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

Exp:

• Nature 566, 354 (2019)
• Nature, 560, 617 (2018)
• PRL, In-Print (2019)
• PRL 121, 092501 (2018)

arXiv: 1811.01823 (accepted to PRL) 1902.06358 (\w PRL)

Theory:

• Physics Letters B 791, 242 (2019)
• Physics Letters B 785, 304 (2018)
• Physics Letters B 780, 211 (2018)
• CPC 42, 064105 (2018)

arXiv: 1812.08051 (\w PLB) 1805.12099 (\w PLB)

2018/19 Publications*

*Just by us. More by others…

• Oct. 2018 Collaboration Meeting

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.

PCM ≪ prel.

• 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: Ψ(rij → 0) − → ϕα(rij) × A(Rij, rk=i,j)

10

Generalized Contact Formalism exploits scale separation.

When two particles are in close proximity: Ψ(rij → 0) − → ϕα(rij) × A(Rij, rk=i,j) ρ2(rij) − →

• α

Cα|ϕα(rij)|2

11

Generalized Contact Formalism exploits scale separation.

When two particles are in close proximity: Ψ(rij → 0) − → ϕα(rij) × A(Rij, rk=i,j) ρ2(rij) − →

• α

Cα|ϕα(rij)|2 When two particles have high relative momentum: ˜ ρ2(kij) − →

• α

Cα| ˜ ϕα(kij)|2

12

Universal ϕα functions are Schr¨

• dinger solutions

for a given NN potential.

0.5 1 1.5 2 2.5 3 |ϕ(r)|2 r [fm] for AV18 pp/nn, s = 0 np, s = 0 np, s = 1

13

Universal ϕα functions are Schr¨

• dinger solutions

for a given NN potential.

1 2 3 4 5 6 7 8 9 10 | ˜ ϕ(r)|2 k [fm−1] for AV18 pp/nn, s = 0 np, s = 0 np, s = 1

14

Generalized Contact Formalism exploits scale separation.

When two particles are in close proximity: ρ2(rij) − →

• α

Cα|ϕα(rij)|2 When two particles have high relative momentum: ˜ ρ2(kij) − →

• α

Cα| ˜ ϕα(kij)|2

15

Contacts can be determined from fits to ab initio calculations.

0.5 1 1.5 2 2.5 3 n p a b i n i t i

• p

p a b i n i t i

• ρ2(rij)

r [fm] Contact Fits Total np np, s = 1 pp, s = 0

16

These fits faithfully reproduce high-momentum tails.

17

. . . and short-distance two-body densities.

0.01 0.02 0.03 0.04 0.05 0.06 ρNN(r)/Z This work

40Ca, pp/nn 40Ca, pn 16O, pp/nn 16O, pn

CVMC

40Ca, pp/nn 40Ca, pn 16O, pp/nn 16O, pn

0.01 0.02 0.03 0.04 0.05 0.06 −10% +10% 0.5 1 1.5 2 2.5 3 Residuals r [fm] −10% +10% 0.5 1 1.5 2 2.5 3

• R. Cruz-Torres, A. Schmidt et al., PLB 785 p.304 (2018)

18

Different NN interactions can lead to very different two-body densities.

r [fm] 1 2 3 0.5 1 1.5 2

LO distributions normalized to AV18 distributions at r = 1 fm)

(N

s=0 s=1

AV18 LO (1.0 fm)

2

N LO (1.2 fm)

2

N

LO distributions normalized to AV18 distributions at r = 1 fm)

(N

Figure courtesy of Reynier Cruz-Torres

19

Different NN interactions can lead to very different two-body densities.

]

• 1

k [fm 1 2 3 4 5

5 −

10

3 −

10

1 −

10 10

3

10

5

10

7

10 (s=1 scaled x100) s=0 s=1

AV18 LO (1.0 fm)

2

N LO (1.2 fm)

2

N

(s=1 scaled x100)

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

A E1',p1' E2,p2 E1,p1 E1+E2,pCM pCM

2 + (mA-2+E*)2,–pCM

22

We can use GCF to calculate this plane-wave reaction.

e e'

ω,q

A E1',p1' E2,p2 E1,p1 E1+E2,pCM pCM

2 + (mA-2+E*)2,–pCM

pCM ≪ prel ≪ q

23

GCF allows us to calculate a spectral function

• r a decay function.
• R. Weiss et al., PLB 790 p 241 (2019)

Two-nucleon knockout: D(E1, p1, p2) =

• α

Cα|ϕα(prel)|2n(pCM)δ(Ei − Ef )

24

GCF allows us to calculate a spectral function

• r a decay function.
• R. Weiss et al., PLB 790 p 241 (2019)

Two-nucleon knockout: D(E1, p1, p2) =

• α

Cα|ϕα(prel)|2n(pCM)δ(Ei − Ef ) Single-nucleon knockout: S(E1, p1) =

• α

Cα

• d3

p2 (2π)3 |ϕα(prel)|2n(pCM)δ(Ei − Ef )

25

GCF allows us to calculate a spectral function

• r a decay function.
• R. Weiss et al., PLB 790 p 241 (2019)

Two-nucleon knockout: D(E1, p1, p2) =

• α

Cα|ϕα(prel)|2n(pCM)δ(Ei − Ef ) Single-nucleon knockout: S(E1, p1) =

• α

Cα

• d3

p2 (2π)3 |ϕα(prel)|2n(pCM)δ(Ei − Ef ) dσ ∝ σeN · S(E1, p1)

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) A

10

2

10

[MeV/c]

c.m.

σ

50 100 150 200

He

4

C Al Fe Pb

This Work BNL (p,2pn) Hall-A (e,e'pp) Hall-A (e,e'pn) Ciofi and Simula Colle et al. (All Pairs) pairs) S

1

Colle et al. ( Fermi-Gas (All Pairs)

29

We can compare to data from the CLAS EG2 experiment.

5 GeV e− beam C, Al, Fe, Pb CLAS detector

e– b e a m Scintillators (timing) Drift chambers (tracking) Calorimeters (energy) Cherenkov (e– ID) Target ≈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.

Isobar Config.

e e' A Lead Recoil A-2

FSI within pair

e e' A Lead Recoil A-2

Meson-exchange curr.

A e e' Lead Recoil A-2

FSI with nucleus

e e' A Lead Recoil A-2

33

We’ve selected events to minimize competing reactions.

Isobar Config.

e e' A Lead Recoil A-2

FSI within pair

e e' A Lead Recoil A-2

Meson-exchange curr.

A e e' Lead Recoil A-2

FSI with nucleus

e e' A Lead Recoil A-2

xB > 1.2 High Q2

34

We’ve selected events to minimize competing reactions.

Isobar Config.

e e' A Lead Recoil A-2

FSI within pair

e e' A Lead Recoil A-2

Meson-exchange curr.

A e e' Lead Recoil A-2

FSI with nucleus

e e' A Lead Recoil A-2

xB > 1.2 High Q2 Anti-parallel kinematics

35

SRC events are selected in kinematics that minimize final-state interactions.

Missing Momentum = p1 - q Leading Proton (High mom.) Recoil (Low mom.) 36

• pmiss is anti-parallel to

q for C, Al, Fe, Pb.

Missing Momentum = p1 - q

Figure courtesy of M. Sargsian

200 400 600 180◦ 150◦ 120◦ 90◦ Counts (normalized to C) cos θpm,q C Al Fe Pb FSI peak

37

We remain anti-parallel over our pmiss range.

100 200 300 400 500 600 700 180◦ 150◦ 120◦ FSI peak 400 < pmiss < 500 Counts (normalized to C) cos θpm,q 100 200 300 400 500 600 700 180◦ 150◦ 120◦ FSI peak 500 < pmiss < 600 Counts (normalized to C) cos θpm,q 50 100 150 200 250 300 350 400 180◦ 150◦ 120◦ FSI peak 600 < pmiss < 700 Counts (normalized to C) cos θpm,q 50 100 150 200 250 300 180◦ 150◦ 120◦ FSI peak 700 < pmiss < 1000 Counts (normalized to C) cos θpm,q

38

Connecting the model to data

Data Model Radiative corrections Acceptance corrections FSI corrections, etc... 39

Connecting the model to data

Data Model Radiative corrections Acceptance corrections FSI corrections, etc... Transparency, SCX Radiative effects Detector model 40

We forward propagate the model to the data.

1 Generate events according to

model

e e'

ω,q

A E1',p1' EA-2,–pCM pCM E2,p2 E1,p1 41

We forward propagate the model to the data.

1 Generate events according to

model

2 Radiative effects

e e'

ω,q

A E1',p1' EA-2,–pCM pCM E2,p2 E1,p1 42

We forward propagate the model to the data.

1 Generate events according to

model

2 Radiative effects 3 Transparency/SCX using

Glauber

43

We forward propagate the model to the data.

1 Generate events according to

model

2 Radiative effects 3 Transparency/SCX using

Glauber

4 Detector acceptance

0◦ 60◦ 120◦ 180◦ 240◦ 300◦ 20◦ 60◦ 100◦ 140◦ φ θ Protons at 1 GeV/c 0◦ 60◦ 120◦ 180◦ 240◦ 300◦ 20◦ 60◦ 100◦ 140◦ 1 Acceptance

44

We forward propagate the model to the data.

1 Generate events according to

model

2 Radiative effects 3 Transparency/SCX using

Glauber

4 Detector acceptance 5 Same event selection as data

Missing Momentum = p1 - q

45

We compare our GCF calculation to several reactions.

12C(e, e′np)

0.4 < pmiss < 1.0 GeV/c Only a few dozen neutron events arXiv:1810.05343, just accepted to PRL

12C(e, e′p) and 12C(e, e′pp)

0.4 < pmiss < 1.0 GeV/c Few hundred to few thousand events Analysis under review (still preliminary!)

46

12C(e, e′pp)/12C(e, e′np)

| [GeV/c]

recoil

|P

0.4 0.6 0.8 1

[%]

n

σ (e,e'np)/

A

σ

p

σ (e,e'pp)/2

A

σ

5 10 15 20 25

GCF

C, with SCX corrections)

(

Data

C Al Fe Pb AV18

loc

N2LO

non-loc

N3LO

Old New

• M. Duer, A. Schmidt et al., accepted to PRL (2019)

47

Comparison to 12C(e, e′p) and 12C(e, e′pp)

Carbon data only

Contacts determined from fits to ab initio VMC

48

Comparison to 12C(e, e′p) and 12C(e, e′pp)

Carbon data only

Contacts determined from fits to ab initio VMC

NN interactions

AV18 Local χPT N2LO (1 fm cut-off)

49

Comparison to 12C(e, e′p) and 12C(e, e′pp)

Carbon data only

Contacts determined from fits to ab initio VMC

NN interactions

AV18 Local χPT N2LO (1 fm cut-off)

Model uncertainty from: Contacts σCM SCX prob. Transparency A − 2 excitation E ∗

• prel. cut-off

e− res. p res.

50

The model accurately predicts kinematics.

C(e, e′p)

C(e, e′pp)

51

Missing momentum distributions show sensitivity to the NN interaction.

C(e, e′p)

C(e, e′pp)

52

We can verify no significant FSIs.

Different pmiss dependence for e′p, e′pp events

53

We can verify no significant FSIs.

Different pmiss dependence for e′p, e′pp events No excess transverse missing momentum

100 200 300

0.4 < pmiss < 0.5

Counts 50 100 150 200

0.5 < pmiss < 0.6

Counts 50 100

0.6 < pmiss < 0.7

Counts 20 40 60 80 0.2 0.4 0.6 0.8 1

0.7 < pmiss < 1.0

Counts Transverse component of pmiss [GeV/c]

54

We can verify no significant FSIs.

Different pmiss dependence for e′p, e′pp events No excess transverse missing momentum No A-dependence in distributions!

200 400 600 180◦ 150◦ 120◦ 90◦ Counts (normalized to C) cos θpm,q C Al Fe Pb FSI peak

55

Missing-momentum and missing-energy

0.4 < pmiss < 0.5 GeV/c

0.5 < pmiss < 0.6 GeV/c

0.6 < pmiss < 0.7 GeV/c

• 0.1

0.7 < pmiss < 1.0 GeV/c

• 0.1

56

(e, e′pp)/(e, e′p) ratio

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 0.1 0.2 #epp/#ep Data AV18 χ-LocalN2LO 57

Isospin-dependence of the repulsive core

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 0.1 0.2 0.3 0.4 #epp/#ep Scalar Limit AV18 N2LO N2LO AV18 With experimental corrections Calculated Ratio Data

58

To recap:

1 Generalized Contact Formalism

0.5 1 1.5 2 2.5 3 np ab initio p p a b i n i t i

• ρ2(rij)

r [fm] Contact Fits Total np np, s = 1 pp, s = 0

59

To recap:

1 Generalized Contact Formalism 2 GCF cross sections

e e'

ω,q

A E1',p1' E2,p2 E1,p1 E1+E2,pCM pCM

2 + (mA-2+E*)2,–pCM

60

To recap:

1 Generalized Contact Formalism 2 GCF cross sections 3 Comparisons to data

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 1 10 100 1000 Counts 12C(e, e′p) Data AV18 χ-LocalN2LO

61

SRC data can constrain the NN interaction up to 1 GeV/c!

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 1 10 100 1000 Counts 12C(e, e′p) Data AV18 χ-LocalN2LO

62

Different observables have different scale and scheme dependence.

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 1 10 100 1000 Counts 12C(e, e′p) Data AV18 χ-LocalN2LO

63

Different observables have different scale and scheme dependence.

0.4 0.5 0.6 0.7 0.8 0.9 1 pmiss [GeV/c] 0.1 0.2 #epp/#ep Data AV18 χ-LocalN2LO

64

Different observables have different scale and scheme dependence.

65

We now have a consistent scale-separated view of SRCs.

Three important properties: Pair abundances Pair CM motion Pair relative motion

66

Other talks at this meeting:

In this session: Or Hen Later today: Dien Nguyen (D15) Sunday Morning: Rey Cruz-Torres (G05) Florian Hauenstein (H15) Holly Szumila-Vance (H15) Sunday Afternoon: Afroditi Papadopoulou (J12) Eli Piasetzky (L05) Holly Szumila-Vance (L05) Monday: Holly Szumila-Vance (S01)

67

BACK-UP

68

Model cross section

d8σ dQ2dxBdφed3 pCMdΩ2 = σeN 32π4 n( pCM)J

• α

Cα| ˜ ϕα(| prel|)|2 J = E ′

1E2p2 2

|E2(p2 − Z cos θZ,2) + E ′

1p2|

ω 2EbeamEexB

• Z ≡

q + pCM

69

Leading and recoil protons are distinct.

0.5 1 1.5 2 20◦ 40◦ 60◦ 80◦ 100◦ 120◦ Momentum [GeV/c] θ Leading protons 0.5 1 1.5 2 20◦ 40◦ 60◦ 80◦ 100◦ 120◦

70

Leading and recoil protons are distinct.

0.5 1 1.5 2 20◦ 40◦ 60◦ 80◦ 100◦ 120◦ Momentum [GeV/c] θ Recoil protons 0.5 1 1.5 2 20◦ 40◦ 60◦ 80◦ 100◦ 120◦

71

Leading and recoil protons are distinct.

0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 Missing momentum [GeV/c] Leading proton momentum [GeV/c] 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 Line of ambiguity

72

Missing momentum distributions show sensitivity to the NN interaction.

C(e, e′p)

C(e, e′pp)

73

Implementation of single charge exchange (SCX) and transparency

Colle, Cosyn, Ryckebusch, PRC 034608 (2016)

Glauber calc of avg. probabilities: Leading p ↔ n Recoil p ↔ n Transparency factor for NN Transparency factor for N

e'NN

e'NN e'NN e'NN e'NN e'NN e'NN e'NN

SCX Transp.

74

Inclusive scaling relies on kinematical assumptions.

200 400 600 800 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 pmiss [MeV] xB

4He, σCM = 0 4He, σCM = 50 4He, σCM = 100 4He, σCM = 150 12C, σCM = 0 12C, σCM = 50 12C, σCM = 100 12C, σCM = 150

200 400 600 800 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

75

Inclusive scaling relies on kinematical assumptions.

200 400 600 800 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 pmiss [MeV] xB

4He, E∗ = 0 4He, E∗ = 15 4He, E∗ = 30 12C, E∗ = 0 12C, E∗ = 15 12C, E∗ = 30

200 400 600 800 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

76