unraveling the -nucleus cross-section
TRANSCRIPT
Unraveling the ν-Nucleus Cross-Section
Omar Benhar
INFN and Department of Physics, “Sapienza” UniversityI-00185 Roma, Italy
Workshop on ν-Nucleus Interaction in a Few-GeV RegionKEK, Tokai Campus, November 18-19, 2017
OUTLINE
? The riddle of the flux integrated neutrino-nucleus cross section
? The issue of degeneracy between different models of the inclusivecross section in the 0π channel
? Exploit exclusive channels to resolve the degeneracy
? The (e, e′p) cross section and the nuclear spectral function
? The Ar, T i(e, e′p) experiment at Jefferson Lab
? Summary & outlook
1 / 21
THE ISSUE OF FLUX AVERAGE
? The energy-transfer dependence of the cross section of theprocess
e+A→ e′ +X
at fixed beam energy and electron scattering angle displays acomplex landscape.
? The contributions of the main reaction mechanisms—involvingboth nuclear and nucleon structure—can be clearly identified
2 / 21
? In neutrino interactions, e.g.
νµ +A→ µ− +X
the energy of the incoming particle is spread according to abroad distribution, and different reaction mechanisms contributeto the cross section at fixed muon energy and emission angle
? This feature clearly emerges from the analysis of the availableelectron-scattering data
3 / 21
WHERE WE ARE
? Even if we restrict ourselves to the 0π sector, the interpretation ofthe signals measured by neutrino detectors require theunderstanding of the different reaction mechanisms contributingto the neutrino-nucleus cross section: single-nucleon knock out,coupling to meson-exchange currents (MEC), and excitation ofcollective modes
? Over the ∼ 15 years since the first NuINT Workshop—that wemay characterize as the post Fermi-gas age—a number of moreadvanced models have been developed
? Electron scattering data, mainly inclusive cross sections, havebeen exploited to derive or validate the some of proposedmodels
? Several models have achieved the degree of maturity requiredfor a meaningful comparison between their predictions and themeasured neutrino-nucleus cross sections
? Very accurate results have been also obtained from QuantumMonte Carlo calculations. However, this approach is isinherently non relativistic, and its applicability is limited
4 / 21
12C(e, e′): FACTORIZATION vs SUPERSCALING
I N. Rocco et al
where dσ denotes the cross section in the absence of FSI,the effects of which are accounted for by the foldingfunction
fqðωÞ ¼ffiffiffiffiffiffiTA
pδðωÞ þ ð1 −
ffiffiffiffiffiffiTA
pÞFqðωÞ: ð10Þ
The above equations show that inclusion of FSI involvesthree elements: (i) the real part of the optical potential UVextracted from proton-carbon scattering data [28], respon-sible for the shift in ω, (ii) the nuclear transparency TAmeasured in coincidence ðe; e0pÞ reactions [29], and (iii) afunction FqðωÞ, sharply peaked at ω ¼ 0, whose width isdictated by the in-mediumNN scattering cross section [27].A comprehensive analysis of FSI effects on the electron-
carbon cross sections has been recently carried out by theauthors of Ref. [15]. In this work we have followed closelytheir approach, using the same input.Figure 3 illustrates the effects of FSI on the electron-
carbon cross section in the kinematical setups of Fig. 2. InFig. 3(a), both the pronounced shift of the quasielastic peakand the redistribution of the strength are clearly visible, andsignificantly improve the agreement between theory anddata. For larger values of Q2, however, FSI play a lessrelevant, in fact almost negligible, role. This feature isillustrated in Fig. 3(b), showing that at beam energy Ee ¼1.3 GeV and scattering angle θe ¼ 37.5 deg, correspond-ing toQ2 ∼ 0.5 GeV2, the results of calculations carried out
with and without inclusion of FSI give very similar results,yielding a good description of the data.Note that, being transverse in nature, the calculated two-
nucleon current contributions to the cross sections exhibit astrong angular dependence. At Ee ¼ 1.3 GeV, we find thatthe ratio between the integrated strengths in the 1p1h and2p2h sectors grows from 4% at electron scattering angleθe ¼ 10 deg to 46% at θe ¼ 60 deg.The results of our work show that the approach based on
the generalized factorization ansatz and the spectral func-tion formalism provides a consistent framework for aunified description of the electron-nucleus cross section,applicable in the kinematical regime in which relativisticeffects are known to be important.The extension of our approach to neutrino-nucleus
scattering, which does not involve further conceptualdifficulties, may offer new insight into the interpretationof the cross section measured by the MiniBooNECollaboration in the quasielastic channel [30,31]. Theexcess strength in the region of the quasielastic peak isin fact believed to originate from processes involvingtwo-nucleon currents [32–34], whose contributions areobserved at lower muon kinetic energy as a result of theaverage over the neutrino flux [35]. The strong angulardependence of the two-nucleon current contribution mayalso provide a clue for the understanding of the differencesbetween the quasielastic cross sections reported by theMiniBooNE Collaboration and the NOMAD Collaboration[36], which collected data using neutrino fluxes withvery different mean energies: 880 MeV and 25 GeV,respectively [35].As a final remark, it has to be pointed out that a clear-cut
identification of the variety of reaction mechanisms con-tributing to the neutrino-nucleus cross section will require acareful analysis of the assumptions underlying differentmodels of nuclear dynamics. All approaches based on theindependent particle model fail to properly take intoaccount correlation effects, leading to a significant reduc-tion of the normalization of the shell-model states [37], aswell as to the appearance of sizable interference terms inthe 2p2h sector. However, in some instances these twodeficiencies may largely compensate one another, leadingto accidental agreement between theory and data. Forexample, the two-body current contributions computedwithin our approach turn out to be close to those obtainedwithin the Fermi gas model.The development of a nuclear model having the pre-
dictive power needed for applications to the analysis offuture experiments—most notably the Deep UndergroundNeutrino Experiment (DUNE) [38]—will require that thedegeneracy between different approaches be resolved. Asystematic comparison between the results of theoreticalcalculations and the large body of electron scattering data,including both inclusive and exclusive cross sections, willgreatly help to achieve this goal.
(a)
(b)
FIG. 3. (a) Double differential electron-carbon cross section atbeam energy Ee ¼ 680 MeV and scattering angle θe ¼ 36 deg.The dashed line corresponds to the result obtained neglecting FSI,while the solid line has been obtained within the approach ofRef. [15]. The experimental data are taken from Ref. [24].(b) Same as (a) but for Ee ¼ 1300 MeV and θe ¼ 37.5 deg.The experimental data are taken from Ref. [25].
PRL 116, 192501 (2016) P HY S I CA L R EV I EW LE T T ER Sweek ending13 MAY 2016
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I Megias et al
0 0.05 0.1 0.150
1e+05
2e+05
0 0.05 0.1 0.15 0.23
0.23
0.24
0.24
0.25E=400 MeV, θ=36
o, qQE=239 MeV/c
0 0.05 0.10
10000
20000
30000
40000
50000
0.24
0.25
0.26
0.27
0.28
0.29E=280 MeV, θ=60
o, qQE=263.739 MeV/c
0 0.1 0.2 0.30
25000
50000
75000
1e+05
0.28
0.3
0.32
0.34
E=480 MeV, θ=36o, qQE=286.4 MeV/c
0 0.05 0.1 0.150
10000
20000
30000
0.27
0.28
0.29
0.3
0.31
0.32
0.33
E=320 MeV, θ=60o, qQE=299.4 MeV/c
0 0.1 0.2 0.3 0.40
2e+05
4e+05
6e+05
8e+05
0.3
0.35
0.4
0.45
0.5E=1500 MeV, θ=11.95
o, qQE=311 MeV/c
0 0.1 0.2 0.3 0.40
10000
20000
30000
40000
50000
60000
70000
0.32
0.34
0.36
0.38
0.4
0.42
0.44
E=560 MeV, θ=36o, qQE=332.9 MeV/c
0 0.05 0.1 0.15 0.20
5000
10000
15000
20000
25000
0.31
0.32
0.33
0.34
0.35
0.36E=361 MeV, θ=60
o, qQE=335.7 MeV/c
0 0.1 0.2 0.3 0.4 0.50
1e+05
2e+05
3e+05
4e+05
5e+05
6e+05
0.50.2
0.3
0.4
0.5
0.6
0.7
0.8E=1650 MeV, θ=11.95
o, qQE=343 MeV/c
0 0.1 0.2 0.3 0.40
1e+05
2e+05
3e+05
4e+05
0.3
0.35
0.4
0.45
0.5
0.55
E=1500 MeV, θ=13.5o, qQE=352 MeV/c
0 0.05 0.1 0.150
2000
4000
6000
8000
0.3
0.32
0.35
0.37
E=280 MeV, θ=90o, qQE=352 MeV/c
0 0.1 0.2 0.3 0.40
10000
20000
30000
40000
50000
0.37
0.4
0.42
0.45
0.47
E=620 MeV, θ=36o, qQE=367 MeV/c
0 0.05 0.1 0.15 0.2 0.250
5000
10000
15000
0.34
0.36
0.38
0.4E=401 MeV, θ=60
o, qQE=370.8 MeV/c
0 0.1 0.2 0.3 0.4 0.50
1e+05
2e+05
3e+05
ω (GeV)
0.4
0.5
0.6
E=1650 MeV, θ=13.5o, qQE=388 MeV/c
0 0.1 0.2 0.3 0.4 0.5ω (GeV)
0
10000
20000
30000
40000
0.35
0.4
0.45
0.5
0.55E=680 MeV, θ=36
o, qQE=402.5 MeV/c
0 0.05 0.1 0.15 0.2 0.250
5000
10000
15000
0 0.05 0.1 0.15 0.2 0.25ω (GeV)
0.38
0.39
0.4
0.41
0.42
0.43
0.44E=440 MeV, θ=60
o, qQE=404.7 MeV/c
FIG. 5. Comparison of inclusive 12Cðe; e0Þ cross sections and predictions of the QE-SuSAv2 model (long-dashed red line), 2p-2hMEC model (dot-dashed brown line) and inelastic-SuSAv2 model (long dot-dashed orange line). The sum of the three contributions isrepresented with a solid blue line. The q dependence with ω is also shown (short-dashed black line). The y axis on the left representsd2σ=dΩ=dω in nb=GeV=sr, whereas the one on the right represents the q value in GeV=c.
G. D. MEGIAS et al. PHYSICAL REVIEW D 94, 013012 (2016)
013012-6
0 0.1 0.2 0.3 0.4 0.50
500
1000
1500
2000
2500
0.58
0.6
0.62
0.64
0.66
0.68
E=680 MeV, θ=60o, qQE=610 MeV/c
0 0.1 0.2 0.3 0.4 0.50
5000
10000
15000
20000
25000
0.65
0.7
0.75
0.8
E=2130 MeV, θ=18o, qQE=640 MeV/c
0.1 0.15 0.2 0.25 0.3 0.350
100
200
300
400
500
600
700
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8E=440 MeV, θ=145
o, qQE=650 MeV/c
0 0.2 0.4 0.6 0.80
5000
10000
15000
20000
25000
30000
0.7
0.8
0.9
E=2500 MeV, θ=15o, qQE=658.6 MeV/c
0.2 0.4 0.60
1000
2000
3000
4000
0.65
0.7
0.75
0.8
E=1108 MeV, θ=37.5o, qQE=674.6 MeV/c
0.1 0.2 0.3 0.40
2000
4000
6000
8000
10000
12000
14000
16000
0.7
0.72
0.74
0.76
E=2020 MeV, θ=20o, qQE=700.2 MeV/c
0.2 0.4 0.6 0.80
500
1000
1500
2000
0.8
0.85
0.9
0.95
E=1299 MeV, θ=37.5o, qQE=792 MeV/c
0.2 0.3 0.4 0.50
100
200
300
400
500
0.65
0.7
0.75
0.8
0.85
E=560 MeV, θ=145o, qQE=795 MeV/c
0.2 0.3 0.4 0.5 0.6 0.7 0.80
250
500
750
1000
0.9
0.95
1
1.05
1.1
E=1501 MeV, θ=37.5o, qQE=917 MeV/c
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
1000
2000
3000
1
1.25
1.5
1.75
E=3595 MeV, θ=16o, qQE=1044.3 MeV/c
0 0.2 0.4 0.6 0.8 10
500
1000
1500
2000
2500
1
1.1
1.2
1.3
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E=4045 MeV, θ=15o, qQE=1113.8 MeV/c
0.2 0.4 0.6 0.80
100
200
300
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600
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1.25
1.3
1.35
1.4
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E=3595 MeV, θ=20o, qQE=1316 MeV/c
0.4 0.8 10
50
100
150
0.6ω (GeV)
1.5
1.55
1.6
1.65
1.7
1.75
1.8E=3595 MeV, θ=25
o, qQE=1640 MeV/c
0.6 0.8 1 1.2 1.4 1.6 1.8 2ω (GeV)
0
10
20
30
40
50
2
2.1
2.2
2.3
2.4
2.5E=4045 MeV, θ=30
o, qQE=2247 MeV/c
2.4 2.6 2.8 3ω (GeV)
0
1
2
3
4
5
3.35
3.4
3.45
3.5
3.55
3.6E=4045 MeV, θ=55
o, qQE=3432.2 MeV/c
FIG. 7. As for Fig. 5, but now for kinematics corresponding to the highest qQE values considered.
G. D. MEGIAS et al. PHYSICAL REVIEW D 94, 013012 (2016)
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? Mechanisms other than single nucleon knock-out and leading tothe appearance of 2p2h final states (ground state correlations,final state interactions and coupling to MEC) play a significantrole 5 / 21
12C(νµ, µ−): VALENCIA MODEL vs SUPERSCALING
? Comparison to the flux-integrated cross section measured by theMiniBooNE Collaboration.
I Nieves et al5
0.5 1 1.5Tµ (GeV)
0
0.5
1
1.5
2
d2 !/d
T µ d
cos" µ
(10-3
8 cm
2 /GeV
) Full ModelFull QE (with RPA)MultinucleonNo RPA, No Multinuc.No RPA,No Multin., MA=1.32
0.80 < cos "µ< 0.90
MA=1.049 GeV
FIG. 3: Muon angle and energy distribution d2σ/d cos θµdTµ for 0.80 < cos θµ < 0.90. Experimental data from Ref. [5] andcalculation with MA = 1.32 GeV are multiplied by 0.9. Axial mass for the other curves is MA = 1.049 GeV.
with electron, photon and pion probes and contains no additional free parameters. RPA and multinucleon knockouthave been found to be essential for the description of the data. Our main conclusion is that MiniBooNE data are fullycompatible with former determinations of the nucleon axial mass, both using neutrino and electron beams in contrastwith several previous analyses. The results also suggest that the neutrino flux could have been underestimated.Besides, we have found that the procedure commonly used to reconstruct the neutrino energy for quasielastic eventsfrom the muon angle and energy could be unreliable for a wide region of the phase space, due to the large importanceof multinucleon events.
It is clear that experiments on neutrino reactions on complex nuclei have reached a precision level that requires for aquantitative description of sophisticated theoretical approaches. Apart from being important in the study of neutrinophysics, these experiments are starting to provide very valuable information on the axial structure of hadrons.
Acknowledgments
We thank L. Alvarez Ruso, R. Tayloe and G. Zeller for useful discussions. This research was supported by DGIand FEDER funds, under contracts FIS2008-01143/FIS, FIS2006-03438, and the Spanish Consolider-Ingenio 2010Programme CPAN (CSD2007-00042), by Generalitat Valenciana contract PROMETEO/2009/0090 and by the EUHadronPhysics2 project, grant agreement n. 227431. I.R.S. acknowledges support from the Ministerio de Educacion.
[1] C. F. Perdrisat, V. Punjabi and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 59, 694 (2007).[2] V. Bernard, L. Elouadrhiri and U. G. Meissner, J. Phys. G 28 (2002) R1.
I Megias et al
13
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
5
10
15
20
dσ/d
T µ/d
cosθ
µ (1
0-39 cm
2 /GeV
)
0.9 < cosθµ < 1.0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
5
10
15
20
25
MiniBooNEQE+MECQEMEC
0.8 < cosθµ < 0.9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
5
10
15
200.7 < cosθ
µ < 0.8
0 0.2 0.4 0.6 0.8 10
5
10
15
20
d2 σ/d
T µ/d
cosθ
µ (1
0-39 cm
2 /GeV
)
0.6 < cosθµ < 0.7
0 0.2 0.4 0.6 0.8 1 1.20
2
4
6
8
10
12
14
16
0.5 < cosθµ < 0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
150.4 < cosθ
µ < 0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
2
4
6
8
10
12
d2 σ/d
T µ/d
cosθ
µ (1
0-39 cm
2 /GeV
)
0.3 < cosθµ < 0.4
0 0.2 0.4 0.6 0.80
2
4
6
8
10
12
0.2 < cosθµ < 0.3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
120.1 < cosθ
µ < 0.2
0 0.1 0.2 0.3 0.4 0.5 0.6Tµ (GeV)
0
2
4
6
8
10
d2 σ/d
T µ/d
cosθ
µ (1
0-39 cm
2 /GeV
)
0.0 < cosθµ < 0.1
0 0.1 0.2 0.3 0.4 0.5 0.6Tµ (GeV)
0
2
4
6
8
10-0.1 < cosθ
µ < 0.0
0 0.1 0.2 0.3 0.4 0.5Tµ (GeV)
0
2
4
6
8
10-0.2 < cosθ
µ < -0.1
FIG. 6. (Color online) MiniBoone flux-folded double differen-tial cross section per target nucleon for the νµ CCQE processon 12C displayed versus the µ− kinetic energy Tµ for variousbins of cos θµ obtained within the SuSAv2+MEC approach.QE and 2p-2h MEC results are also shown separately. Dataare from [1].
? The degeneracy issue: The result of Nieves et al show asignificant contribution arising from the excitation of nuclearcollective modes (RPA), which is not included in the approach ofMegias et al
6 / 21
UNRAVELING THE NEUTRINO-NUCLEUS CROSS SECTION
? An accurate description of the 2p2h sector and collectiveexcitations, providing a ∼ 20% contribution to the nuclear crosssection, is only relevant to the extent to which the remaining∼ 80%, arising from processes involving 1p1h final states, is fullyunderstood. The ability of the models to explain single-nucleonknock out needs to be assessed
? Fifty years of (e, e′p) experiments, in which the scattered electronand the outgoing proton are detected in coincidence, haveprovided a wealth of information on single nucleon knock-outprocesses, associated with 1p1h final states, as well as clear-cutevidence of the coupling between the 1p1h and 2p2h sectors
? The large database of (e, e′p) cross sections—measured mainly atSaclay, NIKHEF-K and Jefferson Lab—must be exploited to testthe theoretical approaches employed to study neutrino-nucleusinteraction, and assess their predictive power
7 / 21
THE (e, e′p) REACTION
I Consider the process
e+A→ e′ + p+ (A− 1)
in which both the outgoing electronand the proton, carrying momentump′, are detected in coincidence, andthe recoiling nucleus can be left in aany (bound or continuum) state |n〉with energy En
e e′
p′
q,ω
I In the absence of final state interactions (FSI)—which can betaken into acount as corrections—the the measured missingmomentum and missing energy can be identified with themomentum of the knocked out nucleon and the excitationenergy of the recoiling nucleus, En − E0
pm = p′ − q , Em = ω − Tp′ − TA−1 ≈ ω − Tp′
8 / 21
(e, e′p) CROSS SECTION AND NUCLEAR SPECTRAL FUNCTION
I In the absence of FSI (to be discussed at a later stage)
dσAdEe′dΩe′dEpdΩp
∝ σepP (pm, Em)
I Kallen-Lehman representation of the spectral function
P(pm, Em) = PMF(pm, Em) + Pcorr(pm, Em)
I In the kinematical region corresponding to knock-out from theshell-model states (Em <∼ 50 MeV and |pm| <∼ 250 MeV)
P(pm, Em) ≈ PMF(pm, Em) =∑α∈F
Zα |φα(pm)|2 Fα(Em − εα)
I According to the nuclear shell model
Zα →2jα + 1
Z, Fα(Em−εα)→ δ(Em−εα) , Pcorr(pm, Em)→ 0
9 / 21
P (k, E) WITHIN THE LOCAL DENSITY APPROXIMATION (LDA)
? Bottom line: the tail of themomentum distribution, arisingfrom the continuum contributionto the spectral function, turns outto be largely A-independent forA > 2
n(k) =
∫dE P (k, E)
? Spectral functions of complex (isospin symmetric) nuclei havebeen obtained within the local density approximation (LDA)
PLDA(k, E) = PMF(k, E) +
∫d3r ρA(r) PNMcorr (k, E; ρ = ρA(r))
using the MF contributions extracted from (e, e′p) data? The continuum contribution PNMcorr (k, E) can be accurately
computed in uniform nuclear matter at different densities10 / 21
OXYGEN SPECTRAL FUNCTION
I FG model: P (p, E) ∝ θ(pF − |p|) δ(E −√|p|2 +m2 + ε)
I shell model states account for ∼ 80% of the strenghtI the remaining ∼ 20%, arising from NN correlations, is located at
high momentum and large removal energy (more on this later)
11 / 21
PINNING DOWN THE 1P1H SECTOR
I At moderate missing energy—typically Em <∼ 50 MeV—therecoiling nucleus is left in a bound state
I The final state is a 1p1h state of the A-nucleon systemI The missing energy spectrum exhibits spectroscopic lines,
corresponding to knock out from the shell model states.However the normalization of the shell model states issuppressed with respect to the predictions of the independentparticle model.
I The momentum distributions of nucleons in the shell modelstates can be obtained measuring the missing momentumspectra at fixed missing energy
I Consider 12C(e, e′p)11B, as an example. The expected 1p1h finalstates are
|11B(3/2−
), p〉 , |11B(1/2−
), p〉 , . . .
12 / 21
C(e, e′p) AT MODERATE MISSING ENERGY
I Missing energy spectrum of12C measured at Saclay in the1970s
QUASI-FREE (e, e’p) 473
8% PG 180 M&J/”
MISSIffi ENERGY (McV)
Fig. 9. Missing energy spectra from “C(e, e’p), (a) 0 S P 5 36 MeV/c, (b) SO $ P 5 180 MeV/c and (c) 0 s P s 60 MeV/c for 20 5 E 5 60 MeV.
3OG E< 50 MeV
0 50 la, ls0 2co 250 300 RECOIL MOMENTUM (M&/c)
Fig. 10. Momentum ~s~ibution from “C(e, e’p); (a) I5 s E 4 21.5 MeV and (b) 30 5 E s 50 MeV. The solid and dashed lines represent DWIA and PWIA ~lcula~ons respectively, with nonfiction
obtained by a fit to the data.
shells of “C. The lp, shell, at a separation energy of 16 MeV (fig. 9), exhibits the expected I = 1 distribution having a zero at P = 0 and a single maximum at PW 100 MeVJc. The two lines occurring in S(E, P) at 18 and 21 MeV correspond
I P - state momentumdistribution. Solid line: LDAspectral function
13 / 21
DETERMINATION OF THE SPECTROSCOPIC FACTOR
? The spectroscopic factor of the p-state with j = 3/2 is obtainedfrom
Zp =Z
(2j + 1)
∫∆k
d3k
(2π)3
∫∆E
dE PLDA(|k|, E) = 0.64
with
Zp =
∫d3k
(2π)3
∫dE PLDA(|k|, E) = 1
and∆k ≡ [0–310] MeV , ∆E ≡ [15–22.5] MeV
? The result obtained from the LDA spectral function—which iswithin 2 % of the experimental value—implies that dynamicaleffects not taken into account within the independent particlemodel reduce the average number of protons in the p-shellfrom 4→ 2.5
14 / 21
WHERE IS THE MISSING 1P1H STRENGTH?
? The correlation strength in the 2p2h sector arises from processesinvolving high momentum nucleons, with |pm| >∼ 400 MeV. Therelevant missing energy scale can be easily understoodconsidering that momentum conservation requires
Em = Ethr +√|pm|2 +m2 −m
? Scattering off a nucleon belonging to a correlated pair entails astrong energy-momentum correlation
15 / 21
MEASURED CORRELATION STRENGTH
? The correlation strength in the 2p2h sector has been investigatedby the JLAB E97-006 Collaboration using a carbon target
0.2 0.3 0.4 0.5 0.6pm [GeV/c]
10-3
10-2
10-1
n(p m
) [fm
3 sr-1
]? Measured correlation strength
6
0.2 0.3 0.4 0.5 0.6pm [GeV/c]
10-3
10-2
10-1
n(p m
) [fm
3 sr-1
]Figure 6. Momentum distribution of the data(circles) compared to the theory of refs. [3] (dots),[4] (solid) and [24] (dashed). The lower integra-tion limit is chosen as 40 MeV, the upper one toexclude the ∆ resonance.
Experiment 0.61 ±0.06Greens function theory [3] 0.46CBF theory [2] 0.64SCGF theory [4] 0.61
Table 1Correlated strength (quoted in terms of the num-ber of protons in 12C.)
shape of the spectral function for C, Al, and Feist quite similar. For Au a larger contributionfrom the broader resonance region is obvious andthe maximum of the spectral function is shiftedto higher Em. The correlated strength for Al, Feand Au is 1.05, 1.12 and 1.7 times the strengthfor C normalized to the same number of pro-tons. This increase cannot be solely explainedby rescattering but MEC’s have probably takeninto account. Another contribution may be com-ing from the stronger tensor correlations in asym-metric nuclear matter [26,27].
REFERENCES
1. P.K.A. deWitt Huberts, J. Phys. G 16 (1990)507.
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4. T. Frick and H. Muther, Phys. Rev. C 68(2003) 034310.
5. D. Rohe, Habilitationsschrift, UniversityBasel, 2004.
6. R. Ent et al., Phys. Rev. C 64 (2001) 054610.7. C. Barbieri, this proceeding8. C. Barbieri, D. Rohe, I. Sick and L. Lapikas,
Phys. Lett. B 608 (2005) 47.9. C. Barbieri, private communication.10. T. de Forest, Nucl. Phys. A 392 (1983) 232.11. D. Rohe, O. Benhar et al., Phys. Rev. C 72
(2005) 054602.12. T.G. O′Neill et al., Phys. Lett. B 351 (1995)
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5072.14. K. Garrow et al., Phys. Rev. C 66 (2002)
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Sick, Nucl. Phys. A 579 (1994) 493.17. J. Mougey et al., Nucl. Phys. A 262 (1976)
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Phys. Rev. C 41 (1990) R24.21. H. Muther and I. Sick, Phys. Rev. C 70 (2004)
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182501.23. T. Frick, Kh.S.A. Hassaneen, D. Rohe,
H. Muther, Phys. Rev. C 70 (2004) 024309.24. O. Benhar, A. Fabrocini, S. Fantoni and I.
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MORE (e, e′p) DATA IS ON ITS WAY
? Jlab experiment E12-12-14-012 has measured the Ar,Ti(e, e′p)cross section. These data will allow the determination of thespectral functions needed for the analysis of both ν and νinteractions in liquid argon detectors
? Collaboration involving 38 physicists, including few theorists,from 8 institutions
? Approved by the Jefferson Lab PAC42 in July, 2014, withscientific grade A-
? Experimental readiness review passed in July, 2016
? Data taking in February-March 2017
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JLAB E12-14-012 KINEMATICS
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PRELIMINARY 12C(e, e′) RESULTSPreliminary results
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SCHEDULE
? Inclusive cross sections of C and Ti analysed: December 2017
? Inclusive cross section of Ar analysed: Early 2018
? (e, e′p) analysis: 2018
? First data release: End of 2018
? Spectral functions of Argon and Titanium: Mid 2019
? Data release: End of 2019
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SUMMARY & OUTLOOK
? A number of advanced models of the electroweak nuclear crosssection the 0π sector have been developed and extensively tested
? The degeneracy between models based on different physics mustbe resolved. The available electron scattering data in exclusivechannels can play a critical role in this context
? (e, e′p) data at low missing energy and low missing momentumprovide model independent information on single-nucleonknock out, which is known to provide the dominant contributionto the cross section in quasi-elastic kinematics
? The upcoming models of the Argon and Titanium spectralfunctions, based on the data collected by the JLab E12-14-012experiment, will allow to pin down the contribution ofsingle-nucleon knock out processes in neutron-rich nuclei, thedescription of which involves non trivial difficulties
? Note that, being an intrinsic property of the target, the spectralfunction is needed to obtain the nuclear cross sections in both theelastic and inelastic channels
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Backup slides
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THE E12-14-012 EXPERIMENT AT JEFFERSON LAB
? The reconstruction of neutrino and antineutrino energy in liquidargon detectors will require the understanding of the spectralfunctions describing both protons and neutrons
? The Ar(e, e′p) cross section only provides information on protoninteractions. The information on neutrons can be obtained fromthe Ti(e, e′p), exploiting the pattern of shell model levels
16
Physics MotivationExperimental Goals
Experimental conditionsTitanium idea
Physics motivation
Use few hours of beam time investigating the feasibility of runningon a titanium target, as suggested by the PAC.The neutron spectral function of argon is needed to modelquasielastic neutrino scattering. In pion production both neutronsand protons take part in charged-current interactions.
4018Ar
p’s n’s
4822Ti
p’s n’s
C. Mariani for E12-14-012 Collaboration Spectral function of 40Ar through the (e, e0p) reaction23 / 21