neutrino cross sections in few hundred mev energy region
DESCRIPTION
Neutrino cross sections in few hundred MeV energy region. Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with A. Ankowski and J. Nowak). Plan of the talk: Introduction Quasi-elastic scattering off free target (form-factors, axial mass). - PowerPoint PPT PresentationTRANSCRIPT
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.
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 3
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 4
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 5
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 6
Quasi-elastic reaction
The limiting value depends onthe axial mass
Under assumption of dipole vector form-factors:
(from Naumov)
(A. Ankowski)
Huge experimental uncertainty
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 7
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)
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 8
Quasi-elastic reaction – first step
Free target cross sections:
)(
)(,)(
)(
ee
RR
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 9
Quasi-elastic reaction - uncertainties
Do theoretical/experimental uncertainties: • axial mass
• electromagnetic form-factors
have an impact on cross-section ratios?
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 10
Axial mass …
… no change!
Quasi-elastic reaction - uncertainties
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 11
… no change!
Electromagnetic form-factors …
Quasi-elastic reaction - uncertainties
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 12
Single pion production - kinematics
Threshold for the pion production
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 13
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 14
Single pion productionWhat is a significance of spp channels in few hundred MeV energy region?What is their impact on total cross sections ratios?
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 15
Relevance of single pion production
)()1(21
)()1()( 1
qelRqelR
qelRqelRR
)()1(21
)()1()( 1
qelRqelR
qelRqelRR
)(
)(,)(
)(
ee
RR
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 16
Relevance of single pion production
)()1(21
)()1()( 1
qelDRqelDR
qelDRqelDRDR
)(
)()(
)(
e
eDR
Target: free nucleons
Relevant at <0.35% levelfor E<500MeV.
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 17
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.
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 18
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 (?).
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 19
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 20
(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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 21
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.
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 22
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
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 23
Spectral function - results
??? ???
??? ???
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 24
Effective potential – results
??? ???
??????
PreliminaryPreliminary
PreliminaryPreliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 25
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.
???
???
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 26
Effective potential – ratios
???
???
)(
)(,)(
)(
ee
Preliminary
Preliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 27
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)(
???
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 28
Effective potential – ratios
???
???
Measure of relevance ofnuclear effects:
freenuclear
freenuclear
RR
RRR
2
1)(
freenuclear
freenuclear
RR
RRR
2
1)(
Preliminary
Preliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 29
Effective potential – ratios
Measure of relevance ofnuclear effects:
freenuclear
freenuclear
RR
RRR
2
1)(
freenuclear
freenuclear
RR
RRR
2
1)(
Preliminary
Preliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 30
Spectral function – double ratios
)(
)()(
)(
e
eDR
Targets: free nucleons and water
???
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 31
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%
???
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 32
Effective potential – double ratios
???
)(
)()(
)(
e
eDR
Targets: free nucleons and water
Preliminary
Preliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 33
Effective potential – double ratios
)(
)()(
)(
e
eDR
freenuclear
freenuclearnuclear
DRDR
DRDRR
2
1)(
Targets: free nucleons and water
???
Preliminary
Preliminary
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 34
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.
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 35
The end
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 36
Fermi gas – dependence on Fermi momentum
(the same value of binding energy: 27 MeV)
Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006 37
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