NUCLEAR EFFECTS IN NEUTRINO STUDIES

Transcription

1 NUCLEAR EFFECTS IN NEUTRINO STUDIES Joanna Sobczyk June 28, 2017, Trento 1

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4 OUTLINE Motivation: neutrino physics Neutrino oscillation experiments: why nuclear physics is important Lepton-nucleus scattering: quasielastic mechanism Fermi Gas model Additional nuclear effects Comparison Conclusions 4

5 NEUTRINO OSCILLATIONS Neutrinos change their identity because mass eigenstates are not flavour eigenstates, = e, µ, i = mass eigenstates P! 6=0 i i = X U i, i different basis i (t)i = e i(et ~p~x) i (0)i mass eigenstates propagate 5

6 NEUTRINO OSCILLATIONS P! = h (t) i 2 = X U iu i e im2 i L/2E 2 PMNS matrix: e µ 1 A = c 23 s 23 A 0 s 23 c 23 c 13 0 s 13 e i s 13 e i 0 c 13 1 A 1 c 12 s 12 0 s 12 c 12 0A A There are 6 parameters in the SM which influence oscillations. Various oscillation experiments are sensitive to different parameters (we can play with L and E) 6

7 EXPERIMENTS P! =sin 2 (2 )sin m2 L E [ev 2 ][km] [GeV ] given by the experimental setup At the experiment one has to: distinguish events that are triggered by different neutrino types be able to make energy reconstruction to get E (neutrino beams are not monoenergetic!) 7

8 NEUTRINO PHYSICS - OPEN QUESTIONS STANDARD MODEL sin 2 (2 13 )=0.093 ± sin 2 (2 12 )=0.846 ± sin 2 (2 23 ) > 0.92 CP violation phase - still big uncertainty BEYOND STANDARD MODEL sterile neutrinos? more flavours? Which model is correct? Further question: are neutrino Majorana particles? But this cannot be answered by neutrino oscillation experiments. 8

9 EXPERIMENT - THEORY EXPERIMENT THEORY neutrino flux (blured) detector (target): carbon, oxygen, argon, iron, etc. Monte Carlo event generator Good knowledge of of neutrino-nucleus cross-section is needed! SM parameters or BSM theories

10 NEUTRINO-NUCLEUS CROSS SECTION We need a precise model to calculate cross-section for neutrino scattering of various nuclei (carbon, oxygen, argon ) We can check the models for electron scattering instead of neutrino scattering (much more data!) e e e e W + different vertex of interaction the same nuclear response 10

11 INCLUSIVE CROSS SECTION d /d de (nb/sr/gev) Barreau:1983ht We have precise data for the electron scattering e + 12 C! e + X E=560 MeV, θ=60 o (GeV) Barreau:1983ht Different dynamic mechanisms 11

12 CROSS SECTION Barreau:1983ht 5000 d /d de (nb/sr/gev) (GeV) Barreau:1983ht QUASIELASTIC MECHANISM 12

13 QUASIELASTIC MECHANISM lepton Impulse Approximation: only one interacting nucleon Barreau:1983ht It is correct if momentum transfer ~ inter-nucleons distance in nuclei fm = 200 MeV/c 0 d /d de (nb/sr/gev) giant resonances (GeV) 13

14 QE PEAK S POSITION d /d de (nb/sr/gev) Barreau:1983ht Suppose the elementary process is en en (GeV) Barreau:1983ht QUASIELASTIC MECHANISM Energy-momentum conservation 4E 2 sin 2 2 = 2M +4Esin 2 2 ) = 129MeV 14

15 QE PEAK S POSITION d /d de (nb/sr/gev) Barreau:1983ht Suppose the elementary process is en en (GeV) Barreau:1983ht = 4E2 sin MB 2M 2B +4Esin 2 2 B2 Energy-momentum conservation, B = 25MeV! = 150MeV binding energy 15

16 QE PEAK S WIDTH Barreau:1983ht 6000 d /d de (nb/sr/gev) (GeV) Peak s width arises due to Fermi motion Peak's width tells us about the Fermi momentum Barreau:1983ht 16

17 FERMI GAS The most basic approach: statistical correlations + constant binding energy H = X i2nucleons p 2 i 2M We know with a very good precision how describe the interaction e + N! e + N For neutrinos there is a room for improvement (axial form-factor) 17

18 FERMI GAS Clearly, it is not possible to find a good parametrisation (binding energy and Fermi momentum) in terms of (L)FG 18

19 TURN-ON INTERACTION We need to employ a more sophisticated model for nucleons in the nuclei. non-relativistic propagator: G(E,p, ) = E p 2 2M 1 (E,p, ) we include the SELF-ENERGY which is complex ImΣ(E,p) - particle width 19

20 SPECTRAL FUNCTION This is described by means of a spectral function: E<µ S h (E,p)= 1 ImG(E,p) E>µ S p (E,p)= 1 ImG(E,p) S h/p (E,p)=± 1 Im (E,p) [E p 2 /2M Re (E,p)] 2 +[Im (E,p)] 2 It can be shown that hole spectral function is the probability density for removing a particle with momentum k, with the removal energy E from the ground state. 20

21 E. OSET AND F. DE CORDOBA SEMIPHENOMENOLOGICAL MODEL A simple, semi-phenomenological approach to calculate nucleon self-energy in nuclear matter We calculate the SF for the infinite nuclear matter at constant density. Then we use LDA (local density approximation), meaning we integrate SF with a density profile function to model the nucleus. The calculation is non-relativistic which is OK for the hole SF but might be poor for the particle SF.

22 III. MODEL FOR THE NUCLEON SELF-ENERGY n self-energy which rely upon static NN potentials. tion (3) certainly requires the inclusion of this chans soon as the energy allows it. However, one must be e that for some practical applications the inclusion is channel might be relatively irrelevant. Indeed, for scattering, the region of energies where pion producis allowed is dominated by the 5 resonance and the The diagrammatic meaning of Eq. (1) is given in Fig. 2, series leading to the NN where the Lippmann-Schwinger t matrix is shown explicitly. Figure 2(a) does not contribute to the imaginary part of X, while all the others do. In order to evaluate it, we concentrate on Fig. 2(b). The self-energy for this diagram is given by E. OSET AND F. DE CORDOBA SEMIPHENOMENOLOGICAL MODEL I 4 (2m ) k q c(k q)+ i e k q c(k q) ie + + a} b) c) d} FICz. 7. Reordering of the series of Fig. 6 leading to (F. de Cordoba, E. Oset, PRC 46, 5) of the figure where the serrated line indicates t diagrama NN FIG. 2. Ladder sum for the nucleon self-energy. The dashed lines indicate potential. um t matrix. calculate the nucleon self-energy by summing Lippmann-Schwinger series approximate t matrix with the free NN scattering matrix (average over angles section) 1701 APPROACH TO NUCLEON... SEMIPHENOMENOLOGICAL 46 -> use NN cross the density modifications will come At this point we would like to raise a word of caution not to use Eq. (4), for the second-order diagram, to evaluate the real part of the nucleon self-energy by replacing V(q) by the r matrix, as we have done to calculate ImX. This would lead to double counting since two interaction lines on the upper part of the diagram and one in the lower will be counted twice when we consider also one interaction line in the upper part and two in the lower. from medium polarization FIG. 8. Self-energy diagram including the effects um polarization. of the medi-

23 SPECTRAL FUNCTION ~ 5 ( ( I I I I ( I I I I t I ) ) ) I K = 1.6gfm-' K,= (.4 fm-' ~4 I Particle spectral function at a density such that Fermi momentum kf=1.4 fm -1 =280 MeV t 3 0) ~ 1 For a particle of momentum k=1.61 fm -1 =320 MeV the largest probability is for kinetic energy ~17 MeV higher then the Fermi level I 0 20 (kinetic energy) - (Fermi level) I I I I I ) a g(.me& (F. de Cordoba, E. Oset, PRC 46, 5)

24 SPECTRAL FUNCTIONS IN THE CROSS-SECTION d d!d = Z d 3 p (2 ) 3 nucleon s momentum Z des h (E,~p)S p (w E,~p + ~q)l µ W µ removal energy energy transfer scattering angle lepton tensor hadron tensor e (!, ~q) N ~p ~p + ~q e N For large energy-momentum transfer this nucleon becomes relativistic

25 SPECTRAL FUNCTIONS IN THE CROSS-SECTION d d!d = Z d 3 p (2 ) 3 Z des h (E,~p)S p (w E,~p + ~q)l µ W µ This is difficult to calculate numerically so some approximations can be done, e.g. S h/p (E,p)=± 1 Im (E,p) [E p 2 /2M Re (E,p)] 2 +[Im (E,p)] 2 neglect the width: Im (E,p)! 0 S h / (E Ē(p)) (µ E) Ē(p) = p2 2M Re (Ē(p),p)

26 RESULTS giant resonances not reproduced relativistic effects are small the long tail comes from imaginary part of spectral functions (J.E.S. arxiv: ) 26

27 RESULTS relativistic effects are huge

28 RESULTS giant resonances not visible (large momentum transfer) relativistic effects are huge other mechanism overlap with the QE peak: 2p2h + delta prod. (J.E.S. arxiv: )

29 IDEAS TO TAKE HOME We need a precise knowledge of neutrino-nucleus interaction. Nuclear effects are crucial for the analysis of neutrino experimental data First we should see how the models work for electron scattering. One has to account for different mechanisms: quasielastic, 2p2h, delta excitation The fact that we are dealing with high energy transfer is a challenge 29

30 THANK YOU!