The Proton Polarizability Contribution: Lamb Shift and Elastic Scattering

Transcription

1 The Proton Polarizability Contribution: Lamb Shift and Elastic Scattering Gerald A. Miller, University of Washington It is Thursday 11 am, so and you all know what the proton radius puzzle is The Lamb shift measurement of muonic hydrogen gives a different proton radius than that of electronic hydrogen.

2 Pohl s Table of calculations Lamb shift: vacuum polarization many, many terms proportional to lepton mass 4

3 muon electron Lamb shift?

4 Possible resolutions Electron- H experiments not so accurate (Pohl) Muon interacts differently than electron Strong interaction effect in two photon exchange diagram for muon only ( ) If correct, most electronic scattering and H-atom results can stand

5 Analysis Extract the proton radius from the transition energy, compare measured ξ to the following sum of contributions: ξ= (32) mev -One measured number ξ = (45) r 2 p r3 p mev three computed numbers To explain puzzle: increase mev by 0.31 mev= MeV

6 Our idea l l k l lepton P P proton lepton propagator provides term so that energy shift is proportional to lepton mass 4

7 The Controversy- our effect is 20 times that of Pachucki, Martynenko... Carlson & Vanderhaeghan Conventional approach Pachucki l l k l E α 5 m 3 R d 4 q q 4 T µν l µν (m) T µν is forward virtual-photon proton scattering amplitude, l µν (m) is lepton-tensor T µν (q, P )= i R d 4 xe iq x P T (j µ (x)j ν (0) P P +crossed photons P T µν (q, P )= (g µν )T 1 +(P µ )(P ν )T 2 Im(T 1,2 ) W 1,2 Measured structure functions Cauchy plus data answers rock solid (?) T 1,2 (q P/M, q 2 )=T 1,2 (q 0,Q 2 )

8 T 1,2 (q P/M, q 2 )=T 1,2 (q 0,Q 2 ) ImT 1,2 W 1,2 q 0 ν W 2 1/ν, W 1 ν large ν Dispersion integral involving W2 converges Dispersion integral involving W1 diverges- subtraction needed at all Q 2 Hill & Paz 2011 : dispersion approach uncertainty order of mag larger than stated

9 Features need subtracted dispersion relation for T1 subtraction function (q 0 = 0, all q 2 ) mainly unknown T 1 (0,Q 2 ) asymptotic ~1/Q 2 so we tried EFT power series in Q off-shell effects 2 1. Miller, Carroll, Thomas, Rafelski Phys.Rev. A84 (2011) Disagrees with existing constraints- Carlson/VDH 2. Miller, Carroll, Thomas better offshell, but ruled out by (e,e p) nuclear reactions two strikes- swing and misses

10 Alternate: unknown T 1 (0,Q 2 ) E subt = α2 m Ψ2 S(0) 0 dq 2 Q 2 h(q2 )T 1 (0,Q 2 ) lim Q 2 h(q2 ) 2m2 Q 2, chiral PT : T 1(0,Q 2 )= β M α Q2 + Logarithmic divergence T 1 (0,Q 2 ) β M α Q2 F loop (Q 2 ) Cuts off integral Birse & McGovern : T 1 (0,Q 2 )= β M α Q2 (1 Q2 M 2 β β M α Q2 1 (1 + Q2 2M 2 β ) 2 M β = 460 ± 50 MeV, E subt =4.1µ ev very small High Q 2 behavior is ASSUMED Miller PLB O(Q 4 ))

11 Arbitrary functions T 1 (0, Q 2 )= β M α Q2 F loop (Q 2 ). ( ) n F ds the energy shift to be loop (Q 2 Q )= 2 1 M 0 2 (1 + aq 2, n 2, N n + 3, ) N T 1 (0,Q 2 ) 1 Q 4 or faster, β M β E subt 3α 2 mφ 2 (0) β α γn B(N, n), γ 1 M 2 0 a. If we take N = 5, n = 2 so that B(5, 2) =1/12, and β = 10 3 fm 3, a value of γ = 30.9 reproduces E = 0.31 mev. If we take M 0 = 0.5 GeV (as in [20]), then a 1 = 15.4 GeV 2, and that the contribution to the integral comes from the region of very high values of Q 2.

12 Another example n=23,n=26, 1/a=0.44 GeV 2 F loop Q2 GeV 2

13 EFT of µp interaction Compute Feynman diagram, remove log divergence using dimensional regularization include counter term in Lagrangian Caswell Lepage 86 q q M2 DR = 3 2 i α2 m β M [2 α ɛ + log µ2 m γ E + log 4π ] u f u i U f U i, = i α 2 m β M α (λ + 5/4) u f u i U f U i Choose λ to get 0.31 mev shift

14 E DR = α 2 m β M α φ2 (0)(λ + 5/4). ev in E the DR above =0.31 mev equation λ = requires 769 th λ seems large but β M (mag. polarizability) = fm 3 very small Natural units β M /α 4π/(4πf π ) 3 Butler & Savage 92 M2 DR = i 3.95 α 2 m 4π Λ 3 u f u i U f U i. χ 3.95 =natural

15 So what? A Proposal for the Paul Scherrer Institute πm1 beam line Studying the Proton Radius Puzzle with µp Elastic 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. Weinstein 18 PSI proposal R photon exchange idea is testable

16 muon scattering M = M (1) + M (2) + Is contact interaction too large??

17 Observable Effect in µ p Scattering R R =2 Re[(M(1) ) M (2) ] M (1) ] 2 Form Factor 200 MeV/c 100 MeV/c R EFT Dim Reg Θ cm Θ cm Definitive test -two theories same effect in scattering

18 Deuteron radius from µd and µp (preliminary) H-D isot.-shift: rd 2 r2 p = (65) fm 2 µp : r p = (39) fm r d = (22) fm Directly from µd spectroscopy using predictions of polarizabiliy with mev uncertainty µd Borie+Pachucki+Ji+Friar µd Borie+Ji µd Borie+Pachucki µd Martynenko µp + iso(1s-2s) PRELIMINARY CODATA-2010 CODATA D + e-d e-d scatt. n-p scatt Deuteron charge radius [fm] A. Antognini ECT, Trento p. 22

19 Deuteron as a test Need polarizability effect on neutron two versions of the hypothesis form factor and EFT form factor- effect on neutron= effect on proton, otherwise n-p mass different becomes gigantic, then in Deuteron the TPE contribution to the Lamb shift effect is doubled -Aldo TPE contribution about the same EFT- the unknown short distance mu-n interaction needs an unknown interaction constant, can t predict Deuteron

20 Deuteron radius from µd and µp (preliminary) H-D isot.-shift: rd 2 r2 p = (65) fm 2 µp : r p = (39) fm r d = (22) fm Directly from µd spectroscopy using predictions of polarizabiliy with mev uncertainty µd Borie+Pachucki+Ji+Friar µd Borie+Ji µd Borie+Pachucki µd Martynenko µp + iso(1s-2s) Width allows ~1/2 the effect for FF PRELIMINARY CODATA-2010 CODATA D + e-d e-d scatt. n-p scatt Deuteron charge radius [fm] A. Antognini ECT, Trento p. 22

21 Summary Integrand for subtraction term log diverges Subtraction function needed Flexibility in subtraction function may resolve puzzle FF, EFT version of subtraction function resolve puzzle TESTS NEEDED mu p- scattering ~5% effect in mu p scattering FF, EFT mu D- FF reduced by a factor of 2, EFT not changed

22 spares follow

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24 Experiment: Basic idea The Experiment Muonic Hydrogen 2P 1/2 E 2S 2P Lamb 2S 1/2 2S 1/2, 2P 1/2 states are degenerate Schroedinger, Dirac eqns. The Lamb shift is the splitting of the degenerate 2S 1/2 and 2P 1/2 eigenstates, due to vacuum polarization Dominant in μh 205 of 206 mev ( ) Dominant in eh E = ψ S V C ψ S = 2 3 πα ψ S(0) 2 r 2 p lepton mass 3

25 The experiment: results disagree with previous measurements & world average 7 CODATA-06 Our value The 1S-2S transition in H has been measured to 34 Hz, that is, relative accuracy. Only an error of about 1,700 times the quoted experimental uncertainty could account for our observed discrepancy. 6 e p scattering Delayed / prompt events (10 4 ) H 2 O calibration Laser frequency (THz) Rock Solid!

26 Experimental summary Pulsed laser spectroscopy measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find r p (67) fm, which differs by 5.0 standard deviations from the CODATA value 3 of (69) fm. Our result implies that either the Rydberg constant has to be shifted by 2110 khz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient. Rydberg is known to 12 figures Puzzle- why muon H different than e H?

27 Electronic Hydrogen -Pohl 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 µp : fm 1S-2S + 1S - 3S 1/2 2 measurements get r p,r proton charge radius (fm)

28 µ e Marciano, INT Talk summer 2010-massive photon, violate mu-e universality, matter effects in neutrino oscillations too big by Barger et al We consider exotic particles that couple preferentially to muons, and mediate an attractive nucleon-muon interaction. Many constraints from low energy data disfavor new spin-0, spin-1 and spin-2 particles as an explanation.prl 106, Brax, Burrage Combining these constraints with current particle physics bounds, the contribution of a scalar field to the recently claimed discrepancy in the proton radius is negligible. Phys.Rev.D83:035020,2011 Batell, McKeen, Pospelov PRL 107, 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-ofmagnitude of the parity-violating asymmetries in the scattering of low-energy muons on nuclei. Related to muon g-2 Barger et al, PRL108, , previous BMP model is constrained by K decays if new particles are long lived Carlson, Rislow, arxiv: Conclusions: New physics with fine tuned couplings may be entertained as a possible explanation for the Lamb shift discrepancy.

29 Form factor with QCD limit at high Q 2 F loop (Q 2 )= Q4 M 4 G 1 (1+a Q 2 ) 3 Prompted by Hill & Paz 1/a 100GeV 2 Lamb shift and scattering results not changed