LNS Laboratory for Nuclear Science 1 Short-range correlations - PowerPoint PPT Presentation

Recent developments in understanding short-range correlations Axel Schmidt MIT April 13, 2019 LNS Laboratory for Nuclear Science 1

Short-range correlations produce a complicated picture. 2

The short-distance part of the NN -interaction is not well-constrained by data. Figure courtesy of Reynier Cruz-Torres 3

Short-range correlations produce a complicated picture. 4

We now have a consistent scale-separated view of SRCs. Three important properties: Pair abundances Pair CM motion Pair relative motion 5

Oct. 2018 Collaboration Meeting 2018/19 Publications * Exp: Theory: • Nature 566, 354 (2019) • Physics Letters B 791, 242 (2019) • Nature, 560, 617 (2018) • Physics Letters B 785, 304 (2018) • PRL, In-Print (2019) • Physics Letters B 780, 211 (2018) • PRL 121, 092501 (2018) • CPC 42, 064105 (2018) arXiv: 1811.01823 arXiv: 1812.08051 (\w PLB) (accepted to PRL) 1805.12099 (\w PLB) 1902.06358 (\w PRL) * Just by us. More by others…

In my talk today: 1 Generalized Contact Formalism Scale-separated description of SRCs 2 Moving from GCF to cross sections Modeling abundances, CM motion, relative motion 3 Comparisons to data Constraining the short-range NN interaction 7

We have lots of data to compare to! 8

Generalized Contact Formalism exploits scale separation. P CM ≪ p rel . R. Weiss, R. Cruz-Torres et al., PLB 780 211–215 (2018) 9

Generalized Contact Formalism exploits scale separation. When two particles are in close proximity: → ϕ α ( r ij ) × A ( R ij ,� Ψ( r ij → 0 ) − r k � = i , j ) 10

Generalized Contact Formalism exploits scale separation. When two particles are in close proximity: → ϕ α ( r ij ) × A ( R ij ,� Ψ( r ij → 0 ) − r k � = i , j ) � C α | ϕ α ( r ij ) | 2 ρ 2 ( r ij ) − → α 11

Generalized Contact Formalism exploits scale separation. When two particles are in close proximity: → ϕ α ( r ij ) × A ( R ij ,� Ψ( r ij → 0 ) − r k � = i , j ) � C α | ϕ α ( r ij ) | 2 ρ 2 ( r ij ) − → α When two particles have high relative momentum: � ϕ α ( k ij ) | 2 ρ 2 ( k ij ) − ˜ C α | ˜ → α 12

Universal ϕ α functions are Schr¨ odinger solutions for a given NN potential. for AV18 pp/nn , s = 0 np , s = 0 np , s = 1 | ϕ ( r ) | 2 0 0 . 5 1 1 . 5 2 2 . 5 3 r [fm] 13

Universal ϕ α functions are Schr¨ odinger solutions for a given NN potential. for AV18 pp/nn , s = 0 np , s = 0 np , s = 1 ϕ ( r ) | 2 | ˜ 0 1 2 3 4 5 6 7 8 9 10 k [fm − 1 ] 14

Generalized Contact Formalism exploits scale separation. When two particles are in close proximity: C α | ϕ α ( r ij ) | 2 � � ρ 2 ( r ij ) − → α When two particles have high relative momentum: ϕ α ( k ij ) | 2 � � ρ 2 ( k ij ) − ˜ → C α | ˜ α 15

Contacts can be determined from fits to ab initio calculations. Contact Fits Total np np , s = 1 pp , s = 0 n ρ 2 ( r ij ) p a b i n i t i o p p a b i n i t i o 0 0 . 5 1 1 . 5 2 2 . 5 3 r [fm] 16

These fits faithfully reproduce high-momentum tails. 17

. . . and short-distance two-body densities. 0 . 06 0 . 06 0 . 05 0 . 05 0 . 04 0 . 04 ρ NN ( r ) /Z 0 . 03 0 . 03 0 . 02 0 . 02 This work CVMC 40 Ca, pp/nn 40 Ca, pp/nn 0 . 01 0 . 01 40 Ca, pn 40 Ca, pn 16 O, pp/nn 16 O, pp/nn 16 O, pn 16 O, pn 0 0 Residuals +10% +10% − 10% − 10% 0 0 0 . 5 0 . 5 1 1 1 . 5 1 . 5 2 2 2 . 5 2 . 5 3 3 r [fm] R. Cruz-Torres, A. Schmidt et al., PLB 785 p.304 (2018) 18

Different NN interactions can lead to very different two-body densities. 2 2 (N (N LO distributions normalized to AV18 distributions at r = 1 fm) LO distributions normalized to AV18 distributions at r = 1 fm) 2 AV18 2 N LO (1.0 fm) 2 N LO (1.2 fm) 1.5 s=0 1 0.5 s=1 0 0 1 2 3 r [fm] Figure courtesy of Reynier Cruz-Torres 19

Different NN interactions can lead to very different two-body densities. (s=1 scaled x100) (s=1 scaled x100) 7 10 AV18 2 N LO (1.0 fm) 5 10 2 N LO (1.2 fm) s=1 3 10 10 s=0 − 1 10 − 3 10 − 5 10 0 1 2 3 4 5 -1 k [fm ] Figure courtesy of Reynier Cruz-Torres 20

Relative SRC pair abundances are largely scale and scheme independent. Adapted from J. Lynn et al., arXiv:12587 (2019) 21

We can use GCF to calculate this plane-wave reaction. e' e ω ,q E 1 ,p 1 E 1 ',p 1 ' E 1 +E 2 ,p CM E 2 ,p 2 A 2 + (m A-2 +E*) 2 ,–p CM p CM 22

We can use GCF to calculate this plane-wave reaction. e' e ω ,q E 1 ,p 1 E 1 ',p 1 ' E 1 +E 2 ,p CM E 2 ,p 2 A 2 + (m A-2 +E*) 2 ,–p CM p CM p CM ≪ p rel ≪ q 23

GCF allows us to calculate a spectral function or a decay function. R. Weiss et al., PLB 790 p 241 (2019) Two-nucleon knockout: � C α | ϕ α ( p rel ) | 2 n ( p CM ) δ ( E i − E f ) D ( E 1 , p 1 , p 2 ) = α 24

GCF allows us to calculate a spectral function or a decay function. R. Weiss et al., PLB 790 p 241 (2019) Two-nucleon knockout: � C α | ϕ α ( p rel ) | 2 n ( p CM ) δ ( E i − E f ) D ( E 1 , p 1 , p 2 ) = α Single-nucleon knockout: d 3 � p 2 � � ( 2 π ) 3 | ϕ α ( p rel ) | 2 n ( p CM ) δ ( E i − E f ) S ( E 1 , p 1 ) = C α α 25

GCF allows us to calculate a spectral function or a decay function. R. Weiss et al., PLB 790 p 241 (2019) Two-nucleon knockout: � C α | ϕ α ( p rel ) | 2 n ( p CM ) δ ( E i − E f ) D ( E 1 , p 1 , p 2 ) = α Single-nucleon knockout: d 3 � p 2 � � ( 2 π ) 3 | ϕ α ( p rel ) | 2 n ( p CM ) δ ( E i − E f ) S ( E 1 , p 1 ) = C α α d σ ∝ σ eN · S ( E 1 , p 1 ) 26

Ingredients to the GCF cross section Relative momentum − → NN interaction SRC pair abundances − → estimate from ab initio calcs. Pair center-of-mass motion 27

We measured the CM momentum distribution and confirmed its width is small. E.O. Cohen et al., PRL 121 092501 (2018) 28

We measured the CM momentum distribution and confirmed its width is small. E.O. Cohen et al., PRL 121 092501 (2018) 200 Pb Fe Al C 150 [MeV/c] 4 He 100 c.m. σ This Work Ciofi and Simula 50 BNL (p,2pn) Colle et al. (All Pairs) Hall-A (e,e'pp) 1 Colle et al. ( S pairs) 0 Hall-A (e,e'pn) Fermi-Gas (All Pairs) 0 2 10 10 A 29

We can compare to data from the CLAS EG2 experiment. Scintillators (timing) Cherenkov (e – ID) Drift chambers (tracking) e – b e a m 5 GeV e − beam Target Calorimeters (energy) C, Al, Fe, Pb CLAS detector ≈ 8m 30

CLAS’s large-acceptance is crucial for detecting multi-particle final states. electron proton 31

CLAS’s large-acceptance is crucial for detecting multi-particle final states. electron neutron 32

We’ve selected events to minimize competing reactions. Meson-exchange curr. Isobar Config. e' e' e e Lead Lead Recoil Recoil A A-2 A A-2 FSI with nucleus FSI within pair e' e' e e Lead Lead Recoil Recoil A A A-2 A-2 33

We’ve selected events to minimize competing reactions. Meson-exchange curr. Isobar Config. e' e' e e Lead Lead Recoil x B > 1 . 2 Recoil A A-2 A High Q 2 A-2 FSI with nucleus FSI within pair e' e' e e Lead Lead Recoil Recoil A A A-2 A-2 34

We’ve selected events to minimize competing reactions. Meson-exchange curr. Isobar Config. e' e' e e Lead Lead Recoil x B > 1 . 2 Recoil A A-2 A High Q 2 A-2 FSI with nucleus FSI within pair e' e' e Anti-parallel kinematics e Lead Lead Recoil Recoil A A A-2 A-2 35

SRC events are selected in kinematics that minimize final-state interactions. Missing Momentum = p 1 - q Leading Proton Recoil (High mom.) (Low mom.) 36

� p miss is anti-parallel to � q for C, Al, Fe, Pb. Missing Momentum = p 1 - q 600 C Al Fe Counts (normalized to C) Pb 400 FSI peak 200 0 90 ◦ 120 ◦ 150 ◦ 180 ◦ cos θ p m ,q Figure courtesy of M. Sargsian 37

We remain anti-parallel over our p miss range. 700 400 Counts (normalized to C) Counts (normalized to C) 350 600 400 < p miss < 500 600 < p miss < 700 300 500 250 400 200 FSI peak FSI peak 300 150 200 100 100 50 0 0 120 ◦ 150 ◦ 180 ◦ 120 ◦ 150 ◦ 180 ◦ cos θ p m ,q cos θ p m ,q 700 300 Counts (normalized to C) Counts (normalized to C) 600 500 < p miss < 600 700 < p miss < 1000 250 500 200 400 150 FSI peak FSI peak 300 100 200 50 100 0 0 120 ◦ 150 ◦ 180 ◦ 120 ◦ 150 ◦ 180 ◦ cos θ p m ,q cos θ p m ,q 38

Connecting the model to data Radiative corrections Acceptance corrections FSI corrections, etc... Model Data 39

Connecting the model to data Radiative corrections Acceptance corrections FSI corrections, etc... Model Data Transparency, SCX Radiative e ff ects Detector model 40

We forward propagate the model to the data. e' 1 Generate events according to model e ω ,q E 1 ,p 1 E 1 ',p 1 ' p CM E 2 ,p 2 A E A-2 ,–p CM 41

We forward propagate the model to the data. e' 1 Generate events according to model e ω ,q 2 Radiative effects E 1 ,p 1 E 1 ',p 1 ' p CM E 2 ,p 2 A E A-2 ,–p CM 42

We forward propagate the model to the data. 1 Generate events according to model 2 Radiative effects 3 Transparency/SCX using Glauber 43