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 Dalitz decay :

From theory….  Dalitz decay :. lagrangian. eVdm. …to HADES experimental spectra. preliminary. B. Ramstein, IPN Orsay In collaboration with J. Van de Wiele. GSI, HADES Collaboration Meeting , 05/07/08. Dalitz decay in transport codes: C+C 2 GeV. IQMD. Dalitz pn. No medium effects.

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 Dalitz decay :

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  1. From theory…  Dalitz decay: lagrangian eVdm …to HADES experimental spectra preliminary B. Ramstein, IPN Orsay In collaboration with J. Van de Wiele GSI, HADES Collaboration Meeting , 05/07/08

  2. Dalitz decay in transport codes:C+C 2 GeV IQMD • Dalitz pn No medium effects HSD Me+e-(GeV/c2) Thomère,Phys ReV C 75,064902 (2007) E. Bratkovskaya nucl-th 07120635 Important issue for understanding intermediate mass dilepton yield

  3. q2 = M2inv(e+e-) = M*2 > 0 Time Like  - N transition: Complementary probes of electromagnetic structure of N -  transition Space Like N -  transition : extraction of electromagnetic form factors GE(q2), GM(q2), GC(q2) e- e- q2 = M* = - Q2 < 0 * p D+ →Np Lots of data, Mainz, Jlab Pion electro/photo-production  Dalitz decay : intrinsic interest of the measurement  Dalitz decay p D+ * e+ Branching ratio not measured experimental challenge e-- e--

  4. N- Dalitz decay dilepton yield: ingredients of the calculation Strong interaction model • 1) N N N : • Mass dependent width Breit-Wigner, with possible cut-offs • model for t dependence or angular distribution QED N N • 2 )  N e- e + • exact field theory calculation • 3 independent amplitudes: • e.g. Electric, Magnetic and Coulomb p N D+ * QCD e+ q2 = M*2 > 0 3) electromagnetic form factors GM(q2),GE(q2),GC(q2)  Dalitz decay e--

  5. N  N- em transition : what do we know? « Photon point » : q2=0 GM(0)=3, GE(0)~0 • at q2=0, mainly M1+ (magnetic) transition • At finite q2, many recent data points from Mainz, Jlab: • multipole analysis of ° or + electroproduction (%) GM(q2) related to GE(q2 ) (%) related to GC( q2 ) Many models: dynamical models (Sato,Lee), EFT (Pascalutsa and Vanderhaeghen), Lattice QCD, two component modelQ. Wan and F. Iachello What about time-like region ?

  6. N- transition em structure: what about time-like region? • Problems in Time-like region • No data • Electromagnetic form factors are complex But,… •  decay width doesn’t depend on phases of form factors • q2 stays small in  Dalitz decay at M =1232 MeV/c2 ,q2 < 0.09 GeV/c2 Space Like: q2<0 Time Like: q2>0 complex GTL(q2) Analytic continuation : real GSL(q2) Models constrained by data eg. GTL(q2) = GSL(-q2) or GTL(q2) = GSL(-q2ei),… • 2 options: • take constant form factors HSD, UrQMD, IQMD • use models for form factors GE(q2),GM(q2),GC(q2) : VDM,eVDM, (RQMD)two component Iachello model

  7. GM(q2) M=1.3 GeV/c2 0.6m2 M=1.1 GeV/c2 __ pure QED __ Iachello FF M=1.5 GeV/c2 M=1.7 GeV/c2 Sensitivity to Iachello form factor • two component model: • Unified description of all baryonic transition form factors • Direct coupling to quarks + coupling mediated by  • Analytic formula • 4 parameters fitted on • elastic nucleon FF (SL+TL) • SL N- transition GM

  8. PLUTO simulations: sensitivity to Iachello’s form factor in pe+e- events from  Dalitz decay E. Morinière, PHD thesis pp @ 1.25 GeV pe+e- events Normalisation problem now solved →no sensitivity at E=1.25 GeV

  9. N- Dalitz decay dilepton yield: ingredients of the calculation Strong interaction model • 1) N N N : • Mass dependent width Breit-Wigner, with possible cut-offs • model for t dependence or angular distribution QED N N • 2 )  N e- e + • exact field theory calculation • 3 independent amplitudes: • e.g. Electric, Magnetic and Coulomb p N D+ * QCD e+ q2 = M*2 > 0 3) electromagnetic N- transition form factors GM(q2),GE(q2),GC(q2)  Dalitz decay e--

  10.  Dalitz decay in « reference » papers Jones and Scadron convention • form factor conventions (including or not isospin factor of the amplitude) • choices of form factors • analytic formula for differences See Krivoruchenko et al. Phys.Rev.D 65, 017502 « remarks on  radiative and Dalitz decays »

  11. X4 (misprint) Comparing different  Dalitz decay dilepton spectra: • analytic formula for • and form factors values at q2=0 from 4 papers  compare dilepton spectra for M=1232 MeV/c2

  12.  mass dependence factor 1.5 factor 1.7 factor 2.2 factor 2 Me+e-( GeV/c2) Discrepancy increases with  mass But also off-shell effects problem at high  mass

  13. Branching Ratio Expt « Wolf »: HSD before 2007, IQMD, UrQMD « Ernst » HSD after 2007 « Krivoruchenko » RQMD Zetenyi PLUTO Radiative decay (10-3) 5.6± 0.4 6.0 8.7 7.05 (HSD) 5.6 5.6 Dalitz decay (10-5) ? 4.6 6.5 5.3 (HSD) 4.12 (const.GM) 4.25 (e-VDM) 4.12 4.4 Pretty well! Radiative decay width OK Check: radiative decay width values M=1232 MeV/c2 For M* =0 radiative decay width Dalitz decay width

  14. Direct effect:different normalisation of  Dalitz decay dilepton spectrum Same « Ernst » formula Pluto BR(+→pe+e-) = 4.4 10-5 HSD BR (+→pe+e-) =5.3 10-5

  15. Field theory calculation: Leptonic current • Amplitude Same as for →N hadronic current E,M,C : eg Krivoruchenko « standard normal parity set »: eg Wolf • Spin ½ projector (Dirac spinors) • spin 3/2 projector (Rarita-Schwinger spinors) • Traces of products of  matrices Calculation of JH(..) JH ’*(..)* JL’(..) JL(…) * phase space From reference papers and Jacques Van de Wiele’s work • Differential decay width: • Electromagnetic hadronic current: 2 sets of covariants can be used:

  16.  Dalitz decay width calculation: results • Jacques Van de Wiele’s calculation → same analytical function as Krivoruchenko’s • Can also be expressed in terms of g1,g2,g3: • Shyam and Mosel; Kaptari and Kämpfer: • g1=5.42, g2=6.61, g3=7 equivalent to GM=3.2 GE=0.04 GC~0.2 • Zetenyi and Wolf: g1=1.98, g2=0,g3=0 • fitted to reproduce radiative decay width • →same Dalitz decay width as Van de Wiele/Krivoruchenko q2 dependence negligible for  Dalitz decay

  17.  Dalitz decay width calculation: results and suggestions for new PLUTO inputs p D+ * e+ q2 = M*2  Dalitz decay e-- • * angular distribution • « helicity distribution » • Krivoruchenko/Van de Wiele ( or « Zetenyi » ) expression for • Electromagnetic N- transition form factors • Branching ratio Ok with E. Bratkovskaya, Phys. Lett. B348 (1995) 283 M=1232 MeV/c2

  18. N- Dalitz decay dilepton yield: ingredients of the calculation Strong interaction model • 1) N N N : • Mass dependent width Breit-Wigner, with possible cut-offs • model for t dependence or production angular distribution QED N N • 2 )  N e- e + • exact field theory calculation • 3 independent amplitudes: • e.g. Electric, Magnetic and Coulomb p N D+ * QCD e+ q2 = M*2 > 0 3) electromagnetic form factors GM(Q2),GE(q2),GC(Q2)  Dalitz decay e--

  19. e+ Same as in  photoproduction e-- N N N model:  polarisation effects  Dalitz decay N • polarization 4x4 density matrix ms= -3/2,-1/2,1/2,3/2 N N D+ * Anisotropy of * angular distribution p Spin-isospin excitation 1 exchange  +  exchange Effective interaction,… Long. polarization : (pure 1 exch.) 1/2 1/2 =  -1/2 -1/2 =1/2 others ij=0 Transv. polarization : ( exch.) 3/2 3/2 =  -3/2 -3/2 =1/2 others ij=0 Jacques Van de Wiele’s result

  20. e+ e- p p , N p p p p pD p e+ , N e- pp ppe+e- interference effects Interference between all graphs including either a Delta or a nucleon + ….. + , cf Kaptari and Kämpfer,…. In PLUTO: factorization of NN → N cross section and (→Ne+e-): p p 1 No Bremstrahlung two exit protons are distinguishable p2 D+ p e+ q2=M2inv(e+e-)=M* e-

  21. Origin of high dilepton mass tails HSD  HSD p+p 1.25 GeV PLUTO HSD PLUTO 12C+12C 1 AGeV  tail at high dilepton mass: absent in PLUTO ? absent in pp and pn ? Different  mass distributions ?

  22. pp@1.25 GeV + from p° W. Przygoda’s talk  from e+e-p M(e+e-)>140 MeV/c2 Ania Kozuch’s talk q2=0.02 (GeV/c)2 q2=0.2 (GeV/c)2 Delta mass distribution in PLUTO: • Dmitriev’s mass distribution parametrisation • but with Moniz vertex form-factors Mass distribution Teis = 300 MeV/c Dmitriev = 200 MeV/c M(MeV/c2) d/dM high mass dilepton yield is sensitive to high  mass E. Morinière, PHD thesis

  23. Quite well known, can be improved with our data N- Dalitz decay dilepton yield: ingredients of the calculation Strong interaction model • 1) N N N : • Mass dependent width Breit-Wigner, with possible cut-offs • model for t dependence or angular distribution QED N N Exact calculation, But offshell effects? • 2 )  N e- e + • exact field theory calculation • 3 independent amplitudes: • e.g. Electric, Magnetic and Coulomb p N D+ * QCD e+ q2 = M*2 > 0 No sensitivity at E=1.25GeV, Important at E=2.2 GeV or in -p E=0.8 GeV/c 3) electromagnetic form factors GM(q2),GE(q2),GC(q2)  Dalitz decay e--

  24. Ania Kozuch’s talk pp → pp ° E=1.25 GeV Tingting’s talk pp →pn+ E=1.25 GeV • Experiment • Simulation total • Simulation D++ • SimulationD+ • SimulationN* Normalized yield simulation total Marcin Wisniovski pp → pp ° pp → pn + E=2.2 GeV Sexperiment =1.39*106 events Ssimulation =1.37*106 events Very good agreement

  25. „pure ” pp→ppe+e-, pn →ppe+e-Challenging data ? Tetyana Witold + (p,e+,e-) invariant mass dilepton angle, helicity angle,…

  26. Conclusion • A lot of different models to describe HADES data • Different results , but we need to understand the reasons • Some investigations for  Dalitz decay • A lot of other questions about other processes • Let’s start the discussions…

  27. Results of simulations for  Dalitz decay Possibility to reduce ° background to 20% 1500 e+e-p events In HADES acceptance 7 days of beam time Better sensitivity to discriminate pp bremstrahlung

  28. MD

  29. Efficiency and acceptance corrected pp data,comparison to transport model calculation IQMD preliminary Δ→e+e-N seems to explain e+e- yield in p+p at 1.25 GeV

  30. Dalitz decay in transport codes:p+p and pn at 1.25 GeV Isospin effects

  31. Analytic continuation : Time Like: Space Like: analytic continuation to Time-Like region: 3) Intrinsic form factor: Space Like: Time Like: Q2  - q2 ei phase : • removes singularity at q2=1/a2 (~ 3.45 (GeV/c)2) •  =53° fitted to elastic nucleon form factors Time Like data • same value taken for N -  transition

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