Neutrino cross sections in few hundred MeV energy region Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with

Neutrino cross sections in few hundred MeV energy

region

Jan T. SobczykInstitute of Theoretical Physics,

University of Wrocław

(in collaboration with A. Ankowski and J. Nowak)

Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 2

Plan of the talk:

1. Introduction

2. Quasi-elastic scattering off free target (form-factors, axial mass).

3. Significance of single pion production.

3. Nuclear effects – general remarks.

4. Nuclear effects – numerical results (models: Fermi gas, spectral function, momentum dependent effective potential).

5. Conclusions.


Total neutrino – nucleon CC cross sections

We distinguish:

• quasi-elastic• single pion production („RES region”, e.g. W<=2 GeV)• more inelastic („DIS region”)

Focus on few hundred MeV neutrino energies:quasi-elastic region.

Plots from Wrocław MC generator

neutrino anti-neutrino


The aim of analysis

)(

)()(

)(

e

eDR

„Double ratio”:

Targets: water (argon computations are not yet finished).

Basic problem: How sensible the double ratio is to nuclear effectsin the energy range of few hundred MeV?

As intermediate step also „ratios”: )(

)(,)(

)(

ee

RR


Quasi-elastic reaction - theory

nlp

pln

CVC – use electromagnetic data

PCAC

We need the axial form-factor; the standard dipole form

gA =1.26 from neutron decay;MA a free parameter (the only one)

The value of axial mass is obtained from experimental data.

M

QFqQF

M

QFqiQF P

A

)()(

2

)()(

2

52

5

222

1

22

222 )(2)(

Qm

QFMQF A

P

2

2

2

2

1

)(

A

AA

M

Q

gQF


Quasi-elastic reaction

The limiting value depends onthe axial mass

Under assumption of dipole vector form-factors:

(from Naumov)

(A. Ankowski)

Huge experimental uncertainty


Quasi-elastic reaction

One can find better fits to the existing data,BBBA2005

Dipole electromagnetic form-factors:

7.4)91.1(79.21 neutronproton

(from R. Bradford talk at NuInt05)


Quasi-elastic reaction – first step

Free target cross sections:

)(

)(,)(

)(

ee

RR


Quasi-elastic reaction - uncertainties

Do theoretical/experimental uncertainties: • axial mass

• electromagnetic form-factors

have an impact on cross-section ratios?


Axial mass …

… no change!



… no change!

Electromagnetic form-factors …



Single pion production - kinematics

Threshold for the pion production


Single pion production

3 CC channels for neutrino and 3 CC channels for anti-neutrino reactions.

The characteristic feature is that the dominant contribution comes from resonance excitation (mainly Δ):

nlln

nllp

pllp00

0

nlln

plln

pllp0


Single pion productionWhat is a significance of spp channels in few hundred MeV energy region?What is their impact on total cross sections ratios?


Relevance of single pion production

)()1(21

)()1()( 1

qelRqelR

qelRqelRR

)()1(21

)()1()( 1

qelRqelR

qelRqelRR

)(

)(,)(

)(

ee

RR


Relevance of single pion production

)()1(21

)()1()( 1

qelDRqelDR

qelDRqelDRDR

)(

)()(

)(

e

eDR

Target: free nucleons

Relevant at <0.35% levelfor E<500MeV.


Nuclear effects – general remarks

The treatment is energy-dependent:

• low energies: shell model• intermediate energies: CRPA• higher energies: impulse approximation (Fermi gas, spectral function)

What does it mean: „low”, „intermediate”, „higher”?!

Peter Vogel (nucl-th/9901027):

For electron neutrino energies starting from ≈ 200 MeV CRPA and FG give rise to very similar total and differentialcross-sections.

Giampaolo Co’:

Impulse approximation methods make sense for momentum transfer > 400 MeV.


Nuclear effects – general remarks

The methods well justified in GeV region will be used and …

… the results which follow should be treated with caution.

Impulse approximation based computations will be presented.

The hope is that ratios are not very much sensitive to details of nuclear effects modelling.

The methods are reliable for E>250 MeV (?).


Impulse approximation

(from Ch. Maieron, XX Max Born Symposium)

• neutrino interacts with an individual (bound) nucleons

• „final state interactions” (FSI) follows (does not change inclusive cross-section)

The simplest realization:Fermi gas model defined by 2 parameters.

Step 1: Fermi gasStep 2: Spectral function


(from O. Benhar et al. hep-ph/0516116)

Spectral function

Realistic distribution of momenta

(from A. Ankowski)

Short range correlations (SRC):correlated pairs of nucleons


Spectral function

Spectral function for oxygen

1s

1p (1/2)1p (3/2)

(from O. Benhar)

Spectral function approachis parameter free.But FSI/Pauli blockingeffects must beadded.


Effective (momentum dependent) potential

(from Juszczak, Nowak, Sobczyk, Eur. Phys. J. C39 (2005) 195)

(from Leitner, Alvarez-Ruso, Mosel, nucl-th/0601103)

Step 1: LDA (Fermi gas + nucleus density profile)Step 2: LDA + effective potential


Spectral function - results

??? ???

??? ???


Effective potential – results

??? ???

??????

PreliminaryPreliminary

PreliminaryPreliminary


Spectral function - ratios

FG – Fermi gas modelSF – spectral function with Pauli blocking

)(

)(,)(

)(

ee

Binding energy 27 MeVis very important at low energies.The model is obviously not appropriateat low energies.

???

???


Effective potential – ratios

???

???

)(

)(,)(

)(

ee

Preliminary

Preliminary


Spectral function - ratios

freenuclear

freenuclear

RR

RRR

2

1)(

FG – Fermi gas modelSF – spectral function with Pauli blocking

Measure of relevance ofnuclear effects:

freenuclear

freenuclear

RR

RRR

2

1)(

???



???

???


freenuclear

freenuclear

RR

RRR

2

1)(

freenuclear

freenuclear

RR

RRR

2

1)(

Preliminary

Preliminary




freenuclear

freenuclear

RR

RRR

2

1)(

freenuclear

freenuclear

RR

RRR

2

1)(

Preliminary

Preliminary


Spectral function – double ratios

)(

)()(

)(

e

eDR

Targets: free nucleons and water

???


Spectral function – double ratiosTargets: free nucleons and water

freenuclear

freenuclearnuclear

DRDR

DRDRR

2

1)(

At 250 MeV the reduction of DR is ~5%At 300 MeV the reduction of DR is ~2.5%

???


Effective potential – double ratios

???

)(

)()(

)(

e

eDR


Preliminary

Preliminary


Effective potential – double ratios

)(

)()(

)(

e

eDR

freenuclear

freenuclearnuclear

DRDR

DRDRR

2

1)(


???

Preliminary

Preliminary


Conclusions

The energy region 250-500 MeV has been investigated.

The caution is necessary: the methods are well justified only at higher energies.

„Ratios” R (and automatically also „double ratios” - DR)are not sensitive to uncertainties of free quasi-elastic description.

Pion production changes DR by less than ~0.4%.

For energies ~250 MeV nuclear effects can reduce DR by 2-6%.

The sensitivity of DR to nuclear effects seems to decrease quicklyfor higher energies.


The end


Fermi gas – dependence on Fermi momentum

(the same value of binding energy: 27 MeV)


Comparison with Amaro-Nieves group

(very recent paper: hep-ph/0604042)

FG – Fermi gas modelSF – spectral function with Pauli blockingLDA – local density approximationOxygen – effective potential

Documents

Neutrino cross sections in few hundred MeV energy region Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with