04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 11

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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 22

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)

eV 044.0725.7576 23

322

0

F

mNc

2. Recent calculations beyond the chiral anomaly

NLO calculations in ChPT (include ud 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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 33

Physics motivation

Experimental scenario for and

0 1 2 3 4 5 6 7 80.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.510(26) keV

0.324(46) keV

Cornell (Primakoff-effect)

JADECBALASP

MD1

PDG average

(keV

)

Experiments

PrimEx proposal

Precision measurements of and representstringent tests of fundamental quantities in QCD

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 44

The Primakoff method

22

NINCi

P TTeTd

d

22

4

43

3

22

sin)(~8

QFQ

k

m

ZT em

PPP

222

22sin)(

~LQFAT NNC

22)( neffNI TQfAT

P

A A

NuclearCoherent

P

A A*

NuclearIncoherent

Primakoff P

A A

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 55

Inelastic background of pseudo-scalar mesons

Main features included in the MCMC intranuclear cascade model:

Relativistic and time-dependent multicollisional algorithm;

The elementary mechanism ( NN ) in terms of a Regge

model;

Realistic MD for light nuclei ((e,e´p) knock-out reactions);

Non-stochastic Pauli-blocking in a multiple scattering scenario;

Photon shadowing effects via a VMD model;

Realistic angular distributions for the elastic scattering

NN;

Multiple meson productionduring 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)

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 66

Inelastic background of pseudo-scalar mesons

The elementary mechanism ( NN )

)()()()( 21 pNpPpNk

2

21

)(

)(

pkt

pks

P

N N

b1

3213

2

22

314

23

2

212

4

22

2

232

2

16

54

2422

2

21642432

1

Fpm

spF

p

sF

m

FF

sp

kt

spm

FF

m

F

m

FF

kt

m

FF

dt

d

NN

NNNN

N

() A. Gasparian and S. Gevorkyan, Theoretical part of PrimEx, 2004

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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 77

Inelastic background of pseudo-scalar mesons

0.0 0.5 1.0 1.5 2.0

0.01

0.1

BONN-DESY J. Dewire

k = 4.0 GeV

+ p + p

0.0 0.5 1.0 1.5 2.01E-3

0.01

0.1 SLAC

k = 5.5 GeV

0.0 0.5 1.0 1.51E-3

0.01

0.1

1

k = 9.0 GeV

- t (GeV2) - t (GeV2)

0.0 0.5 1.0 1.5

0.01

0.1

1

k = 6.0 GeVd/d

t (b

/GeV

2 )

0 1

0.01

0.1

1

k = 6.5 GeV

0.0 0.5 1.0 1.50.01

0.1

1

k = 8.0 GeV

The elementary mechanism ( NN )

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 88

1E-5 1E-4 1E-3 0.01 0.1 10.1

1

10

100

k = 4.0 GeV + p 0 + p

d/d

t (

b/G

eV2 )

1E-5 1E-4 1E-3 0.01 0.1 10.1

1

10

100

k = 5.0 GeV

Strong Total (strong+Coulomb)

BONN-DESY

1E-5 1E-4 1E-3 0.01 0.1 10.01

0.1

1

10

100

k = 5.8 GeV

d/d

t (

b/G

eV2 )

- t (GeV2)

1E-5 1E-4 1E-3 0.01 0.1 10.01

0.1

1

10

100k = 6.0 GeV

SLAC

- t (GeV2)

The elementary mechanism ( NN )

Inelastic background of pseudo-scalar mesons

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 99

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

Inelastic background of pseudo-scalar mesons

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1010

Results: photoproduction

Angular distribution due to incoherent photoproduction (inelastic BG in Cornell's data)

0 1 2 3 4 50

10

20

30

40

Be PWIA with Pauli-blocking with FSI with FSI and Shadowing

polar angle (deg.)

d/d

(b

/sr)

0 1 2 3 4 50

50

100

150

200

250A Xk = 8.5 GeV

polar angle (deg.)

Cu

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1111

)()(2)()()()( NCPNCPNININCNCPP SSaaSaSaSan )cos(

0 10 20 30 400

20

40

60

80Be Cornell data

Primakoff Nuclear Coherent Nuclear Incoherent Interference Total

polar angle (mrad)

eve

nts

0 10 20 30 400

10

20

30

40

50

Be

polar angle (mrad))(

)(

Cornellbb

MCMCNINI

na

Sa

Results: photoproduction

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1212

0 1 2 3 4 5 6 70.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8MCMC NI backgroundIsotropic NI background

0.324(46) keV

PDG average

(

keV

)

Cornell

JADECBALASP

MD1

Experiment

0 1 2 3 4 5 6 70.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.510(26) keV

0.476(62) keV

Experiment

MD1

ASPCBALJADE

Cornell

Results: photoproduction ( decay width)

T. E. Rodrigues et al., Phys. Rev. Lett. 101, 012301 (2008)

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1313

Results: 0 photoproduction

Angular distribution of “quasi-elastic” neutral pions:Nuclear incoherent photoproduction in PrimEx

k

0 1 2 3 4 5 60

40

80

120

160

200

12C 0Xk = 5.2 GeV: []

d

/d

(b

/sr)

0 polar angle (deg.)

dPWIA

dPB

dFSI

dFSI+SHAD

0 1 2 3 4 50

500

1000

1500

2000

2500

3000

3500

0 polar angle (deg.)

d/d

(b

/sr)

208Pb 0Xk = 5.2 GeV: []

dPWIA

dPB

dFSI

dFSI+SHAD

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1414

Results: 0 photoproduction

Double differential cross section for incoherent photoproduction

4900 5000 5100 5200 53000.00

0.02

0.04

0.06

0 = 0.750

0 = 0.250

d/d

dE

(b/

rad.

MeV

)

4900 5000 5100 5200 53000.00

0.05

0.10

0.15

0 = 1.250

4900 5000 5100 5200 53000.0

0.1

0.2

0.3

0.4

0 = 1.750

4900 5000 5100 5200 53000.0

0.1

0.2

0.3

0.4

0 = 2.250

4900 5000 5100 5200 53000.0

0.2

0.4

0.6

0.8

0 = 2.750

4900 5000 5100 5200 53000.0

0.2

0.4

0.6

0.8

0 = 3.250

4900 5000 5100 5200 53000.0

0.2

0.4

0.6

0.8

(5.2 GeV) + 12C 0 + X

0 = 3.750

E0 (MeV)4900 5000 5100 5200 5300

0.0

0.2

0.4

0.6

0 = 4.250

4900 5000 5100 5200 53000.0

0.1

0.2

0.3

0.4 0 = 4.750

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1515

Results: 0 photoproduction

12C 208Pb

Preliminary

PrimEx Collaboration

Preliminary results from PrimEx experiment(Three independent analyses in progress)

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1616

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

PreliminaryPreliminary

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1717

Results: 0 photoproduction

PrimEx results (Current and future)

eV 2.3% 1.6%

1.4%

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1818

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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 1919

1 2 3 4 5 6 7 8 9100

101

102

103

104

105

year 2000

Pho

ton

ener

gy (

MeV

)

GDR

QD(1232)VMD

(1)

Zn

(,n)(,np)

(2)

(,n)

Sn, Ce,Ta, Pb

(3)

(,0)

C, Pb

(,0)

C, Pb

(4)

(,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!

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2020

Introduction (Physics motivation: decay)

Possible cause for discrepancy:Inadequate treatment of the nuclear incoherent contribution (inelastic background)

Typical yield curve at EB = 9 GeV (Cornell)

Primakoff

BackgroundA0.75

0 1 2 3 4 5 6 7 80.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.510(26) keV

0.324(46) keV

Cornell (Primakoff-effect)

JADECBALASP

MD1

PDG average

(

keV

)

Experiments

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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2121

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

Summary of the Monte Carlo calculations Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2222

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

Meson photoproduction from the nucleon Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2323

)(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

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 invariantamplitudes (A) from dispersion relations (CGLN)

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2424

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

Meson photoproduction from the nucleon

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

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2525

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

Meson photoproduction from the nucleon Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2626

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.

Meson photoproduction from the nucleon Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2727

The elementary meson photoproduction

: , 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 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2828

0 photoproduction photoproduction

2-

3

111

20

,

33

42

11111

GeV 20.1

5.13

2.55 ,4.115

GeV 0.1

9.045.0)(

0 ,

a

GeV

b

bb

s

tt

FF

FF

FFFFF

cut

cut

cut

Ccut

GeV

baa

GeV

b

GeV

b

bb

s

tttt

F

mFFFFF

FFFFF

b

cut

cut

b

bcut

Ccut

05.69 ,GeV 976.1

595.7 ,89.23

06.149 ,09.42

GeV 0.1

9.0342.0)( ,0.139.0)(

0

2

12-

333

111

20

1,

4

123333

11111

The elementary meson photoproduction

Fitting parameters and approximations

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 2929

Electromagnetic form factor with FSI

Nuclear/Charge density for light nuclei (shell-model distribution(1))

46

1 ),(65.1or )(71.1 ,1

4)( 02

0

2

3

0

20

2

ACBeaea

r

ar a

r

22

0

2')',(

2

0

122

322

0

12

)(),( ,),(

),(),()(

)()(4

)(~

zbdzzbA

ttt

drrrzbfezbG

dzJbzbzbfzbGbg

dbbgbqJbqA

qF

z

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

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3030

0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

12C, k = 5.6 GeV

Fem

(Q)

Meson polar angle (deg.)

EMFF with FSI

Electromagnetic form factor with FSI Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3131

FSI not considered (PWIA)

)()( 3 xxedqF xqiN

)()()(~

21 qFqFqFN

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

zdzzbAxqi exxedqF

')',(23

1 )()(

z

dzzbA

tt

dzdb

zbddzezbbdbbqJ

q

AqF z ''

)'',(),()()(

')',(2

0

12

absorption Re-scattering

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3232

Nuclear form factor with FSI

Main Goal: to calculate the distortion effects in the MCMC framework

Main Advantage: local density fluctuations are effectively included

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

12C, k = 5.6 GeV

FN(q)

0 (deg.)

PWIA with FSI (MCMC) F

1(q)

F1(q) + F

2(q)

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3333

Results – meson energy spectra (all processes)

11.980 11.985 11.990 11.995 12.00010-3

10-2

10-1

100

101

102

103

k = 12 GeV

+ 12C 0 + X

d/d

E0 (b

/GeV

)

0 energy, lab. frame (GeV)

Primakoff Nuclear Coherent Nuclear Incoherent All

8.980 8.985 8.990 8.995 9.00010-3

10-2

10-1

100

101

102

k = 9 GeV

+ 9Be + X

d/d

E

(b/

GeV

) energy, lab. frame (GeV)

Primakoff Nuclear Coherent Nuclear Incoherent All

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3434

-Nucleus FSI

N channels included in the MCMC (*)

1.5 2.0 2.5 3.0 3.51E-3

0.01

0.1

1

10

100

0p X (MCMC)

C

ross

se

ctio

n (

mb

)

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

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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

-Nucleus FSI

N channels included in the MCMC (*)

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3636

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

Meson-nucleus Final State Interactions Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3737

N total cross section

Meson-nucleus Final State Interactions

2

TotalNTotalNTotalN C

Our

assumption:C ~ 1 (experiments using multiple targets may constrain this factor)

4 6 8 10 12 140

10

20

30

40

50

60

C

ross

sec

tion

(mb)

p (GeV/c)

-p Total (PDG) Fitting

4 5 6 7 8 9 10 11 120

10

20

30

40

50

Cro

ss s

ectio

n (m

b)

p (GeV/c)

+p Total (PDG) Fitting

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3838

Cornell’s kinematics(1):GeV 5.1, 0

201 kk

B02

01 6.0 Ekk

3938.0 rad, 137.0T

21

GeVEB 0.9

),( 0 pp

21),( 1

01 kk

),( 202 kk

z

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

36.0 cm

45.0 cm

45.0 cm

36.0 cm

Counter hodoscopes

z

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 3939

Results (energy spectra)mesonmeson 00

targettarget 1212CC

EnergyEnergy 5.2 GeV5.2 GeV

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

/dE

(b

/GeV

)

0 total energy (GeV)

Primakoff Nuclear Coherent Nuclear Incoherent Total

PrimEx energy range

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 4040

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)

Previous results near the (1232) Extra slides

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Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 4242

Results: The “fate” of the nucleus

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

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Results: 0 photoproduction

Double differential cross section for incoherent photoproduction

4900 5000 5100 5200 53000.0

0.2

0.4

0.6

0.8

0 = 0.250

0 = 0.750

4900 5000 5100 5200 53000.00.20.40.60.81.01.21.4

0 = 1.250

(5.2 GeV) + 208Pb X + 0

4900 5000 5100 5200 53000.0

0.4

0.8

1.2

1.6

2.0

0 = 1.750

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

0 = 3.2500 = 2.7500 = 2.250

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

0 = 3.750

d/d

dE

(b/

rad.

MeV

)

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

0 = 4.250

E0 (MeV)

4900 5000 5100 5200 53000.0

0.5

1.0

1.5

2.0

2.5

0 = 4.750

Extra slides

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GeVin ,),( 21 08.02

6.11 kekCekCtk

dt

d tbtb

N

0.0 0.2 0.4 0.6 0.8 1.010-1

100

101

102

p p

k = 2.8 GeV

SLAC

d/d

t (b

/GeV

2 )

0.0 0.2 0.4 0.6 0.8 1.010-1

100

101

102

k = 3.29 GeV

2/n.d.f = 60.4/51 CLAS

0.0 0.2 0.4 0.6 0.8 1.010-1

100

101

102

k = 3.83 GeV

0.0 0.2 0.4 0.6 0.8 1.010-1

100

101

102

k = 4.7 GeV

0.0 0.1 0.2 0.3 0.4 0.5 0.610-1

100

101

k = 8.9 GeV

Cornell Fitting

-t (GeV2)

d/d

t (b

/GeV

2 )d

/dt (b

/GeV

2 )

0.0 0.2 0.4 0.6 0.8 1.010-2

10-1

100

101

k = 9.3 GeV

-t (GeV2)

Elementary omega photoproduction Extra slides

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Extra slides

d/dt for Carbon (Rochester 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

Exp. Data: H. –J. Behrend et al., Phys. Rev. Lett. 24, 1246 (1970)(d/dt was not published)

photoproduction from nuclei

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 4646

0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02

102

103

104

d2 /dd

x (

b/r

ad

)

x E0/k

k = 5.2 GeV0 = 2.25 deg.

CC (Coherent)

CX (Incoherent)

C X (Omega decay) Total

Inelastic background of neutral pions: decay

0.85 0.90 0.95 1.00 1.05102

103

104

x E0/k

d2

/dd

x (

b/r

ad

) k = 5.2 GeV0 = 2.25 deg.

PbX (Incoherent)

Pb X (Omega decay) Total

Extra slides

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Results: 0 photoproduction

Preliminary results from PrimEx experiment(Three independent analyses in progress)

PrimEx CollaborationPreliminary

Extra slides

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The direct method to obtain The direct method to obtain Decay Length MeasurementsDecay Length Measurements

Measuring 0 decay length (1x10-16 sec) for ultra-relativistic pions:

i.e. For E0 = 1000 GeV, we have L = vE/m 100 μm

(very challenging experiment)

CERN experiment, 1984: 450 GeV proton beam(0) 7.34eV 3.1% Major limitations of method:

unknown P0 spectrum needs higher energies for

improvement

Extra slides

04/21/2304/21/23 Tulio E. Rodrigues - XXXI RTFNB - Maresias - BrazilTulio E. Rodrigues - XXXI RTFNB - Maresias - Brazil 4949

ee++ee-- Collider Experiment Collider Experiment

e+e-e+e-**e+e-0e+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 q2 for **

Extra slides