Problems In Quasi-Elastic Neutrino-Nucleus Scattering

Gerry GarveyLos Alamos Nat. Lab.

ECT Trento December 14,2011

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• 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??

Outline

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• QES is a model in which the results of elastic lepton-nucleon 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.

What is Quasi-elastic Scattering?

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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 naively treated (by experimentalists) as readily calculable, experimentally identifiable and allowing assignment of the neutrino energy. Some 40 calculations published since 2005 Neutrino Osc Length: 1.27Δmij

2(ev2)× (L(km)/Eν(GeV)) atmos. Scale : Δm23

2=10-3 L≈103 E≈103 LBNE sterile Scale: Δm2S

2=1 L≈1 E≈1 SBNE

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“ *** LSND effect rises from the dead… ?“

Long-Baseline News, May 2010:

Sterile neutrinos

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.

And it’s Getting Worse!!

Cosmology, decay of sterile neutrino (dark matter), calibration of Ga solar neutrino detectors, increased flux from reactors, larger

HIDDEN CLUE: Pulsars, including one inside this "guitar nebula," provide evidence of sterile neutrinos. Scientific American

e

e p n e cross section,

C

Ni

Pb

QES in NP originated in e-Nucleus Scattering

Moniz et al PRL 1971

Simple Fermi Gas 2 parameter , SE, pF

Impulse Approximation

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Inclusive Electron Scattering

Electron BeamΔ/E ~10-

3

Magnetic Spectograph

Scattered electron

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

(E,0,0, p), (E ', p 'sin,0, p 'cos )

E E '

rq

rp

rp '

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(d / de )Mott 2 cos2( / 2)/ E sin4( / 2)

p ', N J p, N i

uN (p ') | [F1

N (q2 ) F2N (q2 ) q ] | uN (p)

Fi 3 (q2 )

1

2(Fi

S (q2 ) 3FiV (q2 )) 2mF2

S (0) 'p n 0.120

F1S (0) 1 F1

V (0)=1 2mF2V (0) 'p n 3.706

dde

Mott

E '

E0

GEN ,2 (q2 ) GM

N ,2 (q2 )

1 2GM

2 (q2 ) tan2 (2

)

GE (q2 ) F1(q2 ) F2 (q2 ) GM (q2 ) F1(q

2 ) F2 (q2 )

Quasi-Elastic Electron Scattering

Q2 q2 2 q2 2

Q2

4M 2Single nucleon vector currentSingle nucleon vector current

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Scaling in Electron Quasi-elastic Scattering (1) The energy transferred by the electron (ω), to a single nucleon with initial Fermi momentum

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.

The scaling function F(y,q) is formed from the measured cross section at 3- momentum transfer q, dividing out the incoherent single nucleon contributions at that three momentum transfer.

Instead of presenting the data as a function of q and ωit can be expressed in terms of a single variable y.

F(y,q) d 2

dd

EXP

1

Z ep (q) N en (q)

ddy

k TN Es TR

[(rk

rq)2 m2 ]

1

2 m Es Erecoil

[k||2 2k||q q2 k

2 m2 ]1

2 m Es Erecoil

neglect Es , Erecoil ,k

k|| 2 2m q y

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Scaling in Electron Quasi-elastic Scattering (2) 3He

Raw data Scaled

Excuses (reasons) for failure y > 0: meson exchange, pion production, tail of delta resonance.

At y 2 2m q 0

q2 2 2m 2 Q2 kinimatics for scattering off a nucleon at rest

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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)

yRFG

kFermi

mN

kFermi

( 1 1 )

2mN , Q2 / 4mN

2 , q / 2m

A new dimensionless scaling variable is employed

Note linear scale: not bad for 0

Serious divergence above 0

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Separating Super Scaling into its Longitudinal and Transverse Responses Phys. Rev. C60, 065502 (1999)

Longitudinal

Transverse

The responses are normalized so that in a Relativistic Fermi Gas Model:

fL ( ) fT ( )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

Transverse

Trouble even with the GOLD standard 13

Contrast of e-N with ν-N Experiments

Electron BeamΔ/E ~10-3

Magnetic Spectograph

Scattered electron

Neutrino Beam ΔE/<E>~1 l -

Very Different Situation from inclusive electron scattering!!

Electron

Neutrino-Mode FluxNeutrino

What’s ω ??? Don’t know Eν !!!

What’s q ????QE peak???

Eν

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Zero π contributions ??

MiniBooNE Setup

neutrino mode: νμ→ νe oscillation search

antineutrino mode: νμ→ νe oscillation search

ν mode flux

ν mode flux

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While inclusive electron scattering and CCQE neutrino experiments are very different, the theory hardly changes.

ddQ2

GF

2 cos2 C

8E2

A(Q2 ) B(Q2 )s u

M 2

C(Q2 )

s u

M 2

2

A(Q2 ) Q2

4f1

2 (Q2

M 2 4) f1 f2 (

4Q2

M 2) f2

2 (Q2

M 2

Q4

4M 4) g1

2 (4 Q2

M 2)

B(Q2 ) Q2 ( f1 f2 )g1

C(Q2 ) M 2

4( f1

2 f22 Q2

4M 2 g1

2 )

s u 4ME Q2

Neutrino (+), Anti-Neutrino(-) Nucleon CCQE Cross Section

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/MA

2). MA=1.02±.02

Charged lepton mass=0

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NUANCE Breakdown of the QE Contributions to the MB Yields

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MiniBooNE

Theoryconsensus

What is Observed?

CCQE 12 C 7 p,5n( )

EQE

2(M n Es ) (M n Es )2 m2 M p

2

2(M n Es E E2 m

2 cos)

Experiment assigns the neutrino energy as if the neutrino scatters off a neutron at rest

ΔE

QE is due solely to the neutron’s Fermi gas momentum.

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MA=1.35

Other Experimental Results from CCQE

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Some RPA p-h diagrams from Martini et al.PR C80, 065501

External interactionnucleonnucleon-

hole

deltavirtual SRI π,ρ, contact

Particle lines crossed by are put on shell

Exchange Current and pionic correlation diagrams in Amaro et al. PR C82 044601

Exchange

Correlation

Diagrams of Some Short Range Correlations

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Martini et al.

Enhanced: Tranverse Axial ??

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CCQE (,12 C) CCQE ( ,12 C)

Martini et al RPA

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Further ReactionAmaro 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

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MORE RPAJ.Nieves, I. Ruiz and M.J. Vincente Vacas arXiv: 1102.2777 [hep-ph]

MiniBooNE

SciBooNE

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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:1103.0636Relativistic descriptions of quasielastic charged-current neutrino-nucleus scattering: application to scaling and superscaling ideasAndrea Meucci, J.A. Caballero, C. Giusti, J.M. Udias

OTHER INTERESTING APPROACHES: Relativistic Potentials-FSI

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How could the CCQE Cross Section/N Exceed the Free N Cross Section?

J. Carlson et al, PR C65, 024002 (2002)

Back to scaling the e-N QE cross section:

F(y,q) d 2

dd

EXP

1

Z ep (q) N en (q)

ddy

y 2 2m q Scaling variable

Scaled function

GL qm

Q2ZGEp

2 NGEn2

GT Q2

2qmZGMp

2 NGMn2

fL ,T kF

RL ,T

GL ,T

In Relativistic FG fL fT

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PR C65, 024002 (2002) Investigated the increased transverse response between 3He and4He

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Euclidian Response Functions: PR C, 65, 024002 (cont.)

0 :Nuclear gs, E=E0 calculated with realistic NN and NNN interactions

H: True Hamiltonian with same interactions as above

RT, L(|q|,ω): Standard response functions from experiment.

τ: units (MeV)-1, determines the energy interval of the response function

NOTE: The group doing the WF calculations are extremely successful in reproducing all features in light nuclei; Masses, energy spectra, transition rates, etc. for A≤12.

E(|rq |, ) e ( E0 )

th

RT ,L (|rq |, )d

%E(|rq |, ) can be calculated as follows

%EL (|rq |, ) 0 (

rq)e (H E0 )(

rq) 0 e

q22 Am 0(

rq) (

rq) 0

%ET (|rq |, ) 0

rjT (

rq)e (H E0 )

rjT (

rq) 0 e

q22 Am 0(

rq)

rjT (

rq) 0

Is presented, removing the trivial kinetic energy dependence of the struck nucleon, and the Q2 dependence of the nucleon FF

ET ,L (q, ) e

q22m

(1Q2 / 2 )4%ET ,L (q, )

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What are the EM Charge and Current Operators??Covariant single nucleon vector current

j uN (p ') F1N (Q2 ) F2

N (Q2 )i q

2muN (p) N n, p

i,NR(1) (

rq) ie

irqg

rr

rji

(1)(rq)

i

2m{rpi ,e

irqg

rr }

iia

2m(rqi

r i )e

irqg

rr

neglecting relativistic corrections

Current Conservation requires:

grj (

rq)

(rq)

t

rqg

rj (

rq) [H ,] H

rpi

2

2mi Vij

i j Vijk

i jk

rqg

rji

(1)(rq) [

rpi

2

2m,i,NR

(1) (rq)]

rqg

rjij

(2)(rq) [Vij ,i,NR

(1) (rq) j ,NR

(1) (rq)] A 2-body current

J jii ji,m

im

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Results of Calculation for fixed q

4He T

E( ) E( )

Note: QE data stops here

Note: QE data stops here

ET ,L (q, )

eq22m

(1Q2 / 2 )4%ET ,L (q, )

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ET(τ)

Let’s Look more carefully

SRC produce interactions requiring large values of ω.SRC + 2-body currents produce increased yield.

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How Big are these Effects Relative to Free Nucleons?

Sum Rule at fixed 3 momentum transfer q:

ST ,L (q) ST ,L (q, ) th

d CT ,L 0 %OT ,L (

rq)OT ,L (

rq) 0 | 0 OT ,L (

rq) 0 |2

CT 2m2

Z p2 Nn

2, CL

1

Z

ST ,L (q) CT .LET ,L (q, 0)

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Further Info from PR C65 024002

Small effect of 2-body currents evaluated in the Fermi Gas:!!!

Effect is due to n-p pairs

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“In contrast to earlier speculations [21] that the large enhancement from two-body currents was due to the presence of strong tensor correlations in the ground state, it is now clear that this enhancement arises from the concerted interplay of tensor interactions and correlations in both ground and scattering states. A successful prediction of the longitudinal and transverse response functions in the quasielastic region demands an accurate description of nuclear dynamics, based on realistic interactions and currents.”

[21] J. Carlson and R. Schiavilla, Phys. Rev. C 49, R2880 (1994)

Conclusion from P.R. C65 024002 (2002)

Can such effects be reliably simulated with RPA with plane wave initial and final states?

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Some More EvidenceAmaro, et al, PHYSICAL REVIEW C 82, 044601 (2010)

56Fe, q=0.55GeV/c

One body RFG

Meson Exchange Diagrams. Correlation Diagrams.2p-2h fin. sts.

Meson exchange

Correlation

Electron Scattering

Knowing the incident neutrino energy to 10% or better is crucial to neutrino oscillation experiments!.

Fully relativistic calculation!!!

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http://arxiv.org/abs/1107.3771

Mosel, Lalakulich, Leitner

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Eν a Critical Issue for Oscillation Experiments

e+d inclusive scattering

The d the rms charge radius is 2 fm. pF≅50MeV/c

Absolute Normalization of the Flux

pp

pppn

p’p

Spectator proton (pp) spectrum

With ω and Eμ known, Eν is determined!!With q and ω known, y=(ω+2mω)1/2 - q < O can be selected.

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Conclusions• (NR)Impulse approximation is inadequate to calculate ν-nucleus CCQE, correlations and 2-body currents must be included. Transverse vector response and interference terms most important.

• Experimentalists must carefully specify what they term QE.

• Reliably assigning the incident neutrino energy is very important for neutrino oscillation experiments.

• Measured Cross Sections are essential. ν flux determination absolutely necessary. Requires a reliable 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 well above the QE peak.

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An Experimentalist’s Questions Why are no errors provided with cross section calculations?

How are large enhancements obtained with plane wave I&F final states?

A MB neutrino energy scale is clearly wrong. How to do better? (Eμ(θμ) Dist (Eν))

Are effects shown in PR C82, 044601 (2010) correct? They are frighteningly large!

Does pion exchange enhance the amplitude of the transverse axial current??

Given the critical role of the transverse vector amplitude shouldn’t all neutrino CS calculation check that amplitude against electron scattering

How well can be calculated? When both p are detected?

Why are experimentalists so cavalier about their knowledge of neutrino flux?

d 2 p

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