Unraveling the ν-nucleus Cross-Section

Transcription

1 Unraveling the ν-nucleus Cross-Section Omar Benhar INFN and Department of Physics, Sapienza University I Roma, Italy Workshop on ν-nucleus Interaction in a Few-GeV Region KEK, Tokai Campus, November 18-19, 2017

2 OUTLINE The riddle of the flux integrated neutrino-nucleus cross section The issue of degeneracy between different models of the inclusive cross 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

3 THE ISSUE OF FLUX AVERAGE The energy-transfer dependence of the cross section of the process e + A e + X at fixed beam energy and electron scattering angle displays a complex landscape. The contributions of the main reaction mechanisms involving both nuclear and nucleon structure can be clearly identified 2 / 21

4 In neutrino interactions, e.g. ν µ + A µ + X the energy of the incoming particle is spread according to a broad distribution, and different reaction mechanisms contribute to the cross section at fixed muon energy and emission angle This feature clearly emerges from the analysis of the available electron-scattering data 3 / 21

5 WHERE WE ARE Even if we restrict ourselves to the 0π sector, the interpretation of the signals measured by neutrino detectors require the understanding of the different reaction mechanisms contributing to the neutrino-nucleus cross section: single-nucleon knock out, coupling to meson-exchange currents (MEC), and excitation of collective modes Over the 15 years since the first NuINT Workshop that we may characterize as the post Fermi-gas age a number of more advanced models have been developed Electron scattering data, mainly inclusive cross sections, have been exploited to derive or validate the some of proposed models Several models have achieved the degree of maturity required for a meaningful comparison between their predictions and the measured neutrino-nucleus cross sections Very accurate results have been also obtained from Quantum Monte Carlo calculations. However, this approach is is inherently non relativistic, and its applicability is limited 4 / 21

6 significantly improve the agreement 4000 between theory and two-nucleon currents [32 34], whose contributions are data. For larger values of Q , however, FSI play a less observed at lower muon kinetic energy as a result of the relevant, in fact almost negligible, 2000 role. This feature is average500 over the neutrino flux [35]. The strong angular dependence of the two-nucleon current contribution may GeV and scattering angle θ e 0¼ 37.5 deg, corresponding to Q 2 N. also provide a clue for the understanding of the differences Rocco GeV , the etresults al of calculations carried out between the quasielastic cross sections reported by the Megias et al MiniBooNEE=2500 Collaboration MeV, θ=15 o, and q the NOMAD Collaboration E=1650 MeV, θ=13.5 o, q QE =388 MeV/c E=680 MeV, θ=36 [36], which collected data o QE =658.6 MeV/c, q QE =402.5 MeV/c 4000 E=1108 M E=440 MeV 3e using neutrino 0.55fluxes with very different mean energies: 880 MeV0.9 and 25 GeV, (a) respectively [35] e As a final remark, it has to be pointed out that a clear-cut identification of the variety of reaction mechanisms 0.45 contributing to the neutrino-nucleus cross section will 1e require a careful analysis of the assumptions underlying 0.4 different 0.4 models of nuclear dynamics. All approaches based on the independent 0 particle 0.2 model 0.4 fail0.6to properly take into ω (GeV) account correlation effects, ω (GeV) leading to a significant reduction of the normalization of the shell-model states [37], as (b) FIG. 5. Comparison of inclusive 12 Cðe; well e 0 E=1299 MeV, θ=37.5 o, q Þascross to the sections appearance and predictions QE =792 MeV/c E=560 Me 2000 of sizableof interference the QE-SuSAv2 500 termsmode in MEC model (dot-dashed brown line) and theinelastic-susav2 2p2h sector. However, model (long in dot-dashed some instances orange 0.95 these line). two The s 400 represented with a solid blue line. The deficiencies q dependence 1500 may withlargely ω is also compensate shown (short-dashed one another, black leading line). T d 2 σ=dω=dω in nb=gev=sr, whereas the to one accidental on the right agreement represents between the q value theoryin0.9 and GeV=c. 300 data. For example, 1000the two-body current contributions computed within our approach turn out to be close to those obtained within the 500 Fermi gas model The development of a nuclear model having 0.8 the predictive power0.2 needed 0.4 for applications to the analysis0.2of future experiments most notably the Deep Underground 0 0 FIG. 3. (a) Double Mechanisms differential electron-carbon other than crosssingle section at nucleon knock-out and leading to Neutrino Experiment (DUNE) [38] will require that the beam energy the E e ¼ 680 appearance MeV and scattering of 2p2h angle θ e final ¼ 36 deg. states degeneracy (ground E=3595 between state MeV, θ=16 different correlations, o, q QE = MeV/c E=4045 M approaches be resolved. A The dashed line corresponds to the result obtained neglecting FSI, while the solid line has been obtained within the approach of systematic 3000 comparison between the results1.75 of 2500 final state interactions and coupling to MEC) play a significant theoretical Ref. [15]. The experimental data are taken from Ref. [24]. calculations and the large body of electron scattering 2000 data, role (b) Same as (a) but for E ¼ 1300 MeV and θ ¼ 37.5 deg. including 2000both inclusive and exclusive cross 1.5sections, 5 will / illustrated C(e, e in ): Fig. FACTORIZATION 3(b), showing that at beam energy vs ESUPERSCALING e ¼ 0.3 0

7 12 C(ν µ, µ ): VALENCIA MODEL vs SUPERSCALING Comparison to the flux-integrated cross section measured by the MiniBooNE Collaboration. dσ/dt d 2!/dT µ d cos" µ (10-38 cm 2 µ /dcosθ µ (10-39 cm 2 /GeV) Nieves et al < cosθ µ < 1.0 Full Model Full QE (with RPA) Multinucleon No RPA, No Multinuc. No RPA,No Multin., M A =1.32 M A =1.049 GeV 0.80 < cos " µ < T µ (GeV) Megias et al 0.8 < cosθ µ < 0.9 MiniBooNE QE+MEC QE MEC FIG. 3: Muon angle and energy distribution d 2 σ/d cos θµdtµ for 0.80 < cos θµ < Experimental data from Ref. [5] and calculation 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 knockout have been found to be essential for the description of the data. Our main conclusion is that MiniBooNE data are fully compatible with former determinations of the nucleon 0.6 axial < mass, cosθ both using neutrino and electron beams in contrast with several previous analyses. The results also suggest that the neutrino flux could have been underestimated. Besides, we20 µ < 0.7 have found that the procedure commonly used to reconstruct the neutrino energy for quasielastic events from the muon angle and energy could be unreliable for a wide region of the phase space, due to the large importance of multinucleon events. It is clear that experiments on neutrino reactions on complex nuclei have reached a precision level that requires for a quantitative description of sophisticated theoretical approaches. Apart from being important in the study of neutrino physics, these experiments are starting to provide very valuable information on the axial structure of hadrons cm 2 /GeV) 15 The degeneracy issue: The result of Nieves et al show a significant contribution arising from the excitation 0.5 < cosθ µ of < 0.6 nuclear 16 collective modes (RPA), which is not included in the approach of 14 Megias et al Acknowledgments We thank L. Alvarez Ruso, R. Tayloe and G. Zeller for useful discussions. This research was supported by DGI / 21

8 UNRAVELING THE NEUTRINO-NUCLEUS CROSS SECTION An accurate description of the 2p2h sector and collective excitations, providing a 20% contribution to the nuclear cross section, is only relevant to the extent to which the remaining 80%, arising from processes involving 1p1h final states, is fully understood. The ability of the models to explain single-nucleon knock out needs to be assessed Fifty years of (e, e p) experiments, in which the scattered electron and the outgoing proton are detected in coincidence, have provided a wealth of information on single nucleon knock-out processes, associated with 1p1h final states, as well as clear-cut evidence of the coupling between the 1p1h and 2p2h sectors The large database of (e, e p) cross sections measured mainly at Saclay, NIKHEF-K and Jefferson Lab must be exploited to test the theoretical approaches employed to study neutrino-nucleus interaction, and assess their predictive power 7 / 21

9 THE (e, e p) REACTION Consider the process e + A e + p + (A 1) e e in which both the outgoing electron and the proton, carrying momentum p, are detected in coincidence, and the recoiling nucleus can be left in a any (bound or continuum) state n with energy E n In the absence of final state interactions (FSI) which can be taken into acount as corrections the the measured missing momentum and missing energy can be identified with the momentum of the knocked out nucleon and the excitation energy of the recoiling nucleus, E n E 0 q,ω p p m = p q, E m = ω T p T A 1 ω T p 8 / 21

10 (e, e p) CROSS SECTION AND NUCLEAR SPECTRAL FUNCTION In the absence of FSI (to be discussed at a later stage) dσ A de e dω e de p dω p σ ep P (p m, E m ) Kállën-Lehman representation of the spectral function P ( p m, E m ) = P MF (p m, E m ) + P corr (p m, E m ) In the kinematical region corresponding to knock-out from the shell-model states (E < m 50 MeV and p m < 250 MeV) P ( p m, E m ) P MF (p m, E m ) = Z α φ α (p m ) 2 F α (E m ɛ α ) α {F } According to the nuclear shell model Z α 2j α + 1 Z, F α (E m ɛ α ) δ(e m ɛ α ), P corr (p m, E m ) 0 9 / 21

11 P (k, E) WITHIN THE LOCAL DENSITY APPROXIMATION (LDA) n(k) = de P (k, E) Bottom line: the tail of the momentum distribution, arising from the continuum contribution to the spectral function, turns out to be largely A-independent for A > 2 Spectral functions of complex (isospin symmetric) nuclei have been obtained within the local density approximation (LDA) P LDA (k, E) = P MF (k, E) + d 3 r ρ A (r) Pcorr NM (k, E; ρ = ρ A (r)) using the MF contributions extracted from (e, e p) data The continuum contribution Pcorr NM (k, E) can be accurately computed in uniform nuclear matter at different densities 10 / 21

12 OXYGEN SPECTRAL FUNCTION FG model: P (p, E) θ(p F p ) δ(e p 2 + m 2 + ɛ) shell model states account for 80% of the strenght the remaining 20%, arising from NN correlations, is located at high momentum and large removal energy (more on this later) 11 / 21

13 PINNING DOWN THE 1P1H SECTOR At moderate missing energy typically E m < 50 MeV the recoiling nucleus is left in a bound state The final state is a 1p1h state of the A-nucleon system The missing energy spectrum exhibits spectroscopic lines, corresponding to knock out from the shell model states. However the normalization of the shell model states is suppressed with respect to the predictions of the independent particle model. The momentum distributions of nucleons in the shell model states can be obtained measuring the missing momentum spectra at fixed missing energy Consider 12 C(e, e p) 11 B, as an example. The expected 1p1h final states are 11 B(3/2 ), p, 11 B(1/2 ), p, / 21

14 C(e, e p) AT MODERATE MISSING ENERGY Missing energy spectrum of 12 C measured at Saclay in the 1970s P - state momentum distribution. Solid line: LDA spectral function 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 MeV/c and (c) 0 s P s 60 MeV/c for 20 5 E 5 60 MeV. 13 / 21

15 DETERMINATION OF THE SPECTROSCOPIC FACTOR The spectroscopic factor of the p-state with j = 3/2 is obtained from Z d 3 k Z p = (2j + 1) k (2π) 3 de P LDA ( k, E) = 0.64 E with and Z p = d 3 k (2π) 3 de P LDA ( k, E) = 1 k [0 310] MeV, E [ ] MeV The result obtained from the LDA spectral function which is within 2 % of the experimental value implies that dynamical effects not taken into account within the independent particle model reduce the average number of protons in the p-shell from / 21

16 WHERE IS THE MISSING 1P1H STRENGTH? The correlation strength in the 2p2h sector arises from processes involving high momentum nucleons, with p m > 400 MeV. The relevant missing energy scale can be easily understood considering that momentum conservation requires E m = E thr + p m 2 + m 2 m Scattering off a nucleon belonging to a correlated pair entails a strong energy-momentum correlation 15 / 21

17 2. O. Benhar, Nucl. Phys. MEASURED CORRELATION 10-2 STRENGTH 3. H. Műther, Rev. C 52 (1 The correlation strength in the 2p2h sector has been investigated 4. T. Frick and by the JLAB E Collaboration using a carbon target n(p m ) [fm 3 sr -1 ] 10-1 (2003) D. Rohe, Basel, p m [GeV/c] 6. R. Ent et al. 7. C. Barbieri, C. Barbieri, Phys. Lett. B Figure 6. Momentum distribution of the data 9. C. Barbieri, (circles) compared to the theory 10-3 of refs. [3] (dots), 10. T. de Forest [4] (solid) and [24] (dashed). The lower integration limit is chosen as 40 MeV, 11. D. Rohe, O. 0.2 the upper 0.3 one 0.4 to 0.5 (2005) exclude the resonance. p m [GeV/c] 10-3 Measured correlation strength n(p m ) [fm 3 sr -1 ] Experiment 0.61 ±0.06 Greens function theory [3] 0.46 CBF theory [2] 0.64 SCGF theory [4] 0.61 Table T.G. O Neill D. Abbott e K. Garrow G. Garino et 16. O. Benhar, Sick, Nucl. P 17. J. Mougey e / 21

18 MORE (e, e p) DATA IS ON ITS WAY Jlab experiment E has measured the Ar, Ti(e, e p) cross section. These data will allow the determination of the spectral functions needed for the analysis of both ν and ν interactions in liquid argon detectors Collaboration involving 38 physicists, including few theorists, from 8 institutions Approved by the Jefferson Lab PAC42 in July, 2014, with scientific grade A- Experimental readiness review passed in July, 2016 Data taking in February-March / 21

19 JLAB E KINEMATICS 18 / 21

20 PRELIMINARY 12 C(e, e ) RESULTS Preliminary results 19 / 21

21 SCHEDULE Inclusive cross sections of C and T i 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 / 21

22 SUMMARY & OUTLOOK A number of advanced models of the electroweak nuclear cross section the 0π sector have been developed and extensively tested The degeneracy between models based on different physics must be resolved. The available electron scattering data in exclusive channels can play a critical role in this context (e, e p) data at low missing energy and low missing momentum provide model independent information on single-nucleon knock out, which is known to provide the dominant contribution to the cross section in quasi-elastic kinematics The upcoming models of the Argon and Titanium spectral functions, based on the data collected by the JLab E experiment, will allow to pin down the contribution of single-nucleon knock out processes in neutron-rich nuclei, the description of which involves non trivial difficulties Note that, being an intrinsic property of the target, the spectral function is needed to obtain the nuclear cross sections in both the elastic and inelastic channels 21 / 21

23 Backup slides 22 / 21

24 Physics Motivation Experimental Goals Experimental conditions THE E EXPERIMENT Titanium idea AT JEFFERSON LAB Physics motivation The reconstruction of neutrino and antineutrino energy in liquid argon detectors will require the understanding of the spectral Use few hours of beam time investigating the feasibility of running functions describing both protons and neutrons on a titanium target, as suggested by the PAC. The Theneutron Ar(e, e p) spectral cross section functiononly of argon provides is needed information to model on proton quasielastic interactions. neutrino The information scattering. onin neutrons pion production can be obtained both neutrons from and theprotons Ti(e, e p), take exploiting part in charged-current the pattern of shell interactions. model levels p s 40 18Ar n s p s 48 22Ti n s C. Mariani for E Collaboration Spectral function of 40 Ar through the (e, e 0 p) reaction 23 / 21 16