SEARCH FOR THE ONSET OF COLOR TRANSPARENCY ELECTROPRODUCTION ON NUCLEI. Outline

Transcription

1 SEARCH FOR THE ONSET OF COLOR TRANSPARENCY THROUGH ρ 0 ELECTROPRODUCTION ON NUCLEI Outline 1 introduction 2 Theoretical introduction 3 Experiments 4 CLAS EG2 5 Results 6 Future ρ 0 measurements at JLAB 7 Conclusions 8 Backup Lorenzo Zana The University of Edinburgh L. El Fassi, K. Hafidi, M. Holtrop, B. Mustapha W. Brooks, H. Hakobyan, CLAS collaboration June 8, 2015

2 Introduction Color Transparency is a QCD phenomenon which predicts a reduced level of interaction for reactions where the particle state is produced in a point-like configuration.

3 Introduction Color Transparency is a QCD phenomenon which predicts a reduced level of interaction for reactions where the particle state is produced in a point-like configuration. EG2 experiment using the CLAS detector at Jefferson Lab The Nuclear Transparency was measured in ρ 0 electro-production through nuclei. A signal of Color Transparency will be an increase of the Nuclear Transparency with a correspondent increase in Q 2

4 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Coherence Length effect with the Glauber model An approximation of scattering through Quantum Mechanics High-Energy collision theory, by R.J. Glauber Using hadron picture for Nuclear Interaction.

5 Coherence Length effect with the Glauber model K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production

6 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup QCD model and Color Transparency What is missing in the previous model? In the Glauber model, that gives a Quantum mechanical description of the interaction with matter, there is no mention of the particles to be considered as a composite system of quarks.

7 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup QCD model and Color Transparency What is missing in the previous model? In the Glauber model, that gives a Quantum mechanical description of the interaction with matter, there is no mention of the particles to be considered as a composite system of quarks. Glauber model No other Q 2 dependence other than the one due to the coherence length effect

8 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration.

9 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration. Momentum Each quark, connected to another one by hard gluon exchange carrying momentum of order Q should be found within a distance of the order of Q1

10 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration. Momentum Each quark, connected to another one by hard gluon exchange carrying momentum of order Q should be found within a distance of the order of Q1 Color Transparency Such an object is unable to emit or absorb soft gluons its interaction with the other nucleons is significantly reduced

11 A lot of EXPERIMENTS since 1988 Quasi-elastic A(p,2p) [Brookhaven] Quasi-elastic A(e,ep) [ SLAC and Jlab] Di-jets diffractive dissociation. [Fermilab] Quasi-elastic D(e,ep) [Jlab - CLAS] Pion Production 4 He,( γ n p π ) [Jlab] Pion Production A(e,eπ + ) [Jlab] ρ 0 lepto production. [Fermilab, HERMES] ρ 0 lepto production & D(e,ep) [ Jlab - CLAS ]

12 OTHER EXPERIMENTS, Thomas Jefferson Lab: Hall A D. Dutta, PRC 68, (2003) Pion photo-production on 4 He, ( γ n p π ) at θ π cm = 70 at θπ cm = 90

13 Thomas Jefferson Lab: Hall C B. Clasie, PRL 99, (2007) Pion e-production on 2 H, 12 C, 27 Al, 63 Cu and 197 Au, ( γ p n π + ) T = ( Ȳ ȲMC ) A Ȳ ( ) Ȳ H MC T = A α 1, with α 0.76

14 HERA positron storage ring at DESY: HERMES A. Airapetan, PRL 90, (2003) Measurement of the Nuclear Transparency, incoherent ρ 0 prod. T A = P 0 + P 1 Q 2,with P 1 = (0.089 ± ± 0.020)GeV 2

15 Thomas Jefferson Lab: CLAS EG2 experiment Electron Beam 5GeV (50 days) & 4GeV (7days) Targets: D&Fe, D&C, D&Pb Luminosity 2x10 34 cm 2 s 1

16 Eg2 experiment target

17 Eg2 experiment target

18 Author information Reprints and permissions information is available a Correspondence and requests for materials should be addressed to K.H. (kawtar@anl.gov). introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ 0 measurements at JLAB Conclusions Backup Reaction

19 Reaction Variables and kinematical cuts N Data Selection: q _ q t N 0 Q 2 = (q µ γ )2 4E e E e sin 2 ( θ 2 ) ν = E e E e t = (q µ γ pµ ρ 0 ) 2 W 2 = (q µ γ + pµ N )2 Q 2 + M 2 p + 2M p ν W > 2GeV, to avoid the resonance region t > 0.1GeV 2 to exclude coherent production off the nucleus t < 0.4GeV 2 to be in the diffractive region z = Eρ ν > 0.9 to select the elastic process

20 Mππ invariant mass, showing ρ 0 peak Kinematical cuts: Select the physics of interest Enhance the ρ 0 peak Cut a lot of data

21 Mππ invariant mass, showing ρ 0 peak Invariant mass for H 2, C and Fe

22 Extraction of the Nuclear Transparency The goal of the experiment is to determine the Nuclear Transparency T ρ0 A as a function of Q2 and l c T ρ0 A = ( N ρ 0 A L int A ) ( Nρ0 D ) L int D where L int A is the integrated luminosity for the target A L int A = nnucleons A Q int q e

23 Nuclear Transparency for Iron and Carbon l c dependence of Nuclear Transparency C 56 Fe 0.7 Nuclear Transparency ( 0.77) l c (fm) Nuclear Transparency

24 Nuclear Transparency for Iron and Carbon 12 C 56 Fe C 56 Fe ( 0.77) Nuclear Transparency 0.55 FMS Model FMS Model (CT) function of l c.the 0.45 the outer ones are stematic uncertainnormalization sysor iron (not shown btraction being the a factor 0.77 to fit Q 2 (GeV 2 ) GKM Model GKM Model (CT)

25 Nuclear Transparency for Iron and Carbon Table 1: Fitted slope parameters of the Q 2 -dependence of the nuclear transparency for carbon and iron nuclei. The results are compared with theoretical predictions of KNS [37], GKM [38] and FMS [39]. Measured Slopes Model Predictions Nucleus GeV 2 KNS GKM FMS C ± stat ± syst Fe ± stat ± syst B. Z. 261 Kopeliovich, J. Nemchik and I. Schmidt, Phys. 313 Rev. C , (2007) K. Gallmeister, 264 M. Kaskulov and U. Mosel, Phys. Rev. 316 C 83, (2011) L. Frankfurt, 267 G. A. Miller and M. Strikman, Private Communication based on Phys. Rev. C 78, (2008) but somewhat larger than the Frankfurt-Miller-Strikman (FMS) [39] calculations. While the KNS and GKM models yield an approximately linear Q 2 dependence, the FMS calculation yields a more complicated Q 2 dependence as shown in Fig. 4. The measured slope for carbon corresponds to a drop in the absorption of the ρ 0 from 37% at Q 2 = 1GeV 2 to 32% at Q 2 = 2.2 GeV 2,inreasonableagreementwiththecalculations. Despite the differences between these models in the assumed production mechanisms and SSC interaction in the nuclear medium, they all support the idea that the observed Q 2 dependence is clear evidence for the of the SSCs. Suc by future measure additional nuclei an We thank M. Sar the Fermi motion eff the outstanding effo the Physics Divisio experiment possible by the U.S. Depart Physics, under co and No. DE-FG02- CYT grants , BASAL FB082 the Italian Istituto French Centre Nat the French Comm National Research ence and Technolo the Physics Depart The Jefferson Scie Thomas Jefferson N

26 Thomas Jefferson Lab 12GeV upgrade: CLAS12 in Hall-B Up to 20 times more luminosity than CLAS Improved particle identification Access to higher masses Much larger kinematical range

27 Future ρ 0 measurements with CLAS12 at JLAB

28 Future ρ 0 measurements with CLAS12 at JLAB

29 Conclusions We see a rise in the Transparency of ρ 0 electro-production with increasing Q 2 We have different model calculations by KNS, GKS, FMS which well interpret the data.

30 Conclusions We see a rise in the Transparency of ρ 0 electro-production with increasing Q 2 We have different model calculations by KNS, GKS, FMS which well interpret the data. Approved experiment with CLAS12 at the future 12GeV upgraded Jefferson Laboratory with increased Q 2 range

31 Conclusions We see a rise in the Transparency of ρ 0 electro-production with increasing Q 2 We have different model calculations by KNS, GKS, FMS which well interpret the data. Approved experiment with CLAS12 at the future 12GeV upgraded Jefferson Laboratory with increased Q 2 range Thank you for your time

32 Backup Slides Glauber model l c effect l c effect Hermes data l c effect Hermes, EG2 data QCD model PLC definition PLC and Nuclear filtering Color Transparency Data Analysis Lengths in the reaction Kinematical cuts Diffractive region test Simulation, Background,Acceptance Extraction of the Nuclear Transparency Results FMS Model GKM Model KNS Model Comparison ρ 0 data and π data (FMS)

33 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Glauber model An approximation of scattering through Quantum Mechanics High-Energy collision theory, by R.J. Glauber Using hadron picture for Nuclear Interaction.

34 Glauber model Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 k ( j) (c) V Nucleus Nucleons

35 Glauber model Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 k ( j) (c) * z>z j (b s j ) V V s j z j b z

36 Glauber model Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 k ( j) (c) * z>z j (a) (b s j ) s j z j b V z V Γ γ V N ( b s j ) is the vector meson photo-production amplitude on a nucleon

37 Glauber model * Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 z>z j (b) k ( j) (c) Considering the quantities Longitudinal and transverse to the axis z of symmetry, (b s j ) V V q L = p γ L p V L = Q2 + M 2 V 2ν s j z j b z l c = 1 q L = 2ν Q 2 +M 2 V for (z j 1 z j 2) < l c contributions will add coherently

38 Glauber model Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 k ( j) (c) * z>z j (b) (b s j ) V V l c = 1 q L = 2ν Q 2 +M 2 V s j z j b z The γ interacts simultaneously with all the target nucleons within a distance l c

39 Glauber model * Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 z>z j (c) k ( j) (c) small scattering ( k k ) on the nuclei with z k > z j k k ẑ = ( k k ) ẑ (b s j ) V V Γ( b) = (e iχ( b) 1) and χ VV tot = m χvv m ( b s m) s j z j b z e i m χvv m ( b s m) = m (1 Γ VV m ( b s m))

40 Glauber model Γ γ V A ( b) = (a) (b) {}}{ A {}}{{}}{ Γ γ V N ( A [ b s j ) e i q Lz j 1 Γ VV N ( ] b s k ) θ(z k z j ) j=1 k ( j) (c) * z>z j (c) (b s j ) s j z j b V z V with this easy model ( J.Hüfner et al., Phys. Lett. B383 (2996) 362) were able to parameterize the Q 2 and ν dependence of the Nuclear Transparency due to Coherence length effect

41 Glauber model (c) with this easy model ( J.Hüfner and oth., arxiv:nucl-th ) were able to parameterize the Q 2 and ν dependence of the Nuclear Transparency due to Coherence length effect

42 HERA positron storage ring at DESY: HERMES K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production

43 HERA positron storage ring at DESY: HERMES K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect 2l c l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production: 1 Inter-nuclear spacing

44 HERA positron storage ring at DESY: HERMES K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production 1 Inter-nuclear spacing (< r 2 > 1/2 0.8fm)

45 HERA positron storage ring at DESY: HERMES K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production 2l c 1 Inter-nuclear spacing (< r 2 > 1/2 0.8fm) 2 Atom size

46 HERA positron storage ring at DESY: HERMES K. Ackerstaff, PRL 82, 3025 (1999) Exclusive ρ 0 electro-production, Coherence length ( l c ) effect l c = 2ν M 2 V +Q2 Cross section dependence on l c Mimics CT signal for incoherent ρ 0 production 1 Inter-nuclear spacing (< r 2 > 1/2 0.8fm) 2 Atom size

47 EG2 and HERMES kinematical range HERMES experiment kinematical range: 0.8GeV 2 < Q 2 < 4.5GeV 2 5GeV < ν < 24GeV

48 EG2 and HERMES kinematical range ) 2 (GeV 2 Q EG2 experiment kinematical range: 0.9GeV 2 < Q 2 < 2GeV 2 2.2GeV < ν < 3.5GeV ν (GeV)

49 EG2 and HERMES kinematical range EG2 experiment kinematical range: 0.9GeV 2 < Q 2 < 2GeV 2 2.2GeV < ν < 3.5GeV

50 EG2 experimental l c dependence? l c vs Q 2 range for Iron target

51 EG2 experimental l c dependence? l c vs Q 2 range for Iron target 1.0GeV 2 < Q 2 < 1.6GeV 2 T l c (GeV )

52 EG2 experimental l c dependence? l c vs Q 2 range for Iron target 1.0GeV 2 < Q 2 < 2.2GeV 2 T l c (GeV )

53 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration.

54 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration. Momentum Each quark, connected to another one by hard gluon exchange carrying momentum of order Q should be found within a distance of the order of Q1

55 introduction Theoretical introduction Experiments CLAS EG2 Results Future ρ0 measurements at JLAB Conclusions Backup Point like configuration What is it? High Q 2 in the reaction will select a very special configuration of the hadron wave function, where all connected quarks are close together, forming a small size color neutral configuration. Momentum Each quark, connected to another one by hard gluon exchange carrying momentum of order Q should be found within a distance of the order of Q1 Color Transparency Such an object is unable to emit or absorb soft gluons its interaction with the other nucleons is significantly reduced

56 Point like configuration: The distribution amplitude The distribution amplitude is (Lepage and Brodsky, PRD 22, 2157) φ(q 2, x) = Q 2 0 d 2 k T ψ(k T, x) ; (x = Longitudinal momentum fraction)

57 Point like configuration: The distribution amplitude The distribution amplitude is (Lepage and Brodsky, PRD 22, 2157) φ(q 2, x) = Q 2 0 d 2 k T ψ(k T, x) ; (x = Longitudinal momentum fraction) if we expand this expression in Fourier series φ(q 2, x) = Q 2 0 d 2 k T d 2 b T e i b T k T ψ(bt, x)

58 Point like configuration: The distribution amplitude The distribution amplitude is (Lepage and Brodsky, PRD 22, 2157) φ(q 2, x) = Q 2 0 d 2 k T ψ(k T, x) ; (x = Longitudinal momentum fraction) if we expand this expression in Fourier series φ(q 2, x) = Q 2 0 d 2 k T and assume cylindrical symmetry around k T d 2 b T e i b T k T ψ(bt, x) φ(q 2, x) = (2π) 2 db Q J 1 (Qb) ψ(b T, x) 0

59 Point like configuration: The distribution amplitude φ(q 2, x) = (2π) 2 0 db Q J 1(Qb) ψ(b T, x) 2 (Q J (Qb)) Q b

60 Point like configuration: The distribution amplitude φ(q 2, x) = (2π) 2 0 db Q J 1(Qb) ψ(b T, x) (Q J 2 (Qb)) At high Q 2 the distribution amplitude tends to evaluate the wave function at points of small transverse space separation ( b T ) Q b

61 Point like configuration: The distribution amplitude φ(q 2, x) = (2π) 2 0 db Q J 1(Qb) ψ(b T, x) (Q J 2 (Qb)) At high Q 2 the distribution amplitude tends to evaluate the wave function at points of small transverse space separation ( b T ) Short distance is a statement about a dominant integration region Q b

62 Point like configuration: The distribution amplitude φ(q 2, x) = (2π) 2 0 db Q J 1(Qb) ψ(b T, x) (Q J 2 (Qb)) At high Q 2 the distribution amplitude tends to evaluate the wave function at points of small transverse space separation ( b T ) Short distance is a statement about a dominant integration region Q b Each quark, connected to another one by hard gluon exchange carrying momentum of order Q should be found within a distance O( 1 Q )

63 Color Interaction: Simple model (P. Jain et al., PR271, 93) See P. Jain et al., Physics Report 271 (1996) 93 q x 1 PLC x 1 q b T y 1 y 1 PLC x 2 u y 2 x 2 d y 2 x u 2 y 2

64 Color Interaction: Simple model (P. Jain et al., PR271, 93) x 1 q y 1 x 1 q y 1 PLC x 1 q b T y 1 PLC PLC b T PLC x 1 q y x 2 y 2 q x 2 y 2 q x 1 q y 1 PLC b T PLC x 1 q y 1 x 1 q y 1 PLC b T PLC x 1 q y = x 2 y 2 x 2 y 2 q q K(x i, x j ) { }} { V (x 1 x 2 )V (x 1 x 2 ) V (x 1 x 2 )V (x 1 x 2) + V (x 1 x 2)V (x 1 x 2) V (x 1 x 2)V (x 1 x 2 )

65 Color Interaction: Simple model (P. Jain et al., PR271, 93) K(x i, x j ) [V (x 1 x 2) V (x 1 x 2 )] 2 for (b T = x 1 x 1 0), I have f (x 1 ) f (x 1) x 1 x 1 df dx 1 K(x i, x j ) {b T [V (x 1 x 2 )]} 2

66 Color Interaction: Simple model (P. Jain et al., PR271, 93) K(x i, x j ) [V (x 1 x 2) V (x 1 x 2 )] 2 for (b T = x 1 x 1 0), I have f (x 1 ) f (x 1) x 1 x 1 df dx 1 K(x i, x j ) {b T [V (x 1 x 2 )]} 2 K(x i, x j ) (b T ) 2

67 Finally: Color Transparency (1) At the time of the reaction, the hadron has to fluctuate to a Point Like configuration

68 Finally: Color Transparency (1) At the time of the reaction, the hadron has to fluctuate to a Point Like configuration (2) This configuration will experience a reduced interaction in the nucleus

69 Finally: Color Transparency (1) At the time of the reaction, the hadron has to fluctuate to a Point Like configuration (2) This configuration will experience a reduced interaction in the nucleus (3) A signature of Color Transparency will be an increase in nuclear transparency T A with an increase in the hardness of the reaction, driven by Q 2

70 Lengths in the reaction, order of magnitude Fluctuation q q ν Q _ q q N t N fm nucleon R 1.1 A 1/3 Carbon Iron fm

71 Lengths in the reaction, order of magnitude Formation length ρ 0 2E ρ 0 M 2 ρ 1 M2 ρ _ q q N t N fm nucleon R 1.1 A 1/3 Carbon Iron fm

72 Kinematical cuts W > 2GeV, to avoid the resonance region

73 Kinematical cuts W > 2GeV, to avoid the resonance region

74 Kinematical cuts W > 2GeV, to avoid the resonance region t > 0.1GeV 2 to exclude coherent production off the nucleus t < 0.4GeV 2 to be in the diffractive region

75 Kinematical cuts W > 2GeV, to avoid the resonance region t > 0.1GeV 2 to exclude coherent production off the nucleus t < 0.4GeV 2 to be in the diffractive region

76 Kinematical cuts W > 2GeV, to avoid the resonance region t > 0.1GeV 2 to exclude coherent production off the nucleus t < 0.4GeV 2 to be in the diffractive region z = Eρ > 0.9 to select the ν elastic process

77 Kinematical cuts W > 2GeV, to avoid the resonance region t > 0.1GeV 2 to exclude coherent production off the nucleus t < 0.4GeV 2 to be in the diffractive region z = Eρ > 0.9 to select the ν elastic process

78 Diffractive ρ 0 production Diffractive ρ 0 production. Fit to: Ae bt 10 6 (3.58 ± 0.5) 10 6 (3.67 ± 0.8) N 10 5 (3.72 ± 0.6) N C H Fe C t (GeV/c) t (GeV/c) 2 -t dependence show the rapid fall expected for incoherent diffractive ρ 0 production, consistent with CLAS data: (2.63 ± 0.44) Morrow JLAB-PHY , arxiv: PINAN11, Marrakech, 2011 Maurik Holtrop - University of New Hampshire 23 Tuesday, September 27, 11 23

79 Background Study and Simulation ρ 0 (GeV) ρ 0 REC bin 1 Liquid target χ 2 =246 for DF= As event generator used the one implemented by B. Mustapha (ANL) Tune to the Eg2 experiment configurations Radiative Effects, Fermi motion of target Possibility of using experimental cross section (D.Cassel, Physical Review D, 24 (1981)) for tuning the different contributions in our kinematics Background assumed composition: 1 γ + p = ++ + π 2 γ + p = 0 + π + 3 γ + p = p + π + + π ρ 0 (GeV) ρ 0 bin 1 Liquid target χ 2 =68 for DF=57

80 Acceptance correction In CLAS comprehensive of: Acceptance: Geometry of CLAS is not 4π Efficiency: considering together: 1 Detectors 2 Reconstruction protocol 3 Analysis

81 Acceptance correction Unexpectedly large effect of acceptance Due to: 1 tight kinematic cuts, 2 complicated detector 3 targets not at identical location (5 cm from each other)

82 Acceptance correction Iron at 4GeV T 0.54 Determined the correction 0.52 with 2 methods green: bin to bin red: bin to migration consider as systematic 0.42 error Q (GeV /c)

83 Extraction of the Nuclear Transparency The goal of the experiment is to determine the Nuclear Transparency T ρ0 A as a function of Q2 and l c T ρ0 A = ( N ρ 0 A L int A ) ( Nρ0 D ) L int D

84 Extraction of the Nuclear Transparency The goal of the experiment is to determine the Nuclear Transparency T ρ0 A as a function of Q2 and l c T ρ0 A = ( N ρ 0 A L int A ) ( Nρ0 D ) L int D where L int A is the integrated luminosity for the target A L int A = nnucleons A Q int q e

85 L. Frankfurt, G.A. Miller, M. Strikman Model L. Frankfurt, G.A. Miller, M. Strikman, arxiv: v2 [nucl-th] Glauber based calculation. Includes experimental conditions. Includes the ρ 0 decay. With of without the Color Transparency effect.

86 L. Frankfurt, G.A. Miller, M. Strikman Model dσ dt = n=0 dσn dt = T A = dσ dt A dσγ V dt = n=0 dσn dt A dσγ V dt = n=0 T n The full cross section will be given by the sum of all the possible different number of elastic re-scattering ( n in equation)

87 L. Frankfurt, G.A. Miller, M. Strikman Model dσ dt = dσ n n=0 dσ 0 dt = = T dt A = dσ dt (a) A dσγ V dt = n=0 dσn dt A dσγ V dt = n=0 Tn {}}{ V { }}{ A dσγ d 2 b dz ρ(b, z) (1 dz σ totρ(b, z )) A 1 dt (a) represents the sum of all the possible contributions for scattering a Vector meson from a γ in a target with density given by ρ(b, z ) (b) refers to the probability of not having an elastic re-scattering (1 dz σ z totρ(b, z )) from all the remaining nucleons (A 1) starting from the point z of the vector meson s creation z (b)

88 L. Frankfurt, G.A. Miller, M. Strikman Model dσ dt dσ 0 dt = dσ n n=0 = A dσγ V dt = T dt A = dσ dt d 2 b σ D eff (z z, p ρ 0) =σ tot(p ρ 0) A dσγ V dt = n=0 dz ρ(b, z)(1 z [( n 2 < kt 2 > + σ tot(p ρ 0) [ + 2σ πn ( p ρ 0 2 ) dσn dt A dσγ V dt = n=0 Tn dz σ totρ(b, z )) A 1 Q 2 + z l h (1 n2 < k 2 T > θ((z z) l h ) exp [ θ((z z) l h ) ( ( ) ] ) θ(l Q 2 h (z z)) )] Γ ρ 0 (z z) γ pρ 0 1 exp ( Γ ρ 0 (z z) γ pρ 0 ))].

89 L. Frankfurt, G.A. Miller, M. Strikman Model [( σeff D (z n 2 < kt 2 > z, p ρ 0) =σ tot(p ρ 0) [ + σ tot(p ρ 0) + 2σ πn ( p ρ 0 2 ) Q 2 + z l h (1 n2 < k 2 T > θ((z z) l h ) exp [ θ((z z) l h ) ( ( ) ] ) θ(l Q 2 h (z z)) )] Γ ρ 0 (z z) γ pρ 0 1 exp ( Γ ρ 0 (z z) γ pρ 0 ))]. Point Like Configuration interaction

90 L. Frankfurt, G.A. Miller, M. Strikman Model [( σeff D (z n 2 < kt 2 > z, p ρ 0) =σ tot(p ρ 0) [ + σ tot(p ρ 0) + 2σ πn ( p ρ 0 2 ) Q 2 + z l h (1 n2 < k 2 T > θ((z z) l h ) exp [ θ((z z) l h ) ( ( ) ] ) θ(l Q 2 h (z z)) )] Γ ρ 0 (z z) γ pρ 0 1 exp ( Γ ρ 0 (z z) γ pρ 0 ))]. PLC evolution in θ(l h (z z)) l h = 2p ρ 0/ M 2 is the formation time tot PLC z l h z

91 L. Frankfurt, G.A. Miller, M. Strikman Model [( σeff D (z n 2 < kt 2 > z, p ρ 0) =σ tot(p ρ 0) [ + σ tot(p ρ 0) + 2σ πn ( p ρ 0 2 ) Q 2 + z l h (1 n2 < k 2 T > θ((z z) l h ) exp [ θ((z z) l h ) ( ( ) ] ) θ(l Q 2 h (z z)) )] Γ ρ 0 (z z) γ pρ 0 1 exp ( Γ ρ 0 (z z) γ pρ 0 ))] PLC evolution in θ(l h (z z)) l h = 2p ρ 0/ M 2 is the formation time fm

92 L. Frankfurt, G.A. Miller, M. Strikman Model [( σeff D (z n 2 < kt 2 > z, p ρ 0) =σ tot(p ρ 0) [ + σ tot(p ρ 0) + 2σ πn ( p ρ 0 2 ) Q 2 + z l h (1 n2 < k 2 T > θ((z z) l h ) exp [ θ((z z) l h ) ( ( ) ] ) θ(l Q 2 h (z z)) )] Γ ρ 0 (z z) γ pρ 0 1 exp ( Γ ρ 0 (z z) γ pρ 0 ))]. Vector meson interaction + decay Interaction of decay product

93 GKM Model GMK Model Gallmeister, Kaskulov, Mosel. PRC 83, (2011) Coupled channel Giessen Boltzmann-Uehling- Uhlenbeck (GiBUU) transport equation. Includes rho decay and subsequent pion absorption. Includes experimental cuts and acceptance. With and without CT effects. PINAN11, Marrakech, 2011 Maurik Holtrop - University of New Hampshire 37

94 KNS Model KNS Model Kopeliovich, Nemchik, Schafer, Tarasov PRC 65 (2002) Light Cone QCD Formalism for q q-bar dipole. σ(qq) - Universal dipole cross section for q q-bar interaction with a nucleon, fit to proton structure functions over a large range of x, Q 2. LC wave function for q q-bar fluctuation of photon. LC wave function for vector meson. Parameter free (apart from initial fit). Will add the rho decay soon. PINAN11, Marrakech, 2011 Maurik Holtrop - University of New Hampshire 35

95 Comparison ρ 0 data and π data (FMS) Rho and Pion CT compared Using the same ingredients the FSM (LSM) model agrees well with both data sets.! FMS: Frankfurt, Miller and Strikman, PRC 78: , 2008 LSM: Larson, Miller and Strikman, PRC 74, (2006) PINAN11, Marrakech, 2011 Rho data FMS Model (CT) FMS Model (NO CT) 0.76 Pion data 0.74 LMS Model (CT) 0.72 LMS Model (NO CT) Q 2 (GeV/c) 2 Maurik Holtrop - University of New Hampshire 45 Tuesday, September 27, 11 45