12/14/2015 tulio rodrigues – nn2012 – san antonio – usa 1 11 th international conference on...

04/21/2304/21/23 Tulio Rodrigues – NN2012 – San Antonio – USATulio Rodrigues – NN2012 – San Antonio – USA 11

11th INTERNATIONAL CONFERENCE ON NUCLEUS-NUCLEUS COLLISIONSSan Antonio, Texas, May 27 thru June 1, 2012

Hadrons in a Cold Nuclear MediumTulio Rodrigues, University of São Paulo, Brazil


oThe nucleus as a QCD laboratory

• Chiral anomaly of QCD (2 decay of pseudoscalar

mesons)

• Chiral symmetry restoration in nuclei

o Forward angle meson photoproduction in nuclei (MCMC

model)

o Confronting theory and experiment

• pseudoscalar mesons (Cornell and PrimEx @ JLab)

• vector mesons (TAPS and g7a @ JLab)

o Conclusions and future prospects

O

U

T

L

I

N

E

11th INTERNATIONAL CONFERENCE ON NUCLEUS-NUCLEUS COLLISIONSSan Antonio, Texas, May 27 thru June 1, 2012


oThe nucleus as a QCD laboratory

• Chiral anomaly of QCD (theoretical scenario for 0

decay)

used as input to obtain beyond the LO chiral anomaly

LO chiral LO chiral anomaly anomaly ((NNcc = =

3)3)

NLO ChPT NLO ChPT andand

1/1/NNcc

expansionexpansion

NNLONNLO

two flavor two flavor ChPTChPT

QCDQCD

sum rulesum rule

Bell & JackiwNC A 60, 47 (1969)

AdlerPR 177, 2426 (1969)

Goity, Bernstein and Holstein

PRD 66, 076014 (2002)

(1) Ananthanarayan & Moussallam

JHEP 0205, 052 (2002)

(2) Kampf & Moussallam

PRD 79, 076005 (2009)

Ioffe & Oganesian PLB 647, 389 (2007)

0

eV 044.0725.7

64

23

32

F

m

1.0%eV 10.8 (1) 1.0%eV 06.8 (2) 1.4%eV 09.8

1.5%eV .937

MOTIVATION


22

NINCi

PA TTeT

d

d

22

22sin)(

~QFAT NNC

P

A A

NuclearCoherent

dTAdT NeffNI

22

P

A A*

NuclearIncoherent

22

4

43

3

22

sin)(~8

QFQ

k

m

ZT em

PPP

Coulomb(Primakoff)

P

A A

• Chiral anomaly of QCD: P via the Primakoff method

MOTIVATION


• Chiral anomaly of QCD: 0 decay

revisited

Figure: R. Miskimen, Annu. Rev. Nucl. Part. Sci. 61, 1 (2011)

PrimEx data: I. Larin et al., Phys. Rev. Lett. 106, 162303 (2011)

MOTIVATION


• Chiral anomaly of QCD: decay revisited

PDG: K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)

Cornell: A. Browman et al., Phys. Rev. Lett. 32, 1067 (1974)

0 1 2 3 4 5 6 7 80.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

E xperiments

0.510(26) keV

0.324(46) keV

Cornell (Primakoff-effect)

JADECBALASP

MD1

PDG average

Dec

ay W

idth

(k

eV)

Removed from the PDG world average

20 year old puzzle!MOTIVATION

(1)



Hatsuda et al., PRL 55, 158 (1985)Weise et al., NPA 553, 59 (1993)

...8

100

00222

2

0

,

fmf

T

qq

qqNT

NPB 321, 387 (1989)PRC 45, 1881 (1992)PLB 357, 199 (1995)

s partially restored

Hadron properties (mass, width, etc…) are supposed to change in hot and/or dense nuclear matter

(1) Chaden Djalali, Modification of hadrons in the medium, talk in the VIII LASNPAP, December 15 - 19, 2009, Santiago de Chile.

MOTIVATION


MesoMesonn

Mass (MeV)Mass (MeV) (MeV(MeV))

cc (fm)(fm) Main decayMain decay VNVN (mb) (mb)

~ 775~ 775 ~ 150~ 150 ~ 1.3~ 1.3 (~ 100%)(~ 100%) ~ 30~ 30

~ 783~ 783 ~ 8~ 8 ~ 23~ 23 (~ (~ 90%)90%) ~ 30~ 30

~ 1019~ 1019 ~ 4~ 4 ~ 46~ 46 KK++KK-- (~ 50%) (~ 50%) ~ 10~ 10

Light vector meson properties IN VACUUM

HADESHADES , , pp AA XX (VM (VM e e++ ee--))

Jlab – g7aJlab – g7a AA A*A* (VM (VM e e++ e e--))

KEKKEK pp AA XX (VM (VM e e++ e e--))

SPring-8SPring-8 AA A*A* (( K K++ K K--))

TAPSTAPS AA XX (( 00))

Few experiments with nucleus close to equilibrium


MOTIVATION


In-medium width of vector mesons via nuclear transparency measurements

Cross section scaling(Incoherent)

NA A eff

Low density theorem

*0*inel 0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

inel= 25 mb

inel= 30 mb

A

TA/T

C

Transparency ratios

)(

)(12

T

T

eff

eff

CA

AA

AC

A

Nuclear transparency

A

A

A

A

A N

N

N

AA

effeffT


MOTIVATION


THE

MODEL

o Concept of the time-dependent multicollisional MCMC cascade

t < 0, Lab Frame

(k)

t = 0, CM Frame

N (p1)

P (q)

N (p2)

P

k

qp2

kF

t = 0, Lab Frame

or ,,, with , :decay) (particle

or ,,,,,, with ,)( :)conditions(boundary

and or ,,,,,, with ),()( :)collisionsbinary (

*

*

*2

Nit

NNiRtr

NjNNistb

decayi

Nucleussurfaceii

ijijijij

Pick-up the first occurrence (t + tmin) satisfying the cascade criteria

t = tmin, CM Frame

p2

p1

p'2

p'1

p'1 or p'2 (Lab Frame) occupied Pauli-Blockedinteraction

p'1 and p'2 (Lab Frame) available 4-vectorsupdated


THE

MODEL

o Forward angle meson photoproduction in nuclei

0.01

1

0.01

1

0.01

1

0.01

1

0.01

1

0.01

1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.1

12.0 GeV

9.0 GeV

6.0 GeV

5.8 GeV

5.0 GeV

4.0 GeV

p 0p

DESY

dn/d

t (

b/G

eV2 )

SLAC

15.0 GeV

-t (GeV2)

Elementary photoproduction of pseudoscalar mesons [ NN]

Differential cross sections described via a Regge model assuming VDM ( and exchange)

736.110

...

2

FOD

0.0 0.5 1.0 1.50.01

0.1

1

10

BONN-DESY J. Dewire et al.

k = 4.0 GeV

p p

0.0 0.5 1.0 1.50.01

0.1

1

10

SLAC

k = 5.5 GeV

0.0 0.5 1.0 1.51E-3

0.01

0.1

1

10

k = 9.0 GeV

- t (GeV2) - t (GeV2)

0.0 0.5 1.0 1.5

0.01

0.1

1

10

k = 6.0 GeV

d/d

t (b

/GeV

2)

0.0 0.5 1.0 1.5

0.01

0.1

1

10

k = 6.5 GeV

0.0 0.5 1.0 1.51E-3

0.01

0.1

1

10

k = 8.0 GeV

411.52

...

2

FOD


THE

MODEL

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

160

SAPHIR ABBHHM

d/d

t (b

/GeV

2 )

k = 2.1 GeV

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

k = 2.3 GeV0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

k = 2.5 GeV

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

SLAC

k = 4.0 GeVk = 2.8 GeV

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

Regge Model

Y.Eisenberg et al.

k = 4.3 GeV

B

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

-t (GeV2)

k = 4.7 GeV

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

k = 9.3 GeVk = 5.15 GeV

-t (GeV2)

B

0.0 0.1 0.2 0.3 0.4 0.50

40

80

120

+ p + p

-t (GeV2)

Elementary photoproduction of vector mesons [ NN]

Regge model includes Pomeron and -meson exchange amplitudes

0.0 0.1 0.2 0.3 0.4 0.50

10

0

10

0

10

200

10

200

20

0

20

400

20

40

60

-t (GeV2)

SLAC, k = 9.3 GeV

Cornell, k = 8.9 GeV

(g)

(f)

(e)

SLAC, k = 4.7 GeV

(d)

JLab, k = 3.83 GeV

JLab, k = 3.29 GeV

(c)

(b)

SLAC, k = 2.8 GeV

d/

dt (b

/Ge

V2 )

(a)

p p

JLab, k = 2.363 GeV

4870

...

2

FOD

851.80

...

2

FOD



THE

MODEL

-nucleus Final State Interactions (channels included in the MCMC model)



THE

MODEL

Energy dependence of -nucleon scatterings: MCMC model versus PDG



THE

MODEL

o Forward angle meson photoproduction in nuclei (MCMC*)

PB

A

d

d

PSFSIPB

A

d

d

FSIPB

A

d

d

PauliBlocking

FSI

Photonshadowing

PWIA

AN

d

d

d

dA

N N

P

N N

Normalization and initial sampling of

polar angles

NA A eff

dd

d

ddd

AN

PSFSIPB

A

eff

(*) T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)

Incoherent process: A meson X


RESULTS

Differential cross sections for incoherent 0 photoproduction @ 5.2 GeV (PrimEx kinematics)

T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010).

• pseudoscalar mesons


RESULTS

0 photoproduction yields from PrimEx (MIT/JLab analysis)

Line shapes (MIT/JLab analysis)Coherent: S. Gevorkyan et al., Phys. Rev. C 80, 055201 (2009)Incoherent: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)

Figures from Dustin Mcnulty



RESULTS

Revisiting PrimEx data with the latest (state-of-the-art) on coherent photoproduction

o Coherent: M. Kaskulov and U. Mosel, Phys. Rev. C 84, 065206 (2011)

o PrimEx: I. Larin et al., Phys. Rev. Lett. 106, 162303 (2011)

o Incoherent: MCMC model scaled by 1.35 ± 0.03 0.0 0.5 1.0 1.5 2.0 2.5

-4

-2

0

2

4

0 polar angle (deg)

Carbonresid

ue

0.0 0.5 1.0 1.5 2.0-4

-2

0

2

4

Lead

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

5

10

15

20

25

30

35

40

d/d (b

/rad

)

0 polar angle (deg)DOF = 1.47

C 0Xk = 5.2 GeV: []

Coherent PrimEx Coherent Incoherent

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

-200

0

200

400

600

800

Pb 0Xk = 5.2 GeV: []

DOF = 1.47

d/d

(b/

rad)

0 polar angle (deg)

Coherent PrimEx Coherent Incoherent



RESULTS

Incoherent photoproduction in Cornell: decay width revisited

Cornell: A. Browman et al., Phys. Rev. Lett. 32, 1067 (1974)Calculation: T. E. Rodrigues et al., Phys. Rev. Lett. 101, 012301 (2008)



RESULTS

Incoherent photoproduction in Cornell: decay width revisited



RESULTS

TAPS measurements are reproduced assuming *inel 40

mbMCMC (previous version): T. E. Rodrigues and J.D.T. Arruda-Neto, Phys. Rev. C 84, 021601 (R) (2011)TAPS: M. Kotulla et al., Phys. Rev. Lett. 100, 192302 (2008)

• vector mesons

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

1.2

p ~ 1.1 GeV/c

A Xk = 1.5 GeV

A

TA/T

C

TAPS stat

syst

MCMC (Cinel

= Cel = 1)

MCMC (Cinel

= Cel = 1.3)

Attenuation of mesons in nuclei: MCMC versus TAPS measurements

XC

XA

C

A

A

12

T

T

1 100

5000

10000

15000

Pb X

p ~ 1.1 GeV/c

k = 1.5 GeVC

inel= C

el = 1

polar angle (deg, lab frame)

1 100

250

500

750

1000

C X

(dd)PB+FSI+PS

(dd)PB+FSI+PS+TAPS

(dd)PWIA

(dd)PB

d/d

(b/

sr)

pppppCpCp elVN

inelVN

elVNel

inelVNinelVN 6.0 exp104.5)( 420)( )()()( 22*

G. I. Lykasov et. al, Eur. Phys. J. A 6, 71 (1999)


RESULTS

• vector mesons

Giessen: P. Mühlich and U. Mosel, Nucl. Phys. A773, 156 (2006)Valencia: M. Kaskulov, E. Hernandez, and E. Oset, Eur. Phys. J. A 31, 245 (2007)

In-medium width (nuclear rest frame) from TAPS:MCMC versus Giessen /Valencia models

Giessen/Valencia models

130 150 MeV

MCMC model MeV

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

1.2

p ~ 1.1 GeV/c

A Xk = 1.5 GeV

A

TA/T

C

TAPS stat

syst

MCMC (Cinel

= Cel = 1)

MCMC (Cinel

= Cel = 1.3)


RESULTS

CLAS: M. Wood et al., Phys. Rev. Lett. 105, 112301 (2010)TAPS: M. Kotulla et al., Phys. Rev. Lett. 100, 192302 (2008)Giessen: P. Mühlich and U. Mosel, Nucl. Phys. A773, 156 (2006)Valencia: M. Kaskulov, E. Hernandez, and E. Oset, EPJ A 31, 245 (2007)Glauber: R.J. Glauber and G. Matthiae, Nucl. Phys. B 21, 135 (1970)

• vector mesons

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

1.2

p ~ 1.1 GeV/c

A Xk = 1.5 GeV

AT

A/T

C

TAPS stat

syst

MCMC (Cinel

= Cel = 1)

MCMC (Cinel

= Cel = 1.3)

In-medium width: CLAS (ee ) versus TAPS measurement

200 MeV

inel150 mb

56 MeV

)()(

)()()()(

0

0

0

0

Dalitz

ee

eeee

eeeff

eeeff

eeeff

ee

ee

eeeff

eeeff

ee

ee

eeeff

eeeffDalitz

ee

eeee

eff

eeeffjj

SA

AAS

A

A

SA

AS

A

ASCN


RESULTS

Attenuation of vector mesons in CLAS revisited (preliminary)

Constrained and simultaneous fitting of the e+e- invariant mass spectra

)()()()()()( ,, Dalitzj

DjjDalitzj

Djj SCSCSCSCSCN

Known quantities From MCMC cascadeFitted parameters

)( and )(

and )()()( 0

DalitzDalitz

eeeff

eeeff

eeeff

eeeff

SS

A

A

A

A

Pb) and Ti-Fe C, (d2, targets

and

2)(

)(

22222

2

0

j

mS

eeVeeV

VV

VV

NN

NN

NN

NN

sVsVsj mC

and

and , '''

• vector mesons


RESULTS

Attenuation of vector mesons: MCMC versus CLAS (preliminary)

m = 777.3 MeV

m= 752.8 MeV

m = 1009.9 MeV

= 12.5 MeV

= 117.0 MeV

= 17.4 MeV

C D = 5480

C C = 3200

C Fe-Ti = 1900

C Pb = 950

2 = 209.3

2 /DOF = 1.12

CLAS: M. Wood et al., Phys. Rev. Lett. 105, 112301 (2010)

• vector mesons

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20

100

200

300

400

Cou

nts

e+e- Invariant Mass (GeV)

CLAS (Deuteron)

e+e-) ( e+e-)

e+e-

e+e-) e+e-) e+e-) Total

0.2 0.4 0.6 0.8 1.0 1.20

50

100

150

200

250

300

C

ount

s


CLAS (Carbon)

e+e-) ( e+e-)

e+e-


0.2 0.4 0.6 0.8 1.0 1.20

25

50

75

100

125

150

Cou

nts


CLAS (Fe-Ti)

e+e-) ( e+e-)

e+e-


0.2 0.4 0.6 0.8 1.0 1.20

20

40

60

80

C

ount

s


CLAS (Lead)

e+e-) ( e+e-)

e+e-



RESULTS

peak after subtraction of background: MCMC versus CLAS (preliminary)

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20

10

20

3010203040506020406080

100120

50

100

150

200


Lead

Cou

nts

Cou

nts

Fe-Ti

e+e-

Cou

nts

Carbon

Cou

nts

Deuteron

GiBUU model: M. Effenberger and U. Mosel, Phys. Rev. C 62, 014605 (2000)

x 0.94

x 0.90

x 1.3

x 2.3

MCMC model

CLAS: M. Wood et al., Phys. Rev. Lett. 105, 112301 (2010)

• vector mesons

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

1.2

Preliminary

p ~ 1.1 GeV/c

A X

Cinel = Cel = 1.3

e+e-p ~ 1.7 GeV/c

A

TA/T

C

TAPS stat

syst

MCMC (TAPS kinematics) CLAS MCMC (CLAS kinematics) CLAS (BG from MCMC)


RESULTS

In-medium width and the inelastic N cross section revisited

MCMC versus TAPS/CLAS (preliminary)

CLAS TAPS

decaye

e

p(GeV/c) ~ 1.7 ~ 1.1

*inel (mb) ~ 38 ~ 40

*el (mb) ~ 15 ~ 18

* (MeV) ~ 58 ~ 56

TAPS/CLAS data are mutually consistent with a multiple scattering scenario with *inel ~ 39 mb and * ~ 57 MeV.

• vector mesons


RESULTS

In-medium width and inelastic cross section (summary)

CLAS: M. Wood et al., Phys. Rev. Lett. 105, 112301 (2010)TAPS: M. Kotulla et al., Phys. Rev. Lett. 100, 192302 (2008)Glauber: R.J. Glauber and G. Matthiae, Nucl. Phys. B 21, 135 (1970)Giessen: P. Mühlich and U. Mosel, Nucl. Phys. A773, 156 (2006)Valencia: M. Kaskulov, E. Hernandez, and E. Oset, EPJ A 31, 245 (2007)

Model results versus

measurementsGlauber Giessen Valencia MCMC

Gla/MC

Gie/MC

Val/MC

CLASp

GeV/c

ee

* > 236 MeV

> 210 MeV

~ 58 MeV

> 4.1 > 3.6

*inel > 150 mb ~ 38 mb > 3.9

TAPSp

GeV/c

* ~ 140 MeV

~ 150 MeV

~ 56 MeV

~ 1.3 ~ 1.3

*inel ~ 60 mb ~ 40 mb ~ 1.5 CLAS/TAPS

> 2.5 > 3.4 > 2.8 ~ 1 •Preliminary

• vector mesons


CONCLUSIONS


The MCMC model is a suitable framework for the evaluation of the

nuclear effects in wide ranges of targets and incident energies.

The calculations of the incoherent cross sections for 0 reproduce

with good accuracy the PrimEx data. The fitted parameters obtained

for Carbon (0.69 ± 0.05/1.35 ± 0.03) are strongly dependent (factor

2) on the calculations of the coherent part (S. Gevorkyan et

al./Kaskulov & Mosel).

Our reanalysis of the decay width [0.476(62) keV] is in

line with the PDG average [0.510(26) keV] and ~ 50% higher than

Cornell’s result [0.324(46) keV]. Future and high precision

measurements using the Primakoff method are necessary and could

be focused on the proton (constraint), light nuclei (suitable to

disentangle the Coulomb peak) and heavy targets (to access the

unknown in-medium N cross section).


CONCLUSIONS

The predictions for mesons with inel ~40 mb reproduce quite

well TAPS data, leading to ~ 56 MeV. This result is considerably

lower than the predictions from the Giessen, Valencia and Glauber

models (factors 1.3 to 1.5). In the Glauber model, the effects of

Fermi motion, Pauli-blocking, coupled-channels, nuclear shadowing

and rescattering are neglected.

Recent data from CLAS indicate a much stronger absorption

than TAPS measurements. Calculations using the Giessen, Valencia

and Glauber models could not explain this huge absorption even

assuming 200 MeV and inel 150 mb. Our preliminary analysis

of the e+e- IM spectra suggests that both CLAS and TAPS data are

mutually consistent with a multiple scattering scenario with inel ~

39 mb and ~ 57 MeV.



FUTURE

PROSPECTS

• Short term:

• Delineation of the inelastic background of pseudoscalar

mesons in future experiments dedicated to the chiral anomaly of

QCD via the Primakoff method: [“Precision measurement of with the 12

GeV upgrade @ Jlab”, A. Gasparian et al., JLab exp. E1210011,

http://www.jlab.org/exp_prog/proposals/10prop.html (2010)]

• The investigation of in-medium changes in light vector mesons

surrounded by strongly interacting cold nuclear matter (JLab,

KEK, Spring-8 and TAPS)

• Long term (potentialities/possibilities):

• To extend the calculations for Heavy-Ion Collisions

• Hadronization mechanism

• Color Transparency

• Jets in dense and hot nuclear matter

• Di-lepton channels in relativistic HI collisions

o Future plans


o Collaborators

• João Arruda-Neto (USP, Brazil)

• Joel Mesa (UNESP, Brazil)

• Cesar Garcia and Katherin Shtejer (CEADEN, Cuba)

• Daniel Dale and Philip Cole (ISU/JLab, USA)

• Itaru Nakagawa (RIKEN, Japan)

Thank you !


THE

MODEL

0.01

1

0.01

1

0.01

1

0.01

1

0.01

1

0.01

1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.1

12.0 GeV

9.0 GeV

6.0 GeV

5.8 GeV

5.0 GeV

4.0 GeV

p 0p

DESY

dn/d

t (

b/G

eV2 )

SLAC

15.0 GeV

-t (GeV2)

Elementary photoproduction of pseudoscalar mesons ( NN)

Regge model ( and exchange) plus Regge cuts (absorption due to FSI)

736.110

...

2

FOD

0 5 10 15 20 25 300.01

0.1

1

10

100

p 0p5.8 GeV

0 polar angle, CM frame (deg.)d/

d

(b/

sr)

DESY DATA Total (Strong with cuts + Coulomb) Strong with cuts

Strong without cuts (0.005 < |t| <0.3 GeV2)

Extra slides


THE

MODEL

2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

+ p + p

k (GeV)

(b

)

SAPHIR [Eur. Phys. J. A 23, 317 (2005)] ABBHHM [Phys. Rev. 175, 1669 (1968)] SLAC [Phys. Rev. D 7, 3150 (1973)] DESY [Nucl. Phys. B 47, 463 (1972)] Y. Eisenberg et al. (WIS-71-9-PH) Regge model

Elementary photoproduction of vector mesons ( NN)

Pomeron plus -meson exchange amplitudes are included

851.80

...

2

FOD

Extra slides


THE

MODEL

Parameterization of the total and elastic N cross sections

s

sY

s

sBZs pp

Totalp1

2

2log)()(

0

2

)(

)()( ctbta

Totalp

Totalp

ppe

p

ppd

ppN 2

10

ppNddd

2

10NN C 0

NN Cdd 0

Extra slides


THE

MODEL

Parameterization of the total and elastic VN cross sections (1)

(1) G. I. Lykasov et. al, Eur. Phys. J. A 6, 71 (1999)

mb 12)(

104.5)( ,4

20)(

)()()(

*

6.0

22*)(

VN

pelVN

inelVN

elVNel

inelVNinelN

p

epp

p

pCpCp

NNVNVN

VN

elVNel

inelVNinel

elVNel

elVNel

dd

p

pCprr

pCpC

pCpr

00

*

2

22

2

)()(

)()(

0.5 1.0 1.5 2.0 2.5 3.00

20

40

60

80

100

Cro

ss s

ectio

n (m

b)

Meson momentum (GeV/c)

V

el

V

inel

VN

* (Cel = C

inel = 1)

0.5 1.0 1.5 2.0 2.5 3.00.15

0.20

0.25

0.30

0.35

Meson momentum (GeV/c)

r(pV)

Extra slides


THE

MODEL

The non-stochastic Pauli-blocking mechanism

Extra slides

Fermi surface

px

py

pz

kF

p

t

tt

tt

tt

t

i

i

i

itt00

''0 ),(),(

2/~ pr

t

tt

tt

tt

t

i

i

i

itt00

''0 ),(),(

MCMC: T.E. Rodrigues et al., PRC 69 064611 (2004)

Ref.[7]: J. Cugnon, C. Volant, and S. Vuillier, NPA 620, 475 (1997)


RESULTS

Calculations of the incoherent cross sectionsGroup I: S. Gevorkyan et al., arXiv:0908.1297 [hep-ph]

Group II: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)

Extra slides


RESULTS

Recent developments for coherent photoproduction of pseudoscalar mesons

Calculation: M. Kaskulov and U. Mosel, Phys. Rev. C 84, 065206 (2011)JLab data: I. Larin et al., Phys. Rev. Lett. 106, 162303 (2011)

Extra slides


RESULTS

Scaling of nuclear cross sections for 0 photoproduction within 3 to 9 GeV(Cornell versus MCMC)

MCMC: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)


dtdtd

dtdtd

AA PWIA

SHADFSI

)MCMC(eff

Extra slides


RESULTS


MCMC: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)


Extra slides


RESULTS



3 4 5 6 7 8 91

10

100

Pb

AgCu

C

Be

Al

Aeff

E0 (GeV)

MCMC: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)Cornell: W. T. Meyer et al., Phys. Rev. Lett. 28, 1344 (1972)

Extra slides


RESULTS



3 4 5 6 7 8 91

10

100

Pb

AgCu

C

Be

Al

Aeff

E0 (GeV)

MCMC: T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010)Cornell: W. T. Meyer et al., Phys. Rev. Lett. 28, 1344 (1972)

bdbdzzbNAN

N

0

Geff ),(exp1

20

0

EE00 == 6.4 GeV 6.4 GeV AAeff(MCMC)(MCMC) AAeff(Glauber)(Glauber) M/GM/G

BeBe 5.05.0 6.16.1 0.820.82

CC 5.65.6 7.27.2 0.780.78

AlAl 10.410.4 14.814.8 0.700.70

CuCu 18.618.6 27.027.0 0.690.69

AgAg 27.227.2 38.738.7 0.700.70

PbPb 42.142.1 60.160.1 0.700.70

Extra slides


RESULTS

Future prospects for the decay width

Precision measurement of with the 12 GeV upgrade @ JLab

A. Gasparian et al., JLab exp. E1210011 (proton and 4-He targets) http://www.jlab.org/exp_prog/proposals/10prop.html

(2010)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1

10

100

1000

d

/d

(b/

rad)

polar angle (deg)

Pb Xk = 9.0 GeV0.9 < <1.0

Coherent (K.M.) Incoherent (MCMC) Total

K.M.: M. Kaskulov and U. Mosel, Phys. Rev. C 84, 065206 (2011)

Potentialities of measurements in complex nuclei(Coherent/Incoherent contributions accurately constrained by calculations)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

1

2

3

4

5

6

d/d

(b/

rad)

polar angle (deg)

C Xk = 9.0 GeV0.9 < <1.0

Coherent (K.M.) Incoherent (MCMC) Total

Extra slides


RESULTS

Extracting N via nuclear measurements beyond the coherent peak!

1.50 1.75 2.00 2.25 2.50 2.75 3.002

3

4

5

6

7

C Xk = 9.0 GeV0.9 < <1.0

d/d (b

/rad

)

polar angle (deg)

Incoherent (N 0.50N)

Incoherent (N 0N)

~1 b

2.0

1.5 2.0 2.5 3.00

10

20

30

40

50

60

d

/d

(b/

rad)

polar angle (deg)

Pb Xk = 9.0 GeV0.9 < <1.0

Incoherent (N 0.50N)

Incoherent (N 0N)

~20 b

6.0

•Heavy targets: preferable to access the N cross section(multiple scattering scenario)

•Light targets: preferable to extract (high Z2 in comparison with proton and 4-He)[lower model dependence in comparison with heavy targets, where

the Coulomb (peakmPk) and NC cross sections (peakkR) are

more strongly correlated (form factor effect)]

Extra slides


RESULTS

Double differential cross sections for incoherent 0 photoproduction

T. E. Rodrigues et al., Phys. Rev. C 82, 024608 (2010).

Extra slides

04/21/2304/21/23 4747

Cornell´s analysis*

*A. Browman et al., Phys. Rev. Lett. 32, 1067 (1974)**T. E. Rodrigues et al., Phys. Rev. Lett. 101, 012301 (2008)

Our reanalysis**

polar angles (mrad)

Isotropic NI Background without PB (T A0.75) NI Background from MCMC model

Nuclear Incoherent

Coulomb (~

Extra slides

Tulio Rodrigues – NN2012 – San Antonio – USATulio Rodrigues – NN2012 – San Antonio – USA


RESULTS

Momentum dependent transparency ratios: TAPS versus MCMC

TAPS: M. Kotulla et al., Phys. Rev. Lett. 100, 192302 (2008)MCMC: T. E. Rodrigues and J.D.T. Arruda-Neto, Phys. Rev. C 84, 021601 (R) (2011)

500 1000 15000.2

0.3

0.4

0.5

0.6

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.0

(c)

p (MeV/c)

Pb

r~ 0.2 r ~ 0.4 [~ 30 mb]

(b)

r~ 0.2 r ~ 0.4 [~ 25 mb

TA/T

C

Nb

(a)

CBELSA/TAPS

Ca

Effect of Pauli-blocking for low p and high elastic cross section (<r> ~ 0.4)

Extra Extra slides

04/21/2304/21/23 4949

The elementary meson photoproduction: NN

The cascade “trigger”

)()()()( 21 pNpPpNk

2

21

)(

)(

pkt

pks

N N

spm

FF

m

F

m

FF

kt

m

FF

dt

d

NNNN

N

21642432

1 314

23

2

212

4

22

2

232

2

() A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004.() M. Braunschweig et al., Nucl. Phys. B 20, 191 (1970).

Cross section expanded in t-channel helicity amplitudes (Fi)

iF Calculated using a Regge model ( and exhange) plus Reggeon cuts**

Extra slides

THE

MODEL


04/21/2304/21/23 5050

0 1 2 3 4 5 60

25

50

75

100

125

150

175

200

12C 0Xk = 5.2 GeV: []

d/

d

(b

/sr)

0 polar angle (deg.)

dPWIA (with cuts)

dPWIA (without cuts)

dPB (with cuts)

dPB (without cuts)

dFSI (with cuts)

dFSI (without cuts)

Contribution of Regge cuts on the incoherent cross section

Extra slides


04/21/2304/21/23 5151

Overview of the MCMC plus Evaporation model (Flow Diagram)

Cascade Dynamics (Main Block)

Fermi Gas Model Shell ModelNuclear Ground State

Square Well Potential

Momentum Distribution

Effective Mass

Initial Interaction Mechanism

Relativistic Kinematics

Cross Sections N-N, -N, -N

BoundaryEffects

BinaryScatterings

Energetic Balance

Reflections

Pre-eq. Emissions

Compound Nucleus

Energetic Criterion

Pauli-Blocking

MCMC input

MCMC Structure

Evaporation Step

p-h Configurations


Extra slides

04/21/2304/21/23 5252

Main features included in the MCMC intranuclear cascade model:• Relativistic and time-dependent multicollisional algorithm (18);• Elementary photoproduction ( NmesonN ) included (3-4), (6-8);• Realistic MD for light nuclei ((e,e´p) knock-out reactions) (6-8);• Non-stochastic Pauli-blocking in a multiple scattering scenario (2-8);• Photon shadowing effects via a VMD model (6-8);• Realistic angular distributions for the process meson N meson N (6-8);• Multiple meson productionduring secondary scatterings (3-4),( 6-8).

(1) M. G. Gonçalves, S. de Pina, D. A. Lima, W. Milomen, E. L. Medeiros and S. B. Duarte, Phys. Lett. B 406, 1 (1997).

(2) T. E. Rodrigues, J. D. T. Arruda-Neto, A. Deppman, V. P. Likhachev, J. Mesa, C. Garcia, K. Shtejer, G. Silva, S. B. Duarte, O. A. P. Tavares, Phys. Rev. C 69, 064611 (2004).

(3) T. E. Rodrigues, J. D. T. Arruda-Neto, J. Mesa, C. Garcia, K. Shtejer, D. Dale and I. Nakagawa, Phys. Rev. C 71, 051603(R) (2005).

(4) T. E. Rodrigues, J. D. T. Arruda-Neto, J. Mesa, C. Garcia, K. Shtejer, D. Dale and I. Nakagawa, Braz. J. of Phys. 36, 1366 (2006).

(5) T. E. Rodrigues, M. N. Martins, C. Garcia, J. D. T. Arruda-Neto, J. Mesa, K. Shtejer and F. Garcia Phys. Rev. C 75, 014605 (2007).

(6) T. E. Rodrigues, J. D. T. Arruda-Neto, J. Mesa, C. Garcia, K. Shtejer, D. Dale, I. Nakagawa and P. Cole, Phys. Rev. Lett. 101, 012301 (2008).

(7) T. E. Rodrigues, J. D. T. Arruda-Neto, J. Mesa, C. Garcia, K. Shtejer, D. Dale, I. Nakagawa and P. Cole, Phys. Rev. C 82, 024608 (2010).

(8) T. E. Rodrigues and J.D.T. Arruda-Neto, Phys. Rev. C 84, 021601 (R) (2011)


Extra slides

04/21/2304/21/23 5353

Meson photoproduction at high energies (3 - 12 GeV) andforward angles (1)

)()()()( 21 pNpPpNk

2

21

)(

)(

pkt

pks

*3*

43*2*

32*

41

2

4

2

3

**

21*

43*

32*

41

2

4

2

3

2

2

2

1

cosRecosReRe2

1

2

1

cosRe2ReReRe2

1

2

1

ffffffff

ffffffffffffd

d

p

k

(1) A. Donnachie and G. Shaw, Ann. Phys. 37 (1966) 333

*32

*41

*21

2

432

4

2

2

211

Re222

1ffffffff

kt

kff

d

d


Extra slides

04/21/2304/21/23 5454

)(8

)(8

)(8

)(8

4322

4

4323

43

2

412

43

2

411

AAAmss

mspf

AAAmss

mEmspf

AAms

tAmsA

s

mspf

AAms

tAmsA

s

mEmsf

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 invariantamplitudes (A) from dispersion relations (CGLN)


Extra slides

04/21/2304/21/23 5555

231

4

43

23

221

2

231

1

4

2

4

21

4

2

mt

FmFA

FA

mt

mFF

tmt

FA

mt

mFtFA

(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

Relationship between the invariant amplitudes (Ai) (1,2) and t-channel helicity amplitudes (Fi) (3)


Extra slides

04/21/2304/21/23 5656

smp

FF

m

F

m

FF

kt

m

F

d

d

21644232

1 314

23

2

212

42

4

2

23

)1(

1

(1) A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004(2) J.P. Ader and M. Capdeville, Nucl. Phys. B B3, (1967) 407

)0,(2)0,( 23 tsmFtsFConspiracy relation (2):

Fi’s calculated using a Regge Model (, and meson exchange)

: , 31 FF natural parity t-channel amplitudes (, , exchange)

: , 42 FF unnatural parity exchange ( meson)

: , 21 FF nucleon helicity non-flip

: , 43 FF nucleon helicity flip


Extra slides

04/21/2304/21/23 5757

Two possible scenario at small t

Fi’s defined by single poles exchanges

Fi’s defined taking into account the reggeon cuts (1)

Fi’s have no longer definite parity and F2,3 are non-zero

for t = 0.

(1) A. Capella and J. Tran Thanh Van, Nuovo Cimento Letters 1 (1969) 321.


Extra slides

04/21/2304/21/23 5858

The elementary mechanism ( NN )

: , 31 FF natural parity (, exchange)

unnatural parity (b1 exchange)

: , 21 FF nucleon helicity non-flip

: , 43 FF nucleon helicity flip: , 42 FF

2

1

0

1)0(

033

0

1)0(

011

1)(

033

1112

1)(

011

)()(0543.02

ln)0(22

ln)0(

2

2)(1)()()(22

)(

2)(1)()()(2

qFeVt

mF

ss

e

s

sF

ss

e

s

s

mF

s

sttttt

mF

attF

s

stttt

mF

C

atcutcut

atcutcut

t

bbb

t

1)(

01

1111

)(

2222

2

224

22

2

1

2)(

3)(2)(1)()(

))(sin(

1)(

2 ,

2

24

2

22

2

t

b

bbbb

ti

cmcm

cm

cm

b

s

ust

tttt

t

et

ms

msp

k

ms

smsmk

stmu

mmks

(*) M. Braunschweig et al., Nucl. Phys. B 20, (1970) 191.

Helicity amplitudes calculated using a Regge Model with cuts (*)


Extra slides

04/21/2304/21/23 5959

elementary meson photoproduction

0 photoproduction photoproduction

2-

3

111

20

,

33

42

11111

GeV )12(668.0

)23(23.10

)65(88.33 ,)15(2.127

GeV 0.1

9.045.0)(

0 ,

a

GeV

b

bb

s

tt

FF

FF

FFFFF

cut

cut

cut

Ccut

2-

333

111

20

,

4

3333

11111

GeV )26(059.2

)11(9.8 ,)39(2.27

)24(4.155 ,)51(3.44

GeV 0.1

0.139.0)(

0

a

GeV

b

GeV

b

bb

s

tt

F

FFFF

FFFFF

cut

cut

cut

Ccut

Fitting parameters and approximations


Extra slides

04/21/2304/21/23 6060

1.5 2.0 2.5 3.0 3.51E-3

0.01

0.1

1

10

100

1000

p X

Cro

ss s

ectio

n (m

b)

s1/2 (GeV)

exp (PDG)

Fitting (2/n.d.f. = 1.6) Total (MCMC) Elastic

(1232)0

N(1520)0

N(1680)0

n0

p-+

n20

p-20

p2-0+

n-20+

n-+

p2-+

n2-2+

n-0+

n30

p3-2+

n3-3+

p3-02+

p-30

p2-20+

(+n)nn

Mesonnucleus FSI


Extra slides

04/21/2304/21/23 6161

1.5 2.0 2.5 3.0 3.51E-3

0.01

0.1

1

10

100

0p X (MCMC)

Cro

ss s

ect

ion

(m

b)

s1/2(GeV)

Total (MCMC) Elastic

(1232)+

N(1520)+

N(1680)+

(1950)+

n+

p20

p30

p-20+

n30+

n0+

p-0+

n-02+

n20+

p2-02+

n2-03+

p2-202+

p40

p-30+

(+n)pn

T. E. Rodrigues et al., Phys. Rev. C 71, 051603 (R) (2005).


Extra slides

04/21/2304/21/23 6262

1.5 2.0 2.5 3.0 3.51E-3

0.01

0.1

1

10

100

0n X (MCMC)

C

ross

se

ctio

n (

mb

)

s1/2(GeV)

Total (MCMC) Elastic

(1232)0

N(1520)0

N(1680)0

(1950)0

p-

n20

n30

n-20+

p-30

p-0

n-0+

p2-0+

p-20

n2-02+

p3-02+

p2-202+

n40

n-30+

(+p)np


Extra slides

04/21/2304/21/23 6363

0 5 10 15 20 25 300.0

0.1

0.2

0.3

0.4

0.5

0.6

dt

nd int

4.0

5.5

12

12

208

208

intint

intint

dtdt

ndn

dtdt

ndn

t

CC

t

PbPb

Time derivative of the average number of N interactions


Extra slides

04/21/2304/21/23 6464

energy spectra

5.17 5.18 5.19 5.2010-3

10-2

10-1

100

101

102

103

104

12C, k = 5.2 GeVElasticity = 0.9

d/d

E (b

/GeV

)

0 total energy (GeV)

Primakoff Nuclear Coherent Nuclear Incoherent Total


Extra slides

04/21/2304/21/23 6565

0 incoherent photoproduction from 12C and 208Pb 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).

0 60 120 1800

2

4

6

8

10

12 MCMC (1)

MAMI (2)

208Pb12C

MCMC (1)

MAMI (2)

*0(degrees)

(d/

d*)

/A (b

/sr)

0 60 120 1800

1

2

3

4

5

6

*0(degrees)


Extra slides

04/21/2304/21/23 6666

neutrons protons Probability Excitation energy (MeV)

0 0 7.127400000000000E-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

0*6

)(1212 XC jpinj

ji


Extra slides

04/21/2304/21/23 6767

21210

,,,,,, bbCCAbdt

deff

:parameters Fitting

)(*

.

tGdt

dA

dt

dA

dt

d

dt

d

Neff

Neff

Diff

AA

decay in PrimEx

Coherent photoproduction + A + A

Incoherent photoproduction with

isobar + A + X +

Incoherent photoproduction + A + X

tbedt

d

0

~

PRD 17, 647 (1978)

Pauli-blocking(MCMC cascade)

tbtb ekCekC 21 08.02

6.11~


Extra slides

04/21/2304/21/23 6868

Typical fitting for Carbon nuclei (Rochester unpublished data*)

0.00 0.02 0.04 0.06 0.08 0.1010-3

10-2

10-1

100

101

+ C + Xk = 6.8 GeV

t (GeV2)

d/d

t (m

b/G

eV

2 )

Exp. data (Rochester) Coherent (diffractive) Incoherent with isobar Incoherent Total

82.0...

2.18.5

58

082.0808.0

2

0

fdn

A

b

dt

d

eff

2-

2

GeV

GeV

mb

(*) H. –J. Behrend et al., Phys. Rev. Lett. 24, 1246 (1970)


Extra slides

04/21/2304/21/23 6969

0 1 2 3 4 5 60

1

2

3

4

5

6

+ 12C () + Xk = 5.2 GeVE/k0.92

d

/d (b

/ra

d)

0 polar angle (deg.)

Coherent Incoherent Incoherent with isobar Total

0 1 2 3 4 50

10

20

30

40

50

60

70

+ 208Pb () + Xk = 5.2 GeVE/k 0.92

d

/d (b

/rad

)0 polar angle (deg.)

Coherent Incoherent Incoherent with isobar Total

angular distribution due to photoproduction in complex nuclei(PrimEx pion elasticity cuts are imposed)


Extra slides

04/21/2304/21/23 7070

0.80 0.85 0.90 0.95 1.00 1.050

200

400

600

800

1000

1200

1400

1600

x E0/k

d2 /dd

x (

b/ra

d)

CX (Incoherent)

C X (Omega decay) Total

k = 5.2 GeV0 = 2.25 deg.x = 0.001

elasticity distribution due to incoherent single photoproduction and decay

(PrimEx kinematics)

0.80 0.85 0.90 0.95 1.00 1.050

2000

4000

6000

8000

10000

k = 5.2 GeV0 = 2.25 deg.x = 0.001

d2

/dd

x (

b/ra

d)x E0/k

PbX (Incoherent)

Pb X (Omega decay) Total


Extra slides

12/14/2015 tulio rodrigues – nn2012 – san antonio – usa 1 11 th international conference on...

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