1. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil1 Tulio E. Rodrigues University of São Paulo - Brazil   decay width via the Primakoff method http://www.jlab.org/primex/ PrimEx Collaboration Outline:  Physics motivation  The Primakoff method  Inelastic background of pseudo-scalar mesons  Results   photoproduction (  decay width)   0 photoproduction (PrimEx preliminary)  Conclusions and final remarks

2. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil2  Physics motivation Theoretical developments for  0  decay 1.  0  decay proceeds primarily via the chiral anomaly in QCD: (J. S. Bell and R. Jackiw, Nuovo Cimento 60A, 47 (1969); S. L. Adler, Phys. Rev. 177, 2426 (1969) 2. Recent calculations beyond the chiral anomaly NLO calculations in ChPT (include u  d quark masses and mass difference)     = 8.10 eV  1.0% (J. L. Goity et al., Phys. Rev. D66, 076014 (2002)) QCD sum rule (include  0  mixing)     = 7.93 eV  1.5% (B. L. Ioffe et al., Phys. Lett. B647, 389 (2007)) To obtain     beyond the chiral anomaly we need  

3. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil3  Physics motivation Experimental scenario for    and          PrimEx proposal Precision measurements of     and   represent stringent tests of fundamental quantities in QCD

4. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil4  The Primakoff method  P     A A  Nuclear Coherent  P     A A*A*  Nuclear Incoherent Primakoff  P     A A 

5. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil5  Inelastic background of pseudo-scalar mesons Main features included in the MCMC intranuclear cascade model: R elativistic and time-dependent multicollisional algorithm; T he elementary mechanism (  N    N ) in terms of a Regge model; R ealistic MD for light nuclei ((e,e´p) knock-out reactions); N on-stochastic Pauli-blocking in a multiple scattering scenario; P hoton shadowing effects via a VMD model; R ealistic angular distributions for the elastic scattering    N    N ; M ultiple meson production  during secondary scatterings     X M. G. Gonçalves et al., Phys. Lett. B 406, 1 (1997) T. E. Rodrigues et al., Phys. Rev. C 69, 064611 (2004) T. E. Rodrigues et al., Phys. Rev. C 71, 051603 (R) (2005) T. E. Rodrigues et al., Braz. J. of Phys. 36, 1366 (2006) T. E. Rodrigues et al., Phys. Rev. C 75, 014605 (2007) T. E. Rodrigues et al., Phys. Rev. Lett. 101, 012301 (2008)

6. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil6  Inelastic background of pseudo-scalar mesons The elementary mechanism (  N    N )  P    NN  b1 (  ) A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004 Cross section expanded in t- channel helicity amplitudes  ( F i )

7. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil7  Inelastic background of pseudo-scalar mesons The elementary mechanism (  N  N )

8. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil8 The elementary mechanism (  N    N )  Inelastic background of pseudo-scalar mesons

9. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil9 Meson  nucleus FSI  Inelastic background of pseudo-scalar mesons

10. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil10  Results:  photoproduction Angular distribution due to incoherent  photoproduction (inelastic BG in Cornell's data)

11. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil11  Results:  photoproduction

12. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil12  Results:  photoproduction (  decay width) T. E. Rodrigues et al., Phys. Rev. Lett. 101, 012301 (2008)

13. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil13  Results:  0 photoproduction Angular distribution of “quasi-elastic” neutral pions: Nuclear incoherent photoproduction in PrimEx      k 

14. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil14  Results:  0 photoproduction Double differential cross section for incoherent   photoproduction

15. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil15  Results:  0 photoproduction 12 C 208 Pb Preliminary PrimEx Collaboration Preliminary results from PrimEx experiment (Three independent analyses in progress)

16. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil16  Results:  0 photoproduction Estimated deviation in    due to the nuclear model for incoherent  0 photoproduction (Glauber X Cascade) Deviation in Γ(  0  ) is less than 0.2% PrimEx Collaboration Preliminary

17. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil17  Results:  0 photoproduction PrimEx results (Current and future)    eV  2.3%  1.6%  1.4%

18. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil18  Conclusions and final remarks The MCMC cascade is a sophisticated framework to address the nuclear matter effects within wide ranges of target masses and incident energies. The inelastic BG of Cornell’s data of  photoproduction is consistently attributed to the nuclear incoherent mechanism (not isotropic at all). The result for  so obtained is consistent with the PDG average and is more than 50% higher than the previous value from Cornell. The Monte Carlo method for incoherent meson photoproduction (  0,  ) represents an important tool to delineate the inelastic BG in PrimEx and in future experiments dedicated to the chiral anomaly. Future work (in progress):  Coherent and Incoherent  photoproduction in PrimEx (    decay);  Incoherent   and  photoproduction up to 12 GeV

19. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil19 GDR QD  (1232) VMD (1) Zn ( ,n) ( ,np) (2) ( ,n) Sn, Ce, Ta, Pb (3) (,0)(,0) C, Pb (,0)(,0) (4) (,0)(,0) C, Pb (5) Zr ( ,xnyp) (6) (,)(,) Be, Cu (1) PRC 68, 014618 (2) PRC 69, 064611 (3) PRC 71, 051603 (4) BJP 36, 1366 (5) PRC 75, 014605 (6) PRL 101, 012301 Recent calculations (3) Thank you!

20. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil20  Introduction (Physics motivation:  decay) Possible cause for discrepancy: Inadequate treatment of the nuclear incoherent contribution (inelastic background) Typical yield curve at E B = 9 GeV (Cornell) Primakoff Background  A 0.75 MD1: S. E. Baru et al., Z. Phys. C 48, 581 (1990) ASP: N. A. Roe et al., Phys. Rev. D 41, 17 (1990) CBAL: D. A. Williams et al., Phys. Rev. D 38, 1365 (1988) JADE: W. Bartel et al., Phys. Lett. 160B, 421 (1985) Cornell: A. Browman et al., Phys. Rev. Lett. 32, 1067 (1974)  Extra slides

21. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil21 Overview of the MCMC plus Evaporation model (Flow Diagram) Cascade Dynamics (Main Block) Fermi Gas ModelShell ModelNuclear Ground State Square Well Potential Momentum Distribution Effective Mass Initial Interaction Mechanism Relativistic Kinematics Cross Sections N-N,  -N,  -N Boundary Effects Binary Scatterings Energetic Balance Reflections Pre-eq. Emissions Compound Nucleus Energetic Criterion Pauli-Blocking MCMC input MCMC Structure Evaporation Step p-h Configurations  Summary of the Monte Carlo calculations  Extra slides

22. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil22 Meson photoproduction at high energies (3 - 12 GeV) and forward angles (1) (1) A. Donnachie and G. Shaw, Ann. Phys. 37 (1966) 333  Meson photoproduction from the nucleon  Extra slides

23. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil23  Meson photoproduction from the nucleon CGLN: G.F. Chew, M.I. Goldberg, F.E. Low and Y. Nambu, Phys. Rev. 106, 1345 (1957) Relationship between the Pauli amplitudes (f) and invariant amplitudes (A) from dispersion relations (CGLN)  Extra slides

24. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil24 (1) J.S. Ball, Phys. Rev. 124 (1961) 2014 (2) G.F. Chew, M.I. Goldberg, F.E. Low and Y. Nambu, Phys. Rev. 106 (1957) 1345 (3) A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004  Meson photoproduction from the nucleon Relationship between the invariant amplitudes (A i ) (1,2) and t-channel helicity amplitudes (F i ) (3)  Extra slides

25. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil25 (1)A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004 (2)J.P. Ader and M. Capdeville, Nucl. Phys. B B3, (1967) 407 Conspiracy relation (2) : F i’s calculated using a Regge Model ( ,  and  meson exchange) natural parity t-channel amplitudes ( , , exchange) unnatural parity exchange (  meson) nucleon helicity non-flip nucleon helicity flip  Meson photoproduction from the nucleon  Extra slides

26. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil26 Two possible scenario at small t F i’s defined by single poles exchanges F i’s defined taking into account the reggeon cuts (1) F i’s have no longer definite parity and F 2,3 are non-zero for t = 0. (1)A. Capella and J. Tran Thanh Van, Nuovo Cimento Letters 1 (1969) 321.  Meson photoproduction from the nucleon  Extra slides

27. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil27  The elementary meson photoproduction natural parity ( ,  exchange) unnatural parity (b1 exchange) nucleon helicity non-flip nucleon helicity flip (*) M. Braunschweig et al., Nucl. Phys. B 20, (1970) 191. Helicity amplitudes calculated using a Regge Model with cuts ( * )  Extra slides

28. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil28  0 photoproduction  photoproduction  The elementary meson photoproduction Fitting parameters and approximations  Extra slides

29. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil29  Electromagnetic form factor with FSI Nuclear/Charge density for light nuclei (shell-model distribution (1) ) Electromagnetic form factor with FSI (Glauber theory (2) ) (1)W. T. Meyer et al. Phys. Rev. Lett. 28, 1344 (1972) (2)R. J. Glauber: Lectures in Theoretical Physics, vol. 1 (1959) p.315  Extra slides

30. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil30  Electromagnetic form factor with FSI  Extra slides

31. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil31 FSI not considered (PWIA)FSI considered (Glauber theory) (1-3) (1) R. J. Glauber: Lectures in Theoretical Physics, vol. 1 (1959) p.315 (2) S. Gevorgyan, private comm. (http://www.jlab.org/primex/primex_notes/PR99-014.ps) (3) G. Faldt, Nucl. Phys. B43 (1972) 591  Nuclear form factor with FSI absorptionRe-scattering  Extra slides

32. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil32  Nuclear form factor with FSI Main Goal: to calculate the distortion effects in the MCMC framework Main Advantage: local density fluctuations are effectively included  Extra slides

33. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil33  Results – meson energy spectra (all processes)  Extra slides

34. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil34   -Nucleus FSI  N channels included in the MCMC ( * ) (*)T. E. Rodrigues et al., Phys. Rev. C 71, 051603 (R) (2005).  Extra slides

35. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil35   -Nucleus FSI  N channels included in the MCMC ( * )  Extra slides

36. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil36 Time derivative of the average number of  N interactions  Meson-nucleus Final State Interactions  Extra slides

37. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil37  N total cross section  Meson-nucleus Final State Interactions Our assumption: C ~ 1 (experiments using multiple targets may constrain this factor)  Extra slides

38. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil38 Cornell’s kinematics (1) :  Results (  detection in the Cornell Experiment) (1)A. Browman et al., Phys. Rev. Lett. 32, 1067 (1974) Cornell’s Geometry (1) : Be/Cu Targets 466.1 cm 36.0 cm 45.0 cm 36.0 cm Counter hodoscopes z  Extra slides

39. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil39  Results (energy spectra) meson 0000 target 12 C Energy 5.2 GeV PrimEx energy range  Extra slides

40. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil40  0 incoherent photoproduction from 12 C and 208 Pb at k = 0.33 GeV (1)T. E. Rodrigues et al., Phys. Rev C 71, 051603 (R) (2005). (2)B. Krusche et al., Eur. Phys. J. A 22, 277 (2004).  Previous results near the  (1232)  Extra slides

41. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil41  Extra slides

42. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil42  Results: The “fate” of the nucleus neutronsprotonsProbability Excitation energy (MeV) 0 07.127400000000000E-002 14.9453261696332 0 1 0.369712000000000 19.4509861233355 0 2 2.172500000000000E-002 64.6240038375987 0 3 5.179000000000000E-003 88.3508050836749 1 0 0.368511000000000 19.3918424523630 1 1 4.881500000000000E-002 65.5999372686652 1 2 2.126900000000000E-002 91.7460758820850 1 3 6.857000000000000E-003 116.972074963673 2 0 1.927600000000000E-002 63.6016020666118 2 1 2.033800000000000E-002 92.0391928231057 2 2 1.206400000000000E-002 119.077382335633 2 3 4.837000000000000E-003 143.484196021755 3 0 4.614000000000000E-003 88.2393981604718 3 1 6.352000000000000E-003 117.019413369315 3 2 4.773000000000000E-003 144.802216578445 3 3 2.465000000000000E-003 169.804630963647  Extra slides

43. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil43  Results:  0 photoproduction Double differential cross section for incoherent   photoproduction  Extra slides

44. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil44 Elementary omega photoproduction   Extra slides

45. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil45  Extra slides d  /dt for Carbon (Rochester data) Exp. Data: H. –J. Behrend et al., Phys. Rev. Lett. 24, 1246 (1970) (d  /dt was not published)   photoproduction from nuclei

46. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil46  Inelastic background of neutral pions:    decay  Extra slides

47. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil47  Results:  0 photoproduction Preliminary results from PrimEx experiment (Three independent analyses in progress) PrimEx Collaboration Preliminary  Extra slides

48. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil48  The direct method to obtain    Decay Length Measurements Measuring  0 decay length (    1x10 -16 sec) for ultra-relativistic pions: i.e. For E  0 = 1000 GeV, we have L = v   E  /m   100 μm (very challenging experiment) CERN experiment, 1984: 450 GeV proton beam  (  0  )  7.34eV  3.1% Major limitations of method:  unknown P  0 spectrum  needs higher energies for improvement  Extra slides

49. 12/7/2015Tulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil49 e + e - Collider Experiment  e + e -  e + e -  *  *  e + e -  0  e + e -   e +, e - scattered at small angles (not detected)  only  detected  DORIS II @ DESY  Results: Γ(  0  ) = 7.7 ± 0.5 ± 0.5 eV ( ± 10.0%)  Not included in PDG average  Major limitations of method  knowledge of luminosity  unknown q 2 for  *  *  Extra slides