CORRELATIONS IN QE(LIKE) NEUTRINO- NUCLEUS SCATTERING Natalie - - PowerPoint PPT Presentation

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DEPARTMENT OF PHYSICS AND ASTRONOMY CORRELATIONS IN QE(LIKE) NEUTRINO- NUCLEUS SCATTERING Natalie Jachowicz, T. Van Cuyck, R. Gonzlez-Jmenez, N. Van Dessel, V. Pandey Outline Detailed microscopic cross sections calculations for

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CORRELATIONS IN QE(LIKE) NEUTRINO- NUCLEUS SCATTERING

Natalie Jachowicz, T. Van Cuyck, R. González-Jímenez, N. Van Dessel, V. Pandey

DEPARTMENT OF PHYSICS AND ASTRONOMY

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  • Detailed microscopic cross sections calculations for QE(-like) scattering
  • influence of long-range correlations
  • influence of short-range correlations in 1- and 2-nucleon knockout processes
  • Influence of seagull and pion-in-flight MEC contributions

Outline

  • Scheme-dependent separation
  • Double counting

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Neutrino-hadron scattering

e.g. Dip region : multinucleon mechanisms

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Neutrino-nucleus interactions

Hadron current Lepton tensor

  • 2

̂, ,

  • NATALIE JACHOWICZ

WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Q2 dependence : dipole parametrization

  • r BBBA07 :

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Inclusive QE 1-nucleon knockout cross sections

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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2-nucleon knockout cross sections

2-nucleon knockout : with :

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Cross section calculations Nuclear model

  • Starting point : mean-field nucleus with Hartree-

Fock single-particle wave functions

  • Skyrme SkE2 force used to build the potential
  • Pauli blocking
  • Binding
  • Long- and short-range correlations
  • Meson Exchange Currents

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Packing fraction ~0.012

  • C. Colle, PhD, UGent 2017

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

A model for the nucleus …

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The Fermi gas model

Easiest microscopic independent particle model εF,n εF,p Depth of the potential ~ 41 MeV

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Shell model

Energy first excited state

The mean field model (or shell-model)

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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→ Solve Schrödinger (or Dirac) equation for nucleon in nuclear potential Harmonic oscillator potential spherical

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

The mean field model (or shell-model)

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Shell model

Not too approximate : already quite some correlations : the mean field model (or shell-model)

→Work harder : add spin-orbit term J=l-1/2 J=l+1/2

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

Not too approximate model for nuclei : already quite some correlations : the mean field model (or shell-model)

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Independent particle picture ???

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Woods-Saxon potential :

      −

+ =

a R r

e V r V 1 1 ) (

Not too approximate model for nuclei : already quite some correlations : the mean field model (or shell-model)

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The Hartree-Fock mean field

( )

∑ ∑ ∑ ∑ ∑ ∑

+ =         − + + = + =

i res i i i j i j i i i j i j i i i

H i h H r U V r U T H V T H ) ( ) ( 2 1 ) ( 2 1

, , , ,

  • Nucleons are moving independent

from each other in a mean field

  • How do we obtain a reliable and

consistent field ? Residual interaction

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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The Hartree-Fock recipe : Nucleons fill up a number of orbitals and form a density that can be written in terms of the occupied states as : The potential at a position r’, generated by the nucleon-nucleon two-body interaction V(r,r’) is given by

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Hartree-Fock recipe :Start with an initial guess for either the average field or the wave functions and use V(r,r’) to solve the coupled equations to obtain better values e.g.

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Wave function for the nucleus = Slater determinant Antisymmetrization takes into account the Pauli principle

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Long-range correlations are correlations over the whole size of the

nucleus

  • They can redistribute the incoming energy transfer to the nucleus
  • ver all the nuclear constituents.
  • They manifest themselves in collective excitations such as giant

resonances

Long-range correlations : Continuum Random Phase Approximation

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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https://cyclotron.tamu.edu/research/nuclear-structure/

Long-range correlations = probing collective effects at low energies

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David Bohm & David Pines ‘52 – Condensed matter physics Quantum mechanical interactions interaction between electrons The Hamiltonian corresponding to a system of individual electrons is re- expressed such that the long-range part of the Coulomb interactions between electrons is described in terms of collective fields This leads to the description of organized behavior of electrons brought along by long-range Coulomb interactions that couple together the motion of many electrons simultaneously = plasma oscillations Neglecting the coupling between plasma vibrations of different momenta

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

RPA … What’s in a name

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Single particle propagator

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Dyson Equation : H=H0+U+V Auxiliary potential 2-body interaction Self-energy Hamiltonian :

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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e.g. = Axiliary field U 2-body interaction V …

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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…

Two-particle propagator

Vertex function

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Auxiliary field U interaction V Higher order contributions/different topologies

= + +

Reformulation of the self-energy of a dressed particle

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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The Hartree-Fock mean field

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

Mean field already contains correlations !

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Excited states : Particle-hole or polarization propagator

=

εF

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Higher order RPA diagrams First order

Excited states : Particle-hole or polarization propagator

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Long-range correlations : Continuum RPA

  • Green’s function approach
  • Skyrme SkE2 residual interaction
  • self-consistent calculations

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Solving the RPA equations in coordinate space : What we really need is transition densities : So in the end we have to solve a set of coupled equations, that after discretizing on a mesh in coordinate space, translates into a matrix inversion for the transition densities:

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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2-body interaction V ?

Landau-Migdal interaction

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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2-body interaction V ?

Skyrme

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Regularization of the residual interaction :

Uncorrected dipole

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Final state interactions :
  • taken into account through the calculations of the wave function of the outgoing nucleon in the (real)

nuclear potential generated using the Skyrme force

  • influence of the spreading width of the particle states is implemented through a folding procedure

Bare RPA folding

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Relativistic corrections at higher energies (S. Jeschonnek and T. Donnelly, PRC57, 2438 (1998)):

λ → λλ 1!

Uncorrected Relativistic shift

  • The outgoing nucleon obtains the correct relativistic momentum

" #$ 2%#

  • Shifts the QE peak to the right relativistic position

Shift : Boost :

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Relativistic corrections at higher energies (S. Jeschonnek and T. Donnelly, PRC57, 2438 (1998)):

λ → λλ 1!

Uncorrected Relativistic shift

  • The outgoing nucleon obtains the correct relativistic momentum

" #$ 2%#

  • Shifts the QE peak to the right relativistic position

Shift : Boost :

E=750 MeV, θ=30°

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Coulomb correction for the outgoing lepton in charged-current interactions :

Low energies : Fermi function High energies : modified effective momentum approximation (J. Engel, PRC57,2004 (1998)) Uncorrected MEMA

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Fermi gas Hartree-Fock

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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CRPA : Comparison with electron scattering data

12C( e, e’)

$&/(Ω nb/MeV sr ( MeV!

Hartree-Fock CRPA

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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$&/(Ω nb/MeV sr ( MeV!

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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$&/(Ω nb/MeV sr ( MeV!

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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16O( e, e’)

  • Good overall agreement with e-scattering data
  • P. Barreau et al., Nucl. Phys. A402, 515 (1983), J. S. O’Connell et al., Phys.
  • Rev. C35, 1063 (1987), R. M. Sealock et al., Phys. Rev. Lett.62, 1350

(1989).,D. S. Bagdasaryan et al., YERPHI-1077-40-88 (1988),D. B. Day et al., Phys. Rev. C 48, 1849 (1993).,D. Zeller, DESY-F23-73-2 (1973).

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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MiniBooNe νµ

  • Satisfactory

general agreement

  • Good

agreement for forward scattering

  • Missing

strength for low Tµ , backward scattering

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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MiniBooNe 1̅µ

  • Good general

agreement

  • Good

agreement for forward scattering

  • Missing

strength for high Tµ , backward scattering

  • Better

agreement with data than neutrino cross sections

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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neutrino vs anti neutrinos

E=700 MeV

  • V. Pandey et al, Phys. Rev. C 92, 024606 (2015)

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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T2K νµ

  • General

agreement quite good

  • Missing

strength for low pµ

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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40Ar

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Forward scattering

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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MiniBooNe T2K

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Short-range correlations

  • The short-range repulsive character of

the nuclear force, which correlates with the Pauli exclusion principle, results in a large mean free path of the nucleons with respect to the size of the nucleus

  • In an independent particle model

nucleons move independently from each

  • ther in a mean field
  • This approach fails to capture short-range

features of nucleon-nucleon correlations

  • SRC : short-range repulsive,

tensor component of the nuclear force

  • Individual nucleons receive large

momenta compared to the Fermi momentum IPM single-particle orbitals are depleted by SRC and higher energy levels are populated

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SLIDE 53

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

Independent particle model Two-body density : Correlation function Compare :

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Gearheart (1994) Pieper (1992)

Short-range correlations

with Shifting the complexity induced by correlations from the wave functions to the operators

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  • Short-range

correlations affect 1nucleon and 2- nucleon knockout processes

  • The SRC-prone

nucleon pairs are predominantly in a back-to-back configuration with a small center-of-mass and high relative momentum

  • Final-state interactions

for the outgoing nucleons affect the experimental

  • bservations

To 12C Data : CLAS A(e,e’,pN) data

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • Strength residing

in restricted part

  • f phase space
  • Quasi-deuteron

kinematics

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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To 12C

Data : CLAS A(e,e’,pN)

  • mass dependence ~ A1.12 :soft !
  • Predominantly pn, s-pairs
  • Universal over mass tabel
  • Tensor force dominates at short

distances

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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SRC neutrinos 1p1h

  • Reduction of transverse response
  • Enhancement of Coulomb-longitudinal

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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SRC neutrinos 2p2h

  • Vector and axial contributions have comparable strength
  • Tensor often dominates, but not for all kinematics

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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SRC neutrinos 2p2h

  • Vector and axial contributions have comparable strength
  • Tensor often dominates, but not for all kinematics
  • pn pairs dominate

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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SRC neutrinos 1p1h+2p2h

  • T. Van Cuyck et al
  • Phys. Rev. C 94,

024611 (2016)

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Meson-exchange currents

When an electroweak boson interacts with a pair of nucleons which are correlated through the exchange of a meson, this will cause the knockout of

  • ne or both of the particles from the nucleus. The boson was interacting

with a current consisting of two nucleons, a two-body current, called a MEC Delta currents Seagull Pion in flight

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Correlation currents mπ≈135MeV, mρ≈775MeV, mω≈782MeV Already included in mean field models ! Contributions of heavier mesons :

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • III. MEC in 1p1h and 2p2h

Axial contributions :

12C( e, e’)

  • I. Towner, Nucl. Phys.A542, 631 (1992)

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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  • I. Towner, Nucl. Phys.A542, 631 (1992)
  • Only seagull have axial counterpart
  • timelike
  • Partially constrained by PCAC
  • Non-relativistic reduction not unambiguous

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Seagull and PIF in neutrino 1p1h

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

PRC95, 054611 (2017)

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Seagull and PIF in neutrino 2p2h

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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T2K MiniBooNe

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

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Summary

  • Long- and short-range correlations in QE-like cross

sections

  • CRPA calculations provide extra strength for forward

scattering arising from low-energy excitations

  • This might affect CCQE neutrino cross sections as

measured by MiniBooNe, T2K, …

  • SRC and MEC affect 1- and 2-nucleon knockout

processes

NATALIE JACHOWICZ WINTER WORKSHOP NEUTRINO-NUCLEUS SCATTERING, FERMILAB, NOVEMBER 7 2017

  • Scheme-dependent separation
  • Double counting