1. Time Reversal Invariance in electromagnetic interactions
Alessandra Fantoni
INFN - Laboratori Nazionali di Frascati
Introduction
Processes
Experimental Situation
Perspectives
International Workshop on Nucleon Form Factors, LNF Ottobre 2005

2. Introduction –1-
Invariance of the laws of physics under discrete symmetry operations reflect fundamental properties of matter
Not all processes are invariant under every simmetry operation:
weak interaction violates invariance under space reflection (parity P)
decay of neutral K meson violates invariance under combined charge conjugation (C) and parity operations (CP)
For certain whether C, P and CP conserving interactions are also invariant under time reversal (T): NOT known !!!
T invariance is reflected in the law of conservation of energy for systems with conservative forces

3. Fundamental theorem of relativistic field theory
Introduction -2-
Fundamental theorem of relativistic field theory
All interactions must be invariant under CPT operation
CP invariance T invariance
CP violation T violation
No direct tests of T invariance in CP conserving interactions
Strong interaction Hh: invariant under Ph, Th and Ch
E.m. interaction Hg: invariant under Pg, Tg and Cg

4. Introduction -3- Hh and Hg invariant under Ph = Pg and CgPgTg = ChPhTh
For strong interacting particles no complete theory of electromagnetic interaction exists:
No evidence Hg invariant under Ch or Th
Difficulty of detection Ch or Th violations:
electromagnetic effects well described by lowest order (Born approximation)
Gauge invariance
Test for Th are challenging in electromagnetic interactions of leptons with nucleons

5. W3 ≠ 0 Hg violates Th invariance (and also Ch)
Processes
Literature: Bernstein et al. PR139 (1965) 1650; Christ & Lee PR143 (1966) 1310
Karpman et al PRL16 (1966) 633; Karpman et al. PR174 (1968) 1957
Inelastic lepton scattering on polarised target:
l± + N l± + G
ds ≈ aW1 + bW2 + ST (k × k‘) cW3
W3 ≠ Hg violates Th invariance (and also Ch)
A ≠ 0:
violation of Th invariance
higher order effects (a3) : interference between 1g and 2g amplitudes without requiring T invariance violation:
A(a3) small
A(a3) charge dependent

6. Experimental Situation -1-
Cambridge: J.R.Chen et al. PRL 21 (1968) 1279
J.A.Appel et al. PRD 1 (1970) 1285
Inelastic scattering on h.e. e- from polarized p
Target: 92% C2H5OH, 8% H20 PT=22%
E(e-) = 4, 6 GeV I = 3 nA
Assumption: one-single-photon-exchange
Results:
No asymmetry at Q2 = 0.2 ÷ 0.7
Accuracy = 4 ÷ 12%

7. Experimental Situation -1-
Cambridge: J.R.Chen et al. PRL 21 (1968) 1279
J.A.Appel et al. PRD 1 (1970) 1285

8. Experimental Situation -2-
b) SLAC: S.Rock et al. PRL 24 (1970) 748
Target: 95% butanol, 5% H20 PT=35%
E(e-) = 15, 18 GeV Q2 = 0.4, 0.6, 1.0
E(e+) = 12 GeV Q2 = 0.4
e- , e+ but not covering same kinematic range

9. Experimental Situation -2-
b) SLAC: S.Rock et al. PRL 24 (1970) 748
Data everywhere consistent with A = 0

10. Experimental Situation -2-
b) SLAC: S.Rock et al. PRL 24 (1970) 748
3 bins at 1200 MeV: A = (4.5±1.4)%
difficult
explanation
Data everywhere consistent with A = 0

11. Experimental Situation -3-
Old data NOT very accurate
Conclusions hard to extract
Points still open for discussion
Jlab LoI
How to better investigate the problem ?
What is needed?

12. Perspectives -1- l± + N l± + G
a) Inelastic lepton scattering on polarised target:
l± + N l± + G
no FSI interaction (no hadron detected)
e- and e+ A free of a3 effects
same sign for e+ and e-
≈ a2
e+ and e- in the same kinematic range
Emin (e+/e-) = 1.2 GeV (first resonance)
Edes (e+/e-) = 3 GeV

13. Perspectives -2- l± + N l± + N*
b) Unpolarised target, polarised outgoing particle:
l± + N l± + N*
no FSI interaction (no hadron detected)
detection of polarization vector of outgoing nucleon
same case as before

14. Perspectives -3- l± + N l± + N + p
c) Exclusive process: hadron detected in final state
l± + N l± + N + p
FSI interaction (hadron detected)
need to evaluate A(a3) effects
(2 g exchange)
same sign for e+ and e-
≈ a2
free of FSI
different sign for e+ and e-
Model dependent
access to T-odd GPDs

15. Perspectives inside LNF
LNF is studying perspectives for the future
Increase of energy of DAFNE
Possibility to use upgraded DAFNE Linac

18. Courtesy of SPARC/X Collaboration

19. Courtesy of SPARC/X Collaboration

20. Courtesy of SPARC/X Collaboration

21. Courtesy of SPARC/X Collaboration

22. Courtesy of SPARC/X Collaboration

23. Courtesy of SPARC/X Collaboration

24. Perspectives LNF is studying scenarios for near-mid-long range
MIUR funds for SPARXino R&D
Proposal within beginning 2006 from SPARC/X Collaboration for Dafne Linac upgrade from 800 MeV to GeV
Possibility to E=1.8 GeV under study
(new cavities 11 GHz instead of 3 GHz ; new technology for LNF)
e+ beam available (PC)
Possibility to use these beams for dedicated proposals
such as Time invariance in em interaction
Further developments depend on approval/decisions