2 and the nonrelativistic energy E 0 = 2 n 2 the evp dominates the Lamb shift E L = 2P V vp (r) 2P 2S V vp (r) 2S = mev complete result but without finite size = (5) mev important corrections: second order, two-loop vacuum polarization, and the muon self-energy other corrections are much smaller than the discrepancy of 0.3 mev, while finite nuclear size is 3.9 mev.

11 Leading relativistic correction Breit-Pauli Hamiltonian H BP = p4 p4 8 mµ 3 8 mp π α 3 ( α p i δ ij 2 m µ m p r ( r 2 p mµ mp 2 ) δ 3 (r) + r i r j ) r 3 p j + 2 π α g µ g p s µ s p δ 3 i α sµ (r) g µ g sj p p (δ ij 3 m µ m p 4 m µ m p r 3 3 r i r j ) r 2 + α [ ( ) ( )] gµ (gµ 1) gp (gp 1) r p s 2 r 3 µ + m µ m p mµ 2 + s p + m µ m p mp 2, δ rel E L = 2P 1/2 H BP 2P 1/2 2S 1/2 H BP 2S 1/2 = α 4 m 3 r 48 m 2 p = mev valid for an arbitrary mass ratio quite small and higher order relativistic corrections are negligible

12 Important corrections second order V vp : δe L = mev two-loop vp: δe L = mev three-loop vp: δe L = mev hadronic vp: δe L = (4) mev muon self-energy and muon vp: δe L = mev

13 Small corrections relativistic correction to vp δ vp,rel E L = δ vp H BP + 2 V vp 1 (E H) H BP = mev. If one used the Dirac equation in the infinite nuclear mass limit, the obtained result would be mev muon self-energy combined with evp: δe L = mev light by light diagrams δe L = mev proton (electromagnetic) self-energy

14 Proton self-energy The proton self energy leads to the modification of elastic form factors in such a way that they depend on a fictitious photon mass one takes the simplest possible point of view and use the formula for the low energy part of the proton self-energy δe = 4 m3 r (Z 2 α) (Z α) 4 3 π n 3 mp 2 = mev. ( ( δ l0 ln m p m r (Z α) 2 ) ) ln k 0 (n, l). the high energy part of the Lamb shift is by definition included in the charge radius and the magnetic moment anomaly how this definition corresponds to r p from the electron scattering?

15 Nuclear structure effects if nuclear excitation energy is much larger than the atomic energy, the two-photon exchange scattering amplitude gives the dominating correction the total proton structure contribution δe L = (20) mev is much too small to explain the discrepancy, but its calculation is uncertain [Carlson, Vanderhaeghen, 2011; Pascalutsa et al, 2013]

16 Summary of theoretical predictions E LS = (15) (10) r 2 p + E TPE E FS = mev E 2S 1/2 HFS = (51) mev, (exp. value) E 2P 1/2 HFS = mev E 2P 3/2 HFS = mev = mev E TPE = (20) mev

17 Does e p scatt. and µh measure the same r p? G E ( Q 2 ) = 1 r 2 6 Q 2 + O(Q 4 ) Low energy Hamiltonian with EM field ( R δh = e A 0 2 e 6 + δ ) I M E 2 e 2 Q (Ii I j ) (2) j E i µ B for a scalar particle δ 0 = 0 for a half-spin particle δ 1/2 = 1/8 difference appears at the level of proton self-energy corrections

18 Possible sources of r p puzzle: theory mistake in e H calculations: all corrections calculated independently by at least two groups, uncertainty in the two-loop correction enters at 1 khz level for 1S state, but this discrepancy corresponds to 100 khz mistake in µ H: QED theory is quite simple, dominated by nonrelativistic vacuum polarization, everything checked and verified large Zemach moment (r (2) p ) 3 ruled out by the low energy electron-proton scattering [Friar, Sick, 2005], [Cloët, Miller, 2010], [Distler, Bernauer, Walcher, 2010]

19 Possible sources of r p puzzle: theory underestimation of proton structure correction? many doubts in the literature, but all different calculations lead to similar value, Estimated value is 10 times smaller than the dicrepancy possible new light particles? ruled out by muon g 2 and other low energy Standard Model tests: Barger et al., Phys. Rev. Lett. 106, (2011), 108, (2012) violation of the universality in the lepton-proton interaction of different origin

20 New interactions If discrepancy in r p is to be explained by a new type of interaction between the proton (neutron) and leptons, than we have two options long range λ e, short range 1fm (or shorter), can be seen in µp scatt. Comparison of nuclear charge radii for H,D, 3 He and 4 He will give hints on the range of new interactions If it is local, than discrepancy for all these elements can be parametrized by δe = (Z δr 2 p + (A Z ) δr 2 n ) 2 δ l0 3 n 3 Z 3 α 4 µ 3 Determination of r N from muonic atoms spectra requires an accurate calculation of the nuclear polarizability correction, not necessarily easy task

21 Possible sources of the proton radius discrepancy: experiment the determination of r p from e p scattering data requires extrapolation to q 2 = 0, subject of systematic uncertainties and model dependence, there is an intensive discussion in the literature with contradicting results Horbatsch, at al., arxiv: Bernauer et al, arxiv: Arrington, arxiv: Arrington, Sick, arxiv: Kraus et al., arxiv: Griffioen, et al, Phys. Rev. C 93, (2016) Lorenz, et al, arxiv: S ns, D measurements (mostly from one laboratory, LKB Paris), not confirmed by independent and equally accurate measurements. Highly excited states of H are affected by various systematics. As a result the Rydberg constant might be not as accurate as claimed

22 Experimental results for hydrogen 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 H avg = fm µp : fm proton charge radius (fm)

23 New hydrogen 2S 4P at MPQ! PRELIMINARY! 2S 1/2-2P 1/2 2S 1/2-2P 1/2 2S 1/2-2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 H avg = fm µp : fm proton charge radius (fm) 2S 4P 1/2 and 4P 3/2 cold H(2S) beam optically excited (1S 2S) Δν 2 khz Γ/10 000!!! Beyer, Maisenbacher, Matveev, RP, Khabarova, Grinin, Lamour, Yost, Hänsch, Kolachevsky, Udem, submitted (2016) Randolf Pohl HC2NP, Tenerife, 30 Sept

24 Ongoing experimental tests determine Ry by another accurate measurement in 1S-2S in He + 1S-3S (Paris,... ) transitions between Rydberg states of heavy H-like ions (NIST, N.D. Guise talk) determine r p low Q 2 e-p scattering (PRad) 2S 2P in H (Hessels) µ p elastic scattering (MUSE collaboration) compare charge radii from electronic and muonic spectra of other atomic systems µd data just published, r D from very accurate H-D isotope shift (Garching) µhe, r He charge radius from scattering or 2 3 S 2 3 P transition in He,

25 Deuteron charge radius H/D isotope shift: r 2 d r2 p = (65) fm 2 C.G. Parthey, RP et al., PRL 104, (2010) CODATA 2010 r d = (210) fm r p from µh gives r d = ( 22) fm 7σ from r p Muonic DEUTERIUM r d = ( 13) exp (77) theo fm RP et al., Science 353, 417 (2016) µd µh + iso H/D(1S-2S) e-d scatt. (7σ from µh) CODATA Deuteron charge radius [fm] Randolf Pohl HC2NP, Tenerife, 30 Sept

26 1st resonance in muonic He-4 µ 4 He(2S 1/2 2P 3/2 ) at 813 nm wavelength Events / Prompt e He scattering Preliminary Frequency [THz] Sick, PRD 77, (R) (2008) Borie, Ann. Phys. 327, 733 (2012) Randolf Pohl HC2NP, Tenerife, 30 Sept

27 α charge radius from He 2 3 S 2 3 P E(2 3 S 2 3 P, 4 He) centroid = (2.1) khz, Florence, 2004 finite size effect: E fs = khz since E fs is proportional to r 2 r r = 1 2 δe fs E fs = electron scattering gives r He = 1.681(4) fm, what corresponds to about relative accuracy 10 khz accuracy requires calculation of m α 7 correction

28 2 3 S 2 3 P transition in 4 He in MHz (m/m) 0 (m/m) 1 (m/m) 2 Sum α α α α α (1.0) 8.0(1.0) FNS NPOL Theory (1.00) Exp (2)