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 12-14 Ottobre 2005

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

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

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

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 ≠ 0 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

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%

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

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

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

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

Experimental Situation -3- Old data NOT very accurate Conclusions hard to extract Points still open for discussion Jlab LoI 01-002 How to better investigate the problem ? What is needed?

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

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

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

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

Courtesy of SPARC/X Collaboration

Courtesy of SPARC/X Collaboration

Courtesy of SPARC/X Collaboration

Courtesy of SPARC/X Collaboration

Courtesy of SPARC/X Collaboration

Courtesy of SPARC/X Collaboration

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 1.2-1.5 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