Neutrinos & Nuclei 56th International meeting on Nuclear Physics - - PowerPoint PPT Presentation

Neutrinos & Nuclei

in collaboration with:

• S. Pastore
• A. Lovato
• D. Lonardoni
• S. C. Pieper
• R. Schiavilla
• R. B. Wiringa

56th International meeting on Nuclear Physics Beta Decay Accelerator Neutrinos (Quasi-elastic) Double Beta Decay

Neutrinos

Neutrinos proposed by Pauli in 1930 to conserve energy, momentum, and angular momentum in nuclear beta decay.

In 1956 Reines and Cowan detected anti-neutrinos from Savannah River reactors:

¯ νe + p → n + e+ n → p + e− + ¯ νe

through coincidence of e+e- gamma rays and neutron capture. Reines was a LANL T-division employee at the time. Reines and Cowan were awarded the Nobel Prize in 1995. Reines and Cowan discovered the electron (anti-) neutrino. Later Lederman, Schwartz and Steinberger detected muon neutrino, receiving the Nobel Prize in 1988.

Nuclei

Rutherford Geiger-Marsden apparatus (~1910)

Why study neutrino-nucleus scattering (accelerators) ?

mass differences, 
 mixings from oscillations

SuperK MicroBooNE MINERva

Neutrinos Oscillations and Masses

Neutrinos interact with matter in the flavor basis but propagate in the mass basis ( in vacuum )

Neutrino oscillations first proposed in 1957 by Bruno Pontecorvo, Maki, Nakagawa, and Sakata in 1962

Mixing angles, CP violating phases, Majorana Phases + MSW effect from forward scattering in matter

Majorana

CP-violating phase

Why study Neutrinos and Nuclei

Neutrinos and nuclei are fundamental to some of the largest and most exciting experiments and observations Double Beta decay Majorana nature of the neutrino Supernovae/ Neutron star mergers and nucleosynthesis Accelerator Neutrino Measurements: Coherent neutrino scattering at SNS At high energies resonance and deep inelastic dominate

Recent Theory Status

Until recently our understanding of neutrino nucleus interactions has been very limited

1 2 3 4 5 6 7 8

M0ν

SM St-M,Tk SM Mi IBM-2 QRPA CH QRPA Tu QRPA Jy R-EDF NR-EDF

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 R(GT) Th. R(GT) Exp.

0.77 0.744

Beta Decay Double Beta Decay

• verpredicted: gA quenching 1.27 ➡ ~1

Factor of >2 uncertainty

MiniBooN Theory

Quasielastic Scattering

Under predicted by ~30%

How can we improve

• ur understanding?

LO (ν = 0) NLO (ν = 2) NNLO (ν = 3)

Basic building blocks: Nuclear interactions and currents NN interactions NN currents 3N interactions

1 2 3 4

r (fm)

−300 −200 −100 100 200 300

(MeV) Reid Paris Urbana AV18 vc

0,1 − 4vt 0,1

vc

0,1 + 2vt 0,1

Deuteron Potential Models with Different Spin Orientations

Nuclei: Interactions and Currents

t20 experiment Jlab R. Holt

Forrest, et al, PRC 1996

H = 1 2m X

i

p2

i +

X

i<j

Vij + X

i<j<k

Vijk

J = X

i

j1;i + X

i<j

j2;ij + ...

12C calculations:

GFMC for ground-state

+ current correlation matrix elements

~ 45 M core-hours

2A = 4096 spin amplitudes x 12!/(6!6!) = 924 isospin amplitudes (charge basis) for each sample

ADLB

http://www.mcs.anl.gov/project/adlb-asynchronous-dynamic-load-balancer

Lusk, Pieper, …

computingnuclei.org

Ψ0 = exp [−Hτ] ΨT

Light Nuclear Spectra

15

• 100
• 90
• 80
• 70
• 60
• 50
• 40
• 30
• 20

Energy (MeV)

AV18 AV18 +IL7 Expt.

0+

4He

0+ 2+

6He

1+ 3+ 2+ 1+

6Li

3/2− 1/2− 7/2− 5/2− 5/2− 7/2−

7Li

0+ 2+

8He

0+ 2+ 2+ 2+ 1+ 3+ 1+ 4+

8Li

1+ 0+ 2+ 4+ 2+ 1+ 3+ 4+ 0+

8Be

3/2− 1/2− 5/2−

9Li

3/2− 1/2+ 5/2− 1/2− 5/2+ 3/2+ 7/2− 3/2− 7/2− 5/2+ 7/2+

9Be

1+ 0+ 2+ 2+ 0+ 3,2+

10Be

3+ 1+ 2+ 4+ 1+ 3+ 2+ 3+

10B

3+ 1+ 2+ 4+ 1+ 3+ 2+ 0+ 2+ 0+

12C

Argonne v18 with Illinois-7 GFMC Calculations

• FIG. 2 GFMC energies of light nuclear ground and excited states for the AV18 and AV18+IL7 Hamiltonians compared to

experiment.

Carlson, et al, RMP 2015

+ …

Magnetic Moments and Transitions (q=0, Low energy)

Magnetic Moments EM Transitions

Wiringa, Pastore, Schiavilla, et al

1 2 3 4

q (fm

• 1)

10

• 4

10

• 3

10

• 2

10

• 1

10

|F(q)|

exp ρ1b ρ1b+2b

12C elastic form factor

1 2 3 4 10-4 10-3 10-2 10-1 k (fm-1) fpt(k) VMC GFMC Experiment

0.2 0.4 1 2 3 4 5 6 k2 (fm-2) 6 Z ftr(k) / k2 (fm2)

Hoyle state transition form factor

Electromagnetic form factors

2 Nucleon charge operators (relativistic corrections) are small

Scaling with momentum transfer: ‘y’-scaling incoherent sum over scattering from single nucleons PWIA often good for q >> kF; used in many fields (neutron scattering, …)

d2 dedEe = d de

M

Q4 q4RLq, + 1 2 Q2 q2 + tan2 2RTq,,

Quasi-elastic scattering: higher p, E

Quasi-Elastic electron scattering:


12C transverse/longitudinal response

Scaled longitudinal vs. transverse scattering from 12C

from Benhar, Day, Sick, RMP 2008 data Finn, et al 1984

Single-Nucleon Momentum Distributions

10-5 10-4 10-3 10-2 10-1 100 101 0.0 1.0 2.0 3.0 4.0 np(k) / Z [ fm3 ] k [ fm-1 ]

4He: AV6’ 16O: AV6’ 4He: N2LO R0=1.0 fm 16O: N2LO R0=1.0 fm 4He: N2LO R0=1.2 fm 16O: N2LO R0=1.2 fm

10-5 10-4 10-3 10-2 10-1 100 101 0.0 1.0 2.0 3.0 4.0

Preliminary

Chiral interactions

10-5 10-4 10-3 10-2 10-1 100 101 0.0 1.0 2.0 3.0 4.0 np(k) / Z [ fm3 ] k [ fm-1 ] AFDMC: 4He AV6’ AFDMC: 16O AV6’ CVMC: 40Ca AV18 10-5 10-4 10-3 10-2 10-1 100 101 0.0 1.0 2.0 3.0 4.0

Different Nuclei

Integrated Strength: 
 15-20 % above kF, Amplitude ~ 0.3-0.4

Lonardoni, Gandolfi, Wiringa, Pieper, et al

Scaling of the 1st kind (w/ p) Donnelly & Sick (1999)

Back to Back Nucleons (total Q~0)

E Piasetzky et al. 2006 Phys. Rev. Lett. 97 162504. 
 M Sargsian et al. 2005 Phys. Rev. C 71 044615.
 R Schiavilla et al. 2007 Phys. Rev. Lett. 98 132501.
 R Subedi et al. 2008 Science 320 1475.

np pairs dominate over nn and pp

1 2 3 4 5 10-1 101 103 105

12C

1 2 3 4 5 10-1 101 103 105

10B

1 2 3 4 5 10-1 101 103 105

8Be

1 2 3 4 5 10-1 101 103 105

6Li

1 2 3 4 5 10-1 101 103 105 q (fm-1) ρpN(q,Q=0) (fm3)

4He

2-nucleon momentum distributions

np vs. pp

Wiringa et al.; Carlson, et al, RMP 2015

10-5 10-4 10-3 10-2 10-1 100 101 102 103 0.0 1.0 2.0 3.0 4.0

16O

n12(k) [ fm-1 ] k [ fm-1 ] np, N2LO R0=1.0 fm pp, N2LO R0=1.0 fm np, N2LO R0=1.2 fm pp, N2LO R0=1.2 fm 10-5 10-4 10-3 10-2 10-1 100 101 102 103 0.0 1.0 2.0 3.0 4.0

Lonardoni, et al, preliminary

Electron Scattering: Longitudinal and Transverse Response

RT (q, ω) = X

f

h0| j†(q) |fihf| j(q) |0i δ(w (Ef E0))

Transverse (current) response:

RL(q, ω) = X

f

h0| ρ†(q) |fihf| ρ(q) |0i δ(w (Ef E0))

Longitudinal (charge) response:

Two-nucleon currents required by current conservation Response depends upon all the excited states of the nucleus

j = X

i

ji + X

i<j

jij + ...

π

Sum Rules: Longitudinal Response

S (q) = h 0 | j†(q) j(q) 0 i

Gives an indication of total strength, but not energy dependence

p

p+q

p

final states

PWIA

p

p+

k

p+q -

π

Energy dependence pion exchange final state interaction

p

p+q

p

final states

Sum Rule determined by pp correlations

Vector Response

p

p+q

p

final state

PWIA

Sum Rule: Constructive Interference between 1- and 2-body currents w/ tensor correlations p k

p+q -

π

k p p p p’ + p k

p+q - k

π

k p p’ p’ p’ + k

Large enhancement from combination of initial state correlations and two-nucleon currents similar in axial response

∝ σi · k σi · q (σj · k)2 (τi · τj)2 v2

π(k)

12C EM response

• Longitudinal

Transverse Lovato, et al, PRL, 2016

EM observables well-reproduced What about neutrinos and weak currents? Vector and Axial currents: beta decay 5 response functions in inclusive scattering

Beta Decay in Light Nuclei

1 1.1 1.2

Ratio to EXPT

10C 10B 7Be 7Li(gs) 6He 6Li 3H 3He 7Be 7Li(ex) gfmc 1b gfmc 1b+2b(N4LO) Chou et al. 1993 - Shell Model - 1b

• Contact fit to Tritium beta decay
• Substantial reduction due to two-body correlations
• Modest 2N current contribution
• Good description of experimental data, explains ‘quenching’
• Many calculations with larger nuclei underway

Neutral Current Response/Cross Sections 12C

Response functions Lovato, et al, 2017

2

• Vector

Axial Total

• Cross sections

anti-ν ν

40 1 2 3 4

q (fm

• 1)

1

Sxy (q)

1 2

S0z (q)

1

Szz (q)

1

Sxx (q)

2 4

S00 (q)

Sum rules in 12C: neutral current scattering

Lovato, et. al PRL 2014

EM

Single Nucleon currents (open symbols) versus Full currents (filled symbols)

Longitudinal Transverse

<m>

Quenching in beta decay and Enhancement in QE scattering What about double beta decay?

!" n n p p e e W W

x

[T 0ν

1/2]−1 = G0ν(Q, Z) |M0ν|2 hmββi2

an average of the three neutrino masses, weighted

where hmββi = P

i U 2 eimi

electron neutrino (this is

Matrix Element for light Majorana neutrino exchange) M0ν = g2

A M GT 0ν − g2 V M F 0V

M GT

0V

= hf| X

i<j

R r σi · σj τ +

i τ + j |ii

M F

0V

= hf| X

i<j

R r τ +

i τ + j |ii

Majorana

Rate goes like gA4

Double Beta Decay Matrix Element (light Majorana neutrino exchange) M0ν = g2

A M GT 0ν − g2 V M F 0V

M GT

0V

= hf| X

i<j

R r σi · σj τ +

i τ + j |ii

M F

0V

= hf| X

i<j

R r τ +

i τ + j |ii

corrections from two-nucleon currents, quenching of gA? MC methods sum over all intermediate states

100 200 300 400 500 600 700

p [MeV]

0.000 0.001 0.002 0.003 0.004

CGT(p) [MeV

• 1]

2b 1b

Different from single-beta decay and from inclusive scattering

Engel, Simkovic Vogel (2014)

Double Beta Decay ME in light Nuclei

Pastore, et al, 2017

2 4 6 r [fm]

• 0.1

0.1 0.2 0.3 0.4

C(r) [fm

• 1]

200 400 600 q [MeV]

• 4×10
• 4

4×10

• 4

8×10

• 4

1×10

• 3

2×10

• 3

2×10

• 3

GT-AA with correlations GT-AA without correlations 10He 10Be

C(q) [MeV

• 1]

Double Beta Decay ME in light Nuclei

Pastore, et al, 2017

• 1

1 Norm A=10 A=12 A=48 JM A=76 JM A=76 JH A=136 JM A=136 JH

Fν FNN GTAA GTν GTππ GTπN JM = Javier Menendez private communication JH = Hyv¨ arien et al. PRC91(2015)024613 * Relative size of the matrix elements is approximately the same in all nuclei * Short-range terms approximately the same in all nuclei

Less quenching than in single beta decay

Includes possible short-range contributions

Outlook

• More quantitative understanding of neutrinos and neutrino-nucleus

interactions is being developed


• Good Description of data in light nuclei across a range

• f energy and momenta

• Important to extract neutrino properties from experiment
• Mixing angles
• Hierarchy
• CP violation
• Absolute mass scale

• And to understand astrophysical environments and observations
• R-process nucleosynthesis in supernovae / n-star mergers
• Neutron star cooling
• R-process nucleosynthesis and weak matrix elements