Exclusive study of Short range correlations Eli PiasetzkyTel Aviv University, ISRAEL Hall C Summer Workshop

Short /intermediate Range Correlations in nuclei  1.f Nucleons 2N-SRC 1.7f  o = 0.16 GeV/fm 3 ~1 fm 1.7 fm A~10 57 Cold-Dense Nuclear Matter (from deuteron to neutron-stars). What SRC in nuclei can tell us about: High – Momentum Component of the Nuclear Wave Function. The Strong Short-Range Force Between Nucleons. tensor force, repulsive core, 3N forces Nucleon structure modification in the medium ? EMC and SRC, contribution of non-nucleonic D.O.F to SRC 12 GeV update

A triple – coincidence measurement E / Jlab p p p n EVA / BNL (E07-006) “Redefine” the problem in momentum space JLab / CLAS EG2

he A triple – coincidence measurement “Redefine” the problem in momentum space 3 He

BNL / EVA 12 C(e,e’pn) / 12 C(e,e’p) [ 12 C(e,e’pp) / 12 C(e,e’p)] / 2 [ 12 C(e,e’pn) / 12 C(e,e’pp)] / 2 R. Subedi et al., Science 320, 1476 (2008). Why ? There are 18 ± 5 times more np-SRC than pp-SRC pairs in 12 C.

At MeV/c there is an excess strength in the np momentum distribution due to the strong correlations induced by the tensor NN potential. 3 He V18 Bonn np pn pp pp/np 3 He Schiavilla, Wiringa, Pieper, Carson, PRL 98, (2007). Sargsian, Abrahamyan, Strikman, Frankfurt PR C (2005). Ciofi and Alvioli PRL 100, (2008). MeV S=1 T=0 MeV S=1 T=0S=1 T=1S=0 T=0 S=0 T=1 Argonne V8 potential

n-p pairs p-p pairs n-n pairs C 12 Single nucleons 60-70% 2N-SRC % 10-20% 20±5% 4.75±1% 2N-SRC A(e,e‘p) A(e,e‘) γ p n Egiyan et al. PRC 68, Egiyan et al. PRL. 96, (2006) Tang et al. PRL (2003) Piasetzky, Sargsian, Frankfurt, Strikman, Watson PRL (2006). 12 C(p,2p n) A(e,e‘pN) 4.75±1% Long range (shell model) correlations Summary of Results R. Subedi et al., Science 320, 1476 (2008). Also data from SLAC and Hall C CA 2010

JLab / Hall B 300 < q < 500 MeV/c Q>0 q= MeV/c pp np pp/pn ratio as a function of pair CM momentum Small Q  NN pair in s-wave  large tensor contribution  small pp/np ratio Wiringa, Schiavilla, Pieper, Carlson PRC (2008) Q (fm -1 ) q (fm -1 ) Hall A / BNL Q Q PRL 105, (2010) pair CM momentum Q

F e (e,e’pp) P b (e,e’pp) JLab / CLAS Data Mining, EG2 data set, Or Chen et al. Q 2 =2 GeV/c 2 Ein =5.014 GeV X>1.2

JLab / CLAS Data Mining, EG2 data set, Or Chen et al. Ein =5.014 GeV Q 2 =2 GeV/c 2 X> C(e,e’pp)

F e (e,e’pp) P b (e,e’pp) C(e,e’pp) Hall A data PRL 99(2007) γ p p Directional correlation Hall B JLab / CLAS Data Mining, EG2 data set, Or Chen et al. PRELIMINARY

A new experiment Jan-May 2011 at JLab (E ) Measurement over missing momentum range from 400 to 800 MeV/c. The data are expected to be sensitive to the NN tensor force and the NN short range repulsive force. Lattice QCD (e,e’pp) / (e,e’pn) Chiral effective field Taketani,Nakamura,Saaki Prog. Theor. Phys. 6 (1951) 581.

12 C(e,e’p) “300 MeV/c” “400 MeV/c” “500 MeV/c” E Hall A 2005 E Hall A He(e,e’p)

E Hall A Jan- May He(e,e’p)

Deep Inelastic Scattering (DIS) E E` (,q)(,q) nucleon Final state Hadrons W2W2 Incident lepton E, E’ GeV Q GeV 2 w 2 >4 GeV 2 0 ≤ X B ≤ 1 x B gives the fraction of nucleon momentum carried by the struck parton Information about nucleon vertex is contained in F 1 (x,Q 2 ) and F 2 (x,Q 2 ), the unpolarized structure functions scattered lepton Electrons, muons, neutrinos SLAC, CERN, HERA, FNAL, JLAB

DIS Scale: several tens of GeV Nucleons Nucleon in nuclei are bound by ~MeV Naive expectation : DIS off a bound nucleon = DIS off a free nucleon (Except some small Fermi momentum correction)

The European Muon Collaboration (EMC) effect DIS cross section per nucleon in nuclei ≠ DIS off a free nucleon

SLAC E139 Data from CERN SLAC JLab

J. Seely et al. PRL 103, (2009) JLab / Hall C EMC is a local density or nucleon momentum dependence effect, not a bulk property of nuclear medium

G. Miller: EMC = Every Model is Cool Theoretical interpretations: ~1000 of papers Gessman, Saito,Thomas, Annu. Rev. Nucl. Part. Sci. 45:337 (1995). EMC recent review papers: P.R. Norton Rep Prog. 66 (2003).

A(e,e’)

: EMC slope SRC scaling factor Comparing the magnitude of the EMC effect and the SRC scaling factors Frankfurt, Strikman, Day, Sargsyan, Phys. Rev. C48 (1993) Q 2 =2.3 GeV/c 2 Gomez et al., Phys. Rev. D49, 4348 (1983). Q 2 =2, 5, 10, 15 GeV/c 2 (averaged ) SLAC data:

EMC: J. Seely et al. PRL 103, (2009) SRC: Hall B and Hall C data

Slopes 0.35 ≤ X B ≤ 0.7 EMC SRC Scaling factors X B ≥ 1.4 arXiv: nucl-ex PRL 106, (2011)

Where is the EMC effect ? High local nuclear matter density, large momentum, large off shell. large virtuality ( ) Largest attractive force Mean field SRC OR 80% nucleons (20% kinetic energy) 20% nucleons (80% kinetic energy) np pp nn Possible explanation for EMC / SRC correlation See also talk by S. Strauch on nucleon modification as a function of the nucleon virtuality

0.079±0.06 Deuteron is not a free np pair SRC=0 free nucleons A EMC SRC bound to free n p pairs (as opposed to bound to deuteron) The slopes for 0.35 ≤ X B ≤ 0.7

SRC=0 free nucleons A EMC SRC ±0.06 Deuteron is not a free np pair The slopes for 0.35 ≤ X B ≤ 0.7

In Medium Nucleon Structure Function, SRC, and the EMC Effect Spokepersons: O. Hen (TAU), L. B. Weinstein (ODU), S. A. Wood (JLab), S. Gilad (MIT) Proposal PR PAC 38 Aug Collaboration: Experimental groups from : ANL, CNU, FIU, HU, JLab, KSU, MIT, NRCN, ODU, TAU, U. of Glasgow, U. of Ljubljana, UTFSM, UVa Theoretical support: Accardi, Ciofi Degli Atti, Cosyn, Frankfurt, Kaptari, Melnitchouk, Mezzetti, Miller, Ryckebusch, Sargsian, Strikman

Measurement concept 1.Spectator Tagging:  Selects DIS off high momentum (high virtuality) nucleons 2. cross sections ratio  Minimize experimentaland theoreticaluncertainties No ‘EMC effect ‘ is expected R FSI is the FSI correction factor

Obstacles (FSI) Increase with W’ Decrease with Q 2 Decrease with recoil spectator angle Not sensitive to x’ * Collect data at very large recoil angles (small FSI) and at ~90 0 (large FSI) * look at ratios of two different x’ * Use the low x’ large phase space to check / adjust the FSI calculations (Study the dependence of FSI on Q 2, W' and θ pq ) * Get a large involvement of theoretical colleges at all stages of proposal, measurement, analysis θ pq >107 o 72 o <θ pq <107 o What do we know about FSI: How are we going to minimize (correct for) FSI: PdPdPd PdPd p or n CLAS d(e,e’p s ) vs. PWIA

Large Acceptance Detector (LAD) Use retired CLAS-6 TOF counters to detect recoiling nucleons (protons and neutrons) at backwards angles TOF

Expected Results d(e,e’p)d(e,e’n) Melnitchouk, Sargsian, Strikman Z. Phys. A359 (97) 99. PLC suppression Rescaling model Binding/off shell PLC suppression Rescaling model Binding/off shell

The probability for a nucleon to have momentum ≥ 300 MeV / c in medium nuclei is 20-25% More than ~90% of all nucleons with momentum ≥ 300 MeV / c belong to 2N-SRC. Probability for a nucleon with momentum MeV / c to belong to np-SRC is ~18 times larger than to belong to pp-SRC. Three nucleon SRC are present in nuclei.. PRL. 96, (2006) PRL (2006); Science 320, 1476 (2008). CLAS / HALL B EVA / BNL and Jlab / HALL A Dominant NN force in the 2N-SRC is tensor force PRL 98, (2007). Standard model for short distance structure of nuclei ~80% of kinetic energy of nucleon in nuclei is carried by nucleons in 2N-SRC. 12 Summary I Repulsive force ?

Summary II The magnitude of the EMC effect and SRC scaling factor are linearly related. We speculate that observed correlation arises because both EMC and SRC are dominated by high momentum (large virtuality) nucleons in nuclei. The observed relationship can be used to extract: the free neutron structure function and the d/u ratio for proton The EMC is a local density and / or momentum dependent and/or virtualery effect not a bulk property of the nuclear medium. EMC SRC 0.079±0.06 SRC=0 DIS off the deuteron tagged by high momentum recoil spectator JLab Proposal PR PAC 38 Aug. 2011

12 GeV 0utlook For Q 2 =2 GeV/c 2, x=1.2 SHMS momentum acceptance % 3 missing momentum setting Single setting BigBite 100 msr > 200 msr ~100 QE events ` QE events HrS momentum acceptance ±4.5%

A(e,e’) shows\ a second Plateau. 12 GeV 0utlook What is the role played by non nucleonic degrees of freedom in SRC ? m What is the role played by short range correlation of more than two nucleons ? EMC SRC DIS QE Are bound nucleons in SRC pairs different from free? Higher rate Higher energy

n recoil signal / BG (large x) ~1:20

Ciofi, )

The inclusive A(e,e’) measurements  At high nucleon momentum distributions are similar in shape for light and heavy nuclei: SCALING.  Can be explained by 2N-SRC dominance.  Within the 2N-SRC dominance picture one can get the probability of 2N-SRC in any nucleus, from the scaling factor. Deuterium Q 2 =2 GeV 2 Solution: For fixed high Q 2 and x B >1, x B determines a minimum p i Problem: In A(e,e’) the momentum of the struck proton (p i ) is unknown. e e/e/ q pipi Prediction by Frankfurt, Sargsian, and Strikman: Adapted from Ciofi degli Atti

Deuterium Q 2 =2 GeV 2 e e/e/ q pipi

Estimate the amount of 2N-SRC in nuclei 3 He2.08± He3.47±0.02 Be4.03±0.04 C4.95±0.05 Cu5.48±0.05 Au5.43±0.06 a 2N (A/d) p min For Carbon: a 2N (A/d) calculations measurement This includes all three isotopic compositions (pn, pp, or nn) for the 2N-SRC phase in 12 C.

44 Why several GeV and up protons are good probes of SRC ? Large momentum transfer is possible with wide angle scattering. For pp elastic scattering near 90 0 cm QE pp scattering near 90 0 has a very strong preference for reacting with forward going high momentum nuclear protons. = h/p = hc/pc = 2   GeV-fm/(6 GeV)  0.2 fm. They have small deBroglie wavelength: The s -10 dependence of the p-p elastic scattering preferentially selects high momentum nuclear protons.

45 Why several GeV and up protons are good probes of SRC ? Large momentum transfer is possible with wide angle scattering. For pp elastic scattering near 90 0 cm QE pp scattering near 90 0 has a very strong preference for reacting with forward going high momentum nuclear protons. = h/p = hc/pc = 2   GeV-fm/(6 GeV)  0.2 fm. They have small deBroglie wavelength: The s -10 dependence of the p-p elastic scattering preferentially selects high momentum nuclear protons.

p e e’ n or p p Pm = “300”,”400”,”500” MeV/c 99 ± 5 0 P = MeV/c Ee = GeV Ee’ = GeV Q 2 =2 (GeV/c) 2 q v =1.65 GeV/c , 35.8, p = 1.45,1.42,1.36 GeV/c The kinematics selected for the measurement X=1.245

JLab / Hall B pair CM momentum 300 < q < 500 MeV/c Q>0 q= MeV/c pp np pp/pn ratio as a function of pair CM momentum Small Q  pp pair in s-wave  large tensor contribution  small pp/np ratio Wiringa, Schiavilla, Pieper, Carlson PRC (2008) Q (fm -1 ) q (fm -1 ) Hall A / BNL Q Q PRL 105, (2010)

Very weak Q 2 dependence J. Seely et al. J. Gomez et al.JLabSLAC EMC SRC J. Arrington talk, Minami 2010.

SRC in nuclei: implication for neutron stars At the outer core of neutron stars, ~95% neutrons, ~5% protons and ~5% electrons (β-stability). Neglecting the np-SRC interactions, one can assume three separate Fermi gases (n, p, and e). k Fermi n k p Strong SR np interaction k Fermi e At T=0 Pauli blocking prevent direct n decay

Frankfurt and Strikman: Int.J.Mod.Phys.A23: ,2008 SRC in nuclei: implication for neutron stars Strong SR np interaction

Kinematics optimized to minimize the competing processes High energy, Large Q 2 MEC are reduced as 1/Q 2. Large Q 2 is required to probe high P miss with x B >1. FSI can treated in Glauber approximation. x B >1 Reduced contribution from isobar currents. Large p miss, and E miss ~p 2 miss /2M Large P miss_z E01-015: A customized Experiment to study 2N-SRC Q 2 = 2 GeV/c, x B ~ 1.2, P m = MeV/c, E 2m <140 MeV Luminosity ~ cm -2 s -1 The large Q 2 is required to probe the small size SRC configuration.

Kinematics optimized to minimize the competing processes FSI Small (10-20%). Can be treated in Glauber approximation. Kinematics with a large component of p miss in the virtual photon direction. FSI with the A-2 system: Pauli blocking for the recoil particle. Geometry, (e, e’p) selects the surface. Canceled in some of the measured ratios. FSI in the SRC pair: Conserve the isospin structure of the pair. Conserve the CM momentum of the pair. These are not necessarily small, BUT:

Why FSI do not destroy the 2N-SRC signature ? For large Q 2 and x>1 FSI is confined within the SRC FSI in the SRC pair: Conserve the isospin structure of the pair. Conserve the CM momentum of the pair.

x x 1-2x Assuming in 12 C nn-SRC = pp-SRC and 2N-SRC=100% A virtual photon with x B >1 “sees” all the pp pairs but only 50% of the np pairs.

d distribution at large x Uncertainty due to nuclear effects Adapted from J. F. Owens talk in DIS2011

d 4 He 12 C 56 Fe 197 Au 4%22%20%14% The ‘evolution parameter’ is the amount of 2N-SRC in nuclei The probability to find 2N-SRC in the nucleus Free neutron structure function No ‘free’ neutron target (life time ~ 12 minutes)

0.079±0.06 Deuteron is not a free np pair SRC=0 free nucleons A EMC SRC bound to free n p pairs (as opposed to bound to deuteron) The slopes for 0.35 ≤ X B ≤ 0.7 Conclusion: One should not neglect the EMC effect using deuteron and proton data to extract free neutron properties Phys. Rev. Lett. 106, , 2011

The free neutron DIS cross section

Gessman, Saito,Thomas,Annu. Rev. Nucl. Part. Sci :337 Where is the ratio of cross sections for absorbing a longitudinal to that for a transverse photon.

For 0.35 ≤ X B ≤ 0.7 The free neutron structure function SLAC Data, J. Arrington et al. JPG 36(2009) Extracted from this work Fermi smearing using relativistic deuteron momentum density With medium correction Phys. Rev. Lett. 106, , 2011

The free neutron structure function Compared to CT calculations SLAC Data, Preliminary calculation by :H. l. Lai, P. Nadolsky, J. Pumplin,.P.Yuan Fh07b / fh02c are CT10 / CT10W like Chebyshev fits See talk by J.Pumplin in DIS2011 SU6 pQCD Scalar qq

Compared to CT calculations SLAC Data, Preliminary calculation by :H. l. Lai, P. Nadolsky, J. Pumplin,.P.Yuan Fh07b / fh02c are CT10 / CT10W like Chebyshev fits See talk by J.Pumplin in DIS2011 SU6 pQCD Scalar qq The d / u ratio

The probability for a nucleon to have momentum ≥ 300 MeV / c in medium nuclei is 20-25% More than ~90% of all nucleons with momentum ≥ 300 MeV / c belong to 2N-SRC. Probability for a nucleon with momentum MeV / c to belong to np-SRC is ~18 times larger than to belong to pp-SRC. Three nucleon SRC are present in nuclei.. PRL. 96, (2006) PRL (2006); Science 320, 1476 (2008). CLAS / HALL B EVA / BNL and Jlab / HALL A Dominant NN force in the 2N-SRC is tensor force PRL 98, (2007). Standard model for short distance structure of nuclei ~80% of kinetic energy of nucleon in nuclei is carried by nucleons in 2N-SRC. 12 Summary I

EMC Slopes 0.35 ≤ X B ≤ 0.7SRCScaling factors X B ≥ 1.4 PRL 106, (2011)