Deep Inelastic Scattering (DIS) E E` Incident scattered lepton µ = − = − ω 2 2 2 lepton Q q q q µ ( ω , q ) ω = − E ' E W 2 2 Q = 2 x Q = ( ) B ω 2 m ⋅ 2 ( q p ) T Final state nucleon Hadrons ≤ ≤ 0 x 1 B Electrons, muons, neutrinos x B gives the fraction of nucleon momentum SLAC, CERN, HERA, FNAL, JLAB carried by the struck parton E, E’ 5-500 GeV Q 2 5-50 GeV 2 Information about nucleon vertex is contained in w 2 >4 GeV 2 F 1 (x,Q 2 ) and F 2 (x,Q 2 ), the unpolarized structure 0 ≤ X B ≤ 1 functions
DIS scale: several tens of GeV Nucleon in nuclei are bound by ~MeV (My) Naive expectations : DIS off a bound nucleon = DIS off a free nucleon (Except for small Fermi momentum corrections) Nucleons Deuteron: binding energy ~2 MeV Average nucleons separation ~2 fm Nucleons DIS off a deuteron = DIS off a free proton neutron pair
The European Muon Collaboration (EMC) effect >30 years old σ σ per nucleon in nuclei ≠ per nucleon in deuteron DIS DIS
SLAC E139 EMC collaboration, Aubert et al. PL B 123,275 (1983) Data from CERN SLAC JLab 1983- 2009 SLAC Gomez et al., Phys Rev. D49,4348 (1994) A review of data collected during first decade, Arneodo, Phys. Rep. 240,301(1994)
EMC is a not a bulk property of nuclear medium JLab / Hall C . Seely et al. PRL 103, 202301 (2009)
The European Muon Collaboration (EMC) effect 30 years old Well established measured effect with no consensus as to its origin
Models of the EMC effect Drell-Yan data Binding effects Fermi motion Pions … Vector mesons ∆s Multiquak clusters ‘Photons’ … Nucleus ≠nucleons M*≠M bound N ≠ free N R*≠R Dynamical rescaling Confinement changes Global changes Quark w,f. modification Rare configurations in mean field … review papers: Suppression of PLC Gessman, Saito,Thomas, Annu. Rev. Nucl. Part. Sci. … 45:337 (1995). P.R. Norton , Rep Prog. 66 (2003). Frankfurt and Strikman (2012)
υ = p − 2 2 m
Inclusive electron scattering A(e,e’) A(e,e’)
Inclusive electron scattering A(e,e’) DIS off nucleons DIS off nuclei E E E` E` Incident scattered Incident scattered 2 − μ 2 − 2 lepton lepton Q = q q = q ω lepton lepton μ ( ω , q ) ( ω , q ) − ω = E' E 2 Q 2 Q x = = ' ( x ) W 2 nucleon nucleus B 2mω B ⋅ 2 ( q p ) T Nucleons Final state 0 ≤ x ≤ 1 Hadrons 0 ≤ x ≤ A B B x B gives the fraction of nucleon x B counts the number of momentum carried by the struck nucleons involved parton x > 2 x > 1 B B 2N-SRC 3N-SRC --> scaling --> Counting the number of SRC clusters in nuclei
Comparing magnitude of EMC effect and SRC scaling factors σ Fe SRC This image cannot currently be displayed. σ scaling factor d a N ( Fe / d ) 2 EMC slope : dR EMC dx SLAC data: Frankfurt, Strikman, Day, Sargsyan, Gomez et al., Phys. Rev. D49, 4348 (1983). Phys. Rev. C48 (1993) 2451. Q 2 =2, 5, 10, 15 GeV/c 2 (averaged) Q 2 =2.3 GeV/c 2
υ = p − 2 2 the EMC effect is associated with large virtuality ( ) m EMC SRC PRL 106, 052301 (2011), also PRC 85 047301 (2012)
Is the EMC effect associated with large virtuality ? Hypothesis can be verified by measuring DIS off Deuteron tagged with high momentum recoil nucleon EMC 12 GeV JLab/ Hall C approved υ = p − 2 2 m experiment E 12-11-107 12 GeV JLab/ Hall B approved experiment E12-11-003a Tagged recoil proton measure Tagged recoil neutron measure neutron structure function in the proton structure function BAND LAND
Summary – relevant of Correlations 3N-SRC Symmetry energy Contact term
Summary – proposed experiments JLab Hall C: E12-11-107 JLab Hall A: E12-14-011 Add 8 f7/2 neutrons JLab Hall B: E12-11-003a Dubna GSI / FAIR Migdal jump Add 8 protons
SRC talks Axel Schmidt 15:00-15:30
Acknowledgment I would like to thank the organizers for the invitation. Collaborators: Or Hen, Larry Weinstein, Shalev Gilad, Doug Higinbothan, Steve Wood, John Watson Misak Sargsian, Mark Axel Schmidt Erez Cohen Strikman, Leonid Frankfurt, Gerald Miller
Electrons
Triple coincidence A (p, p p N) measurements complementary to JLab Scattered proton Incident proton Complementary to JLab study with electrons
Why H.E. protons are good probes of SRC ? selective attention to SRC Selective attention . A type of attention which involves focusing on a specific aspect of a scene while ignoring other aspects. → → p p � pp elastic scattering near 90 0 c.m d σ − ∝ s 10 dt QE pp scattering have a very strong preference for reacting with forward going high momentum nuclear protons
A new proton scattering experiment at GSI can yield a high –statistic data set of SRC pairs C.M. Frame : P 1 P Beam P 2
Inverse kinematics at Dubna Same selective attention Target Nucleus SRC Nuclear beam A proposal for a BM@N experiment To study the NN Repulsive Core with Hard inverse kinematic reactions 10 B / 10 Be 12 C A-2 A-2 p/n
triple – coincidence measurements 65
triple – coincidence measurements ? 66
Inverse kinematics 67
E07-006 (2011) 4 He ( 12 C) background Knock-out Recoil Jlab Hall A experiment I. Korover et al. Phys. Rev. Let. 113, 022501 (2014). 68
QE measurement with LAND/R3B@GSI V. Panin et al. PLB 753 (2016) 204. A-2 ~400 MeV
SRC @ Dubna Carbon beam with momentum of 4 GeV/cN 33° ± 5° proton Neutrons /Protons ± 0 beam ( 8 ) A-2 0 ( 0 ) proton 33° ± 5° Get the ratios: − − − np SRC pp SRC np SRC − p p pp SRC + 10 #( B n ) 5 + 10 #( Be p ) 4 70
Proposed experimental setup TOF700 Proportional chambers ZDC Two Target TOF400 ensemble NeuLAND Tracking chambers NeuLAND 71
LH 2 Vs. CH 2 LH 2 : – Length: 15 cm – Interaction probability: ~3% CH 2 : – Length: ~9 cm [equal hydrogen areal density] – Interaction probability: ~10% [7% with C, 3% with H 2 ] Other considerations: – CH 2 has increased BG from C-C interactions. – CH 2 requires extra time for C subtraction. – CH 2 maintenance free. – LH 2 requires safety approval for used in BM@N area.
simulation 12 C Frame
The inclusive A(e,e’) measurements § At high nucleon momentum distributions are similar in shape for = ⋅ n ( k ) C n ( k ) A A D light and heavy nuclei: SCALING. § Can be explained by 2N-SRC dominance. Adapted from Ciofi degli Atti § Within the 2N-SRC dominance picture one can get the probability of 2N-SRC in any nucleus, from the scaling factor. e / In A(e,e’) the momentum of the e p i struck proton (p i ) is unknown. q But: For fixed high Q 2 and x B >1, x B determines a minimum p i µ = − = − ω 2 2 2 Q q q q µ ω = − Prediction by E ' E Frankfurt, Sargsian, 2 Q and Strikman: = x B ω 2 m
Kinematics optimized to minimize the competing processes FSI FSI with the A-2 system: Kinematics with a large component of p miss in Small (10-20%) . the virtual photon direction. Pauli blocking for the recoil particle. Geometry, (e, e’p) selects the surface. Can be treated in Glauber approximation. Canceled in some of the measured ratios. FSI in the SRC pair: These are not necessarily small, BUT: Conserve the isospin structure of the pair . Conserve the CM momentum of the pair.
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: 1 fm Conserve the isospin structure of the pair . > for x 1.3 Conserve the CM momentum of the pair.
( e , e ' pp ) pp - SRC = ± ⇒ = ± 9 . 5 2 % 4 . 75 1 % − ( e , e ' p ) 2 N SRC Assuming in 12 C nn-SRC = pp-SRC and 2N-SRC=100% A virtual photon with x B >1 1-2x “sees” all the pp pairs but only 50% of the np pairs. x x ( e , e ' pp ) x = = 2 x + − ( e , e ' p ) x ( 1 2 x ) / 2
(p,2pn) np - SRC np - SRC = BNL = = (74-100) % (p,2p) np - SRC+2 (pp - SRC) 2N - SRC − (e,e'pn) np SRC = Jlab = (84 - 100)% − (e,e'p) 2 N SRC − (e,e'pp) pp-SRC nn SRC ± = ± Jlab = (9.5 2) % i.e =(5 1)% − (e,e'p) 2N-SRC 2 N SRC − np SRC = (84 - 92)% − 2 N SRC
Implications for Neutron Stars Adapted from: D.Higinbotham , E. Piasetzky, M. Strikman CERN Courier 49N1 (2009) 22 • At the core of neutron stars, most accepted models assume : ~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). • strong np interaction the n-gas heats the p-gas. n n p e k k k Fermi Fermi Fermi See estimates in Frankfurt and Strikman : Int.J.Mod.Phys.A23:2991-3055,2008.
SRC in nuclei: implication for neutron stars • At the core of neutron stars, most accepted models assume : ~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). N = + n p e k k k = = p p e 1 / 3 n k k ( ) k At T=0 Fermi Fermi Fermi Fermi Fermi Fermi N n ρ = ρ ≈ = ≈ n p e 5 k 500 MeV/c, k k 250 MeV/c For 0 , Fermi Fermi Fermi Pauli blocking prevent direct n decay → p + + ν n e e n e p k k k Fermi Fermi Fermi Strong SR np interaction
) Ciofi,
4 He ( e , e ' p ) Polariztion Transfer Copied from S. Strauch talk M. Paolone at al. PRL 105,072001,(1020)
The minimum missing momentum of the D(e,e’)pn reaction from EMC conservation of energy and momentum for quasi-elestic scattering + − = 2 2 ( q p p ) m d n p Q 2 =4,8,10 GeV 2 P min ∞ ∫ = π ⋅ ⋅ ⋅ 2 P ( x ) 2 p n ( p ) dp SRC d B d P min = ⋅ n ( p ) n ( p ) a ( A / d ) A 2 d ∞ ∫ = π ⋅ ⋅ ⋅ 2 P ( x ) 2 p n ( p ) dp A B A P min Direction with respect to q σ − 1 P ( x ) = A A B σ − 1 P ( x ) d d B Higinbotham, Gomez, Piasetzky arXiv:1003.4497 [hep-ph]
Q 2 =10 GeV 2 σ − 1 P ( x ) = a 2 (A/d) A A B interpolation σ − 1 P ( x ) d d B Higinbotham, Gomez, Piasetzky arXiv:1003.4497 [hep-ph]
Data: 3 He, 4 He, 12 C J. Seely et al. PRL 103, 202301 (2009). 56 Fe J. Gomez et al. PR D49, 4348 (1994). interpolation Higinbotham, Gomez, Piasetzky arXiv:1003.4497 [hep-ph]
Very weak Q 2 dependence EMC JLab SLAC J. Gomez et al. J. Seely et al. SRC J. Arrington talk, Minami 2010.
E01-015: A customized Experiment to study 2N-SRC Q 2 = 2 GeV/c , x B ~ 1.2 , P m =300-600 MeV/c, E 2m <140 MeV Luminosity ~ 10 37-38 cm -2 s -1 Kinematics optimized to minimize the competing processes High energy, Large Q 2 The large Q 2 is required to probe the small size SRC configuration. 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
Kinematics optimized to minimize the competing processes FSI FSI with the A-2 system: Kinematics with a large component of p miss in Small (10-20%) . the virtual photon direction. Pauli blocking for the recoil particle. Geometry, (e, e’p) selects the surface. Can be treated in Glauber approximation. Canceled in some of the measured ratios. FSI in the SRC pair: These are not necessarily small, BUT: Conserve the isospin structure of the pair . Conserve the CM momentum of the pair.
The kinematics selected for the measurement p Ee’ = 3.724 GeV e’ Ee = 4.627 GeV 19.5 0 e 50.4 0 40.1, 35.8, 32.0 0 n or p γ * Q 2 =2 (GeV/c) 2 p q v =1.65 GeV/c 99 ± 5 0 X=1.245
Experimental setup HRS HRS EXP 01-015 / Jlab n array p p e n e Big Bite Lead wall
BigBite Spectrometer Neutron Detector EXP 01-015 Dec. 2004 – Apr. 2005 Jlab / Hall A
“300 MeV/c” 12 C(e,e’p) “400 MeV/c” x B >1 “500 MeV/c” 12 C(e,e’p) 11 B “300 MeV/c” “500 MeV/c” “400 MeV/c”
(e,e’pp) P mis =“300” MeV/c (Signal : BG= 1.5:1) (e,e’pp) P mis =“400” MeV/c (Signal : BG= 2.3:1) (e,e’pp) P mis =“500” MeV/c (Signal : BG= 4:1) P mis =“500” MeV/c (e,e’pn) (Signal : BG= 1:7) TOF [ns]
Directional correlation 12 C(e,e’pp) MCEEP Simulation with pair CM motion σ CM =136 MeV/c BG (off peak) p p γ
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