Nucleon Electromagnetic Form Factors: Introduction and Overview

Transcription

1 Nucleon Electromagnetic Form Factors: Introduction and Overview Diego Bettoni Istituto Nazionale di Fisica Nucleare, Ferrara Scattering and Annihilation Electromagnetic Processes Trento, 18- February 013

2 Outline Introduction definitions main properties Space-like Form Factors Rosenbluth separation Polarization transfer Experimental situation Summary and outlook Time-like Form Factors Main properties and predictions Experimental situation Open issues Summary and outlook Conclusions Diego Bettoni Nucleon Form Factors

3 Introduction p 0 k q = p 0 - p p k J µ e F κ M ( ) µ ( ) µν Q γ + F Q iσ q = 1 ν M nucleon mass Q = -q F F p 1 n 1 (0) = 1 (0) = 0 F F p n (0) (0) = 1 = 1 Dirac and Pauli Form Factors Diego Bettoni Nucleon Form Factors 3

4 Sachs Form Factors E M κq F1 + 4M F + κf 1 F Electric form factor Magnetic form factor ( ) ( q q ) p n = ( ) ( ) M E 0 = 1 E 0 = 0 p n ( 0) = +.79 ( 0) = E E M = E and M are Fourier transforms of nucleon charge and magnetization density distributions (in the Breit Frame). q < 0 space-like form factors (elastic en scattering) q > 0 time-like form factors (creation or annihilation of an N N pair) M M Diego Bettoni Nucleon Form Factors 4

5 Form Factors Properties Spacelike form factors are real, timelike are complex. The analytic structure of the timelike form factors is connected by dispersion relations to the spacelike regime. By definition they do not interfere in the expression of the cross section, therefore, in the timelike case, only polarization observables allow to get the relative phase. Diego Bettoni Nucleon Form Factors 5

6 Space-like Form Factors Rosenbluth separation Polarization transfer Experimental Situation Two-photon contribution Future experiments

7 ( ) + Ω = Ω sin cos θ κ θ κ σ σ F F M q F M q F d d d d Rutherford Ω = Ω sin cos 1 θ τ θ τ τ σ σ M M E Rutherford d d d d Ω = Ω tan 1 θ τ τ τ σ σ M M E Mott d d d d 4M q = τ en Elastic Scattering The experimental determination of the nucleon form factors in the space-like region (q < 0) is carried out by studying en elastic scattering d e d e p e p e Diego Bettoni Nucleon Form Factors 7 Rosenbluth Formula

8 Rosenbluth Separation Method dσ dω dσ dω Mott = ( ) + B( q ) A q tan θ Rosenbluth Plot Diego Bettoni Nucleon Form Factors 8

9 Early Measurements p M µ p p E n M µ n p E n En E Scaling laws for the form factors: ( q ) = ( q ) = 0 p M µ ( ) n ( q q ) p = aτ = µ n 1 + bτ M µ ( ) ( q q ) n = ( ) q Diego Bettoni Nucleon Form Factors 9

10 Proton Charge Radius q Dipole formula: ( ) M V = ( 0.84 ev 0 0 ) ρ ( R) ρ e = 0 = 1 + M V M R V 3 ρ0e R d R 0 1 R = = M R 3 M V ρ e d R R R V 1 M 1 q M V The dipole form corresponds to an exponential charge distribution with an rms radius For the proton: = = 0.80 Diego Bettoni Nucleon V Form Factors 10 fm

11 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 11

12 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 1

13 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 13

14 Polarization Transfer Method e + p e + p P = P Ee + E M E T e M L θ tan Diego Bettoni Nucleon Form Factors 14

15 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 15

16 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 16

17 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 17

18 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 18

19 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 19

20 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 0

21 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 1

22 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05

23 R p R p ( Q ) ( Q ) µ pe = Q 1 M ( 0.9) Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 3

24 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 4

25 Diego Bettoni Nucleon Form Factors Mark Jones Nucleon05 5

26 Two-Photon Exchange Investigated both experimentally and theoretically for the past 50 years. Radiative corrections to Rosebluth tecnique normally ignore terms with two hard photons. Can be studied experimentally by measuring the ratio of electron and positron elastic scattering off a proton. Diego Bettoni Nucleon Form Factors 6

27 Space-like FF Outlook Explain discrepancy between Rosenbluth separation method and polarization transfer. Two-photon contribution. Main player will be JLAB at 1 ev. Diego Bettoni Nucleon Form Factors 7

28 Time-like Form Factors Measurement method Main properties and predictions Experimental Situation Open issues Future prospects

29 Diego Bettoni Nucleon Form Factors 9 N N e e = * * sin ) ( 4 ) cos (1 ) ( 4 θ θ β α Ω σ s s m s s C d d E N M + = ) ( ) ( 3 4 s s m s s C E N M πβ α σ 0 = Q > s p p e + e - *

30 C is the Coulomb correction factor, taking into account the QED coulomb interaction. Important at threshold. C 1 = 1 e y y = παm β s N C s 4M N 1 β finite σ π α 3 ( ) 4M = (4M ) 0. nb N E N 1 4M N s (ev ) There is no Coulomb correction in the neutron case. Diego Bettoni Nucleon Form Factors 30

31 Form Factor Properties At threshold E = M by definition, if F 1 and F are analytic functions with a continuous behaviour through threshold. E (4m p ) = M (4m p ) Timelike E and M are the analytical continuation of non spin flip and, respectively, spin flip spacelike form factors. Since timelike form factors are complex functions, this continuity requirement imposes theoretical constraints. Two-photon contribution can be measured from asymmetry in angular distribution. Diego Bettoni Nucleon Form Factors 31

32 Diego Bettoni Nucleon Form Factors 3 Form Factor Properties Perturbative QCD and analyticity relate timelike and spacelike form factors, predicting a continuous transition and spacelike-timelike equalitity at high Q. At high Q PQCD predicts: Naïve prediction for the neutron: ) ( ) ( ) ( ) ( Q Q Q F Q Q Q F s α s α 0.5 = u d p M n M q q

33 Proton Form Factors The moduli of the Form Factors can be derived from measurements of the cross sections for e + e - pp Due to the low value of the cross sections and the consequent limited statistics, most experiments could not determine M and E separately from the analysis of the angular distributions, but extracted M using the (arbitrary) assumption E = M. The magnetic form factor has been derived in this way by many e + e - and pp experiments. The timelike electric form factor is basically unknown. Recently BaBar has attempted to measure M / E by means of ISR, but the final result is quoted using E = M. Diego Bettoni Nucleon Form Factors 33

34 Proton Magnetic Form Factor M The first experiment to produce a positive result for the proton timelike form factor was carried out at ADONE in Frascati e + e - pp The measurement was based on 0. pb -1 of data at 4.4 ev yielding 5 events. Diego Bettoni Nucleon Form Factors 34

35 Proton Magnetic Form Factor M The first measurement of the timelike form factors at threshold is due to the ELPAR experiment at CERN. They observed 34 events of pp annihilation at rest in a liquid H target. The measurement assumes E = M Diego Bettoni Nucleon Form Factors 35

36 Proton Magnetic Form Factor M Various measurements of the proton form factors were carried out at DCI in Orsay using e + e - pp The first experiment was DM1 which recorded 63 events in 4 data points. Diego Bettoni Nucleon Form Factors 36

37 Proton Magnetic Form Factor M At DCI in ORSAY the DM collected data in three data taking runs for a total of 0.7 pb -1. With a total of 11 events in 6 points they attempted to measure the angular distribution, from which they could fit M / E =0.34, but E = M was still allowed. Diego Bettoni Nucleon Form Factors 37

38 Proton Magnetic Form Factor M The first high-statistics measurement of the timelike form factors was carried out at LEAR by the PS 170 collaboration. They recorded a total of 3667 pp e + e - events in 9 data points. The angular distribution is compatible with E = M. First indication of steep rise near threshold. Diego Bettoni Nucleon Form Factors 38

39 Proton Magnetic Form Factor M The E760 experiment at Fermilab produced the first measurement of the form factors at high Q pp e + e - Very difficult measurement due to very small cross section. They recorded 9 events. The measurement assumes E = M. Diego Bettoni Nucleon Form Factors 39

40 Proton Magnetic Form Factor M The FENICE experiment at ADONE, primarily devoted to the measurement of the neutron form factor, produced also a measurement of the proton magnetic form factor with 69 events in 4 points. Diego Bettoni Nucleon Form Factors 40

41 Proton Magnetic Form Factor M E835 at FNAL, continuation of E760, made further measurements at high Q with a total of 06 events in data taking runs. Diego Bettoni Nucleon Form Factors 41

42 Proton Magnetic Form Factor M A new measurement at high Q was recently made by the CLEO at CESR in e + e - pp. It assumes E = M. The measurement is based on 14 events. Diego Bettoni Nucleon Form Factors 4

43 Proton Magnetic Form Factor M Another measurement of the proton timelike form factors has been reported by BES. The measurement covers 9 data points from (.0 ev) to (3.07 ev) using the hypothesis E = M. Diego Bettoni Nucleon Form Factors 43

44 Proton Magnetic Form Factor M BaBar measurement using Initial State Radiation (ISR) Advantages: e + e - pp All energies at the same time fewer systematics CMS boost easier measurement at threshold Disadvantages Luminosity proportional to invariant mass bin L s More background Diego Bettoni Nucleon Form Factors 44

45 Asymptotic Behavior The dashed line is a fit to the PQCD prediction µ M p = s ln C s Λ The expected Q behaviour is reached quite early, however... Diego Bettoni Nucleon Form Factors 45

46 Asymptotic Behavior The dashed line is a fit to the PQCD prediction µ M p = s ln C s Λ The expected Q behaviour is reached quite early, however there is still a factor of between timelike and spacelike. Diego Bettoni Nucleon Form Factors 46

47 E and M angular distributions Diego Bettoni Nucleon Form Factors 47

48 The ratio E / M So far only two experiments have collected enough statistics to analyze the angular distribution and attempt to extract E and M independently. The present accuracy in the ratio E and M is of the order of 50 %. Diego Bettoni Nucleon Form Factors 48

49 Threshold Q Dependence Steep behavior near threshold observed by PS 170 at LEAR (000 events). Diego Bettoni Nucleon Form Factors 49

50 BaBar Measurement using ISR BaBar measurement very near threshold confirms steep rise of Form Factor Diego Bettoni Nucleon Form Factors 50

51 Resonant Structures The dip in the total multihadronic cross section and the steep variation of the proton form factor near threshold may be fitted with a narrow vector meson resonance, with a mass M 1.87 ev and a width 10-0 MeV, consistent with an N N bound state. Diego Bettoni Nucleon Form Factors 51

52 Neutron Timelike Form Factor 1.9 < s <. 55 ev Diego Bettoni Nucleon Form Factors 5 Ldt = 0. 4 pb 1 80 events The neutron form factor is bigger than that of the proton!!!

53 Measuring the Phase between E and M The relative phase ME between M and E can only be measured by means of single- or double-polarization experiments. P P x z P P e e cosδ ME P y = M ( s) (1 + cos sin θ * θ ) + * 4m s N E ( s) sin θ * 4m s N E M sin δ ME It takes the maximum value near scattering angles of 45 0 and and vanishes at Once this phase is known, by measuring the ratio of the two components of the nucleon polarizations in the scattering plane with longitudinally polarized beams, the ratio M / E can be obtained with small systematic uncertainties. Diego Bettoni Nucleon Form Factors 53

54 Summary and Outlook In spite of more than forty years of measurements our knowledge of the timelike nucleon form factors is far from complete. Proton Form Factors Only effective M has been measured. Almost no information on E and phases. Steep behavior near threshold poses interesting challenge (baryonium, dips in hadronic cross sections...). Asymptotic Q regime reached quite early, but still far from spacelike. BaBar data suggest steps rather than smooth behavior. Neutron Form Factor, measured by a single (low statistics) experiment Mn > Mp contrary to expectations Mn >> En Future prospects: BES III, Belle II, VEPP, PANDA. Diego Bettoni Nucleon Form Factors 54

55 Conclusions These considerations strongly support the importance of new measurements of the neutron and proton form factors with much higher statistics than previous work and with the capability of separately determining the electric and magnetic form factors (timelike) and to understand the discrepancy between Rosenbluth separation and polarization transfer measurements. We can look forward to many more years of exciting Form Factor Physics! Diego Bettoni Nucleon Form Factors 55