Incoherent photoproduction of π 0 and η from complex nuclei up to 12 GeV
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1 Incoherent photoproduction of π 0 and η from complex nuclei up to GeV Tulio E. Rodrigues University of São Paulo - Brazil Outline: Physics motivation (chiral anomaly in QCD) Meson photoproduction from complex nuclei (the Primakoff approach) Calculation of the incoherent cross section: γ + Α > η(π 0 ) + X Results Incoherent π 0 photoproduction in PrimEx measured ratio A eff = σ γa /σ γn from Cornell Incoherent π 0 and η photoproduction at GeV Incoherent η photoproduction in Cornell (η > γγ decay width revisited) Conclusions and final remarks /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
2 Physics motivation (chiral anomaly in QCD) Theoretical developments for the π 0 > γγ decay amplitude. π 0 > γγ decay proceeds primarily via the chiral anomaly in QCD: (J. S. Bell and R. Jackiw, Nuovo Cimento 60A, 47 (969); S. L. Adler, Phys. Rev. 77, 46 (969) 3 α N 0 = c mπ = 7.75± ev γγ 3 576π F Γπ. Recent calculations beyond the chiral anomaly π NLO ChPT and /N c expansion to O(p 6 ) Γ π 0 > γγ = 8.0 ev ±.0% [J. L. Goity et al., Phys. Rev. D66, (00)] NNLO two flavor ChPT Γ π 0 > γγ = 8.06 ev ±.0% [B. Ananthanarayan and B. Moussallam, JHEP 005, 05 (00)] Γ π 0 > γγ = 8.09 ev ±.4% [K. Kampf and B. Moussallam, Phys. Rev. D 79, (009)] QCD sum rule (include π 0 η mixing) Γ π 0 > γγ = 7.93 ev ±.5% [B. L. Ioffe et al., Phys. Lett. B647, 389 (007)] To obtain Γ π 0 > γγ beyond the chiral anomaly we need Γ η > γγ /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
3 Physics motivation (chiral anomaly in QCD) Experimental scenario for Γ(π 0 > γγ ) and Γ(η > γγ ) η > γγ Decay Width (kev) MD ASP JADE CBAL Removed from PDG world average! 0.34(46) kev PDG average 0.50(6) kev Cornell (Primakoff-effect) A. Gasparian, EINN Experiments Precision measurements of Γ π 0 > γγ and Γ η > γγ represent stringent tests of fundamental quantities in QCD /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 3
4 Meson photoproduction from complex nuclei (the Primakoff method) Primakoff γ A γ P π 0, η A T P = Γ P γγ 8παZ 3 m P 3 β k 4 Q 4 ~ F em ( Q) sin θ dσ dω = T P + e iϕ T NC + T NI Nuclear Coherent γ A ρ, ω P π 0, η A γ P π 0, η ρ, ω A A * Nuclear Incoherent T NC = A ~ F N ( Q) L sin θ NI T = A eff f ( Q) Tn /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 4
5 Calculation of the incoherent cross section: γ + Α > η(π 0 ) + X Main features included in the MCMC intranuclear cascade model: Relativistic and time-dependent multicollisional algorithm () (6) ; The elementary mechanism (γ + N > η(π 0 ) + N ) in terms of a Regge model (3),(4),(6) ; Realistic MD for light nuclei [(e,e p) knock-out reactions] (6) ; Non-stochastic Pauli-blocking in a multiple scattering scenario () (6) ; Photon shadowing effects via a VMD model (6) ; Realistic angular distributions for the elastic scattering η(π 0 ) + N > η(π 0 ) + N (6) ; Multiple meson production during secondary scatterings (3),(4),(6). () M. G. Gonçalves et al., Phys. Lett. B 406, (997). () T. E. Rodrigues et al., Phys. Rev. C 69, 0646 (004). (3) T. E. Rodrigues et al., Phys. Rev. C 7, 05603(R) (005). (4) T. E. Rodrigues et al., Braz. J. of Phys. 36, 366 (006). (5) T. E. Rodrigues et al., Phys. Rev. C 75, (007). (6) T. E. Rodrigues et al., Phys. Rev. Lett. 0, 030 (008). /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 5
6 /30/009 /30/009 Tulio Rodrigues Tulio Rodrigues VIII LASNPAP VIII LASNPAP Santiago Santiago - Chile Chile 6 The elementary meson photoproduction: γ + N > η(π 0 ) + N The cascade trigger ) ( ) ( ) ( ) ( p N p P p N k + + γ ) ( ) ( p k t p k s = + = γ η (π 0 ) N N ρ, ω Calculation of the incoherent cross section: γ + Α > η(π 0 ) + X s p m F F m F m F F k t m F F dt d N N N N N μ π σ ( ) A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 004. ( ) M. Braunschweig et al., Nucl. Phys. B 0, 9 (970). Cross section expanded in t-channel helicity amplitudes (F i ) i F Calculated using a Regge model (ρ and ω exhange) plus Reggeon cuts**
7 The elementary mechanism: γ + N > π 0 + N γp >π 0 p 0.0 DESY 4.0 GeV 5.0 GeV dσ n /dt (μb/gev ) SLAC 5.8 GeV 6.0 GeV 9.0 GeV.0 GeV GeV t (GeV ) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 7
8 The elementary mechanism: γ + N > π 0 + N Contribution of the Reggeon cuts and the Coulomb amplitude dσ n /dω (μb/sr) DESY DATA Total (Strong with cuts + Coulomb) Strong with cuts Strong without cuts (0.005 < t <0.3 GeV ) γp > π 0 p k = 5.8 GeV π 0 polar angle, CM frame (deg.) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 8
9 The elementary mechanism: γ + N > η + N γ + p > η + p BONN-DESY J. Dewire SLAC dσ/dt (μb/gev ) 0.0 k = 4.0 GeV k = 6.0 GeV k = 5.5 GeV E k = 6.5 GeV k = 8.0 GeV k = 9.0 GeV E t (GeV ) - t (GeV ) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 9
10 Calculation of the incoherent cross section: γ + Α > η(π 0 ) + X Cross section (mb) E-3 Meson nucleus FSI π p > X s / (GeV) exp (PDG) Fitting (χ /n.d.f. =.6) Total (MCMC) Elastic Δ(3) 0 N(50) 0 N(680) 0 nπ 0 pπ - π + nπ 0 pπ - π 0 pπ - π 0 π + nπ - π 0 π + nπ - π + pπ - π + nπ - π + nπ - π 0 π + n3π 0 p3π - π + n3π - 3π + p3π - π 0 π + pπ - 3π 0 pπ - π 0 π + (+n) >nn /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 0
11 Results: Incoherent π 0 photoproduction in PrimEx Motivation: To deliver a sophisticated calculation for incoherent π 0 photoproduction in PrimEx. Kinematics and main features: Photon energy: 5. GeV pion elasticity: [0.9 ] angular range: [0 6] deg targets: C and Pb elementary photoproduction Pauli-blocking photon shadowing π 0 nucleus FSI π 0 N > π 0 N elastic channel single and double differential cross sections /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
12 Results: Incoherent π 0 photoproduction in PrimEx MCMC model calculations for the angular distribution of quasi-elastic π 0`s dσ/dω (μb/sr) γ C > π 0 X k = 5. GeV ε π 0: [0.9.0] dσ PWIA dσ PB dσ FSI dσ FSI+SHAD dσ/dω (μb/sr) γ 08 Pb > π 0 X k = 5. GeV ε π 0: [0.9.0] dσ PWIA dσ PB dσ FSI dσ FSI+SHAD π 0 polar angle (deg.) π 0 polar angle (deg.) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
13 Results: Incoherent π 0 photoproduction in PrimEx MCMC model calculations for the double differential cross section γ(5. GeV) + C > π 0 + X 0.04 θ π 0 = θ π 0 =.5 0 θ π 0 = dσ/dθ π 0dE π 0 (μb/rad.mev) θ π 0 = θ π 0 = θ π 0 = θ π 0 = θ π 0 = θ π 0 = θ π 0 = E π 0 (MeV) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 3
14 Results: Incoherent π 0 photoproduction in PrimEx Results from PrimEx experiment (MIT/JLab analysis plots from Dustin McNulty) (Shad.) ~ 0.76 PrimEx Collaboration /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 4
15 Results: measured ratio A eff = σ γa /σ γn from Cornell MCMC model calculations (solid lines) versus Cornell`s data* 00 Pb Ag Cu A eff 0 Al C Be E 0 π (GeV) * W. T. Meyer et al., Phys. Rev. Lett. 8, 344 (97). /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 5
16 Results: Incoherent π 0 and η photoproduction at GeV dσ n /dω (μb/sr) dσ n /dω (μb/sr) γn > π 0 N γn > ηn MCMC trigger k = GeV meson polar angle, CM frame (deg.) k = GeV dσ/dω (μb/sr) dσ/dω (μb/sr) γbe > π 0 X γbe > ηx MCMC output k = GeV k = GeV meson polar angle, Lab. frame (deg.) dσ/dω (μb/sr) dσ/dω (μb/sr) γc > π 0 X γc > ηx MCMC output k = GeV k = GeV meson polar angle, Lab. frame (deg.) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 6
17 Incoherent η photoproduction in Cornell (η > γγ decay width revisited) MCMC model calculations for the angular distributions γa > ηx k = 8.5 GeV Be Cu PWIA with Pauli-blocking with FSI with FSI and Shadowing dσ/dω (μb/sr) η polar angle (deg.) η polar angle (deg.) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 7
18 n( θ ) = a S ( θ ) + a S ( θ ) + a S ( θ ) + a a cos( φ) S ( θ ) S ( θ ) P P Incoherent η photoproduction in Cornell (η > γγ decay width revisited) NC NC NI NI P NC P NC events 80 Be Cornell data Primakoff Nuclear Coherent Nuclear Incoherent Interference Total Be a NI a n b S MCMC NI Cornell b ( θ) ( θ) η polar angle (mrad) η polar angle (mrad) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 8
19 Incoherent η photoproduction in Cornell (η > γγ decay width revisited) η > γγ Decay Width (kev) Isotropic NI background MD JADE CBAL ASP Cornell 0.34(46) kev Experiments MD MCMC NI background JADE ASP CBAL Cornell () 0.5(90) kev (Be only) Cornell (,) 0.476(6) kev (Be and Cu) PDG average 0.50(6) kev Experiments () The error bars represent the statistical errors from the fits () T. E. Rodrigues et al., Phys. Rev. Lett. 0, 030 (008) /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 9
20 Conclusions and final remarks The MCMC model is a nice framework to address the nuclear matter effects within wide ranges of target masses and incident energies (4 to GeV). The calculations for incoherent π 0 photoproduction fit the PrimEx data at larger angles both for Carbon (χ /n.d.f ~.4) and Lead (χ /n.d.f ~.). The fitted parameters are mutually consistent and reasonably close to unit (~ 0.76). The calculations reproduced with good accuracy both the measured ratio A eff and the inelastic background in Cornell s experiments of π 0 and η photoproduction from complex nuclei, respectively. The MCMC calculations for incoherent π 0 photoproduction show that the proton data (DESY/SLAC) and the complex nuclei data from Cornell (Be, C, Al, Cu, Ag and Pb) are mutually consistent. /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile 0
21 Conclusions and final remarks The result for the η > γγ decay width obtained [0.476(6) kev] is consistent with the PDG average [0.50(6) kev] and approximately 50% higher than the previous value from Cornell [0.34(46) kev]. On the other hand, the result is not supposed to supersede Cornell s result for the following reasons:. The uncertainty of the decay width does not include the systematic errors and represents a lower limit of the analysis;. We analyzed only a fraction of Cornell s data (Be and Cu at 9 GeV) not all the data. The Monte Carlo method represents an important tool to delineate the NI cross section in future experiments to measure the radiative decay width of pseudo scalar mesons via the Primakoff effect. A high precision Primakoff-type experiment to determine the η > γγ decay width and the proton amplitude with better accuracy is highly recommended with the GeV upgrade at Jlab. /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
22 Incoherent photoproduction of π 0 and η from complex nuclei up to GeV Tulio E. Rodrigues University of São Paulo - Brazil Collaborators: João Arruda-Neto (USP, São Paulo, Brazil) Joel Mesa (UNESP, Botucatu, Brazil) Cesar Garcia (CEADEN, Havana, Cuba) Katherin Shtejer (CEADEN, Havana, Cuba) Dan Dale (ISU, Pocatello, USA) Itaru Nakagawa (RIKEN, Japan) Phillip Cole (ISU, Pocatello, USA) Thank you! /30/009 Tulio Rodrigues VIII LASNPAP Santiago - Chile
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