Neutrino-Nucleon Cross-Sections at Energies of Megaton ...€¦ · Neutrino-Nucleon Cross-Sections at Energies of Megaton-Scale Detectors Part II Askhat Gazizov IP NASB, ... scattering

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

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νl+N→ l−+X (CC )

ν̄l+N→ l++X (CC )

νl+N →νl+X (NC )

ν̄l+N →ν̄l+X (NC )

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g

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g

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g

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k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')g

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k =(E , k⃗ )

P=(M , 0⃗)

PX=(EX , p⃗ X)

k '=(E ' , k⃗ ')

S=(k+P)2=M 2

+2M E

g

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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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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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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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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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e

W+

e-

e- e

W+

e-

e- e

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e

W+

e-

e- e

W+

e-

e- e

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e

W+

e-

e- e

W+

e-

e- e

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e

W+

e-

e- e

W+

e-

e- e

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e

W+

e-

e- e

W+

e-

e- e

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e

W+

e-

e- e

W+

e-

e- e

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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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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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σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS


Quasi-elastic scattering (QES) for CC:

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σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS



Single production (RES):

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σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS



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

N* ≤ 1970 MeV

are included.

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σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS




N* ≤ 1970 MeV

are included. Single kaon production: Very small!

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σν Ntot

=σν N(Q )ES

⊗σν N1 π

⊗σν N1 K

⊗σν NDIS




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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22 target medium.

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

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22 target medium.

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

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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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E [GeV]

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Many experimental data differ.

E [GeV]

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

E [GeV]

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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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QES cross-sections grow with axial mass MM

AA increasing.

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AA increasing.

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

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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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At small energies nuclear corrections are important.

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Shown calculations using standard RFGRFG model.

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Note that such targets do not exit. But HH

22OO is close.

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22OO is close.

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

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

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

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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.



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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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 (NC ) (NC )

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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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DIS dominates at E (3 - 5) GeV.

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

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

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

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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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Neutrino-Nucleon Cross-Sections at Energies of Megaton ...€¦ · Neutrino-Nucleon Cross-Sections at Energies of Megaton-Scale Detectors Part II Askhat Gazizov IP NASB, ... scattering