Nuwro - Neutrino MC Event Generator

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NuWro - neutrino MC event generator

Tomasz Golan

28.04.2017, UW HEP Seminar Outline

Neutrino source νe Detector

′ α 1. Motivation να νµ ντ

2. NuWro event generator

3. Final State Interactions

3500 MB data Total 3000 EL on carbon np-nh 2500 EL on hydrogen Irreducible background 2000 Other backgrounds

1500

4. MB NCEL data analysis No. of events 1000

500

0 0 100 200 300 400 500 600 700 Reconstructed kinetic energy (MeV)

Tomasz Golan NuWro @ HEP UW 2 / 61 Introduction Basic properties of neutrinos

■ 1 Three generations 2 -spin, no electric charge, small mass Introduction of fermions H Neutrino properties (extremely hard to detect) I II III PMNS matrix Probability of oscillation u c t γ Neutrino oscillation ■ Measurement idea Interactions with elementary particles

Example: T2K BOSONS

QUARKS s g Energy reconstruction → electroweak theory (Standard Model) d b

MC generators ■ ν νµ ν 0 NuWro Interactions with nucleons e τ Z Final state interactions → form factors e µ τ ± MB NCEL analysis → parton distribution functions LEPTONS W Backup slides ■ Interactions with nuclei → nuclear eﬀects

■ The neutrino ﬂavor state is a superposition of the mass states:

|ναi = i Uαi |νii νe The neutrino producedP in α state να νβ νµ ντ can be measured in β state. The phenomenon is called neutrino oscillation.

Tomasz Golan NuWro @ HEP UW 4 / 61 Pontecorvo-Maki-Nakagawa-Sakata matrix

The PMNS matrix deﬁnes the mass mixing in the lepton sector:

−iδ 1 0 0 c13 0 s13e c12 s12 0 U = 0 c23 s23 0 1 0 −s12 c12 0    iδ    0 −s23 c23 −s13e 0 c13 0 0 1      

cij = cos θij sij = sin θij θij - mixing angels δ - CP phase factor

Measurements:

2 ■ Solar, reactor and accelerator: sin (2θ12) = 0.846 ± 0.021

2 ■ Atmospheric: sin (2θ23) > 0.92

2 ■ Reactor: sin (2θ13) = 0.093 ± 0.008

δ can be measured if and only if all mixing angles are nonzero. If δ 6= 0 CP is violated.

Tomasz Golan NuWro @ HEP UW 5 / 61 Probability of oscillation

Introduction 2 Neutrino properties P (να → νβ) = |hνβ(x)|να(y)i| = δαβ PMNS matrix 2 Probability of oscillation ∗ ∗ 2 ∆mij L Neutrino oscillation − 4 Re U UiβUα U sin Measurement idea αi j jβ 4E Example: T2K i>j Energy reconstruction 2 2 2 X ∆mij ≡ mi − mj 2 MC generators ∆m L + 2 Im U ∗ U U U ∗ sin2 ij NuWro αi iβ αj jβ 2E Final state interactions i>j X MB NCEL analysis

Backup slides

L - traveled distance (ﬁxed), E - neutrino energy (will be discussed)

Measurements:

■ 2 −5 2 Solar neutrinos: ∆m21 = (7.53 ± 0.18) · 10 eV

■ 2 −3 2 Atmospheric neutrinos: |∆m32| = (2.44 ± 0.06) · 10 eV

Tomasz Golan NuWro @ HEP UW 6 / 61 Neutrino oscillation

The probability of neutrino oscillation depends on: Normal hierarchy Inverted hierarchy 2 2 ■ m3 m2 What we want to measure: 2 ∆m21 2 2 ◆ three mixing angles - already measured ∆m32 m1

2 2 ◆ the diﬀerence between squared mass of the mass m2 ∆m31 2 2 states - the sign of ∆m is still unknown, ∆m21 32 2 2 what is the mass hierarchy? m1 m3 ? ? ◆ the CP phase factor - is the CP symmetry broken? 0 0

? P (¯να → ν¯β) = P (νβ → να) = P (να → νβ)

C + − ■ What we need to know: charge conjugation P ◆ the distance traveled by a neutrino + + parity transformation ◆ neutrino energy - this is a problem T + + time reversal

Tomasz Golan NuWro @ HEP UW 7 / 61 How to measure neutrino oscillation?

Neutrino source ν Detector Introduction e Neutrino properties ′ PMNS matrix Probability of oscillation Neutrino oscillation α/α Measurement idea να Example: T2K Energy reconstruction νµ ντ MC generators

NuWro

Final state interactions

MB NCEL analysis Backup slides Disappearance method

Number of α-ﬂavor Number of α-ﬂavor neutrinos charged leptons

Appearance method

Number of α-ﬂavor Number of α′-ﬂavor neutrinos charged leptons

Tomasz Golan NuWro @ HEP UW 8 / 61 Example: T2K

Target Proton beam Decay volume

π + α νµ beam 295 km να 41.4 m µ + 2.5o

39.3 m

■ Oﬀ-axis beam

■ Cherenkov detector (Super-Kamiokande)

■ 50 000 tons of ultra-pure water

■ Only charged leptons and ﬁnal state charged hadrons are visible

■ The neutrino energy is unknown

Tomasz Golan NuWro @ HEP UW 9 / 61 The problem with neutrino energy reconstruction

′ ′ Introduction l(k ) p(p ) Neutrino properties PMNS matrix Probability of oscillation In the case of neutrino scattering oﬀ Neutrino oscillation Measurement idea nucleon at rest neutrino energy can be Example: T2K W Energy reconstruction calculated from lepton kinematics: MC generators ν(k) n(p) NuWro

Final state interactions 2 ′2 ′ 2 Mp = p =(p + k − k ) Quasi-elastic scattering MB NCEL analysis

Backup slides 2 2 2 Mp = ml + Mn − 2MnEl k = (Eν, 0, 0,Eν) + 2Eν(Mn − El + |~pl| cos θl) ′ k = (El, ~pl)

2 2 2 p = (Mp, 0, 0, 0) Mp − Mn − ml + 2MnEl ′ Eν = p = p + q 2(Mn − El + |~pl| cos θl) q = k − k′

Tomasz Golan NuWro @ HEP UW 10 / 61 The problem with neutrino energy reconstruction

Introduction ■ Usually, the energy reconstruction procedure is based on Neutrino properties PMNS matrix quasi-elastic neutrino-nucleon scattering: Probability of oscillation Neutrino oscillation Measurement idea Example: T2K Energy reconstruction 2 2 2 REC Mp − (Mn − EB) − ml + 2(Mn − EB)El MC generators Eν = 2(Mn − EB − El + |~pl| cos θl) NuWro

Final state interactions

MB NCEL analysis

Backup slides Nucleus Impulse Approximation l ν θl

No Fermi motion π nucleon(s) Binding Potential

Tomasz Golan NuWro @ HEP UW 10 / 61 The problem with neutrino energy reconstruction

Final state interactions

MB NCEL analysis

Backup slides Nucleus l Never judge an event ν θl by its ﬁnal state particles! π nucleon(s)

Tomasz Golan NuWro @ HEP UW 10 / 61 Monte Carlo generators Buﬀon’s needle problem

Suppose we have a ﬂoor made of parallel strips of wood, each the same width, and we drop a needle onto the ﬂoor. What is the probability that the needle will lie across a line between two strips?

Georges-Louis Leclerc, blue are good Comte de Buﬀon 18th century red are bad

Monte Carlo without computers

If needle length (l) < lines width (t): MC experiment was performed by Mario Lazzarini in 1901 by throwing 3408 2l P = needles: tπ which can be used to estimate π: 2l · 3408 355 π = = = 3.14159292 2l t · #red 113 π = tP

Tomasz Golan NuWro @ HEP UW 12 / 61 From Solitaire to Monte Carlo method

■ Stanislaw Ulam was a Polish mathematician

■ He invented the Monte Carlo method while playing solitaire

■ The method was used in Los Alamos, performed by ENIAC computer

■ What is a probability of success in solitaire? ◆ Too complex for an analytical calculations

◆ Lets try N = 100 times and count wins

◆ With N → ∞ we are getting closer to correct result

Tomasz Golan NuWro @ HEP UW 13 / 61 MC integration (hit-or-miss method)

Lets do the following integration using MC method: Introduction MC generators 1 1 2 1 Buﬀon’s needle problem 1 1 x 1 From Solitaire to MC f(x)dx = x dx = = Hit-or-miss method 2 2 2 4 Crude method Z0 Z0 0 Methods comparison Accept-reject y MC generators Why do we need them? ■ take a random point from The main problem Cooking generator the [0, 1] × [0, 1] square NuWro 1 1 Final state interactions ■ compare it to your f(x) f(x) = 2 x MB NCEL analysis Backup slides ■ repeat N times

■ count n points below the function

■ you results is given by 1 x

1 n n f(x)dx = P · = N N Z0

Tomasz Golan NuWro @ HEP UW 14 / 61 MC integration (crude method)

Lets do the following integration using MC method once again: Introduction MC generators 1 1 2 1 Buﬀon’s needle problem 1 1 x 1 From Solitaire to MC f(x)dx = x dx = = Hit-or-miss method 2 2 2 4 Crude method Z0 Z0 0 Methods comparison Accept-reject ■ One can approximate y MC generators Why do we need them? integral The main problem Cooking generator b N NuWro b − a f(x)dx ≈ f(xi) 1 Final state interactions N f(x) = x Za i=1 2 MB NCEL analysis X Backup slides where xi is a random number from [a, b]

■ It can be shown that crude method is more accurate x than hit-or-miss

■ We will skip the math and look at some comparisons

Tomasz Golan NuWro @ HEP UW 15 / 61 N = 100 (hit-or-miss) N = 100 (crude) 0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 MC result MC MC result

0.1 0.1

0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 Run number Run number

N = 1000 (hit-or-miss) N = 1000 (crude) 0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2 MC result MC MC result

0.1 0.1

0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 Run number Run number Acceptance-rejection method

fmax Introduction For generating events 0.6 MC generators according to a distribution. Buﬀon’s needle problem 2 From Solitaire to MC 3 −x

y 0.4 Hit-or-miss method f(x) = x · e Crude method Methods comparison Accept-reject 0.2 MC generators ■ Evaluate fmax ≥ max(f) Why do we need them? The main problem Cooking generator 0 Note: fmax > max(f) will 0 0.5 1 NuWro aﬀect performance, but the x Final state interactions result will be still correct MB NCEL analysis

Backup slides ■ Generate random x 0.4

■ Accept x with P = f(x)

f y max 0.2 ◆ generate a random u from [0, fmax]

◆ 0 accept if u < f(x) 0 0.5 1 x

Tomasz Golan NuWro @ HEP UW 17 / 61 Monte Carlo event generators

■ Monte Carlo generators Introduction basically do two things: MC generators Buﬀon’s needle problem From Solitaire to MC ◆ integrate cross Hit-or-miss method Crude method section formulas Methods comparison Accept-reject MC generators ◆ Why do we need them? generate events The main problem Cooking generator using accept-reject method NuWro with many optimization tricks Final state interactions MB NCEL analysis ■ Physicists have been using them since ENIAC Backup slides ■ Some common generators used in neutrino community:

◆ transport of particles through matter: Geant4, FLUKA

◆ neutrino interactions: GENIE, GIBUU, NEUT, NUANCE, NuWro

Tomasz Golan NuWro @ HEP UW 18 / 61 Why do we need them?

Introduction

MC generators Buﬀon’s needle problem From Solitaire to MC Hit-or-miss method Crude method Theory MC generators Experiment Methods comparison Accept-reject MC generators Why do we need them? The main problem Cooking generator

NuWro ■ Final state interactions Monte Carlo event generators connect experiment (what we

MB NCEL analysis see) and theory (what we think we should see)

Backup slides ■ Any neutrino analysis relies on MC generators

■ From neutrino beam simulations, through neutrino interactions, to detector simulations

■ Used to evaluate systematic uncertainties, backgrounds, acceptances...

Tomasz Golan NuWro @ HEP UW 19 / 61 What is the main problem?

“You use Monte Carlo until you understand the problem” Introduction Mark Kac MC generators Buﬀon’s needle problem From Solitaire to MC Hit-or-miss method Crude method Methods comparison Accept-reject MC generators Why do we need them? ■ In perfect world MC The main problem MC Cooking generator generators would contain NuWro “pure” theoretical models Final state interactions MB NCEL analysis ■ In real world theory does Backup slides not cover everything input input

■ Neutrino and non-neutrino data are used to tune generators Data

Tomasz Golan NuWro @ HEP UW 20 / 61 How to build generator

INGREDIENTS: RECIPE:

Phase space

theory ν data other data

educated guesses

Tomasz Golan NuWro @ HEP UW 21 / 61 NuWro NuWro MC event generator

Introduction

MC generators

NuWro NuWro MC Dynamics (Q)EL scattering RES pion production Deep Inelastic Scattering π production formerly known as WroNG Impulse approximation Fermi gas Spectral function Two-body current COH pion production ■ It has been developed at Wroclaw University since 2006 Summary Final state interactions ◆ Currenly involved: Jan Sobczyk, Cezary Juszczak, MB NCEL analysis Krzysztof Graczyk, Tomasz Golan, Kajetan Niewczas Backup slides ◆ Signiﬁcant contribution: Jaros law Nowak, Jakub Zmuda,˙ Artur Kobyli´nski, Maciej Tabiszewski, Pawe l Przewlock i, Patrick Stowell, Luke Pickering

■ The authors were encouraged by prof. Danuta Kie lczewska

■ The open source code: https://github.com/nuwro/

Tomasz Golan NuWro @ HEP UW 23 / 61 “DIS”

“RES” MEC

Interactions

QEL COH

Detector eWro

Experiment NuWro Other

NuWro Beam on-line

Nuclear Fermi Nucleons Eﬀects Gas

Nucleus FSI Model

Spectral Pions Func- tion Implemented dynamics

■ 3 All major interaction channels QEL Total are implemented, for charged and ANL 12-feet [1] BNL 7-feet [4] 2.5 neutral current, covering MiniBooNE [2] Nomad [5] neutrino energy region from RES SciBooNE (NUET) [6] 2 ANL 12-feet [3] SciBooNE (NUANCE) [6] /GeV] a few hundreds MeV 2 DIS MINOS [7] cm (Impulse Approximation limit) 1.5 np-nh T2K [8] -38

to several TeV: [10 ν 1 /E σ

QEL (quasi-)elastic scattering 0.5

RES pion production through 0 a ∆ resonance excitation 0.1 1 10 Eν [GeV]

DIS more inelastic processes [1] PRD 19 (1979) 2521 [5] PLB 660 (2008) 19 [2] PRD 81 (2010) 092005 [6] PRD 83 (2011) 012005 COH coherent pion production [3] PRD 16 (1977) 3103 [7] PRD 81 (2011) 072002 np-nh two body current contribution [4] PRD 25 (1982) 617 [8] PRD 87 (2013) 092003

Tomasz Golan NuWro @ HEP UW 25 / 61 (Quasi-)elastic scattering

■ Llewellyn-Smith model is ν/l N’ Introduction used for charged current MC generators quasi-elastic scattering Z0/W ± NuWro NuWro MC Dynamics ■ (Q)EL scattering Not much diﬀerence here RES pion production between generators (but Deep Inelastic Scattering ν N π production Impulse approximation default parameters) Fermi gas Spectral function Two-body current COH pion production Summary ■ Final state interactions Nucleon structure is MB NCEL analysis parametrized by form Backup slides factors

■ Vector → Conserved Vector Current (CVC)

■ Pseudo-scalar → Partially Conserved Axial Current (PCAC)

■ Axial → dipole form with one free parameter (axial mass, MA)

Tomasz Golan NuWro @ HEP UW 26 / 61 Resonance pion production

Introduction ■ Most of generators (like π MC generators NEUT and GENIE) uses ν/l NuWro ∆ N’ NuWro MC Rein-Sehgal model Dynamics 0 ± (Q)EL scattering Z /W RES pion production Deep Inelastic Scattering ■ RS model describes single π production Impulse approximation pion production through Fermi gas ν N Spectral function baryon resonances below Two-body current COH pion production W = 2 GeV Summary

Final state interactions MB NCEL analysis ■ In NuWro Adler-Rarita-Schwinger formalism is used to Backup slides calculate ∆ resonance explicitly

■ Non-resonant background is estimated using quark-parton model

Tomasz Golan NuWro @ HEP UW 27 / 61 Deep inelastic scattering [DIS]

Introduction ■ Quark-parton model is used MC generators for deep inelastic scattering ν/l NuWro NuWro MC 0 ± Dynamics ■ Z /W (Q)EL scattering Bodek-Young modiﬁcation RES pion production Deep Inelastic Scattering to the parton distributions π production 2 Impulse approximation at low Q is included by Fermi gas ν Spectral function most generators Two-body current COH pion production Summary

Final state interactions MB NCEL analysis Hadronization Backup slides ■ Hadronization is the process of formation hadrons from quarks Hadrons ■ Pythia is widely used at high invariant masses

Tomasz Golan NuWro @ HEP UW 28 / 61 Pion production in NuWro

Introduction π production MC generators

NuWro NuWro MC Dynamics (Q)EL scattering RES pion production Deep Inelastic Scattering π production ∆ resonance Quark-parton Impulse approximation Fermi gas Adler-Rarita-Schwinger model Spectral function Two-body current COH pion production GeV .6 Summary 1 W > 1.6 GeV Final state interactions W < MB NCEL analysis

Backup slides RES DIS

RES/DIS distinguish is arbitrary for each MC generator!

Tomasz Golan NuWro @ HEP UW 29 / 61 Impulse approximation

■ In impulse approximation p Introduction neutrino interacts with a p MC generators n ν n single nucleon p NuWro n NuWro MC p Dynamics n ■ If |~q| is low the impact area p (Q)EL scattering n RES pion production n Deep Inelastic Scattering usually includes many p π production ν Impulse approximation nucleons Fermi gas Spectral function Two-body current ■ For high |~q| IA is justiﬁed COH pion production Summary

Final state interactions ■ MB NCEL analysis Squares of transition matrices are summed up and interference

Backup slides terms are neglected

Z A−Z A σ = σp + σn i=1 i=1 X X ■ High |~q| means more than 400 MeV. However, IA is always assumed

Tomasz Golan NuWro @ HEP UW 30 / 61 Fermi gas

protons potential

Introduction Nucleons move freely neutrons protons EB MC generators within the nuclear vol- neutrons NuWro potential p NuWro MC ume in constant bind- EF n Dynamics EF (Q)EL scattering ing potential. RES pion production Deep Inelastic Scattering π production Impulse approximation Fermi gas Spectral function Global Fermi Gas Local Fermi Gas Two-body current COH pion production Summary ~ 1/3 1/3 Final state interactions 9πN 2 N pF = pF (r) = ~ 3π ρ(r) MB NCEL analysis r 4A A 0 Backup slides 300

Global FG 250 Local FG 200

150

100

Fermi momentum [MeV/c] 50

0 0 1 2 3 4 5 6 7 Distance from the center of nucleus [fm]

Tomasz Golan NuWro @ HEP UW 31 / 61 Spectral function

10 Total Mean Field Part 8 The probability of removing SRC Part 6 of a nucleon with momentum 4

~p and leaving residual nucleus Arbitrary units with excitation energy E. 2 0 0 100 200 300 400 500 600 700 800 P (~p, E) = PMF (~p, E) + Pcorr(~p, E) Momentum [MeV/c]

0.14 0.12 FG l′ 0.1 LFG 0.08 SF

SRC 0.06

Arbitrary units 0.04 spectator l 0.02 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Nucleon momentum [GeV/c]

Tomasz Golan NuWro @ HEP UW 32 / 61 Two-body current interactions

Introduction MC generators Two Body Current NuWro NuWro MC ′ Dynamics l (Q)EL scattering RES pion production Deep Inelastic Scattering π production 2 particles - 2 holes (2p-2h) VM Impulse approximation Fermi gas Spectral function Two-body current COH pion production l Summary Meson Exchange Current (MEC) Final state interactions

MB NCEL analysis

Backup slides Models in generators

■ Nieves model (GENIE, NEUT, NuWro) - CC only

■ Transverse Enhancement model (NuWro) - both CC and NC

Tomasz Golan NuWro @ HEP UW 33 / 61 Two-body current interactions

■ Nieves model is microscopic calculation

■ TE model introduce 2p − 2h contribution by modiﬁcation of the vector magnetic form factors

Total MEC cross section MEC / (QEL + MEC)

10 0.5

x = Nieves 0.4 x = TE ) 1 QEL

σ 0.3 + x σ / GeV / nucleon] 0.1 0.2

Nieves / ( -40 x

TE σ 0.1

[10 QEL σ 0.01 0 0.2 0.5 0.8 1.1 1.4 0.2 0.5 0.8 1.1 1.4 Neutrino energy [GeV] Neutrino energy [GeV]

Tomasz Golan NuWro @ HEP UW 34 / 61 Two-body current interactions

■ Both models provide only the inclusive double diﬀerential cross section for the ﬁnal state lepton

■ Final nucleons momenta are set isotropically in CMS

Nieves Transverse Enhancement

1 1 30 0.8 0.8 6 0.6 0.6 20 4 [GeV] [GeV]

k 0.4 k 0.4 T T 10 0.2 2 0.2 0 0 0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 cosθ cosθ

Tomasz Golan NuWro @ HEP UW 35 / 61 Coherent pion production

■ Rein-Sehgal model is Introduction commonly used for ν/l π MC generators coherent pion production NuWro ± NuWro MC Z0/W Dynamics ■ (Q)EL scattering Note: it is diﬀerent model RES pion production Deep Inelastic Scattering than for RES π production Impulse approximation ν A,Z A,Z Fermi gas ■ Berger-Sehgal model Spectral function Two-body current replaces RS (NuWro, COH pion production Summary GENIE - coming soon) Final state interactions

MB NCEL analysis Backup slides Comments

■ In COH the residual nucleus is left in the same state (not excited)

■ The interaction occurs on a whole nucleus - no ﬁnal state interactions

Tomasz Golan NuWro @ HEP UW 36 / 61 Neutrino interactions - summary

Introduction Neutrino MC generators

NuWro NuWro MC Dynamics (Q)EL scattering RES pion production Deep Inelastic Scattering π production Nucleon (IA*) np-nh (semi-IA) Nucleus Impulse approximation Fermi gas Spectral function Two-body current COH pion production Summary

Final state interactions (Q)EL MEC (2p2h) Coherent π

MB NCEL analysis

Backup slides

RES

Final state interactions

DIS

*IA = Impulse Approximation

Tomasz Golan NuWro @ HEP UW 37 / 61 Final state interactions Final state interactions

FSI describe the propagation of particles created in a primary Introduction neutrino interaction through nucleus MC generators

NuWro

Final state interactions FSI Intranuclear cascade LP eﬀect Formation time NOMAD NC π Summary

MB NCEL analysis

Backup slides

All MC generators (but GIBUU) use intranuclear cascade model

Tomasz Golan NuWro @ HEP UW 39 / 61 Intranuclear cascade

Introduction MC generators ■ In INC model particles NuWro are assumed to be classical Final state interactions FSI and move along Intranuclear cascade LP eﬀect the straight line. Formation time NOMAD NC π ■ Summary The probability of passing

MB NCEL analysis a distance λ (small enough to assume constant nuclear density) Backup slides without any interaction is given by:

˜ P (λ) = e−λ/λ

λ˜ = (σρ)−1 - mean free path

σ - cross section Can be easily handled with MC methods. ρ - nuclear density

Tomasz Golan NuWro @ HEP UW 40 / 61 Landau Pomeranchuk eﬀect

γ γ Introduction ■ The concept of MC generators formation time e e NuWro was introduced by Final state interactions FSI Landau and Pomeranchuk Intranuclear cascade LP eﬀect in the context of electrons γ γ Formation time NOMAD passing through a layer of material. NC π Summary

MB NCEL analysis ■ For high energy electrons they observed less radiated energy Backup slides then expected.

■ The energy radiated in such process is given by:

∞ 2 dI ~ i(ωt−~k·~x(t)) 3 3 ∼ j(~x, t)e d xdt d k −∞ Z

~x(t) describes the trajectory of the electron.

ω, ~k are energy and momentum of the emitted photon.

Tomasz Golan NuWro @ HEP UW 41 / 61 Landau Pomeranchuk eﬀect

■ Assuming the trajectory to be a series of γFormation zone γ straight lines (the current density j ∼ δ3(~x − ~vt)) the radiation integral is: e e

i(~k~v−ω)t ∼ e dt γ γ Zpath

■ Formation time is deﬁned as: ■ If time between collisions t>>tf , there is no interference and total 1 E E 1 t ≡ = = = γT radiated energy is just the average f ~ r.f. ω − k~v kp me ωr.f. emitted in one collision multiplied by k, p - photon, electron four-momenta the number of collisions. ω - photon frequency in the rest r.f. ■ If t<

Tomasz Golan NuWro @ HEP UW 42 / 61 Formation time in INC

■ One may expect a similar eﬀect in hadron-nucleus scattering.

■ In terms of INC it means that particles produced in primary vertex travel some distance, before they can interact.

■ There are several parametrization used in MC generators

■ Ranft parametrization: E · M tf = τ0 2 µT

2 2 2 where E, M - nucleon energy and mass, µT = M + pT - transverse mass

■ SKAT parametrization (similar but with pT = 0)

■ NEUT and GENIE use SKAT parametrization

■ NuWro uses Ranft parametrization for DIS and a model based on ∆ lifetime for RES

Tomasz Golan NuWro @ HEP UW 43 / 61 Comparison with NOMAD data

Introduction ■ Nomad data from π MC generators Nucl. Phys. B609 (2001) 255. NuWro hEν i ∼ 24 GeV Final state interactions ■ FSI The average number Intranuclear cascade π LP eﬀect of backward going negative pions Formation time NOMAD with the momentum π NC π Summary from 350 to 800 MeV/c.

MB NCEL analysis ■ 0.05 Backup slides In this neutrino Nomad data

energy range NuWro w/o formation time − 0.04 Bπ are an NuWro with formation time > - eﬀect of FSI. π 0.03

■ The observable is 0.02 very sensitive

eﬀect. 0 1 10 100 Golan, Juszczak, Sobczyk Q2 [(GeV/c)2] PRC86 (2012) 015505 Tomasz Golan NuWro @ HEP UW 44 / 61 Comparison with data for NC π0 production

0µ

Introduction ■ The cross section hEν i 0π± MC generators for π0 production ∼ 1 GeV NuWro through neutral current 0 Final state interactions 1π FSI is measured by Intranuclear cascade LP eﬀect K2K [1], MiniBooNE [2] and SciBooNE [3] experiments. Formation time NOMAD NC π ■ Summary The signal is deﬁned as: no charged leptons nor charged pions

MB NCEL analysis and one neutral pion (or at least one for ScibooNE) in the ﬁnal Backup slides state.

■ The result depends on primary vertex and FSI, as π can be: ◆ produced in primary vertex;

◆ produced in FSI; [1] Phys. Lett. B619 (2005) 255 ◆ aﬀected by charge exchange; [2] Phys. Rev. D81 (2010) 013005 ◆ absorbed. [3] Phys. Rev. D81 (2009) 033004

Tomasz Golan NuWro @ HEP UW 45 / 61 Comparison with data for NC π0 production

0.3 1200 K2K data SciBooNE data NuWro w/o formation time NuWro w/o formation time 1000 NuWro with formation time NuWro with formation time 0.2 800

600 (arb. units) (arb. units) 400 0.1

200

0 0 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 π0 momentum [MeV/c] π0 momentum [MeV/c]

2.0 8.0 MiniBooNE data MiniBooNE data

NuWro w/o formation time NuWro w/o formation time

1.5 NuWro with formation time 6.0 NuWro with formation time /(MeV nucleon)] /(MeV nucleon)]

2 1.0 neutrino 2 4.0 anti-neutrino cm cm -42 -43 0.5 2.0 /dp [10 /dp [10 σ σ

d 0 d 0 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 π0 momentum [MeV/c] π0 momentum [MeV/c]

Tomasz Golan NuWro @ HEP UW 46 / 61 Neutrino-nucleus interactions

For all channels (but coherent) neutrino interactions are factorized in the following way

p p

n π− n p π− π+ n π0 π0 n n n

p p

π− π+

IA νN hadronization formation time FSI

■ Is the physics really factorized this way?

■ This factorization is common for all generators

■ However, some pieces are done in diﬀerent way

Tomasz Golan NuWro @ HEP UW 47 / 61 The analysis of MB NCEL data (Quasi-)elastic neutrino-nucleon scattering

l(k′) p(p′)

Introduction ■ For (quasi-)elastic neutrino MC generators scattering oﬀ nucleon NuWro the cross section is given by: W Final state interactions MB NCEL analysis µ 2 ν(k) n(p) QEL formalism σ ∼|jµh | Form factors MiniBooNE data np − nh Quasi-elastic scattering Results with np − nh The ratio issue ′ µ Summary jµ =u ¯(k )γ (1 − γ5) u(k) → lepton current

Backup slides ′ µ hµ =u ¯(p )Γ u(p) → hadron current

■ Leptonic vertex can be calculated from the basis.

■ However, due to the complex structure of nucleon, hadronic vertex needs a phenomenological input.

■ Γµ can be parametrized by the functions of Q2, called form factors.

Tomasz Golan NuWro @ HEP UW 49 / 61 Form factors

■ Hadronic vertex can be expressed in terms of form factors: iσµνq Γµ = γµF NC,p(n)(Q2) + ν F NC,p(n)(Q2) − γµγ GNC,p(n)(Q2) NC,p(n) 1 2M 2 5 A

■ Vector form factors are expressed by electromagnetic form factors (Conserved Vector Current - CVC): 1 1 F NC,p(n)(Q2) = ± F p (Q2) − F n (Q2) − 2 sin2 θ F p(n)(Q2) − F s (Q2) 1,2 2 1,2 1,2 W 1,2 2 1,2 ■ Axial form factor is assumed to have a dipole form: axial mass 1 1 −2 GNC,p(n)(Q2) = ± G (Q2) − Gs (Q2)=(±g − gs ) 1 + Q2/M 2 A 2 A 2 A A A A strangeness diﬀerent sign for proton/neutron s gA sensitive to σ(νp)/σ(νn)

Tomasz Golan NuWro @ HEP UW 50 / 61 MiniBoonE data for NCEL

0µ

Introduction ■ The cross section νµ 0π± MC generators for NCEL is measured NuWro by MiniBooNE - 0π0 Final state interactions PRD82 (2010) 092005. MB NCEL analysis QEL formalism Form factors MiniBooNE data ■ The signal is deﬁned as: no charged leptons nor any kind of np − nh Results with np − nh pions in the ﬁnal state. The ratio issue Summary ■ The detector measures the Cherenkov and scintillation light. Backup slides ■ Protons with the kinetic energy of order tens MeV are detectable.

■ Neutrons are visible as an eﬀect of interactions with protons (inside or outside the nucleus).

■ s The MA and gA is extracted from the measurement.

Tomasz Golan NuWro @ HEP UW 51 / 61 MiniBoonE data for NCEL

Introduction

MC generators

NuWro

Final state interactions

MB NCEL analysis QEL formalism Form factors MiniBooNE data np − nh Results with np − nh The ratio issue Summary T stands for the total reconstructed energy of all nucleons in the ﬁnal state. Backup slides ■ s ■ Here assume gA = 0. Here assume MA =1.35 GeV.

■ Best ﬁt for: ■ Best ﬁt for:

s MA = 1.39 ± 0.11 GeV gA = 0.08 ± 0.26

■ Inconsistency with older ■ “νp → νp” stands for measurements events with proton above MA ∼ 1 GeV. Cherenkov treshold.

Tomasz Golan NuWro @ HEP UW 51 / 61 Two body current (or np − nh) contribution

■ The np − nh interactions occur on at least two nucleons.

■ What is the isospin correlation?

■ There are no new particles created, so the ﬁnal state looks the same as in elastic scattering.

■ np − nh is not taken into account in MiniBooNE analysis, which may cause the discrepancy with previous measurements of axial mass.

■ There are two theoretical models of np − nh (IFIC, Lyon), which take care about proper energy transfer distribution. Unfortunately, both are available only for CC channel.

■ The phenomenological Transverse Enhancement (TE) model is used in the calculation. The np − nh contribution is introduced by the modiﬁcation of the vector magnetic form factors. Lepton kinematics is the same as for elastic scattering.

■ The goal is to repeat the analysis with the inclusion if the np − nh contribution.

Tomasz Golan NuWro @ HEP UW 52 / 61 s Simultaneous extraction of MA and gA

3500 MB data Without np -nh contribution Total 0.2 3000 EL on carbon np-nh 2500 EL on hydrogen 0 Irreducible background Other backgrounds -0.2 2000 s A g -0.4 1500

No. of events -0.6 1000 -0.8 500

0 With np -nh contribution 0 100 200 300 400 500 600 700 0.2 Reconstructed kinetic energy (MeV) 0

-0.2 s A g w/o np − nh with np − nh -0.4

+0.18 +0.13 -0.6 MA [GeV] 1.34−0.10 1.10−0.15 s +0.2 +0.5 -0.8 gA −0.5−0.2 −0.4−0.3

800 1000 1200 1400 1600 Golan, Graczyk, Juszczak, Sobczyk PRC86 (2013) 024612 MA H MeVL made in Mathematica Tomasz Golan NuWro @ HEP UW 53 / 61 The ratio issue

0.8 MB data EL on hydrogen Introduction ■ The plot is made 0.7 Total Irreducible bg EL on carbon Other bgs MC generators using best ﬁt values 0.6 np-nh NuWro from the last slide. 0.5 Final state interactions

η 0.4 MB NCEL analysis QEL formalism ■ It turns out that the ratio 0.3 Form factors 0.2 MiniBooNE data is very sensitive − np nh 0.1 Results with np − nh on the energy transfer The ratio issue 0 Summary distribution (No. of 350 400 450 500 550 600 650 700 750 800 protons above threshold). Reconstructed kinetic energy (MeV) Backup slides ■ The Transverse Enhancement does not take care properly of lepton kinematics, which aﬀects the energy distribution of ﬁnal state nucleons. It is not a proper model to analyze this data.

■ This data, however, has a potential to discriminate between IFIC and Lyon models...

■ ... when they appear for neutral current channel.

Tomasz Golan NuWro @ HEP UW 54 / 61 Summary

Introduction

MC generators NuWro ■ MC generators are irreplaceable tools in high-energy physics Final state interactions

MB NCEL analysis QEL formalism ■ People use them before experiment exists (feasibility studies, Form factors MiniBooNE data requirements ...) np − nh Results with np − nh The ratio issue Summary ■ And during data analysis (systematics uncertainties, backgrounds ...) Backup slides ■ NuWro contains all major neutrino-nucleon interaction channels, reliable FSI model and realistic nucleus description - it is a ready tool to use in the investigation of neutrino data

Tomasz Golan NuWro @ HEP UW 55 / 61 Thank you for the attention! Backup slides Formation time in MC generators

Formation time for nucleons Formation time for pions

Introduction

MC generators 2.5 2.5 Neut Nuance Neut Nuance GENIE NuWro (Eν = 1 GeV) GENIE NuWro (Eν = 1 GeV) NuWro 2 2 Final state interactions 1.5 1.5 MB NCEL analysis

Backup slides 1 1 FT in MC generators

Form factors Formation zone [fm] 0.5 Formation zone [fm] 0.5 TE model Cascade algorithm 0 0 300 400 500 600 700 800 250 300 350 400 450 500 550 600 Momentum [MeV/c] Momentum [MeV/c]

■ NUANCE uses constant formation length x = 1 fm.

■ NEUT uses SKAT parametrization (µ2 = 0.08 ± 0.04 GeV2): |~p| x = µ2 ■ GENIE uses Rantf parametrization (assuming transverse momentum p = 0): T E x = τ = τ γ 0 M 0

Tomasz Golan NuWro @ HEP UW 58 / 61 Form factors

iσµνq F (Q2) Γµ (q) = γµF V (Q2)+ ν F V (Q2)−γµγ G (Q2)−qµγ P Introduction CC 1 2M 2 5 A 5 2M MC generators

NuWro ■ Final state interactions Vector form factors are expressed by electromagnetic form MB NCEL analysis factors (Conserved Vector Current - CVC): Backup slides FT in MC generators V 2 p 2 n 2 Form factors F (Q ) = F (Q ) − F (Q ) TE model 1,2 1,2 1,2 Cascade algorithm ■ Axial form factor is assumed to have a dipole form:

2 gA GA(Q ) = 2 2 2 (1 + Q /MA)

■ Pseudoscalar form factor is related to the axial one (Partially Conserved Axial Current - PCAC):

2 2 4M 2 FP (Q ) = 2 2 GA(Q ) mπ + Q

Tomasz Golan NuWro @ HEP UW 59 / 61 Form factors

µν µ µ NC,p(n) 2 iσ qν NC,p(n) 2 µ NC,p(n) 2 Γ = γ F (Q )+ F (Q )−γ γ5G (Q ) Introduction NC,p(n) 1 2M 2 A MC generators

NuWro ■ Vector form factors are expressed by electromagnetic form Final state interactions factors (Conserved Vector Current - CVC): MB NCEL analysis

Backup slides FT in MC generators 1 1 Form factors F NC,p(n)(Q2) = ± F p (Q2) − F n (Q2) −2 sin2 θ F p(n)(Q2)− F s (Q2) TE model 1,2 1,2 1,2 W 1,2 1,2 Cascade algorithm 2 2

■ Axial form factor is assumed to have a dipole form: 1 1 GNC,p(n)(Q2) = ± G (Q2) − Gs (Q2) A 2 A 2 A

■ The axial strange form factor is assumed to have a dipole form:

s s 2 gA GA(Q ) = 2 2 2 (1 + Q /MA)

Tomasz Golan NuWro @ HEP UW 59 / 61 Transverse Enhancement model

■ Introduction In the Transverse Enhancement model the two body current MC generators contribution is introduced by the modiﬁcation of the vector NuWro magnetic form factors: Final state interactions MB NCEL analysis 2 p,n p,n Q p,n Backup slides G → G˜ = 1 + AQ2 exp − G (Q2) FT in MC generators M M M Form factors s B TE model Cascade algorithm ■ A,B are established from the electron data.

■ The cross section for np − nh can be obtained by taking the diﬀerence:

d2σnp−nh d2σQEL d2σQEL ≡ (G˜p,n) − (Gp,n) dqdω dqdω M dqdω M

■ The disadvantage of the model is lepton kinematics (“copied” from the QEL scattering).

Tomasz Golan NuWro @ HEP UW 60 / 61 The algorithm for intranuclear cascade

Calculate: − λ˜(r) = [σρ(r)] 1

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

move particle by

min(λ, λmax)

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Check r′ > R move particle by

R - nucleus radius min(λ, λmax)

r′

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Check r′ > R move particle by

R - nucleus radius min(λ, λmax)

Yes

The particle leaves nucleus.

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Check r′ > R move particle by

R - nucleus radius min(λ, λmax)

Yes No

xmax The particle Check

leaves nucleus. λ < λmax. No

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Check r′ > R move particle by

R - nucleus radius min(λ, λmax)

Yes No

xmax The particle Check

leaves nucleus. λ < λmax. No

Yes

Generate the interaction.

Tomasz Golan NuWro @ HEP UW 61 / 61 The algorithm for intranuclear cascade

Calculate: λ = λ˜ · ln(P ) − λ˜(r) = [σρ(r)] 1 P = rand[0, 1]

Check r′ > R move particle by

R - nucleus radius min(λ, λmax)

Yes No

The particle Check

leaves nucleus. λ < λmax. No

Yes

Check Generate Pauli blocking. the interaction.

Tomasz Golan NuWro @ HEP UW 61 / 61