ciofi a tti - kek · 2009-09-25 · exp erimen tal study of sr c 6. t w o-and three-n ucleon sr c:...

C. CIOFI degli ATTIShort Range Correlations and their impa t on nu lear and parti lephysi s and astrophysi s: re ent advan es and possible studies atJ-PARC

KEK Theory Center workshoponShort-range orrelations and tensor stru ture at J-PARC

C. Cio� degli Atti 1 KEK, September 2009

LIST OF CONTENS1. Introdu tion: two re ent "popular" papers on short range or-relations (SRC)2. The standard model of nu lei3. Relevan e of SRC in di�erent pro esses4. Independent and orrelated nu leons: their smoking guns5. Experimental study of SRC6. Two- and three-nu leon SRC: in lusive A(e,e')X pro esses7. Hadron s attering o� nu lei at high energies (HERA,RHIC,LHC)8. Con lusions


1 Introdu tion: two re ent "popular" papers on short range orrelations (SRC)


SCIENCE 320, 1476 (2008)R. SUBEDI et al Probing Cold Dense Nu lear Matter

The protons and neutrons in a nu leus an form strongly orrelatednu leon pairs. S attering experiments, in whi h a proton is kno kedout of the nu leus with high-momentum transfer and high missingmomentum, show that in arbon-12 the neutron-proton pairs arenearly 20 times as prevalent as proton-proton pairs and, by infer-en e, neutron-neutron pairs. This di�eren e between the types ofpairs is due to the nature of the strong for e and has impli ationsfor understanding old dense nu lear systems su h as neutron stars.


2. THE STANDARD MODEL OF NUCLEI


[

− h2

2m

∑

i ∇2i +

∑

i<j v(i, j) +∑

i<j<k v(i, j, k) + . . .]

Ψo = EoΨ0

vij(xi, xj) =∑

n

v(n)(rij)O(n)ij rij ≡ |ri − rj|

O(n)ij =

[

1 , σi · σj , Sij , (L · S)ij , ...]

⊗[

1 , τ i · τ j]

.

short-range repulsion ( ommon to many systems)

•• intermediate- to long-range tensor hara ter (unique to nu lei)


THE MEAN FIELD APPROXIMATION[

− h2

2m

∑

i ∇2i +

∑

i<j vij

]

Ψo = EoΨo

⇓[

− h2

2m

∑

i ∇2i +

∑

i V i

]

Φo = ǫoΦoIndependent parti le motion → Shell Model

Mean �eld or Shell Model: nu leons o upy all available states belowthe Fermi level; all states above the Fermi level are empty. Greatsu ess (magi numbers, magneti moments, low ex itation levels,et ). Re ent developments: establish the limits of validity by ad-van ed solution of the nu lear many-body problem.


THE "EXACT" MANY-BODY SOLUTIONRe ent developments towards the exa t solution ofHΨo = EnΨo , with vij =

∑

n v(n)(rij) O(n)ijThe same operatorial dependen e appearing in vij is ast onto thetrial fun tion Ψo:

Ψo = FΦowhere Φo is the mean-�eld wave fun tion andF = S

∏

i<j

fij = S∏

i<j

∑

n

f (n)(rij) O(n)ijis a orrelation operator.

Variational monte arlo (Urbana Group)Cluster expansion te hniques ( Here:Alvioli, Cda, Morita)


The orrelation fun tions fij: Central, Spin-Isospin, Tensor . . .

0 1 2 3 4 5

-0.04-0.020.000.020.040.060.080.10 f(r)

4 - 5 - S 6 - S

16O - AV8'

r [fm]

1 - fc (/10) 2 - 3 -

SRC → two nu leons at separation shorter than average separation(≃ 1.7 fm)


THE NOVEL VIEW OF THE ATOMIC NUCLEUS

Nu lei onsist also of drops of old high density matterCru ial question: what is the per entage of SRC? Can we measureit? Why it is important to know it


3. RELEVANCE OF SRC IN DIFFERENT PROCESSES


3.1. Study of ore and tensor orrelationsQuark, gluon or pion des riptions of NN intera tion?

Adapted from: W. Weise, Nu l. Phys. A 805(2008)145


3.2 Transition from hadron to quark gluon des riptions of nu lei

Nu leon radius < r2 >1/2≃ 0.8fm−1 ⇒ Nu leon overlap.

3.3 Medium indu ed modi� ations of hadron properties ??

EMC e�e t and SRC

CdA, L. Kaptari, L. Frankfurt, M. Strikman, Phys. Rev. C 76(2007) 055206


3.4 High energy s attering pro essesThe little bang in the laboratory

Signals depends upon the way hadrons propagated in the medium.SRC do a�e t hadron propagation.


3.5 Formation of old dense nu lear matter in the laboratory

How are neutron star properties a�e ted by SRC?


!"#$%&'($)*(+,-(+.&/-(0)*)(1)&-(&2)*34)1,5)3&"(&6+7*-("1&2%83"13&

'B4."1+,-(3&0-*&=)<$*-(&!$+*3&

y!)EF)FG%)#&.%)&-)'%"F.&')(FB.(H)/&(F)B##%IF%J)/&J%$()B(("/%)DK@6L)'%"F.&'(H)K6L)I.&F&'()

y!)!%M$%#N'M)FG%)'I2345)0'F%.B#N&'(H)&'%)#B')B(("/%)FO&)(%IB.BF%)P%./0)MB(%()

y!)30'#%)'I)0'F%.B#N&')0()$B.M%)#&/IB.%J)F&)''H)')MB()G%BF()FG%)I)MB()

y!)QG0()#&"$J)%R%#F)FG%)"II%.)$0/0F)&')/B(()&-)'%"F.&')B'J)B$$&O)FG%)'%"F.&'()0')FG%)(FB.)J%#BS))))&


4. INDEPENDENT NUCLEONS AND CORRELATEDNUCLEONS: WHICH ARE THE SMOKING GUNS?


.

• Repulsive ore and tensor for e generate high momentum ompo-nents (k >> kF ≃ 1.4 fm−1)

• Properties of nu lear matter at short distan es resemblethe properties of the deuteron (T=0, S=1 proton-neutronpairs)("deuteron s aling")•Wide spe trum of ex itation energy of the nu leus(Spe tral Fun tion)


4.1 High momentum omponents. The role of the ore and thetensor for e0 1 2 3 4

10-7

10-6

10-5

10-4

10-3

10-2

10-1

VMC

Mean Field Central Central

+ Tensor

n(k)

[fm

3 ]

k [fm-1]

16O

Tensor for es a ting in T=0 S=1 states produ e the largest amountof high momentum omponents. Mean �eld distributions drop tozero at k ≥ 1.5− 2 fm−1 (Adapted from Alvioli, CdA, Morita,Phys.Rev. C72(2005)054310)


4.2 High momentum omponents and deuteron s alingdue to NN orrelations the 1-body momentum distributions a quire pe uliarhigh momentum omponents

The high momentum (k > kF ) part of nA(k) an be viewed as theres aled deuteron momentum distribution: nA(k) ≃ CA nD(k).(Adapted from Cda, Simula, Phys. Rev. 53(1996)1689)


Role of orrelations better seen in the2-body momentum distributions0 1 2 3 4 5

10-1

100

101

102

103

104

105

106

n(k re

l,KC

M=0

) [fm

6 ]

krel [fm-1]

12C Total p - p p - n deuteron

0 1 2 3 4 5100101102103104105106107

40Ca

krel [fm-1]

Total p - p p - n deuteron

M. Alvioli, CdA, H.Morita, Phys. Rev. Lett, 100, 162503, (2008)The tensor deuteron-like ( T=0, S=1)dominan e at

krel ≥ 1.5− 2 fm−1o urs both in few-nu leon systems and omplexnu lei.


4.3 High ex itation energy omponents

P0(k,E) P1(k,E)S M (E = ǫα) : 80% Correlations (E ≃ k2/2mN) : 20%S. Simula, CdA - Phys. Rev. C53 (1996) 1689


5. EXPERIMENTAL STUDY OF CORRELATIONS


.CAN THESE RELEVANT DEVIATIONS FROM THE WELLHONORED MEAN FIELD DESCRIPTION OF NUCLEIEXPERIMENTALLY BE DETECTED?YES THEY CAN BY REMOVING THE NUCLEUSCONSTITUENTS AT HIGH ENERGY AND MOMENTUMTRANSFERS

THE A(e, e′N )X and A(e, e′NN )X PROCESSESTHE A(p, p′N )X and A(p, p′NN )X PROCESSESIn double and triple oin iden e experiments the kinemati s isfully determined


Example: the (e,e'p) pro ess on mean �eld and orrelatednu leons.Mean Field:

k1 + kA−1 = 0

The double oin iden e ross se tion:

dσd~e′d~p

∝ σep(~q,~k1 ν)× P0(k1, E)

P0(k1, E) =∑

α nα(k1)δ(E − ǫα)


Correlations:

k1+k2+k3 = 0 k3 ≡ KA−2Simple model:

{

k2 ≃ −k1 k3 ≃ 0 E∗A−2 = 0

E∗A−1 ≃

A−2A−1

k212mNRealisti model:

k3 6= 0 E∗A−2 6= 0

E∗A−1 =

A−22mN (A−1)

[

k1 +A−1A−2 k3

]2+ EA−2The double oin iden e ross se tion:

dσd~e′d~p

∝ σep(~q,~k1 ν)× P1(k1, E)

P1(k1, E) = {models whi h in ludes orrelations} → Morita'stalk


One important aveat


The 12C(e, e′p)X pro ess from its birth to present day1966 LNF (Italy) 1988 NIKHEF (Holland) 2006 JLab (USA)


Re ent Developments (triple oin iden e experiments)

By dete ting 2 Nu leons in the �nal state the initial pair orrelation an be studiedTriple oin iden e experiment A(a, a′NN )X a = {p, e}BNL and JLAB EXPERIMENTS


!"#$%&'($)*(+,-(+.&/-(0)*)(1)&-(&2)*34)1,5)3&"(&6+7*-("1&2%83"13&

/<3$-B"Q)7&G)J)[4=I&L)+3<*)B)($&

•! %";%&NO&$-&B"("B"Q)&Lb/&&&&

•! #fT&$-&3<44*)33&"3->+*&1-($*"><,-(3&

•! +(,94+*+..).&^"()B+,13&$-&3<44*)33&k!'&

H-&3$<78&(<1.)-(&4+"*3&+$&1.-3)&4*-#"B"$8&+(7&$%)"*&1-($*"><,-(3&$-&$%)&.+*;)&B-B)($<B&

$+".&-0&(<1.)-(3&"(&(<1.)"A&

F&4+"*&M"$%&m.+*;)o&*).+,5)&

B-B)($<B&>)$M))(&$%)&(<1.)-(3&

+(7&3B+..&1)($)*&-0&B+33&B-B)($<B&


Momentum onservationq = p + PA−1Missing momentumpm = q− p = {IA} = q− (k1 + q− q) = −k1 = PA−1

Dete t k' , p and pla e a dete tor at the dire tion of PA−1. Sin e if2NC model is orre t we have PA−1 = k2 + PA−2 ≃ −k1, we shoulddete t the orrelated partner of nu leon "1" with momentum pm.


Correlations:

k1+k2+k3 = 0 k3 ≡ KA−2Simple model:

{

k2 ≃ −k1 k3 ≃ 0 E∗A−2 = 0

E∗A−1 ≃

A−2A−1

k212mNRealisti model:

k3 6= 0 E∗A−2 6= 0

E∗A−1 =

A−22mN (A−1)

[

k1 +A−1A−2 k3

]2+ EA−2


BNL p beam 5.9− 7.5GeV/c, 12C targetPhys. Lett. B453 (99) 202; Phys. Rev. C65 (01) 015207; Phys. Rev. Lett. 90(03) 042301


pn

Directional correlation

p

n

Pn>220 MeV/c

Pn<220 MeV/c

The EVA/BNL collaboration

(p,2pn)


R. Subedi et al, S ien e 320,1476 (2008)C. Cio� degli Atti 40 KEK, September 2009

The orrelation pizza in 12C

R. Subedi et al,S ien e 320,1476 (2008)


.

The novel view of the atomi nu leus


6 TWO AND THREE NUCLEON CORRELATIONS:INCLUSIVE A(e, e′)X PROCESSES


TWO-NUCLEON CORRELATIONS::k1 ≃ −k2 large and k3 ≃ 0THREE-NUCLEON CORRELATIONS:

k1 + k2 + k3 = 0 all three momenta are large

Correlations an be linked to the value of the Bjorken s alingvariable xB = Q2

2mN ν ⇒ 2N CORRELATIONS: a kind of "two-bodysystem"; 3N CORRELATIONS: a kind of "three-body systems"s attering on a single nu leon: 0 < xB < 1s attering on 2 orrelated nu leons: 1 < xB < 2s attering on 3 orrelated nu leons: 2 < xB < 3


Measurement of Two- and Three-Nucleon Short-Range Correlation Probabilities in Nuclei

K. S. Egiyan,1,34 N. B. Dashyan,1 M. M. Sargsian,10 M. I. Strikman,28 L. B. Weinstein,27 G. Adams,30 P. Ambrozewicz,10

M. Anghinolfi,16 B. Asavapibhop,22 G. Asryan,1 H. Avakian,34 H. Baghdasaryan,27 N. Baillie,38 J. P. Ball,2

N. A. Baltzell,33 V. Batourine,20 M. Battaglieri,16 I. Bedlinskiy,18 M. Bektasoglu,27 M. Bellis,30,4 N. Benmouna,12

A. S. Biselli,30,4 B. E. Bonner,31 S. Bouchigny,34,17 S. Boiarinov,34 R. Bradford,4 D. Branford,9 W. K. Brooks,34

S. Bultmann,27 V. D. Burkert,34 C. Bultuceanu,38 J. R. Calarco,24 S. L. Careccia,27 D. S. Carman,26 B. Carnahan,5

S. Chen,11 P. L. Cole,34,14 P. Coltharp,11,34 P. Corvisiero,16 D. Crabb,37 H. Crannell,5 J. P. Cummings,30 E. De Sanctis,15

R. DeVita,16 P. V. Degtyarenko,34 H. Denizli,29 L. Dennis,11 K. V. Dharmawardane,27 C. Djalali,33 G. E. Dodge,27

J. Donnelly,13 D. Doughty,7,34 P. Dragovitsch,11 M. Dugger,2 S. Dytman,29 O. P. Dzyubak,33 H. Egiyan,24 L. Elouadrhiri,34

A. Empl,30 P. Eugenio,11 R. Fatemi,37 G. Fedotov,23 R. J. Feuerbach,4 T. A. Forest,27 H. Funsten,38 G. Gavalian,27

N. G. Gevorgyan,1 G. P. Gilfoyle,32 K. L. Giovanetti,19 F. X. Girod,6 J. T. Goetz,3 E. Golovatch,16 R. W. Gothe,33

K. A. Griffioen,38 M. Guidal,17 M. Guillo,33 N. Guler,27 L. Guo,34 V. Gyurjyan,34 C. Hadjidakis,17 J. Hardie,7,34

F. W. Hersman,24 K. Hicks,26 I. Hleiqawi,26 M. Holtrop,24 J. Hu,30 M. Huertas,33 C. E. Hyde-Wright,27 Y. Ilieva,12

D. G. Ireland,13 B. S. Ishkhanov,23 M. M. Ito,34 D. Jenkins,36 H. S. Jo,17 K. Joo,37,8 H. G. Juengst,12 J. D. Kellie,13

M. Khandaker,25 K. Y. Kim,29 K. Kim,20 W. Kim,27,20 A. Klein,27,20 F. J. Klein,27 A. Klimenko,27 M. Klusman,30

L. H. Kramer,10,34 V. Kubarovsky,30 J. Kuhn,4 S. E. Kuhn,27 S. Kuleshov,18 J. Lachniet,4 J. M. Laget,6,34 J. Langheinrich,33

D. Lawrence,22 T. Lee,24 K. Livingston,13 L. C. Maximon,12 S. McAleer,11 B. McKinnon,13 J. W. C. McNabb,4

B. A. Mecking,34 M. D. Mestayer,34 C. A. Meyer,4 T. Mibe,26 K. Mikhailov,18 R. Minehart,37 M. Mirazita,15

R. Miskimen,22 V. Mokeev,23,34 S. A. Morrow,6,17 J. Mueller,29 G. S. Mutchler,31 P. Nadel-Turonski,12 J. Napolitano,30

R. Nasseripour,10 S. Niccolai,12,17 G. Niculescu,26,19 I. Niculescu,12,19 B. B. Niczyporuk,34 R. A. Niyazov,34

G. V. O’Rielly,22 M. Osipenko,16,23 A. I. Ostrovidov,11 K. Park,20 E. Pasyuk,2 C. Peterson,13 J. Pierce,37 N. Pivnyuk,18

D. Pocanic,37 O. Pogorelko,18 E. Polli,15 S. Pozdniakov,18 B. M. Preedom,33 J. W. Price,3 Y. Prok,34 D. Protopopescu,13

L. M. Qin,27 B. A. Raue,10,34 G. Riccardi,11 G. Ricco,16 M. Ripani,16 B. G. Ritchie,2 F. Ronchetti,15 G. Rosner,13 P. Rossi,15

D. Rowntree,21 P. D. Rubin,32 F. Sabatie,27,6 C. Salgado,25 J. P. Santoro,36,34 V. Sapunenko,16,34 R. A. Schumacher,4

V. S. Serov,18 Y. G. Sharabian,34 J. Shaw,22 E. S. Smith,34 L. C. Smith,37 D. I. Sober,5 A. Stavinsky,18 S. Stepanyan,34

B. E. Stokes,11 P. Stoler,30 S. Strauch,33 R. Suleiman,21 M. Taiuti,16 S. Taylor,31 D. J. Tedeschi,33 R. Thompson,29

A. Tkabladze,27,26 S. Tkachenko,27,26 L. Todor,4 C. Tur,33 M. Ungaro,30,8 M. F. Vineyard,35,32 A. V. Vlassov,18

D. P. Weygand,34 M. Williams,4 E. Wolin,34 M. H. Wood,33 A. Yegneswaran,34 J. Yun,27 L. Zana,24 and J. Zhang27

(CLAS Collaboration)

1Yerevan Physics Institute, Yerevan 375036, Armenia

PRL 96, 082501 (2006)P H Y S I C A L R E V I E W L E T T E R S week ending

3 MARCH 2006

,32

22

� �QM

QxB

22 4.1 GeVQ !

The observed “scaling” means

that the electrons probe the

high-momentum nucleons in the

2/3-nucleon phase, and the

scaling factors determine the

per-nucleon probability of the

2/3N-SRC phase in nuclei with

A>3 relative to 3He.

K. Sh. Egiyan et al. PRL. 96, 082501 (2006)

The probabilities for 3-nucleon

SRC are smaller by one order

of magnitude relative to the 2N

SRC.

r(4H

e,3

He

)a)

r(1

2C

,3H

e)

b)

xB

r(5

6F

e,3

He

) c)

1

2

3

1

2

3

4

2

4

6

1 1.25 1.5 1.75 2 2.25 2.5 2.75

New CLAS A(e,e') Result:

3N-SRC Less than 1% of total

K. Sh. Egiyan et al. PRC 68, 014313.

cMeVM

QxB /,. 275P 51

2in

2

t! Q

2N-SRC(np,pp,nn) = 0.20 ± 0.045%

For 12 C:


Mezzetti's talkC. Cio� degli Atti, C.B. Mezzetti, Phys. Rev. C 79 (2009) 051302(R); C.B. Mezzetti, C. Cio�degli Atti, arXiv:0906.5564 (2009)


7 HADRON SCATTERING OFF NUCLEI AT HIGH ENERGIES(HERA, RHIC, LHC)


The total neutron−Nucleus ross se tion at high energies:σtot =

4πk Im [F00(0)] F00(q) =

ik2π

∫

d2bneiq·bn

[

1− eiχopt(bn)]

eiχopt(bn) =

∫ A∏

j=1

drj

A∏

j=1

[1−Γ(bn−sj)] |Ψ0(r1, ..., rA)|2δ

(

1

A

∑ rj) .

The exa t expansion of |Ψ|2 (Glauber, Foldy & Wale ka ):

|Ψ(r1, ..., rA)|2 =

A∏

j=1

ρ(rj) +A∑

i<j=1

∆(ri, rj)A∏

k 6=(il)

ρ(rk) +

+∑

(i<j) 6=(k<l)

∆(ri, rj)∆(rk, rl)∏

m6=i,j,k,l

ρ1(rm) + . . .

∆(ri, rj) = ρ(2)(ri, rj) − ρ(1)(ri) ρ(1)(rj) ;C. Cio� degli Atti 48 KEK, September 2009

|Ψ(r1, ..., rA)|2 =

A∏

j=1

ρ(rj) +A∑

i<j=1

∆(ri, rj)A∏

k 6=(il)

ρ(rk) +

+∑

(i<j) 6=(k<l)

∆(ri, rj)∆(rk, rl)∏

m6=i,j,k,l

ρ1(rm) + . . .

≃A∏

j=1

ρ(rj)

Usual approximation in Glauber-type al ulation: what is itsvalidity?


Glauber + Inelasti shadowing(Di�ra tive ex itation of the proje tile)V. N. Gribov, Sov. JETP 29 (1969) 483;V.A.Karmanov,L.A.Kondratyuk, JETP Lett. 18 (1973) 451;B. Z. Kopeliovi h, I. K. Potashnikova, I. S hmidt, Phys. Rev.C73 (2006)034901NN

AA

fNN N

A A

NX XNfN f N N

A A

NX f XNf f XX

(Glauber) (Inelasti Shadowing)total neutron-Nu leus ross se tion

σtot = 4 πk Im

[

FG00(0)

]

+ ∆σin = σG + ∆σinC. Cio� degli Atti 50 KEK, September 2009

M. Alvioli, C.d.A, I. Mar hino, H. Morita, V. PalliPhys. Rev. C78(R),031601(2008) No free parameters!!10 100

125

130

135

140

145 one body correlations correlations + in

tot [m

b]

plab [GeV/c]

4He

10 100320

340

360

380

400

tot [m

b]

plab

[Gev/c]

mean field correlations correlations +

in

12C

10 100

2900

3000

3100

3200

3300

tot [m

b]

plab

[Gev/c]

mean field correlations correlations +

in

208Pb


Cal ulations of total, elasti , quasi-elasti and di�ra tionhadron-Nu leus ross se tions at HERA, RHIC and LHC energy,taking inelasti Gribov orre tions and SRC into a ount, are inprogress. (Alvioli, CdA, Kopeliovi h, S hmidt, Potashnikova)Experimental data and theoreti al al ulations of this type wouldbe of great relevan e in the �elds of, e.g., high energy heavy ion ollisions, hadronization me hanism, and other phenomena whi h ould be investigated by using the atomi nu leus as a mi rodete tor of QCD e�e ts.


8. CONCLUSIONS


• Advan ed solutions of the nu lear many-body problem lead tonu lear wave fun tions exhibiting a ri h SRC stru ture.• The tensor for e plays a dominant role in reating high momen-tum omponents.

• Reliable experimental information on 2NC and, partly, on 3NCbe ame available on�rming the basi stru ture of SRC, e.g. highrelative momenta of the orrelated pair and small pair CM mo-mentum.

• Correlation pizza ooked out only for 12C. Experiments on othernu lei both with lepton and hadroni probes are alled for.

• SRC have relevant impa t on the stru ture of old dense matterand intermediate and high energy s attering pro esses.


ciofi a tti - kek · 2009-09-25 · exp erimen tal study of sr c 6. t w o-and three-n ucleon sr c:...

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