Mohammad Sajjad Athar

27-06-2012

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CONTENTS
Introduction
Charged Current Quasielastic Scattering
Charged Current One Pion ProductionIncoherent pion production

Coherent pion production
 Charged Current Kaon Production
Charged Current Eta Production
Associated particle production
Charged Current Deep Inelastic Scattering

Conclusions
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Neutrino Event Rates

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ATMOSPHERIC NEUTRINO FLUX

M. Honda

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Most of the neutrino experiments are being performed in the few GeV energyregion. In this energy region the contribution to the cross section comes fromthe quasielastic, inelastic and deep-inelastic processes.

QEX

RES

R
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QUASIELASTIC CHARGED
CURRENT SCATTERING
Phys. Rev. C61 (2000) 028501
Eur. Phys. J. A24 (2005) 459

Phys. Lett. B 641 (2006) 159
Eur. Phys. J. A 43 (2010) 209
J. Phys. G3 7 (2010) 015005
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Quasielastic Charged Current Reaction
Basic l - neutron reaction taking place in nucleus

Matrix elementwhere

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Hadronic current

F1V (q2), F2V (q2), FAV (q2) and FPV (q2) are isovector
form factors

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F1V (0) = 1.0, F2V (0) = 3.7059, Dipole mass Mv = 0.84 GeV
μp = 1.7928473 μN, μn = - 1.9130427 μN, n = 5.6Isovector axial form factor

and pseudoscalar form factor

Axial Charge FA (0) = - 1.26 and axial dipole mass MA = 1.1 GeV

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Different values of MA
World Average Value -NOMAD -1.026 ± 0.02 GeV

1.05 ± 0.02 ± 0.06 GeV

K2K (SciBar detector) -1.14 ± 0.11 GeV

K2K (SciFi detector) - 1.20 ± 0.12 GeV
MiniBooNE experiment - 1.23 ± 0.2 GeV

MiniBooNE experiment - 1.35 ± 0.2 GeV
MINERvA experiment- 1.0GeV
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Axial mass dependence on total cross section

 σ increases by about 15 % when MA is changed from1.05 to 1.21 GeV for neutrino and by about 7- 8 % in
the case of antineutrino at E=1GeV
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The double differential cross section for the process

in the Lab frame is given by

The hadronic tensor is determined by the W± boson self-energyПµνW(q), in the nuclear medium
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First we evaluate the neutrino selfenergy, Σλν(k;ρ) moving in
the nuclear matter of density ρλλλ

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The sum over helicities leads to traces in the Dirac’s space

The neutrino disappears from the elastic flux, by inducing
1p-1h, 2p-2h, Δ-h excitations or creating pions, etc…. at
a rate given by

We get the imaginary part of Σν by using the cutkosky’s rules

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Those states are then placed on shell by taking the imaginary
part of the propagator, self-energy, etc.

Γdtds provides a probability times a differential of area, which
is a contribution to the (νl,l) cross section

The nuclear cross section is given by

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The differential scattering cross section

Which results the hadronic tensor as

when compared with

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Therefore, for 1p1h, one haswith the CC nucleon tensor given byand27-06-2012

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The expression for the hadronic tensor

The d3p integrations above can be analytically done. This is doneby taking the imaginary part of the Lindhard function,

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→Lindhard function corresponding to the p-h excitation

The imaginary part of the Lindhard function isobtained by using the relation

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With these nuclear effects

Due to Coulomb interaction, energy & momentum ofoutgoing lepton gets modified which has been taken
into account in an effective momentum approximation.
Effective energy of the lepton in the coulomb field of the
final nucleus

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Random Phase Approximation (RPA)
In the nucleus there are many nucleons which stronglyinteracts among themselves resulting in a modification of thecoupling strength as compared to the free -N couplingstrength.

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Generally N-N interaction is described by one boson
exchange modelFor  exchange (interaction with a pseudoscalar fieldand for  exchange (interaction with a vector field

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These changes are calculated by considering theinteraction of p-h excitations in the nuclear medium in
Random phase approximation (RPA)
The N-N interaction for the RPA correlations in thenuclear medium
results in the form of geometricseries.
Due to this the Lindhard function modifies to27-06-201223

In the presence of nuclear medium effect, the total
scattering cross section σ(E )27-06-201224

Total cross section for  induced quasielastic process% reduction in thecross section
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Comparison of our local Fermi gas model (FGM) withother versions of Fermi gas model% reduction in thecross section
EPJA 43 (2010)‫‏‬209

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Total Scattering cross section for CCQE process in 12C
AIP Conf. Proc., 1189, 60 (2009)27-06-201227

Differential cross section in the muon kinetic
energy for  induced CCQE process in 12C
AIP Conf. Proc., 1189, 60 (2009)27-06-201228

Differential cross sections averaged over atmosphericneutrino flux
EPJA, 43 209 (2010)‫‏‬Quasielastic process% reduction in the distribution

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Inelastic pion production

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Inelastic pion production
In the neutrino energy region below few GeV, the major
contribution to the lepton event rates would come from thepions produced by theΔ excitation of the nucleon which
subsequently decays into a nucleon and a pion.
Contribution for the one pion production process

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Incoherent Process
In the intermediate energy region of about 1 GeV thepion production from nucleons is dominated by Δ –dominance.

Leptonic current
Hadronic current
Matrix Element27-06-201232

is the N – Δ transitions operators which isequal to the sum of vector and axial vector part

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Parameterization for the N – Δ transitions form factors[Lalakulich et al. PRD 74, 014009(2006)]

where

Axial vector form factor

C3V(0) = 2.13, C4V(0) = -1.51, C5V (0) = 0.48, C5A (0)= 1.2, MV is the vector dipole mass, M A is the axial dipolemass.
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Axial mass dependence on total cross sections

σ increases by about 15 % when MA is changed from1.05 to 1.21 GeV for neutrino and by about 7-8 % in
the case of antineutrino at E = 1GeV
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 In the nuclear medium delta decay mainly through theΔ→N channel. The momenta of the final nucleons have to be
above the Fermi momentum kF of the nucleon in the nucleus
thus inhibiting the decay. This leads to a modification in thedelta decay width In the nuclear medium there are additional decay channels

open due to two body and three body absorption processes
like ΔN →NN and ΔNN→NNN through which Δ disappear in
the nuclear medium without producing a pion while a two bodyΔ absorption process like ΔN → NN gives rise to some morepions.

These nuclear medium effect on the Δ propagation
are included by describing the mass and the decay
width in terms of the self energy of Δ(ΣΔ).
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Due to these changes Ѓ and MΔ modify

E.Oset and L.L.Salcedo, Nucl. Phys. A468 631 (1987);
C.Garcia Recio, E.Oset, L.L.Salcedo, .. Nucl. Phys. A 526 685 (1991).

Final state interaction effects of pions is also taken into
account by using Monte Carlo simulation code given by
Vicente Vacas [ Private Communication].

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Total cross section for induced incoherent
CC1+production process
IJMPE 18, 1469 (2009)% reduction in the cross section

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27-06-201239

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Differential cross section in the pion kinetic energy
for  induced CC1+ production process in 12C with
ME + FSI effect

AIP Conf. Proc.,27-06-2012
1189, 60 (2009)41

Total cross section for  induced CC1 production process in12C with ME + FSI effect

CC Incoherent

AIP Conf. Proc. 1189, 60 (2009)27-06-201242

Incoherent process

EPJA, 43 209 (2010)‫‏‬% reduction in the distribution

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Coherent Process
Nuclear effects in neutrino induced coherent pion production at K2K
and MiniBooNE.

Phys. Rev. Lett. 96 (2006) 241801
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Total cross section for  induced coherent
CC1+ production process

27 June 201245

JPG 37, 015005 (2010)‫‏‬27-06-2012

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Ratio R(E) for Polystyrene(C8H8)
JPG 37, 015005 (2010)‫‏‬27-06-201247

Ratio R(E) in water (H2O): T2K‫‏‬Experiment
JPG 37, 015005 (2010)‫‏‬27-06-2012

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STRANGE PARTICLEPRODUCTION
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Minerva experiment is planning to study strange particle
production with high statistics.

In performing the background studies in the analysis ofneutrino oscillation experiments.
In estimation of atmospheric neutrino ΔS backgrounds
for nucleon-decay searches.
LAGUNA plans to use detectors like GLACIER,
MEMPHYS or LENA to test physics at the GUT scale

Extending the proton (and bound neutron) lifetime
sensitivities up to 1035 years

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K+ life time ~ 12.8 ns and they decay into K+ → μ+ νμ(63.43 %) or K+ → π + + π0 (21.13 %)Main background sources are muon neutrinos produced bycosmic rays interactions

These neutrinos interact with the detector producing
muon in the energy range where search for proton decay
is performed.

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Different types of weak processes accompanying
strange particle/particles
The first category comprises charged current ΔS = 0
reactions:27-06-201252

Different types of weak processes accompanying
strange particle/particles

Strange particle ΔS = 0 associated production canalso proceed via Neutral Current reactions:27-06-201253

Different types of weak processes accompanying
strange particle/particles
Charged-current ΔS = 1 reactions make up a second category. Produced
final state contains single strange K-mesons. The reaction cross sections
are Cabibbo suppressed relative to ΔS = 0 reactions.

(ΔS= 1 processes have no NC contributions as they involve achange in strangeness and therefore in charge.)
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Different types of weak processes accompanying
strange particle/particles
Δ‫‏‬S = Δ‫‏‬Q selection rule restricts Δ‫‏‬S = 1 single hyperon
production to Anti-ν rather than ν reactions

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Single Kaon Production

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Single Kaon Production
PRD 82 (2010) 033001

PRD 85 (2012) 013014

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The basic reaction for the neutrino induced charged
current kaon production isfor which the differential scattering cross section is given by

where M is the matrix element given by

the leptonic current is given by,

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Feynman diagrams for the neutrino induced process: u-channel Kaon inflight , u-channel, contact term, Kaon in flight, pion/eta in flight

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Contributions to the hadronic current forneutrino induced process

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Contributions to the hadronic current for
anti-neutrino induced process

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PRD 82,033001,2010

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PHYSICAL REVIEW D 82, 033001 (2010)27-06-2012

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PRD 82,033001,2010

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PHYSICAL REVIEW D 82, 033001 (2010)27-06-201265

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Flux averaged cross section for ν N →lNK in 10-42 cm2 at MA = 1 GeV

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27-06-201268Eta Production

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Associated Production

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Associated Production

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BACKGROUND TERMS

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DEEP INELASTIC SCATTERING(DIS)

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Phenomenological and Theoretical studies of nuclear
medium effects

Most of the study of nuclear medium effect in the case of
ν(anti-ν)-A DIS has been done phenomenologically by thevarious groups like the works ofHirai et al.(hep-ph/1102.3479)
Eskola et al.(JHEP 04 065 2009)

Kovarik et al.(PRL 106 122301 2011) and others

M S Athar

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There are only a few calculations for the ν(anti-ν)-A DIS where thedynamical origin of nuclear medium effect has been considered.

Kulagin & Petti PRD 76 094023 2007

Our group

PLB 668 133 (2008)

NPA 857 29 (2011)
PRC 84 054610 (2011)
PRC 85 055201 (2012)

These calculations have been performed to understand thecontribution of various effects like Fermi motion, Pauli blocking,shadowing and anti-shadowing and pion and rho cloud contributions.

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Deep Inelastic Scattering

The basic reaction for ν-N scattering is

The differential scattering cross section of ν-N scattering is:

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Hadronic tensor :Leptonic tensor :27-06-201280

Differential scattering cross section:
Fermi coupling constantwhere27-06-2012

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The structure functions F2(x) and F3(x) are given as

Using Callan Gross relation

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We use a theoretical spectral function to describe themomentum distribution of nucleons in nuclei.
The spectral functions has been calculated using Lehmann’srepresentation for the relativistic nucleon propagator.

Nuclear many body theory is used to calculate it for aninteracting Fermi sea in nuclear matter.
A local density approximation is then applied to translatethese results to finite nuclei.
P. Fernandez de Cordoba and E. Oset, Phys. Rev. C 46 1697 (1992).
E. Marco, E. Oset and P. Fernandez de Cordoba, Nucl. Phys. A 611 (1996) 484

M S Athar

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In the present formalism the neutrino – nucleus cross sections areobtained in terms of neutrino self energy Σ(k) in the nuclear
medium:The probability per unit time for the neutrino
to collide with nucleons when travellingthrough nuclear matter is:

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The total cross section for neutrino scattering from an elementof volume d3r and surface dS in the nucleus is given by

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Παβ is the W self energy in the nuclear medium

The imaginary part of the neutrino self energy is evaluated by means of Cutkosky
rules by cutting the Feynman diagram of W self energy along the horizontal line
which puts the particles corresponding to the cut propagators on the mass shellby replacing the fermion and meson propagators by their imaginary part as

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The F2A structure function in nucleus for electromagnetic interactions is:whereThe deuteron structure function has been calculated using the same formalism
as we have used for F2A for a general nucleus , but performing the convolution
with the deuteron wave function squared instead of spectral function which is
written as:

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Electromagnetic structure function in deuteron27-06-201288

Ratio F2Be/F2D vs x and F2C/F2D vs x

M S A, I. Ruiz Simo and M. J. Vicente Vacas Nucl. Phys. A 857, 29 (2011)27-06-2012

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The expression of F2A and F3A structure function due to nuclear
medium effects like Fermi motion and binding energy in thepresent model are obtained as:

Defining γ as

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F2Fe / F2Dvsx in Iron

Nucl. Phys. A 857, 29 (2011)27-06-2012

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F2Fe / F2D

vsx in Iron

PRC 84, 054610 (2011)27-06-2012

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F3Fe / F3D

vsx in Iron

PRC 84, 054610 (2011)27-06-201293

xF3 vs Q2 at different values of x in Iron

PRC 84, 054610 (2011)27-06-201294

Differential scattering cross section at E=65 GeV for Neutrino case in Iron

PRC 84, 054610 (2011)27-06-201295

Differential scattering cross section at E=65 GeV for Antineutrino case in Iron

PRC 84, 054610 (2011)27-06-201296Modified structure functions when target nucleus is treated asnonisoscalar27-06-2012

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F2 vs Q2 at different value of x in Lead

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xF3 vs Q2 at different value of x in Lead

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Differential scattering cross section for Neutrino at Eν=25 GeV in Lead

27-06-2012100Differential scattering cross section for Anti-ν at Eν=25 GeV in Lead

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Conclusions
Total cross section
A. Charged current quasielastic process
The % reduction in the cross section with & without RPA correlations
as compared to the cross section calculated for the neutrino – nucleon
process is following

B. Charged current incoherent pion production process

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C. Charged current coherent pion production process

Axial Mass dependence
We find that  increases by about 15% when MA is changed from 1.05 GeV
to 1.21 GeV in the case of CCQE lepton production process as well as in thecase of charged current incoherent one pion production process.

Form factor dependence
For the quasielastic process ---- very small change in the peak region of Q2

For the incoherent one pion production variation is of about 5% in the peakregion of Q2 .

Kaon Production
1. We have obtained cross sections that are around 2 orders ofmagnitude smaller than for pion production at the neutrinoenergies of 1GeV. For antineutrino induced process thecontribution is larger than in the case of neutrino.

2. These cross sections are large enough to be measured in theMinerva and T2K experiments.
3. In the energy region of atmospheric neutrino experiments or in
the energy region of 0.8-1.2GeV, the studied processes are thedominant source of Kaons.

M. Sajjad Athar, AMU, India

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DIS
Nature of F2EM A/F2EM D and F2W A/F2W D are similar,
while F3W A/F3WD is different.

Nuclear Medium Effects are in better agreement withNuTeV , CDHSW and CHOROUS experimental results.
 Effect of pion and rho cloud contributions are important forx<0.4
The effect is 16-18% in Carbon, 20-22% in Iron and 22-24% in
Lead at x=0.1 which decreases to 6-8% in Iron and Lead atx=0.4.
 Effects of shadowing and anti-shadowing are important for x<0.15
The effect is 12-14% in Carbon, 20-22% in Iron while it is 2224% in Lead at x=0.05 which decreases to 6-7% in Iron andLead at x=0.1.
1027-06-20125

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