Neutrino-Nucleon Cross-Sections at Energies of Megaton ...€¦ · Neutrino-Nucleon Cross-Sections...

Neutrino-Nucleon Cross-Sections Neutrino-Nucleon Cross-Sections at Energies of Megaton-Scale Detectorsat Energies of Megaton-Scale Detectors

Part II Part II

Askhat GazizovAskhat Gazizov

IP NASB, Minsk, BelarusIP NASB, Minsk, Belarus DESY-Zeuthen, GermanyDESY-Zeuthen, Germany

24.06.2015

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KinematicsKinematics

CFA-2015 3

KinematicsKinematics

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

S=(k+P)2=M 2

+2M E

g

CFA-2015 10

KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

Q2=−q2

S=(k+P)2=M 2

+2M E

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

Q2=−q2

S=(k+P)2=M 2

+2M E

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

Q2=−q2

y =q⋅Pk⋅P

=1−E 'E

S=(k+P)2=M 2

+2M E

g

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KinematicsKinematics

νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

Q2=−q2

y =q⋅Pk⋅P

=1−E 'E

S=(k+P)2=M 2

+2M E

x =Q2

2 M E y

g

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Simplest case – Simplest case – eeee-- scattering scattering

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

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Simplest case – Simplest case – eeee-- scattering scattering

e

W+

e-

e- e

W+

e-

e- e

At LO QCD just put a quark mass mq instead of the electron for a

scattering off a nucleon and sum the contributions from all quarks.Valence and sea quarks.

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

Quasi-elastic scattering (QES) for CC:

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

Quasi-elastic scattering (QES) for CC:

Single production (RES):

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

Quasi-elastic scattering (QES) for CC:

Single production (RES): Resonances with masses 1234 MeV ≤ M

N* ≤ 1970 MeV

are included.

CFA-2015 27

Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

Quasi-elastic scattering (QES) for CC:

Single production (RES): Resonances with masses 1234 MeV ≤ M

N* ≤ 1970 MeV

are included. Single kaon production: Very small!

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Contributions to the total cross-sectionContributions to the total cross-section

σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS

Elastic scattering (ES) in case of NC:

Quasi-elastic scattering (QES) for CC:

Single production (RES): Resonances with masses 1234 MeV ≤ M

N* ≤ 1970 MeV

are included. Single kaon production: Very small! Deep inelastic scattering (DIS): > 2 in the final state XX

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ν̄μ+N →μ++X

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νμ+N →μ−+ X

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Ratios Ratios nn//p p and and nn//pp

E [GeV]

Rat

ios

(E)

Rat

ios

(E)

Check model parameteriation using data for such ratios.

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Total Total NN and and

N N Cross-SectionsCross-Sections

E [GeV]

tot(E

) [1

0-3

8 cm

2 ]

Cross-sections grow proportional to E.

At higher energies just power-law growthdue to sea-quarks density increase.

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N N RatiosRatios

E [GeV]

Ra

tios

(E)

Ra

tios

(E)

At low energies ratio is due to kinematics.Both and quark are left-handed: J = 0. Isotropic distribution.

is right-handed: J = 1,

and

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ντ+N →τ−+X

Tevatron protons pro-duce charm mesons.

appears in the charm

decays.

produces 's's in the

nuclear emulsion. 4 -events registered,while 0.2 expected ifno

One event with a kink from the -decay.

DONUT – Direct Observation of the NU TauDONUT – Direct Observation of the NU Tau

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ν̄τ+N →τ++ X

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νl +N →νl +X

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ν̄l +N →ν̄l +X

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MiniBooNEMiniBooNE

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MiniBooNEMiniBooNE

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MiniBooNEMiniBooNEMiniBooNE employs the NUANCE v3 NUANCE v3 event generator to estimate neutrino interaction rates in the CHCH

22 target medium.

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MiniBooNEMiniBooNEMiniBooNE employs the NUANCE v3 NUANCE v3 event generator to estimate neutrino interaction rates in the CHCH

22 target medium.

The most precision expe-riment. 2-differential cross-sections.

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MiniBooNEMiniBooNEMiniBooNE employs the NUANCE v3 NUANCE v3 event generator to estimate neutrino interaction rates in the CHCH

22 target medium.

The most precision expe-riment. 2-differential cross-sections.Discrepancy between different experiments data is significant.

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MiniBooNEMiniBooNEMiniBooNE employs the NUANCE v3 NUANCE v3 event generator to estimate neutrino interaction rates in the CHCH

22 target medium.

The most precision expe-riment. 2-differential cross-sections.Discrepancy between different experiments data is significant.We avoided discussion of low energies.Irrelevant for the future PINGU / ORCA megaton experi-ments.

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ES and QES off proton/neutronES and QES off proton/neutron

Eν , th⩾(ml +MN ' )

2−M N

2

2 MN

≃ml (1+ml

2 MN

)

νl +n→ l−+ p

ν̄l + p→ l−+nνl+ p /n→νl+ p/nQESQES ESES

These processes dominate at low energies.There is practically no threshold energy for the ES.ES.The threshold energy for QES with M

N = m

p or m

n

( mn - m

p ≈ 1.293 MeV )

For τ-lepton production with m/m

16.8, m

/m

N 1.9

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Theoretical approach to QESTheoretical approach to QES

See e.g. A. Strumia & F. Vissani, Phys. Lett. B564:42-54, 2003

In terms of the Mandelstam variables

the differential cross-section of QES

where

A(t), B(t) and C(t) may be expressed in terms of vector and axial vector form factors. They are parametrized by the vectormass and the axial-vector mass M V

2 =0.71 GeV2 M AQES

≈1.02 GeV

with FFAA(0) (0) ≈≈ -1.267 -1.267

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QES Cross Sections vs. DataQES Cross Sections vs. Data

E [GeV]

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QES Cross Sections vs. DataQES Cross Sections vs. Data

E [GeV]

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QES Cross Sections vs. DataQES Cross Sections vs. Data

Many experimental data differ.

E [GeV]

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QES Cross Sections vs. DataQES Cross Sections vs. Data

Many experimental data differ.Different targets, different -flux-es, different methods.

E [GeV]

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QES Cross Sections vs. DataQES Cross Sections vs. Data

Many experimental data differ.Different targets, different -flux-es, different methods.A global fit needs a careful choice of data to be included.

E [GeV]

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Sensitivity of QES to MSensitivity of QES to MAA

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Sensitivity of QES to MSensitivity of QES to MAA

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Sensitivity of QES to MSensitivity of QES to MAA

QES cross-sections grow with axial mass MM

AA increasing.

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Sensitivity of QES to MSensitivity of QES to MAA

QES cross-sections grow with axial mass MM

AA increasing.

The threshold of -production is ~30 times higher than in -production case.

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Sensitivity of QES to MSensitivity of QES to MAA

QES cross-sections grow with axial mass MM

AA increasing.

The threshold of -production is ~30 times higher than in -production case.

At high energies QES cross-sections for and coincide.

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Sensitivity of ES to MSensitivity of ES to MAA

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QES off Oxygen TargetQES off Oxygen Target

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QES off Oxygen TargetQES off Oxygen Target

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QES off Oxygen TargetQES off Oxygen Target

At small energies nuclear corrections are important.

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QES off Oxygen TargetQES off Oxygen Target

At small energies nuclear corrections are important.

Shown calculations using standard RFGRFG model.

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QES off Oxygen TargetQES off Oxygen Target

At small energies nuclear corrections are important.

Shown calculations using standard RFGRFG model.

Note that such targets do not exit. But HH

22OO is close.

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QES off Oxygen TargetQES off Oxygen Target

At small energies nuclear corrections are important.

Shown calculations using standard RFGRFG model.

Note that such targets do not exit. But HH

22OO is close.

The difference is just at small energies lower than interesting for PINGU.

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QES off Oxygen TargetQES off Oxygen Target

At small energies nuclear corrections are important.

Shown calculations using standard RFGRFG model.

Note that such targets do not exit. But HH

22OO is close.

The difference is just at small energies lower than interesting for PINGU.

But for future HyperK lower energies are important.

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ES off Oxygen TargetES off Oxygen Target

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Single Pion Production (RES)Single Pion Production (RES)

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Single Pion Production (RES)Single Pion Production (RES)

Processes are discussed in the framework of the Rein&SehgalRein&Sehgal (RS) approach.

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Single Pion Production (RES)Single Pion Production (RES)

Processes are discussed in the framework of the Rein&SehgalRein&Sehgal (RS) approach.

It is based on the Feynman-Kislinger-RavndalFeynman-Kislinger-Ravndal (FKR) relativistic quark model, applied to -excitations of baryon resonances NN∗∗.

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Single Pion Production (RES)Single Pion Production (RES)

Processes are discussed in the framework of the Rein&SehgalRein&Sehgal (RS) approach.

It is based on the Feynman-Kislinger-RavndalFeynman-Kislinger-Ravndal (FKR) relativistic quark model, applied to -excitations of baryon resonances NN∗∗.

Amplitudes of such processes are a coherentcoherent sum over A's A's of all known NN ∗ ∗ = πNπN resonances.

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Single Pion Production (RES)Single Pion Production (RES)

Processes are discussed in the framework of the Rein&SehgalRein&Sehgal (RS) approach.

It is based on the Feynman-Kislinger-RavndalFeynman-Kislinger-Ravndal (FKR) relativistic quark model, applied to -excitations of baryon resonances NN∗∗.

Amplitudes of such processes are a coherentcoherent sum over A's A's of all known NN ∗ ∗ = πNπN resonances.

Vector and axial-vector transition form-factors GGV,AV,A(Q(Q22) ) are parametrized by the standard vector mass MMVV = 0.84 GeV = 0.84 GeV, the same as in the (Q)ES dipole model, and by axial mass .

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Single Pion Production (RES)Single Pion Production (RES)Processes are discussed in the framework of the Rein&SehgalRein&Sehgal (RS) approach.

It is based on the Feynman-Kislinger-RavndalFeynman-Kislinger-Ravndal (FKR) relativistic quark model, applied to -excitations of baryon resonances NN∗∗.

Amplitudes of such processes are a coherentcoherent sum over A's A's of all known NN ∗ ∗ = πNπN resonances.

Vector and axial-vector transition form-factors GGV,AV,A(Q(Q22) ) are parametrized by the standard vector mass MMVV = 0.84 GeV = 0.84 GeV, the same as in the (Q)ES dipole model, and by axial mass .

The RS model was extended (ExRS) to account for the finite mass of secondary leptons in the case of CC-scattering.

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Nucleon Resonances with M < 2 GeVNucleon Resonances with M < 2 GeV according to PDG-2014

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Nucleon Resonances with M < 2 GeVNucleon Resonances with M < 2 GeV according to PDG-2014

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Nucleon Resonances with M < 2 GeVNucleon Resonances with M < 2 GeV according to PDG-2014

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Nucleon Resonances with M < 2 GeVNucleon Resonances with M < 2 GeV according to PDG-2014

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Single Pion Production (RES), cont.Single Pion Production (RES), cont.

Besides resonances, a non-resonance background is to be added ( general problem!).

Relative normalization of contributions from different resonances is a problem, though 1232) 1232) dominates.

To avoid a double counting with DIS, the maximum mass of the bound πNπN state is to be defined – the WWcutcut.

We find Wcut = 1.4 GeV to be the best fit in our approach.

It's choice is a general problem as well. Experiments also present date for different Wcut from 1.1 GeV up to 2 GeV.

It will be discussed later.

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Sensitivity of RES to MSensitivity of RES to MAA (CC 1) (CC 1)

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Sensitivity of RES to MSensitivity of RES to MAA (CC 1) (CC 1)

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Sensitivity of RES to MSensitivity of RES to MAA (CC 1) (CC 1)

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Sensitivity of RES to MSensitivity of RES to MAA (CC 2) (CC 2)

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Sensitivity of RES to MSensitivity of RES to MAA (CC 3) (CC 3)

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Sensitivity of RES to MSensitivity of RES to MAA (NC ) (NC )

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Sensitivity of CC RES to WSensitivity of CC RES to Wcutcut

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Sensitivity of CC RES to WSensitivity of CC RES to Wcutcut

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Sensitivity of CC RES to WSensitivity of CC RES to Wcutcut

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RES off Oxygen TargetRES off Oxygen Target

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Deep Inelastic ScatteringDeep Inelastic Scattering

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

DIS dominates at E (3 - 5) GeV.

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

DIS dominates at E (3 - 5) GeV.

While (Q)ES and RES cross-sections are constant at high energies due to constraint on Q2, DIS cross-sections grow with energy.

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

DIS dominates at E (3 - 5) GeV.

While (Q)ES and RES cross-sections are constant at high energies due to constraint on Q2, DIS cross-sections grow with energy.

For a q scattering on a quark at rest with

d σ

dQ 2=

GF2

π1

(1+Q2/MW

2)2

⇒ σ(S)=GF

2 MW2

πS

S+MW2

S≃2mq E

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

DIS dominates at E (3 - 5) GeV.

While (Q)ES and RES cross-sections are constant at high energies due to constraint on Q2, DIS cross-sections grow with energy.

For a q scattering on a quark at rest with

At ; at

d σ

dQ 2=

GF2

π1

(1+Q2/MW

2)2

⇒ σ(S)=GF

2 MW2

πS

S+MW2

S≃2mq E

S≪MW2

σ (E)∝E S≫MW2 σ (E)⇒σ0=

GF2 MW

2

π

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Deep Inelastic ScatteringDeep Inelastic ScatteringMore than 2 + N in the final state.

DIS dominates at E (3 - 5) GeV.

While (Q)ES and RES cross-sections are constant at high energies due to constraint on Q2, DIS cross-sections grow with energy.

For a q scattering on a quark at rest with

At ; at

DIS is the sum of cross-sections on all quarks in a nucleon.

d σ

dQ 2=

GF2

π1

(1+Q2/MW

2)2

⇒ σ(S)=GF

2 MW2

πS

S+MW2

S≃2mq E

S≪MW2

σ (E)∝E S≫MW2 σ (E)⇒σ0=

GF2 MW

2

π

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QCD and Structure FunctionsQCD and Structure Functions At LOLO of perturbative QCD nucleon consists of valence quarks, “sea”-quarks and gluons.

Sea quarks are qq-pairs.They arise from qg- and gg-interactions.

For unpolorized nucleons – 5 Sfs.

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Nachtmann Variable

x

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Extrapolations of SFs to small QExtrapolations of SFs to small Q22

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Dependence of Dependence of NNCC DIS on WCC DIS on Wcutcut

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Dependence of Dependence of NNCC DIS on WCC DIS on Wcutcut

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Dependence of Dependence of NNC DIS on WC DIS on Wcutcut

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Optimization of WOptimization of Wcut cut

for for NN

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Optimization of WOptimization of Wcut cut

for for NN

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Kinematic LimitsKinematic Limits

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Kinematic Limits for CC DIS at E=5 GeVKinematic Limits for CC DIS at E=5 GeV

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Kinematic Limits for CC DIS at E=10 GeVKinematic Limits for CC DIS at E=10 GeV

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Kinematic Limits for NC DIS at E=10 GeVKinematic Limits for NC DIS at E=10 GeV

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TMC SFs Dependence on x TMC SFs Dependence on x

PDF are from ABM-11ABM-11 and OPENQCDRAD OPENQCDRAD by Alekhin, Bluemlein, Moch.

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Approach of Bodek&Yang Approach of Bodek&Yang

https://www.jlab.org/conferences/neutrino/talks/yang_uk.pdf

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B&Y Pseudo NLOB&Y Pseudo NLO

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2xF2xF11 and F and F

LL in B&Y Approach in B&Y Approach

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Comparison of B&Y Model with ResonancesComparison of B&Y Model with Resonances

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MC GeneratorsMC Generators Neutrino event generators available in the market.

NEUTNEUT – developed for Kamiokande and used by Super-Kamiokande, K2K, SciBooNE, T2K.

NUANCE NUANCE – developed for the IMB experiment and used by MiniBooNE.

NEUGENNEUGEN - developed for the SOUDAN and updated for MINOS.

ANISANIS – developed for AMANDA and used by IceCube.

General purpose MC generators

FLUKAFLUKA

GENIEGENIE – ArgoNeut, MicroBooNE, MINOS, MINERνA, T2K.Continuously updated.

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GIBUUGIBUU – theorist group approach. It provides an unified transport framework at MeV - GeV energies. Numerous nuclear effects included.

NuWroNuWro - developed by the Wroclaw group. Accounts for the impact of nuclear effects on directly observable quantities with all the final state interactions included.

MC Generators, cont.MC Generators, cont.

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Conclusions

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

Data are controversive and the choice for global fit needs serious expertise.

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

Data are controversive and the choice for global fit needs serious expertise.

With proposed set of models and parameters we fit the known data but at lowest energies.

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

Data are controversive and the choice for global fit needs serious expertise.

With proposed set of models and parameters we fit the known data but at lowest energies.

Uncertainties in the choice of axial masses and Wcut for RES and in extrapolations to small Q2 in DIS are correlated.

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

Data are controversive and the choice for global fit needs serious expertise.

With proposed set of models and parameters we fit the known data but at lowest energies.

Uncertainties in the choice of axial masses and Wcut for RES and in extrapolations to small Q2 in DIS are correlated.

An account for TMC, lepton mass, pQCD corrections are important.

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ConclusionsAccurate account for neutrino-nucleon cross-sections is important.

Data are controversive and the choice for global fit needs serious expertise.

With proposed set of models and parameters we fit the known data but at lowest energies.

Uncertainties in the choice of axial masses and Wcut for RES and in extrapolations to small Q2 in DIS are correlated.

An account for TMC, lepton mass, pQCD corrections are important.

New precision data may change the set of parameters.

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Thank you!

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QES: from Strumia&VissaniQES: from Strumia&Vissani

ξ=k p−k n=3.706 where kp and k

n – anomalous magnetic moments in units

of nuclear magneton μN=e ℏ /2mp

fi and g

i are real function of t = -Q2. Approximation:

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