A. L’vov @ EMIN, 07 Oct, 2015

1. Polarizabilities of nucleons from new data on proton and deuteron Compton scatteringM.I. Levchuk (Minsk), A.I. L’vov (LPI) This not a review of recent or ongoing remarkable experiments on studying RCS and polarizabilities. This is rather a comment on theoretical interpretations of the obtained data and warning on some problems and uncertainties. Part 1. Polarizabilities of the proton from low-energy proton Compton scattering Part 2. Polarizabilities of the neutron from low-energy deuteron Compton scattering (elastic) A. L’vov @ EMIN, 07 Oct, 2015

2. Electromagnetic form factors of nucleons: indicate a space distribution of charge and magnetization in the particles, their size. Schematically, Electromagnetic polarizabilities show a rigidity, the ability of objects to get deformed in external EM fields. Their values is interplay of both the size and the excitation spectrum. Schematically, What is the motivation to know polarizabilities better?

3. 1) Polarizabilities (and, more generally, Compton scattering amplitudes) = convenient matching points for testing and improving Effective Field Theories (such as ChPT) which are now widely used in low-energy nuclear and particle physics as dynamical models for description of strong and electromagnetic N, A, NN, NNN, , N, A … interactions, weak interactions, for extrapolation of lattice QCD predictions, and so on. • There are several predictions of the EFT for the polarizabilities which are waiting for experimental tests. • New experimental possibilities recently appeared for doing single and double polarization experiments and to measuring polarizabilities of higher order (including spin polarizabilities).

4. 2) Physics of two-photon exchanges: polarizabilities come to play. • Examples: • a) Atomic measurements (Lamb shift): • proton radius using electrons 0.8775(51) fm • proton radius using muons 0.84087(39) fm • The difference = 7. • Is it partly related with different response of polarizable proton • to EM field of the lepton? • b) Mass difference of p and n. • Determination of polarizabilities of higher order (including spin polarizabilities) needs a good knowledge of dipole electric and magnetic polarizabilities.

5. Amplitude of low-energy Compton scattering: Said differently: effective interaction of the second order in the E.M. field is Differential cross section of low-energy Compton scattering: How are polarizabilities measured?

6. Determination of polarizabilities from low-energy data and low-energy theorems. Nonlinear effects in ’ beyond  and  are important to fit data above 100 MeV and to determine the slope at =0 (polarizabilities).

7. Baldin sum rule Low-energy experiments: How well do we know polarizabilities? p +  p = 14.0  0.5 (in 104 fm3) n +  n = 15.2  0.5 (in 104 fm3)

8. Recent claims (theory dependent): • McGovern et al (HBChPT + , 2013) • p = 10.65  0.35stat 0.2Baldin 0.3th • p = 3.15 0.35stat 0.2Baldin0.3th • p  p = 7.5  0.7 • ( incredibly small theoretical errors ! ) • Schumacher (2001, 2005, 2013) • (dispersion relations, L.P.S., 1997-2001) • p = 12.0  0.6 • p = 1.9 0.9 • p  p = 10.1  1.1 • Which answer is more correct ?

9. The 250-MeV synchrotron built by V.I. Veksler and his team in 1949 was the biggest in Europe and it provided an excellent base for studying photoproduction of pions and photodisintegration of nuclei. Studies of Compton scattering began in LPI by V.I. Goldansky who came with this idea (barefooted!) to the Veksler laboratory in 1951. Studies of Compton scattering in the Veksler’s lab: the beginning

10. The Goldansky’s initial idea was inspired by reports on R. Hofstadter experiments at Stanford Linear Accelerator of electrons and measurements of form factors and sizes of nuclei (and then nucleons). Using photon scattering is similar to ordinary vision we use to see and learn subjects around us. But: for photons with k ~ 100 - 200 MeV/c  = 2 / k ~ 6 - 12 fm  very pure resolution What can be learnt from such experiments ?! V.I. Goldansky

11. L.D. Landau: elementary particles cannot have a structure: being elementary, they must be rigid, but that is forbidded by special relativity. Goldansky, however, experimentally found that the proton is not rigid and actually measured its deformation (polarizability). [ V.I. Veksler and M.A. Markov are godfathers of the future Goldansky’s discoveries. They blessed Goldansky to work in LPI (1952-1961).] V.I. Veksler (1959) M.A. Markov

12. Several important theoretical results obtained in 1950-1960 helped to understand what information can be inferred from measurements of Compton scattering. • Low-Energy Theorem: F.E. Low and M. Gell-Mann - M.L. Goldberger, (1954). • Extension of the low-energy theorem: A.S. Klein (1955). • terms are described by two parameters. • 3) Dispersion relations: M. Gell-Mann, M.L. Goldberger, W. Thirring (1954). • Explicit formulas for the terms. Polarizabilities. • Baldin sum rule. • A.M. Baldin (1957/1960), V.A. Petrunkin (1961, 1964).

13. Determination of polarizabilities from low-energy data and Low-energy theorems. Nonlinear effects in ’ beyond  and  are important to fit data above 100 MeV and to determine the slope at =0 (polarizabilities).

14. The problem here is: what is really measured? What is the sense of thus measured parameters? Baldin-Petrunkin result (including further improvements): (this pis 40% of the full value of p). Later it was established that only the full value of p enters all observables and should be used as the electric polarizability.

15. The first (of the most precise) experimental results for proton Compton scattering: C. Oxley (Chicago) (1955, 1958). 25-87 MeV He did not try to determine polarizabilities. B.B. Govorkov, V.I. Goldansky (1956) . 75-119 MeV [V.Veksler asked I.Tamm to submit]. V.I. Goldansky et al. (1960) . 40-70 MeV (using a suggested LET and a wisdom concerning p ) the Baldin sum rule was applied (as then saturated): The Goldansky result remained the best until 1974. Cf. contemporary PDG values :  11 for p and 2.5 for p .

16. The next experiment on measuring the polarizabilities was performed in LPI in 1974 by P.S. Baranov, after a long pause of 15 years. Baranov developed a Goldansky idea to use the small-angle monitor reaction e ’e (with radiative corrections) in order to get the absolute cross section of p ’p in the bremsstrahlung experiment with the same ranges of E and E’ = E / [1 + (E /M)(1-cos  ’)]. He got p = 10.7  1.1 and p =0.7 1.6. (But problems with data at 150o) P.S. Baranov et al.

17. After an another long pause low-energy experiments on Compton scattering came to other labs abroad. Most of them have been done with tagged photons (absolute cross sections!). Illinois, 1991: Federspiel et al. 33-70 MeV Mainz, 1992: Zieger et al. 98-132 MeV Saskatoon, 1995: McGibbon et al. 73-145 MeV (with an INR member) Mainz, 2001: Olmos de Leon et al. 59-163 MeV (with LPI and INR members) + theory support of LPI (dispersion relations). Results of these experiments will be shown some later.

18. Nowadays: there are programs in Mainz and HIS (Duke) to measure these and new, so-called spin polarizabilities that determine spin dependence of the Compton scattering cross section (with LPI, INR and JINR members). Compton scattering amplitude, low-energy expansion: T = Born + O(2 [, ]) + O(3 [E1, M1, E2, M2]) + higher orders in . Said differently: effective interaction of the second order in the E.M. field is

19. PDG 2014 double count of the same exp data !! ??

20. Values given by PDG are dominated by a couple of theoretical (ChPT) works, in which theoretical uncertainties are grossly underestimated. Actually this is an average over ChPT theories, not over experiments !!!!

21. PDG 2014 double count of the same exp data !! ??

22. Dispersion theories • (unsubtracted or subtracted) • 2) Effective field theories (Chiral Perturbation Theory, • Heavy Baryon or Covariant, • without or with (1232)) The main theories in the game

23. DR formalism (LPS) for 6 invariant amplitudes Sketch of unsubtracted DR Unitarity Input: SAID / MAID + a model for 2 photoproduction

24. Asymptotic contributions (t-channel poles in the amplitudes A1 and A2) Couplings are adjusted to  as determined from fit to data at low energies: The mass parameter m is denoted in analogy with the mass of the -meson exchanged in the t-channel. Ansatz for A2 that practically works very well (also  and ’)

25. Schematically, DR =

26. Small expansion parameter: m <<  or m ~ 2 and m  mN ~  Sketch of predictions based on ChPT / EFT

28. Where is the difference between DR and EFT (ChPT)? First wonderful predictions of ChPT: contribution of the pion loop gives However, EFT is success if higher orders are small. Is that really so? What e.g. about Delta?

29. EFT is success if higher orders are small. Is that really so? Sometimes no.

31. DR vsChPT’s fit to proton Compton data [McGovern et al, 2013] Spin polarizabilities (without 0, , …) [104 fm4]

32. DR reliably predict all ai except a2 . Hence three combinations of i are predicted reliably.

33. Diagrammatic content of BChPT@ NNLO This is physics of the pion cloud around N and . Is there anything important beyond? Higher orders? Corrections include new LECs. Do they simulate physics of the -exchange with a mass2 well below the chiral energy scale of 1 GeV2 ? Also important to have simultaneously good descriptions of pion photoproduction and Compton scattering using the same couplings.

34. One of HBChPT problems is a wrong position of the pion cusp placed at E = m = 140 MeV instead of the correct m + m2 / 2mN = 150 MeV (HBChPT is sufficiently reliable in that region). Also important to have simultaneously good descriptions of pion photoproduction and Compton scattering using the same couplings what is not the case in actual HBChPT fits.

35. DR is very successful in the very wide energy range, from 0 up to about 800 MeV. DR vs Mainz (2001) data

36. Applicability of ChPT is questionable at relatively low energies and momentum transfers [figure from Beane et al, 2003].

37. Meanwhile DR works very successfully in a very wide energy range

38. DR in the energy region above 

39. DR vs LEGS (BNL) data on the beam asymmetry, 2001 (however, big problems with a description of d/d)

40. Recent Mainz data, arxiv 1408.1576. With LPI, INR, JINR. left: DR DPV (2003) right: DR LPS (1997) with the SAID-11 1 input and E1E1 = 3.37 (net prediction)

41. “Mass” of the  Curves with m = 700, 600 and 500 MeV vs Mainz-LARA data. Fit gives m  600 MeV.

42. Is that  something real? Indirect hint:  quark-level  model gives numerically right f-factor and numerically right -couplings. Quark loop dominates over the pion loop already at moderate t < 0 and gives  +7 to  [at m  2mq  700 MeV] . Interpretation: polarizability of quark vacuum around the nucleon (?).

43. Determination of the proton dipole scalar polarizabilities from fit of data of > 1990’s below pion threshold using DR (LPS) with SAID-2011 photopion input. m = 600 MeV. Two-parameter fit. Normalization uncertainties included.  Poor compatibility of different measurements (?!).  Further high-precision experiments are needed.

44. For comparison: DR (with SAID-2011) fit of some older data. Normalization uncertainties again included. Normalizations of data kj (within normalization uncertainties j ) are determined from fit using chi-squired of the form

45. A good check: let us use only data up to 100 MeV, where model dependence is minimal. Constraint p + p = 14.0  0.5 2/Nd.o.f. = 45.7/ 46 Cf. EFT fits of data points up to 170 MeV: pp = 7.5  0.7 It is not compatible with the above model independent estimate.

46. Polarizabilities of the neutron PDG 2014

47. PDG 2014

48. Polarizabilities of the neutron and low-energy deuteron Compton scattering Schematically: Only the sum of the proton and neutron polarizabilities can be inferred in this way. Said differently, isoscalar nucleon polarizabilities can be found: • s = ½ (p + n ) • s = ½ ( p + n ) • Baldin sum rule s + s = 14.5  0.5 can be imposed. • Neutron polarizabilities then can be inferred from s , s using information of proton polarizabilities.

49. Nonrelativistic description • H = kin + HN, em + VNN + HNN,em + NN,em + retardation • HN, em = charge, magnetic moment, leading relativistic • corrections (SO, polarizability-like effects) • polarizabilities E1, M1, E2, M2, E, M, E1, M1, E2, M2 • (with E1, M1 free; others = DR based) • (very accurate description of the N scattering amplitude) Potential-based model of elastic d scattering(M. Levchuk, A. L.)

50. 2) VNN = nonrelativistic Bonn OBE potential (OBEPR) • (, , , , …; formfactors) • HNN, em associated with these meson exchanges • (currents O(e) and seagulls O(e2) )