Claudio CIOFI degli ATTI DIFFRACTION on NUCLEI ... - QNP2012

<strong>Claudio</strong> <strong>CIOFI</strong> <strong>degli</strong> <strong>ATTI</strong> 

<strong>DIFFRACTION</strong> on NUCLEI 

Effects of Nucleon-Nucleon Correlations and Inelastic 

Shadowing Within an Improved Glauber-Gribov Approach 

INFN and University, Perugia, Italy-UTFSM, Valparaiso, Chile 

Collaboration 

6th International Conference on Quarks and Nuclear Physics 

Palaiseau, France, April 16-20, 2012 

C. Ciofi <strong>degli</strong> Atti 

1 QNP2012, Palaiseau, April 16-20, 2012

AIM and MOTIVATIONS 

• High energy processes involving nuclear targets (hA and AA) provide 

information on: hadronization and confinement, Cronin effect, 

high p T processes, formation of high density matter. 

• Most theoretical approaches to describe the scattering of a multi 

GeV particle impinging on a nucleus are based upon Glauber 

multiple scattering theory and the independent-particle model. 

In our approach: 

. 

• The nucleus is described as a self bound saturated liquid where 

nuclear constituents spend part of their time in strongly correlated 

configurations. 

• Besides Glauber elastic scattering, intermediate hadron-hadron 

inelastic scattering (Gribov inelastic Shadowing) is taken into account. 



1. SHORT RANGE CORRELATIONS IN HADRONIC MATTER 



The two-body density distributions of 16 O 

pp (r), pn (r) (fm-3 ) 

0.06 

0.05 

0.04 

0.03 

0.02 

0.01 

MF 

v 

MF 

pp 

pn 

v 

0 1 2 3 4 5 

r (fm) 

Short Range Correlations 

(SRC): the strong modification 

of the Mean Field 

two-nucleon density distribution 

in the region r ≤ 

1.5 fm due the interplay between 

the core repulsion 

and the tensor attraction. 

At r ≥ 1.5 fm mean field 

(independent particle) motion 

is OK. 

No model dependence. 

Urbana-Argonne Group Phys. Rev. Lett. 98 (2007) 132501. 

Perugia Group Phys. Rev. Lett. 100 (2008) 162503; Phys. Rev. 

Lett. 100 (2008) 122301. 



RECENT EXPERIMENTAL EVIDENCE 

SCIENCE 320, 1476 (2008) 

R. SUBEDI et al Probing Cold Dense Nuclear Matter 

"The protons and neutrons in a nucleus 

can form strongly correlated nucleon pairs. 

Scattering experiments, show that .... the 

neutron-proton pairs are nearly 20 times as 

prevalent as proton-proton pairs.... . This is 

due to the nature of the strong force ." 



2 BEYOND THE GLAUBER APPROXIMATION :THE 

EFFECTS OF SHORT RANGE CORRELATIONS AND GRIBOV 

INELASTIC SHADOWING 



2.1 The h − A elastic amplitude and the "Glauber Approximation" 

Glauber Multiple Scattering in Diagrams 

N 

f NN 

N 

A 

A 



G hA (b) ≡< Ψ 0 |Γ hA (b)|Ψ 0 >= 1 − 

|Ψ 0 (r 1 , ..., r A )| 2 = 

A∏ 

j=1 

[ 

1 − 

∫ 

|Ψ 0 (r 1 . . . r A )| 2 A ∏ 

j=1 

Γ hN 

j (b − s j )d 3 r j 

] 

r i ≡ {s i , z i } (1) 

ρ(r j ) + 

A∑ 

i

2.2 Effects of SRC (all terms of the expansion are considered) 

[ ∫ 

] A 

G hA (b) = 1 − 1 − ρ(r 1 )Γ hN (b − s 1 )dr 1 × 

T hN 

× 

A 

2 ∑ 

m=0 

⇒ 1 − exp 

[ 12 

∫ 

∆(r1 , r 2 )Γ hN (b − s 1 )Γ hN (b − s 2 )dr 1 dr 2 

( 

1 − 

∫ 

ρ(r1 )Γ hN (b − r 1 )dr 1 

) 2 

] m 

⇒ 

[ 

−T hN 

Gl 

T hN 

Gl (b) = 2 

σ NN 

tot 

∫ 

(b) + T 

hN 

SRC (b) ] 

SRC (b) = 

= 1 ∫ 

σtot 

NN d 2 s 1 d 2 s 2 Γ hN (s 1 )Γ hN (s 2 ) 

d 2 s Γ hN (s) T A (b − s) T A (b) = 

∫ ∞ 

−∞ 

∫ ∞ 

∞ 

[ 

A >> 1 

d z ρ(b, z) 

d z 1 d z 2 A 2 ∆(b − s 1 , z 1 ; b − s 2 , z 2 ) 

] 



2.3 Glauber plus Gribov Inelastic Shadowing (IS) 

(lowest and higher orders) 

V. N. Gribov, Sov. JETP 29 (1969) 483; 

J. Pumplin, M. Ross, Phys. Rev. Lett. 21(1968)1778; 

V.A.Karmanov,L.A.Kondratyuk, JETP Lett. 18 (1973) 451; 

B. Z. Kopeliovich, I. K. Potashnikova, I. Schmidt, Phys. Rev. 

C73 (2006)034901 

N 

f NN 

N 

N f N N f 

N 

f NX XN 

NX 

f XX 

f XN 

A 

Glauber 

A 

A 

A 

A 

Inelastic Shadowing 

A 

(Diffractive excitation of the projectile) 



Gribov inelastic shadowing by the light-cone dipole approach 

(Zamolodchikov, Kopeliovich, Lapidus, JEPT Lett. 33 (1981) 612) 

Gribov corrections can be summed to all orders by switching to 

the interaction eigenstates of the propagating hadron; these were 

identified as color dipoles in agreement with the 2-gluon exchange 

interaction in hadron-Nucleon scattering. A certain degree of model 

dependence is introduced, which is reflected in the Key ingredients: 

the universal dipole nucleon cross section, e.g. 

[ ( )] 

σ¯qq (r T , s) = σ 0 (s) 1 − exp − r2 T 

R0 2(s) the light cone wave function of the projectile, e.g.: 

( ) 

|Ψ N (r 1 , r 2 , r 3 )| 2 = 2 

π Rp 

2 exp − 2r2 T 

Rp 

2 



GL plus SRC plus IS BY LIGHT CONE DIPOLES 

Alvioli, CdA, Kopeliovich, Potashnikova, Schmidt, Phys. Rev. C81 

(2010) 025204 

T ¯qq 

Gl+SRC (b, r 1 

T , α) = 

σ¯qq (r T ) × 

∫ 

× d 2 s 1 d 2 s 2 ∆ ⊥ (s 1 , s 2 ) × Re Γ¯qq,N (b − s 1 , r T , α) Re Γ¯qq,N (b − s 2 , r T , α) 

σ pA 

tot = 2 ∫ 

d 2 b 

( [ 

1 − 〈exp − 1 ] ) 

2 σ¯qq(r T , s) T ¯qq 

A (b, r T , α) 〉 

〈. . .〉 = 

∫ 1 

0 

dα 

∫ 

d 2 r T . . . 



3. RESULTS of CALCULATIONS-I 



The total neutron − Nucleus 

cross section at high energies: 

(M. Alvioli, C.d.A, et al Phys. Rev. C78(R),031601(2008) ) 

nA 

tot [mb] 

140 

135 

130 

125 

120 

360 

340 

320 

460 

440 

420 

3200 

3100 

3000 

2900 

4 He 

12 C 

16 O 

208 Pb 

G 

+ G 

10 100 

IS 

p lab 

[Gev/c] 

G 

G SRC 

G SRC IS 

• No free parameters!! 

• Full SRC. 

10 100 

• Gribov inelastic shadowing at 

lowest order. 

• Main result: SRC increase the 

opacity, Gribov IS decreases 

it and depends upon energy, 

the two effects being of about 

the same order in this energy 

range. 

• What about higher order Gribov 

corrections 



SRC plus HIGHER ORDER IS CALCULATIONS of 

(σtot hA, 

σhA el 

, σqe hA , σsd hA, 

σhA dd 

, . . . at HERA B, RHIC and LHC energies ) 

(Alvioli, CdA, Kopeliovich, Potashnikova, Schmidt, Phys. Rev. C81 

(2010) 025204) 

LHC 

208 P b Glauber Glauber q-2q model 3q model 

+SRC +SRC +SRC 

σ tot (mb) 3850.63 3885.77 3833.26 3839.26 

σ el (mb) 1664.76 1690.48 1655.70 1660.67 

σ qe (mb) 120.92 112.65 113.37 113.88 

RHIC 

208 P b GL + SRC q-2q SRC 3q + SRC 

σ tot (mb) 3297.56 3337.57 3155.29 3228.11 3208.92 3262.58 

σ el (mb) 1368.36 1398.08 1246.73 1314.04 1293.75 1343.76 

σ qe (mb) 80.42 74.36 71.99 73.92 



4. RESULTS OF CALCULATIONS II : 

THE EFFECTS OF SRC AND IS ON THE NUMBER OF 

INELASTIC COLLISIONS IN h − A AND A − A SCATTERING 

(CdA, Mezzetti, Kopeliovich, Potashnikova, Schmidt, Phys. Rev. 

C84 (2011) 025205 ) 



4.1 The number of inelastic collisions in hA scattering 

In order to know the absolute value of a hard nuclear cross section, 

the measured fraction of the total number of inelastic events 

is normalized as follows 

Nhard hA /NhA in 

R hard 

A/N = 

σhA in N hA 

hard 

A σ hN 

in 

N hN 

hard 

hard 

Nhard 

hN 

= 1 N hA 

N coll 

, N coll = A σhN in 

σin 

hA 

The number of hard collisions at a given impact parameter should 

be defined as follows 

R hard 

A/N (b) = 

N hA 

hard (b) 

n coll (b) N hN 

hard 

n coll (b) = σhN in 

T A(b) 

P in (b) 

and P in (b) = 1 − exp[−σin 

NNT 

A h b] is the probability for an inelastic interaction 

to occur at impact parameter b; it is affected by both SRC 

and IS through TA h(b): 



p − 208 P b 

GLAUBER 

σin NN [mb] σtot NA [mb] σel NA [mb] σqel NA [mb] σin NA N coll 

RHIC 42.1 3297.6 1368.4 66.0 1863.2 4.70 

LHC 68.3 3850.6 1664.8 121.0 2064.8 6.88 

GLAUBER+SRC 


RHIC 42.1 3337.6 1398.1 58.5 1881.0 4.65 

LHC 68.3 3885.8 1690.5 112.6 2082.7 6.82 

GLAUBER+SRC+GRIBOV IS (q − 2q) 


RHIC 42.1 3228.1 1314.0 71.99 1842.1 4.75 

LHC 68.3 3833.3 1655.7 113.4 2064.2 6.88 

Gribov IS increase N coll , SRC decreases it to the Glauber value. 



4.2 The effects of SRC in A − A scattering 

Collision of two heavy nuclei A and B with nucleon numbers A A 

and A B respectively. Only Γ ′ s having no indexes in common were 

considered. Each nucleon in A interacts with correlated nucleons in 

B and viceversa 

T AB 

Gl (b) = 

∫ 

d 2 b A T A (b A ) T h B (b − b A) 

= 2 ∫ 

σtot 

NN A A A B d 2 b A d 2 b B ρ A (b A )ReΓ NN (b − b A + b B )ρ B (b B ) 

∆T AB 

SRC (b) = 1 ∫ 

σtot 

NN A A A 2 B d 2 b A ρ A (b A ) 

∫ 

× d 2 b B1 d 2 b B2 ∆ ⊥ B (b B1, b B2 )Γ NN (b − b A + b B1 )Γ NN (b − b A + b B2 ) + 

+{A ←→ B} 



T AB (b) = T AB 

Gl 

(b) − 2∆T AB 

SRC (b) 

A -2 AB (b) [fm -2 ] 

~ 

0.010 

0.005 

0.000 

T AB (b) Gl 

T AB (b) SRC 

A -2 TOTAL 

208 

Pb- 208 Pb 

0 2 4 6 8 10 12 14 16 18 20 

b [fm] 

Large effects on the thickness function 



The number of collisions at impact parameter b is 

n AB 

coll 

σhN 

(b) = 

in 

P AB 

in 

T AB(b) 

• σin 

hN T AB(b) is affected neither by SRC nor by IS. 

• how to calculate Pin AB (b) The usual formula 

P AB 

in 

(b) 

(b) = 1 − exp[−σNNT 

AB h (b)] 

misses many terms of the Glauber theory. However, for 

large values of A A and A B the probability of no interaction 

exp[−σin 

NNT 

AB h (b)] is expected to be very small with or without 

the missed terms, the Gribov IS corrections and the effects of 

NN correlations. Except the very peripheral collisions Pin AB(b) 

≃ 1 

and it seems therefore that n AB 

coll 

is practically not affected by NN 

correlations and IS . 

in 



5. CONCLUSIONS 



• The Nucleus is neither a Fermi gas nor a system of independent 

particles but a self-bound saturated correlated liquid which nowadays 

can theoretically be described with high degree of confidence. 

The SRC structure of nuclei has been experimentally unveiled and 

its systematic investigation is under way. 

• A reliable theoretical approach has been developed to treat simultaneously 

SRC NN correlations and Gribov inelastic shadowing 

in high energy nuclear collisions. 

• In the considered processes the effects from NN correlations are 

of the same order of the effects of Gribov inelastic shadowing, the 

two effects acting in the opposite directions. 

• Calculations for relativistic heavy ion scattering are in progress.

Claudio CIOFI degli ATTI DIFFRACTION on NUCLEI ... - QNP2012

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