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Lo Low-energy energy ne neut utrino rino-nucleus nucleus cross ross se sections ctions N. Jachowicz Ghent University Department of Physics and Astronomy natalie.jachowicz@UGent.be Low-energy neutrino-nucleus cross sections Intro

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Lo Low-energy energy ne neut utrino rino-nucleus nucleus cross ross se sections ctions

  • N. Jachowicz

Ghent University Department of Physics and Astronomy

natalie.jachowicz@UGent.be

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Neutrino energies

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Intro

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Neutrino-hadron scattering

  • little experimental data is available
  • small cross sections
  • no monochromatic neutrino beams

N.J. et al, PRC66, 065501 (2002) ;

  • E. Kolbe et al, PRC63, 025802 (2001) ;
  • J. Engel et al, PRD67, 013005 (2001)
  • one has to rely on theoretical predictions,
  • uncertainties induced by model dependence,

and more fundamental uncertainties … Uncertainties :

208Pb

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Intro

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What can we learn from these neutrinos ?

  • Electroweak tests
  • Nuclear structure information
  • Astrophysical neutrinos : a.o. core-collapse supernovae
  • Oscillations
  • Neutrinonucleosynthesis

How can we learn from these neutrinos ?

  • Detect them
  • Neutrino-electron scattering
  • Neutrino-hadron scattering
  • Study their interactions : theory + experiment

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Intro

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Modeling neutrino-nucleus cross sections @ low energies :

E r

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Formalism

Continuum RPA

  • Green’s function approach
  • Skyrme II residual interaction
  • ground state : Hartree-Fock

single-particle wave functions (Skyrme)

  • non-relativistic
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Lepton tensor Hadronic current Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Formalism

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Continuum Random Phase Approximation (CRPA)

16O(n50 MeV , n’) 16O*

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Basic features

  • Axial contribution dominant
  • Transverse contribution dominant
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Low-energy neutrino-nucleus cross sections

12C

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Basic features

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Higher order multipoles important : Low-energy neutrino-nucleus cross sections

16O

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Basic features

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Low-energy neutrino-nucleus cross sections

Contribution of different single-particle channels in 12C

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Basic features

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Neutrinos versus antineutrinos Low-energy neutrino-nucleus cross sections neutrinos antineutrinos

16O

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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Helicity dependence of the cross section: For neutrinos : S+hA = S-A, is small S-hA = S+A, is large h-h-* dominates

16O

For antineutrinos : S+hA = S+A, is large S-hA = S-A, is small h+h+* dominates

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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Adding antineutrinos to the picture :

  • Neutrinos

favor ‘spin down’ nucleon knockout

  • Antineutrinos

mainly induce ‘spin up’ knockout reactions

  • Polarization

differences increase with incoming neutrino energies

16O

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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The asymmetry and the dissimilarities between neutrinos and antineutrinos are most clear considering the angular cross section : The asymmetry is most prominent for forward nucleon knockout, and remains large over a broad angular range. For the suppressed backward scattering reactions, the asymmetry is completely reversed

208Pb

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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Neutrinos Antineutrinos Antineutrinos Neutrinos

208Pb

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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Longitudinal pola

lariza izatio ion asym ymmetry ry :

  • For antineutrinos, Al is

large and positive

  • For neutrinos, Al is large

and negative

16O

  • N. Jachowicz, K. Vantournhout, J. Ryckebusch, K. Heyde, PRL

93, 082501 (2004) ; N. Jachowicz, K. Vantournhout, J. Ryckebusch, K. Heyde, PRC71, 034604 (2005).

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 ν versus antiν

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Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Dependence on MA is very small at very low neutrino energies …

12C(νe ,e-)

Eν=50 MeV MA @ low energies

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Strangeness in the nucleon

Axial form factor : Weak vector form factors : Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Strangeness

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  • strangeness contribution to the weak vector formfactors : Parity Violating Electron Scattering

(Sample, Happex, G0, …)

  • strangeness contribution to the axial current : neutrino scattering

Traditionally :

  • vector current contributions are suppressed
  • no radiative corrections

Correlated !

Low-energy neutrino-nucleus cross sections

N.J., P. Vancraeyveld, P. Lava, J. Ryckebusch, PRC76, 055501 (2007).

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Strangeness

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  • Generally : net strangeness effect

vanishes for isoscalar targets

  • close to particle knockout threshold the

influence becomes larger due to binding energy differences between protons and neutrons

  • differential cross sections differ,

energy of reaction products can be very different

Neutrino cross sections including strangeness

16O

CRPA

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Strangeness

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  • differences up to 20%
  • opposite effect for protons

and neutrons

proton/neutron cross sections

16O

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Strangeness

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Supernova neutrino spectra :

Experimentally : Michel spectra : Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Energy dependence of the cross section

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Supernova neutrino spectra :

Low-energy neutrino-nucleus cross sections spectrum<ε>=18MeV, w=.7 spectrum<ε>=18MeV, w=.9 folded cross section ω=12 MeV cumulative folded cross section Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Energy dependence of the cross section

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Experiments at intermediate energies

Intermediate energies : 100 MeV - … GeV Energy distribution ! Quasi-elastic processes : Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 MiniBooNe

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Cross sections at low Q2

Comparison between inclusive cross sections

  • btained

within a relativistic Fermi gas calculation, a relativistic plane wave impulse approximation (RPWIA) approach, a mean-field calculation, and a calculation including CRPA correlations implemented using a Skyrme parametrization as residual interaction.

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 MiniBooNe

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Cross sections at low Q2

Q2 dependence as

a function of incoming energy

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 MiniBooNe

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Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 Comparison with MiniBooNe data cosθ =0.95 cosθ =0.65 cosθ =0.35 MiniBooNe

MiniBooNe + CRPA ▪ Hartree-Fock ▪ MiniBooNe + CRPA ▪ Hartree-Fock ▪ MiniBooNe + CRPA ▪ Hartree-Fock ▪

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Beta-beam neutrino spectra :

  • β-decay of a primary boosted

nuclear beam generates intense neutrino beams,

  • with average energy and precise

shape of the spectrum determined by the boost factor γ of the primary beam

  • First proposed to produce high energy neutrinos in oscillation experiments

(P.Zuchelli, Phys.Lett.B 532, 166 (2002). Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Low-energy neutrino-nucleus cross sections 18Ne Natalie Jachowicz NuInt12, Rio, October 22-27 2012

  • At lower gamma factor, the neutrino

energy becomes very suitable for neutrino-nucleus scattering investigations

(C. Volpe, J.Phys. G30, 1 (2004)).

  • A detector away form the main axis of

the storage ring will detect the least energetic neutrinos

(R.Lazauskas et al. PRD76, 053006)

→Suited for nuclear structure studies, studies of supernova neutrino responses …

LowE β-beams

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Cross section as a function of the boost factor γ of the beam

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Procedure :

  • linear combinations of normalized beta-beam spectra :
  • fitting the constructed energy distribution to the supernova-

neutrino spectrum by minimizing the expression, varying the expansion parameters ai and the boost factors γi Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Total folded cross sections :

  • 16O : CRPA calculation
  • deuteron : S. Nakamura, T. Sato, S. Ando et al.,
  • Nucl. Phys. A 707 (2002)

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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… differential folded cross sections

16O

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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… differential folded cross sections –multipole contributions Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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This very satisfying agreement suggests that it is possible to reconstruct supernova-neutrino signal using the results of the beta-beam measurement directly, without going through the intermediate step of using a nuclear structure calculation

  • For each set of beta-beam data at a given g, there will be a measured response in the

detector

  • Taking appropriate linear combinations of the measured response provides a very

accurate picture of the response of the detector to an incoming supernova-neutrino spectrum Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Energy ‘resolution’ Width ‘resolution’

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Reconstructing the supernova neutrino spectrum ? Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Inversion of the method : reconstructing the supernova neutrino energy spectrum

Supernova neutrino signal in a terrestrial detector Fit with linear combination of beta beam responses :

aγi, γi

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Inversion of the method – reconstruction in terms of average energy and width of the spectrum

curves : 90% confidence levels for spectra with 5 and 10 % uncertainty on the expansion parameters Low-energy neutrino-nucleus cross sections

N.J., G. McLauglin, PRL96, 172301 (2006) ; N.J., G. McLaughlin, C. Volpe, PRC77, 055501 (2008)

Natalie Jachowicz NuInt12, Rio, October 22-27 2012 LowE β-beams

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Summary

Low-energy neutrino-nucleus cross sections Natalie Jachowicz NuInt12, Rio, October 22-27 2012

Neutrino cross sections in the 10s of MeV energy range

  • Nuclear structure effects are important
  • Strongly energy dependent
  • Dominated by axial, transverse contributions
  • Strangeness influence can be important
  • Low-energy beta beams would provide an

excellent opportunity to study the nuclear response in this energy range, important for e.g. supernovaneutrinos