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Mi MicroBooN oBooNE cr cross-se secti tion ons s fr from om an osc oscillati tion ons s persp specti tive NUFACT 2017 Xiao Luo, Yale University On behalf of MicroBooNE collaboration 1 Mi Micr croBooNE and and FNA NAL L ne


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SLIDE 1

Mi MicroBooN

  • BooNE cr

cross-se secti tion

  • ns

s fr from

  • m an osc
  • scillati

tion

  • ns

s persp specti tive

NUFACT 2017

Xiao Luo, Yale University On behalf of MicroBooNE collaboration

1

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SLIDE 2

Mi Micr croBooNE and and FNA NAL L ne neutr utrino ino be beam am

Fermilab Booster Neutrino Beam (BNB)

Energy (GeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

POT

6

/10

2

/50MeV/m

MicroBooNE

)

  • (
  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10

ยต

  • ยต
  • e
  • e
  • BNB Neutrinos:
  • Mainly ๐œ‰๐œˆ
  • ๐œ‰๐œˆ energy (~700MeV)
  • <1% ๐œ‰# contamination.

Oct 2015 May 2017 Detector upgrade

Collecting BNB Neutrino Data for 17 months, ~ 6.5e20 POT collected.

~ 170 k ๐œ‰๐œˆ CC interactions

LArTPC ~170 tons, surface detector

2

slide-3
SLIDE 3

LAr LArTPC Working princi ciple โ€“ sig signals als

  • Charged particles lose energy through

Ar excitation (scintillation light) and ionization (drift electrons)

  • Electrons drift towards anode wire

planes under E field.

  • MicroBooNE LArTPC has two induction

planes and one collection plane.

  • 3D reconstruction from drift-time (X)

and wire-plane matching (Y,Z).

  • Number of electrons collected indicates

the amount of energy loss from ionization.

z

X Y

3

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SLIDE 4

LAr LArTPC Wo Working princi ciple

4

Advantages:

High Z target: large active volume -> lots of nu interactions. Finely segmented detector:

  • High spatial resolution: 3mm wire spacing -> mm vertex accuracy.
  • High calorimetric resolution: trace the charged particle ionization

Strong particle identification power to tag

  • Tracks: muon, proton, charged pions, kaons, etc.
  • Showers: electron, gamma, pi0.
  • Cold electronics: Low noise -> low threshold.

Challenges:

  • Cosmic background rejection: ionization chamber is slow (~2ms

drift). Surface detector -> ~20 cosmic tracks in 4.8 ms readout window

  • High Z target: Nuclear effects affect nu cross-sections.
  • Non-uniform detector response: unresponsive channels, shorted

wire region.

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SLIDE 5

75 cm Run 3493 Event 41075, October 23rd, 2015

Birdโ€™s eye view From BNB trigger stream

Time ticks (X) Collection wire number (Z)

MICROBOONE-NOTE-1002-PUB

5

๐‹

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SLIDE 6

Mi MicroBooNE us uses es thes these bea e beauti utiful ful i images es t to s study tudy neutr neutrino no os

  • sci

cillation

  • n
  • Goal I: Understand the nature of the MiniBooNE low energy excess of

EM events

  • Goal II: SBN (together with SBND and ICARUS) search for sterile

neutrinos (โˆ†๐‘›( ~ 1 ๐‘“๐‘Š2) with 5๐‰ sensitivity.

  • Goal III: Provide ๐ƒ-Ar cross-section measurements for DUNE.

6

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SLIDE 7

Go Goal al I: : go

  • after

er Mi MiniBooNE NE Lo Low Ene Energy gy Ex Excess ss

  • MiniBooNE sees 2.8 ๐œ and 3.4 ๐œ event excess in ๐ƒ๐‚ โŸถ ๐ƒ๐’‡

and ๐ƒ๐‚ โŸถ ๐ƒ๐’‡

  • Significant background is from ๐œŒ8 misid and ๐›ฟ from delta radiative

decay.

  • Detector can not distinguish e from ๐›ฟ.

MicroBooNE primary goal: determine if the nature of the excess events are ๐œน like or e like.

MiniBooNE MicroBooNE Common features Neutrino source: BNB Detector location: ~540 from the source Flux, L/E Differences Detector Cherenkov detector e/๐›ฟ separation NO LAr TPC e/๐›ฟ separation Yes Target Mineral oil (CH2) (806 tons) Liquid Argon (Ar) (180 tons)

7

  • Phys. Rev. Lett. 110, 161801 (2013)
slide-8
SLIDE 8

Go Goal al II II: : go

  • after

er St Sterile Ne Neutri trino search - SBN SBN progr gram

ICARUS T600 MicroBooNE SBND

ICARUS

LArTPC: 600m, 476t

MicroBooNE

LArTPC: 470m, 87t

SBND

LArTPC:110m, 112t

Fermilab Short Baseline Neutrino program:

  • Shared neutrino beam (BNB) reduce flux

uncertainty.

  • All LArTPC detectors: reduce cross-section

uncertainty

Goal: 5๐‰ sensitivity for sterile neutrino search at โˆ†๐’๐Ÿ‘ ~ 1eV2

8

slide-9
SLIDE 9

Go Goal al III III: : go go after cr cross-se section n unc uncertainty in n Dune une

Dune Far detector is LArTPC. MicroBooNE can give direct cross-section constrain (particularly in low energy region) for Dune oscillation precision measurements.

  • Precision measurements of neutrino
  • scillation parameters.
  • Neutrino Mass Hierarchy
  • CP violation: ๐œ€>?

9

~2X exposure Dune CDR arXiv:1512.06148

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SLIDE 10

Osci cillation signals ๐ƒ๐‚ โ†’ ๐ƒ๐‚, , ๐ƒ๐‚ โ†’ ๐ƒ๐’‡

Signal selection ๐ƒ energy reco.

  • Syst. Uncertainty

10

  • ๐ƒ๐‚CC inclusive
  • CC๐†๐Ÿ
  • ๐ƒ๐‚CC inclusive
  • Charged particle multiplicity,

CC0๐†

  • NC proton identification
  • CC0๐†
  • CC๐†๐Ÿ
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SLIDE 11

Cr Cross-se section n impa pact on n Osc scillation n

๐ƒ๐‚CC inclusive -> ๐ƒ signal selection, Systematic uncertainty

11

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SLIDE 12

๐ƒ๐‚CC CC inc inclus lusiv ive cr cross ss-se sect ction

  • Relatively simple event signature โ€“ tag long muon

track as the product of the neutrino interaction.

  • Muon kinematics is insensitive to FSI.
  • A standard channel to compare with other neutrino

experiments.

12

First channel in MicroBooNE cross-section program: ๐œ‰๐œˆ CC inclusive: Impact on oscillation:

  • Signal selection of ๐œ‰C disappearance channel.
  • ๐œ‰๐œˆ CC help to constrain the ๐œ‰๐‘“ rate.

ArgoNeuT is the only existing ๐ƒ-Ar cross-section

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SLIDE 13

๐ƒ๐‚CC CC inc inclus lusiv ive

  • Purity: 65%, Efficiency: 30%
  • Improved analysis:
  • Scintillation light to improve the selection

efficiency

  • Muon PID to reduce background

Differential cross-section is on the way, stay tuned!

Note: efficiency = # of ๐ƒ๐‚๐ƒ๐ƒ events after selection / All ๐ƒ๐‚๐ƒ๐ƒ events inside of FV

Selection

๐ƒ๐‚๐ƒ๐ƒ 65% Cosmic 26%

13

Track Length (cm)

100 200 300 400 500 600 700 800 900 1000

  • No. of Events

100 200 300 400 500 600 700 800 900 1000

Data: Beam On- Beam Off Simulation: CC+bkgd

ยต

ฮฝ selected bkgd

ยต

ฮฝ bkgd

e

ฮฝ +

e

ฮฝ NC bkgd Cosmic bkgd CC true vertex Out of FV bkgd

ยต

ฮฝ

MicroBooNE preliminary

See Marco Del Tuttoโ€™s talk Tue. WG2 talk Check out MicroBooNE public note MICROBOONE-NOTE-1010-PUB for details.

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SLIDE 14

Ne Neutri trino oscillati tion Vs Cross-se section

CC๐†๐Ÿ -> ๐ƒ signal selection, Systematic uncertainty, ๐ƒ Energy reconstruction

14

slide-15
SLIDE 15

๐‘ซ๐‘ซ๐ƒ๐’‡ select

ction

๐ƒ๐’‡

โ€œInclusiveโ€ search (1 e + 0๐†) Exclusive QE like (1e + 1 p)

15

๐ƒ๐’‡

hadrons p

  • Higher statistics
  • Directly compatible to

MiniBooNE

  • Less model dependency
  • Simpler topology
  • Lower backgrounds
  • Easier ๐‘ญ๐ƒ

determination

slide-16
SLIDE 16

๐‘ซ๐‘ซ๐ƒ๐’‡ select

ction

Challenges:

  • Suppress photon backgrounds:

NC๐œŒ8, CC๐œŒ8, resonant ๐œ‰ interactions in dirt-> ๐›ฟ

  • e/๐œน separation

โ€œInclusiveโ€ search (1 e + 0๐†)

  • Simpler topology
  • Lower backgrounds
  • Easier ๐‘ญ๐ƒ

determination

๐†๐Ÿ misID โˆ†โ†’ ๐‘ถ๐œน

  • Higher statistics
  • Directly compatible to

MiniBooNE

  • Less model dependency

Exclusive QE like (1e + 1 p)

16

p

๐ƒ๐’‡ ๐ƒ๐’‡

hadrons

slide-17
SLIDE 17

CC CC๐†๐Ÿ cr cross-se section measu surement

Impact on oscillation physics:

  • Easiest channel to provide large pi0 sample
  • Utilize the pi0 for shower automated reconstruction development.
  • Enable us to study photon background for the ๐œ‰# appearance channel.

Challenging channel:

  • โ€œShowerโ€ reconstruction is difficult especially in

the low energy range.

  • Strategy: tagging muon and look for two

showers

The first CC ๐†๐Ÿ cross-section result is on the way, stay tuned!

๐œน ๐œน CC๐›’๐Ÿ ๐๐›๐จ๐ž๐ฃ๐ž๐›๐ฎ๐Ÿ ๐Ÿ๐ฐ๐Ÿ๐จ๐ฎ

17

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SLIDE 18

BNB DATA : RUN 5360 EVENT 45. MARCH 8, 2016.

PID PID โ€“ sh shower ers ( s (e/ e/๐œน) )

e-

BNB DATA : RUN 5536 EVENT 1612. MARCH 22, 2016.

dE/dx at start of the shower?

  • e-: 1MIP
  • ๐›ฟ: 1MIP if Compton

scattering, 2MIP if converting to e+e-

Gaps from vertex?

  • ๐›ฟ: yes
  • e-: no

๐›’๐Ÿ โ†’ ๐›…๐›…

What Impact PID?

  • Require good vertexing.
  • Use both dE/dx and gap handles -> better e- tagging.
  • Study the energy dependence of ๐›ฟ contamination.

Note: ArgoNeuT electron like sample has 20% photon contamination with higher energy NuMI beam. ArgoNeuT PhysRevD.95.072005

Electron Vs Gamma

๐ƒ๐’‡ Signal ๐ƒ๐’‡ Background

Gaps No Gap

18

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SLIDE 19

Ne Neutri trino oscillati tion Vs Cross-se section

NC elastic -> ๐ƒ Energy reconstruction

19

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SLIDE 20

NC NC e elastic c โ€“ pr proton n iden dentification

  • Take advantage of LArTPC PID strength, include hadron calorimetry of the final states in energy

reconstruction.

  • ๐œ‰ โˆ’ ๐ต๐‘  NC elastic cross-section help identify protons and their energy reconstruction

40 MeV threshold

NC elastic cross-section

  • ultimate goal: โˆ†๐‘ก.
  • Signature: single short proton

track (challenging to select)

  • Employed BDT to identify

protons

  • Continue push to lower

proton energy threshold. Check out our public note for more details: link

Example of selected NC proton from BNB data. ~60MeV proton

20

slide-21
SLIDE 21

Ne Neutri trino oscillati tion Vs Cross-se section

Charged particle multiplicity -> Systematic Uncertainty from nuclear effects CC0๐† -> ๐ƒ Energy reconstruction, Systematic Uncertainty from nuclear effects

21

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SLIDE 22

Ch Charged p particle multiplicity y analysisโ€“ Mo Motivation

๐›—๐›Ž ๐— ๐›Ž- ๐จ ๐ช+ ๐›—๐›Ž ๐— ๐›Ž- ๐ช, ๐จ ๐šฌ ๐›—๐›Ž ๐— ๐›Ž- (๐จ, ๐ช) ๐˜ ๐˜ ๐ช, ๐จ ๐›’

CCQE Resonant DIS

22 BNB trigger, Run 5831 Event 4262, Apr. 8th , 2016

๐‚

25cm

BNB trigger, Run 3469 Event 53223, Oct. 21st, 2015

๐‹ p ๐†

30cm

BNB trigger, Run 3493 Event 41075, Oct. 23rd, 2015

๐‹ beam ๐‹ ๐‚

Nuclear Effects:

  • Fermi motion
  • Nucleon correlation
  • Final state interaction

Observables are instead final state particles. Direct count of the number of tracks from ๐œ‰CCC events serves as experimental contribution to tuning models for generators, can be a standard measurement

  • n different targets.

Track Multiplicity = 2 Track Multiplicity = 3 Track Multiplicity = 4

slide-23
SLIDE 23

Charged particl cle multiplici city analysis โ€“ pr prelimina nary r resul ult

More details about the analysis method and preliminary results can be found in the MicroBooNE public note: MICROBOONE-NOTE-1024-PUB

23

  • Good agreement between MC and data.
  • High energy threshold (82MeV for p,

37MeV for ๐œˆ, ๐œŒ)

  • Subset of the data sample, stat. limited

for high multiplicity.

  • Will reduce the energy threshold and

increase statistics.

slide-24
SLIDE 24

CC CC 0๐† / proton multiplici city

Several active exclusive cross- section analyses with final state topologies:

  • 1muon + 1 proton
  • 1 muon + 2 proton
  • 1 muon + n protons, n>2

Direct cross-section measurements, provide handle to constrain nuclear effects (MEC, 2p2h, FSI) in Ar.

p p p

24

3 protons

slide-25
SLIDE 25

25

Nuclear effects impact on Oscillation phys.

  • Oscillation is measured as function
  • f ๐‘ญ๐ƒ๐ฎ๐ฌ๐ฏ๐Ÿ
  • ๐‘ญ๐ƒreco -> ๐‘ญ๐ƒ๐ฎ๐ฌ๐ฏ๐Ÿ unfolding using MC
  • Different models -> different ๐นltrue

shape -> different oscillation param.

  • MicroBooNE proton multiplicity

measurements will provide constrains

  • f nucleon correlation/FSI in Ar.
  • O. Lalakulich K. Gallmeister U. Mosel

arxiv 1203.2935

Nucl clear Effect cts affect ct Osci cillation - ๐‘ญ๐ƒ un unfoldi ding ng

slide-26
SLIDE 26

Pr Proto ton multiplicity -> > CP CP violation

From Ornella Palamara NUINT 15 talk

  • Effects are different for neutrino and anti-neutrino
  • Enter systematic uncertainty of ๐œ€>? measurement in DUNE
  • MicroBooNE measures proton multiplicity in Ar with more stat.

26

Neitrno mode GENIE predicted 64% higher than ArgoNeuT data Anti-Neitrno mode GENIE predicted 22% higher than ArgoNeuT data ๐œ‰C ๐ท๐ท0๐œŒ ๐œ‰C๐ท๐ท0๐œŒ

slide-27
SLIDE 27

Co Conclusi sion

  • MicroBooNE targets to understand the MiniBooNE Low energy

excess, search for ~1eV2 sterile neutrino in Femilabโ€™s SBN program and set cross-section constrains for DUNE.

  • MicroBooNE has an active ๐œ‰-Ar cross-section program which will

significantly contribute to achieving oscillation goals

  • CC inclusive
  • Track multiplicity
  • CC 0pi, proton multiplicity
  • CCpi0
  • NC proton
  • Stay tuned for results in the near future!

27

slide-28
SLIDE 28

Back up slides

28

slide-29
SLIDE 29

Other cr cross-sect ction effort useful for osc

  • sc.

. phy hys.

๐ƒ๐’‡๐‘ซ๐‘ซ cross-section from NuMI beam

  • MicroBooNE detector sits on 8ยฐ off-axis NuMI beam.
  • Larger ๐œ‰# fraction in NuMI (~5%) than BNB (~0.6%).
  • Potential cross check for the BNB low energy excess

analysis.

  • Currently no ๐œ‰#CC results on Lar, will be valuable to

DUNE.

Neutrino

Measure High energy ๐ƒ๐‚ rate

  • > constrain the kaon flux
  • > constrain the intrinsic ๐œ‰#

from kaon decay

29

NuMI ๐ƒ๐’‡ like event

slide-30
SLIDE 30

Ne Neutr utrino ino in interac actio tions ns

hadrons

Charged Current

Signal channel, tag lepton gives the flavor of the neutrino ๐ƒ๐’‡ ๐ƒ๐‚

hadrons

๐ƒ๐’‡,๐‚,๐Š

hadrons

Neutral Current

Background, can provide total neutrino flux

T2 K CNGS NOvA DUNE

BNB (0.2 -2 GeV)

30

Tag shower Tag track Tag hadrons

slide-31
SLIDE 31

Requirements on the detector:

  • Large detector active volume:
  • Increase # of interactions.
  • Capture complete info. of the
  • interactions. (containment)
  • High signal/background ratio:
  • Low noise, cold electronics
  • Underground to prevent cosmic

rays.

  • Strong particle identification power:
  • Event topology โ€“ spacial resolution
  • Calorimetry โ€“ energy resolution
  • Segmented detector is highly

preferred.

  • Low threshold:
  • High efficiency for detect and

reconstruct low energy particles.

LA LArTPC TPC Working princi ciple โ€“ No Noise

  • In MicroBooNE, <400 electron equivalent

noise charge (ENC)

  • Great Signal/Noise ratio, ~20 (raw data)

and ~38 (noise filtered). (https://arxiv.org/abs/1705.07341)

  • Misconfigured channels (~8%) and dead

(~4%) channels are problematic in MicroBooNE.

  • Robust channel recovery is needed for

future large scale LArTPC for all cold electronics.

31

slide-32
SLIDE 32

Accel cceler erator r neu eutri rino osci scillation

๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ Near Detector ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐‚ ๐ƒ๐Š ๐ƒ๐Š ๐ƒ๐’‡ ๐ƒ๐’‡ ๐ƒ๐Š ๐ƒ๐‚ Far Detector Propagate as mass eigenstate ๐ƒ๐’‹ ๐ƒ๐‚ ๐ƒ๐Š ๐ƒ๐‚ L/E (km/GeV)

  • Precision measurements of neutrino oscillation mixing angles: ๐ƒ๐‚

disappearance (๐œ„(v), ๐ƒ๐‚ โ†’ ๐ƒ๐’‡ (๐œ„wv), etc. Amplitude of the oscillation probability.

  • Neutrino Mass Hierarchy: determine the sign of โˆ†๐‘›(v

( (๐ƒ๐‚ โ†’ ๐ƒ๐‚ or ๐ƒ๐‚ โ†’ ๐ƒ๐Š)

  • r โˆ†๐‘›wv

( (๐ƒ๐’‡ โ†’ ๐ƒ๐’‡ or ๐ƒ๐‚ โ†’ ๐ƒ๐’‡). Frequency of oscillation probability.

  • CP violation: non-zero phase ๐œ€>? generates asymmetry between neutrino
  • scillation and anti neutrino oscillation.

Requires to correctly detect the flavor and energy of neutrinos in the detectors with high Efficiency.

32

๐ƒ๐‚

slide-33
SLIDE 33

PID PID โ€“ track cks (muon, pion, proton)

๐‚

25cm

BNB trigger, Run 3469 Event 53223, Oct. 21st, 2015

๐‹ p ๐†

๐›—๐›Ž ๐— ๐›Ž- ๐ช, ๐จ ๐šฌ ๐ช, ๐จ ๐›’

Goal: Identify particle type and reconstruct the energy. Tool Box:

  • Bethe Bloch laws (dEdx Vs Residual

range) -> PID

  • Straggling effect: heavier incoming

particle has narrower dE/dx distribution.

  • Track range, Multiple Column

Scattering -> Kinetic energy

  • Delta rays, Bragg peak -> track
  • direction. (Cosmic rejection)

33

By Ornella Palamara

(JINST), 2013 JINST Vol. 8 P08005. https://arxiv.org/abs/1703.06187

CC๐œ‰Cresonant

slide-34
SLIDE 34

BNB DATA : RUN 5360 EVENT 45. MARCH 8, 2016.

PID PID โ€“ sh shower ers( s(e/ e/gamma mma)

e-

BNB DATA : RUN 5536 EVENT 1612. MARCH 22, 2016.

Goal: Tag e- from CC ๐œ‰# events. NCpi0 events are background. Tool Box:

  • dE/dx of the start of the shower.
  • Gap or no Gap from the vertex.
  • Warning: each handle alone is not sufficient

to tag electrons, especially in low energy range.

๐›’๐Ÿ โ†’ ๐›…๐›…

34

By Mark Messier, From INSS2017

PhysRevD.95.072005 Electron Vs Gamma

slide-35
SLIDE 35

PID PID โ€“ summary at ~GeV neutrino interact ctions

e/๐œน ๐‚ยฑ/๐†ยฑ Hadrons p, K, d neutrons EM shower (GeV) Track like at the shower start. Long tracks Short tracks Invisible except scattering caused dot-like nucleus recoil Electron: 1 MIP <dE/dx> Gamma: 1 or 2 MIP <dEdx> MIP <dE/dx> for through going tracks Bragg peak for stopping tracks Highly ionized particle Higher dE/dx Less straggling (narrower dE/dx distribution) Mostly under energy threshold Shower Cone gives the direction KE is basically proportional to range. MCS, bragg peak, delta rays for directionality. Should have good separation from the MIP tracks in PIDA Difficult to reconstruct the full energy: Stochastic nature, low threshold, incompleteness Easy to reconstruct individual tracks, hard to separate muon and charged pions Challenging to reconstruct short tracks. Missing track multiplicity Missing energy for the neutrino energy reconstruction

35

slide-36
SLIDE 36

CC inclusive: selection efficiency

36

[MeV] ยต P

500 1000 1500 2000 2500

Acceptance Efficiency

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

efficiency of CCQE efficiency of CCRes efficiency of CCDIS

MicroBooNE simulation preliminary

slide-37
SLIDE 37

LA LArTPC TPC Working princi ciple โ€“ cosmic c ray back ckground

  • Surface LArTPCs are exposed with cosmic rays constantly, e.g.

comic rate in MicroBooNE LArTPC(~70m3) with rate of 5kHz!

  • Pros: Good energy calibration source (MIP muons, Michel e-)

for low energy electron reconstruction development.(arXiv 1704.02927)

  • Cons: difficult to find neutrino interactions. Strict cosmic

rejection significantly lower the neutrino selection efficiency.

  • LArTPCs in the SBN program are using Cosmic

ray tagger to tag and remove cosmic background.

  • DUNE far detector will be underground with

1.5 km rock shielding, the rate of cosmic ray in the detector will be reduced by more than factor of 500,000.

37

slide-38
SLIDE 38

Reconstruction

38

slide-39
SLIDE 39

Ro Roadmap to ๐œ‰๐œˆ CC c CC cros

  • ss-se

sect ction measu surement

  • Systematics Uncertainties in NBG and acceptance

efficiency ๐‘ :

  • Flux uncertainty (dominant uncertainty)
  • Detector uncertainty: space charge, purity, recombination.
  • Model uncertainty.
  • Reconstruction efficiency: Reco vs true unsmearing matrix
  • ๐‘ธ๐‚ reconstruction for differential cross-section.
  • Contained track: from range
  • Uncontained track: from multiple scattering
  • 1. Flux integrated cross-section
  • 2. Single differential cross-section
  • 3. Double differential cross-section

39

From MiniBooNE

slide-40
SLIDE 40

NuMI and BNB

40

Energy (GeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

POT

6

/10

2

/50MeV/m

MicroBooNE

)

  • (
  • 5

10

  • 4

10

  • 3

10

  • 2

10

  • 1

10

ยต

  • ยต
  • e
  • e