Problems In Quasi-Elastic
Neutrino-Nucleus Scattering
JLAB
September 9,2011
Gerry Garvey
Los Alamos Nat. Lab.
Outline
• What is quasi-elastic scattering (QES)?
• Why has neutrino-nucleus QES Become Interesting?
• Inclusive Electron QES; formalism and results.
(longitudinal and transverse, scaling)
• Extension to neutrino-nucleus QES processes.
• Differences between electron and neutrino QES
experiments.
• Problems with impulse approximation.
• Possible remedies and further problems.
• Determining the neutrino flux??
What is Quasi-elastic Scattering?
• QES is a model in which the results of elastic leptonnucleon scattering (neutral or charge changing, (n p))
is applied to the scattering off the individual nucleons
in the nucleus. The cross-section is calculated as the
square of the incoherent sum of the scattering
amplitudes off the individual nucleons. Pauli exclusion
is applied and a 3-momentum transfer q > 0.3GeV/c is
required to resolve individual nucleons.
Why has QES ν-N become Important?
Research involving neutrino oscillations has required the
extension of QES (CCQE) to neutrino-nucleus interactions.
For 0.3<Eν< 3.0 GeV it is the dominant interaction.
CCQE provides essential information for neutrino
oscillations, neutrino flavor and energy.
CCQE is treated as readily calculable, experimentally
identifiable and allowing assignment of the neutrino
energy.
Some 40 calculations published since 2005
Oscillation period: 1.27Δmij2(ev2)× (L(km)/Eν(GeV))
atmos: Δm232=10-3 L/E≈103 LBNE
sterile: ΔmAS2=1 L/E≈1 SBNE
Long-Baseline News, May 2010:
“ *** LSND effect rises from the dead… ?“
Sterile
neutrinos
And it’s Getting Worse!!
New Subatomic Particle Could Help
Explain the Mystery of Dark Matter. A
flurry of evidence reveals that "sterile
neutrinos" are not only real but common,
and could be the stuff of dark matter.
HIDDEN CLUE: Pulsars, including one inside
this "guitar nebula," provide evidence of
sterile neutrinos. Scientific American
Cosmology, decay of sterile neutrino (dark matter), calibration of Ga
solar neutrino detectors, increased  e flux from reactors, larger

 e  p  n  e cross section,
QES in NP originated in e-Nucleus Scattering
Moniz et al PRL 1971
C
Simple Fermi Gas 2 parameter , SE, pF
Impulse Approximation
Ni
Pb
Inclusive Electron Scattering
Electron Beam /E ~10-3
Scattered
electron

Magnetic
Spectograph

(E , 0, 0, p ), (E ', p 'sin  , 0, p ' cos  )
  E  E'
r r r
q  p  p'
Because the incident electron beam is
precisely known and the scattered
electron well measured, q and ω are
precisely known without any
reference to the nuclear final state
Quasi-Elastic Electron Scattering
Q  q 
2
2
2
 q 
2
2
2
4M
2
( d  / d e ) Mott   cos ( / 2) / E sin ( / 2)
2
p ', N J  p, N 

Q
 
Single nucleon
vector current
Fi 3 (q )
2
1
2
F1 (0 )  1
S
d
d e
i
2
4
 u N ( p ') | [ F1 (q )
N

2
( Fi (q )   3 Fi (q ))
S
2
V
S
2 m F2 (0 )   ' p   n   3 .7 0 6
V
V
E '  GE

E0 
N ,2
(q )   G M (q )
2
N ,2
1
G E (q )  F1 (q )   F2 (q )
2
2
2
2 m F2 (0 )   ' p   n   0 .1 2 0
2
F1 (0 )=1
  M ott
 F2 (q )  q  ] | u N ( p ) 
N

2
2
2
2
2  
 2  G M (q ) tan ( ) 
2 
G M (q )  F1 (q )  F2 (q )
2
2
2
Scaling in Electron Quasi-elastic Scattering (1)
The energy transferred by the electron (ω), to a single nucleon with initial Fermi
momentum k
 T E T
N
s
R
TN is the kinetic energy of the struck nucleon, Es the separation energy of
the struck nucleon, ER the recoil kinetic energy of the nucleus.
1
r
r 2
2 2
  [( k  q )  m ]  m  E s  E reco il
1
 [ k  2 k || q  q  k
2
||
2
2

 m ] 2  m  E s  E reco il
2
n eg lect E s , E reco il , k 
k || 

2
 2 m  q  y
Instead of presenting the data as a function of q and ω,it can be expressed
in terms of a single variable y.

 d
 d 2 
1
F ( y, q )  



 d  d   E X P  Z  ep (q )  N  en (q )  dy
The scaling function F(y,q) is formed from the measured cross section at 3momentum transfer q, dividing out the incoherent single nucleon contributions at
that three momentum transfer.
Scaling in Electron Quasi-elastic Scattering (2)
3He
Raw data
Scaled
At y    2 m   q  0
2
q    2 m    Q
2
2
2
2
kinim atics for scattering off a nucleon at rest
Excuses (reasons) for failure y > 0: meson exchange, pion
production, tail of delta resonance.
Super Scaling
The fact that the nuclear density is nearly constant for A ≥ 12 leads one to ask, can
scaling results be applied from 1 nucleus to another? W.M. Alberico, et al Phys.
Rev. C38, 1801(1988), T.W. Donnelly and I. Sick, Phys. Rev. C60, 065502 (1999)
A new dimensionless scaling variable
is employed
 
y RFG

k F erm i
 
mN
( 1  
1
)
k F erm i
  Q / 4mN ,   q / 2m
2
2mN ,
2
Note linear scale: not bad for
 0
Serious divergence above
 0
Separating Super Scaling into its Longitudinal and
Transverse Responses Phys. Rev. C60, 065502 (1999)
Longitudinal
Transverse
Transverse
The responses are normalized so that in a Relativistic Fermi Gas Model:
f L ( )  f T ( )
fL satisfies the expected Coulomb sum rule. ie. It has the expected value.
fT has mostly excuses (tail of the Δ, meson exchange, pion production etc.)
Fine for fixed q and different A. Note divergence, even below ψ’=0
Trouble even with the GOLD standard
Contrast of e-N with ν-N Experiments
Electron
Electron Beam /E ~10-3

Scattered
electron
Magnetic
Spectograph
Neutrino
Neutrino-Mode Flux

Eν
Neutrino Beam ΔE/<E>~1
l-

Don’t know Eν !!!
What’s ω ???
What’s q ????
QE peak???
Very Different Situation from inclusive electron scattering!!
MiniBooNE Setup
ν mode
flux
neutrino mode:
ν mode
flux
νμ→ νe oscillation search
antineutrino mode: νμ→ νe oscillation search
While inclusive electron scattering and CCQE neutrino
experiments are very different, the theory hardly changes.
Neutrino (+), Anti-Neutrino(-) Nucleon CCQE Cross Section
Charged lepton mass=0
2
2
2

G F cos  C 
2
2 s  u 
2 s  u  

A
(Q
)

B
(Q
)

C
(Q
)

2
2
 M2 
 M2  
dQ
8  E  



 
d
Q  2 Q
A (Q ) 
 f1 (
4 
M
2
2
 4 )  f1 f 2 (
2
2
4Q
2
M
2
) f (
2
2
Q
2
M
2

Q
4
4M
)  g (4 
4
2
1

)
2 
M 
Q
2
B (Q )  Q ( f1  f 2 )g 1
2
C (Q ) 
2
2
M
4
2
( f1  f 2
2
s  u  4 M E  Q
2
Q
2
4M
 g1 )
2
2
2
The f1 and f2 are isovector vector form factors that come from electron
scattering. g1 is the isovector axial form factor fixed by neutron beta
decay with a dipole form, 1.27/(1+Q2/MA2). MA=1.02±.02
NUANCE Breakdown of the QE Contributions to the MB Yields
What is Observed? CCQE
   C    7 p, 5 n (  )
12
MiniBooNE
Theory
consensus
Note: MiniBooNE Eν
inferred from μ- energy.
Assumes a symmetric
uncertainty do to Fermi
momentum.
Other Experimental Results from CCQE
Diagrams of Some Short Range Correlations
nucleonnucleon
hole
Some RPA p-h
diagrams
from Martini et al.
PR C80, 065501
External
interaction
Particle lines
crossed by
are put on shell
delta
virtual SRI π,ρ, contact
Correlation
Exchange Current and pionic
correlation diagrams in Amaro et al.
PR C82 044601
Exchange
 C C Q E ( , C )   C C Q E ( , C )
12
Martini et al RPA
12
Further Reaction
Amaro et al; Phys. Lett. B696 151(2011). arXiv:1010.1708 [nucl-th]
Included Meson Exchange into their SuperScaling (L) Approach
Straight impulse App.
Meson Exchange Included
Angular Dependence
Experiment shows
surplus yield at
backward angles,
and low energy
MORE RPA
J.Nieves, I. Ruiz and M.J. Vincente Vacas arXiv: 1102.2777 [hep-ph]
MiniBooNE
SciBooNE
OTHER INTERESTING APPROACHES: Relativistic Potentials-FSI
arXiv:1104.0125 Scaling Function, Spectral Function and Nucleon Momentum
Distribution in Nuclei A.N. Antonov, M.V. Ivanov, J.A. Caballero, M.B. Barbaro, J.M.
Udias, E. Moya de Guerra, T.W. Donnelly
arXiv:1103.0636
Relativistic descriptions of quasielastic charged-current neutrino-nucleus scattering:
application to scaling and superscaling ideas
Andrea Meucci, J.A. Caballero, C. Giusti, J.M. Udias
Can the CCQE Cross Section/N Exceed the Free N Cross
Section?
J. Carlson et al, PR C65, 024002 (2002)
Returning to the scaling of e-N QE cross section
Scaling variable
  2 m  q
y
2

 d
 d 2 
1
F ( y, q )  



 d  d   E X P  Z  ep (q )  N  en (q )  dy
Scaling function
LongitudinalTransverse
f L ,T  k F
R L ,T
In R elativistic FG f L  fT
G L ,T
GL 
GT 
qm
Q
2
ZG
2
Ep
2

2
ZG

2 qm
Q
 N G En
2
Mp
 N G Mn
2

PR C65, 024002 (2002) Investigated the increased transverse response between 3He and4He
Euclidian Response Functions:
r
E (| q |,  ) 


e
 (  E 0 )
PR C, 65, 024002 (cont.)
r
R T , L (| q |,  )d 
 th
r
E%(| q |,  ) can b e calcu lated as fo llo w s
q 
2
r
r  ( H  E 0 ) r
E%L (| q |,  )  0  ( q )e
 (q ) 0  e

r
r
0 (q )  (q ) 0
2 Am
q 
r r  ( H  E ) r r

r
r r r
0
2 Am
%
E T (| q |,  )  0 j T ( q )e
jT ( q ) 0  e
0 ( q ) jT ( q ) 0
2
q 
2
E T , L (q,  ) 
e 2m
(1  Q /  )
2
2 4
E%T , L (q,  )
Is presented, removing the trivial kinetic
energy dependence of the struck nucleon,
and the Q2 dependence of the nucleon FF
RT, L(|q|,ω): Standard response functions from experiment.
0 :Nuclear gs, E=E0 calculated with realistic NN and NNN interactions
H: True Hamiltonian with same interactions as above
τ: units (MeV)-1, determines the energy interval of the response function
NOTE: The group doing these calculation are extremely successful in
reproducing all the features of light nuclei; Masses, energy spectra,
transition rates, etc. for A≤12.
What are the EM Charge and Current Operators??
Covariant single nucleon vector current



j  u N ( p ') F1 (Q )  F (Q )
N
2
N
2
2
i q 
2m
N  n, p
uN ( p)
r r
r
(1 )
i q gr
neglecting relativistic corrections
 i, NR (q )   i e
a
r (1 ) r
r r
r
 i r iqr grr
i i r
i q gr
ji ( q ) 
{ pi , e } 
( q i   i )e
2m
2m
Current Conservation requires:
r
r r
 (q )
 gj ( q ) 
t
r r r
q gj ( q )  [ H ,  ]
H 
r2
pi
 2m   V
i
r2
pi
r r (1 ) r
r
(1 )
q gj i ( q )  [
,  i , N R ( q )]
2m
r r (2 ) r
r
r
(1 )
(1 )
q gj ij ( q )  [V ij ,  i , N R ( q )   j , N R ( q )]
J 

i
ji 

im
ji , m
i j
ij


V ijk
i jk
A 2-body current
q 
2
Results of Calculation for fixed q E
E( )
T ,L
(q,  ) 
e 2m
(1  Q /  )
2
2 4
E%T , L (q,  )
E( )
Note: QE
data
stops
here
Note: QE
data stops
here
4He
T
Let’s Look more carefully
ET(τ)
SRC produce interactions requiring large values of ω.
SRC + 2-body currents produce increased yield.
How Big are these Effects Relative to Free Nucleons?
Sum Rule at fixed 3 momentum transfer q:


S T , L (q ) 
r
r
r

2
S T , L (q,  )d   C T , L  0 O%T , L ( q )O T , L ( q ) 0  | 0 O T , L ( q ) 0 | 
 th
CT 
2m
2
, CL 
2
Z  p  N n
2
1
Z
S T , L (q )  C T .L E T , L (q,   0 )
Further Info from PR C65 024002
Effect is due to n-p pairs
Small effect of 2-body currents evaluated in the Fermi Gas:!!!
Some More Evidence
Amaro, et al, PHYSICAL REVIEW C 82, 044601 (2010)
Meson Exchange Diagrams.
2p-2h fin. sts.
Correlation Diagrams.
Knowing the incident neutrino energy to 10% or better
is crucial to neutrino oscillation experiments!.
Electron Scattering
56Fe,
q=0.55GeV/c
Meson
exchange
One body RFG
Correlation
Mosel, Lalakulich, Leitner
http://arxiv.org/abs/1107.3771
Absolute Normalization of the Flux
The d the rms charge radius is 2 fm.
pF≅50MeV/c
Spectator proton (pp) spectrum
pn
pp
pp
p’p
e+d inclusive scattering
With ω and Eμ known, Eν is determined!!
With q and ω known, y=(ω+2mω)1/2 - q <
O can be selected.
Conclusions
• Impulse approximation is inadequate to calculate ν-nucleus CCQE,
correlations and 2-body currents must be included. Transverse
vector response most important
• Experimentalists must carefully specify what they term QE.
•Establishing the incident neutrino energy is a very serious issue,
especially for neutrino oscillation experiments.
• Measured Cross Sections are essential. ν flux determination
absolutely necessary. Requires a good calculation of ν-d cross
section (<5%).
• More work, theory and experiment on e-N transverse response
might be the most fruitful avenue to pursue. Need to know the q
and ω of QE-like events for ω above the QE peak.
MINOS arxiv: 1104.0344 [hep-ex]
They’re Catching On
1107.3771
Mosel et al
1106.5374
Nieves et al