CCCCππ+ + Cross Section Results Cross Section Results from MiniBooNEfrom MiniBooNE

Mike WilkingMike Wilking

TRIUMF / University of ColoradoTRIUMF / University of Colorado

NuIntNuInt

22 May 200922 May 2009

CCCCππ++ in Oscillation Experiments in Oscillation Experiments The next generation The next generation

of of νν oscillation oscillation experiments lie at experiments lie at low, mostly low, mostly unexplored unexplored νν energies energies

CCQE is the signal CCQE is the signal process for oscillation process for oscillation measurementsmeasurements

At these energies, At these energies, CCCCππ++ is the dominant is the dominant charged-current charged-current backgroundbackground

T2K NOνA

CCπ+

CCQE DIS

Charged Current Cross Sections

Previous CCPrevious CCππ++ MeasurementsMeasurements

The plot shows previous The plot shows previous absolute cross section vs Eabsolute cross section vs Eνν measurementsmeasurements

(not including K2K; (not including K2K; revisited in a few slides)revisited in a few slides)

Fewer than 8,000 events have Fewer than 8,000 events have been collected in all of these been collected in all of these experiments combinedexperiments combined

Only one experiment was Only one experiment was performed on a nuclear targetperformed on a nuclear target(with E(with Eνν > 3 GeV) > 3 GeV)

Next-generation oscillation Next-generation oscillation experiments use nuclear experiments use nuclear targetstargets

T2K NOνA

The MiniBooNE The MiniBooNE DetectorDetector

Particle reconstruction is based Particle reconstruction is based primarily on detection of Cherenkov primarily on detection of Cherenkov radiation (additional information is radiation (additional information is gained from delayed isotropic light)gained from delayed isotropic light)

The tank is filled with 800 tons of The tank is filled with 800 tons of ultra-pure mineral oil (modeled as ultra-pure mineral oil (modeled as CHCH22))

1280 8” phototubes are attached to 1280 8” phototubes are attached to the inside surface of the tank (10% the inside surface of the tank (10% coverage)coverage)

Outside the main tank is a thin Outside the main tank is a thin spherical shell containing 240 spherical shell containing 240 phototubes to veto entering particlesphototubes to veto entering particles

MiniBooNE CCMiniBooNE CCππ++/CCQE /CCQE MeasurementMeasurement

The ratio of the The ratio of the CCCCππ++ cross cross section to CCQE has been section to CCQE has been measured at several neutrino measured at several neutrino energiesenergies

Neutrino energies are Neutrino energies are determined from the determined from the reconstructed muon kinematicsreconstructed muon kinematics

Results are in agreement with Results are in agreement with previous measurements from previous measurements from K2K and ANLK2K and ANL

Results were recently Results were recently submitted to PRLsubmitted to PRL

See poster by J. NowakSee poster by J. Nowak

arXiv:0904.3159

Reconstruction Reconstruction ImprovementsImprovements

In the MiniBooNE In the MiniBooNE detector, the muon and detector, the muon and pion produced in CCpion produced in CCππ++ interactions are often interactions are often both above Cherenkov both above Cherenkov thresholdthreshold

To better reconstruct To better reconstruct each event, both the each event, both the muon and pion can be muon and pion can be included in a included in a simultaneous fitsimultaneous fit

In addition to In addition to reconstructing both reconstructing both particles, we further particles, we further need the ability to need the ability to distinguish the muon distinguish the muon from the pionfrom the pion

Monte Carlo predicted muon and pion kinetic energy

Event Reconstruction Event Reconstruction OverviewOverview

The reconstruction relies on a detailed analytic The reconstruction relies on a detailed analytic model of extended-track light production in the model of extended-track light production in the detectordetector

Each track is defined by 7 parameters:Each track is defined by 7 parameters:

vertex (X,Y,Z,T)vertex (X,Y,Z,T) direction (direction (θθ,,φφ)) energy (E)energy (E)

For a given set of track parameters, the charge For a given set of track parameters, the charge and time probability distributions are determined and time probability distributions are determined for each PMTfor each PMT

Fitting routine varies these parameters to best fit Fitting routine varies these parameters to best fit the measured charges and timesthe measured charges and times

Particle Particle IdentificationIdentification

The one track fit requires a The one track fit requires a particle hypothesisparticle hypothesis(e.g. (e.g. μμ or e) or e)

Particle identification is Particle identification is achieved by comparing fit achieved by comparing fit likelihoods from different likelihoods from different track hypothesestrack hypotheses

The ratio of the The ratio of the μμ and e and e hypothesis fit likelihoods vs hypothesis fit likelihoods vs fit energy provides nice fit energy provides nice separation between separation between electrons (top) and muons electrons (top) and muons (bottom)(bottom)

arXiv:0902.2222

Pion ReconstructionPion Reconstruction In addition to reconstructing the pion kinematics, the goal of a In addition to reconstructing the pion kinematics, the goal of a

pion fitter is to provide a means by which pions can be pion fitter is to provide a means by which pions can be distinguished from muonsdistinguished from muons

Pions and muons propagate in a very similar fashion (similar Pions and muons propagate in a very similar fashion (similar masses)masses)

To separate, must exploit any differencesTo separate, must exploit any differences

Pions tend to travel in very straight paths (much like muons) Pions tend to travel in very straight paths (much like muons) except that they occasionally interact hadronically and abruptly except that they occasionally interact hadronically and abruptly change directionchange direction

Since the nuclear debris emitted in these interactions usually Since the nuclear debris emitted in these interactions usually doesn't produce any light, the pion trajectories are straight lines doesn't produce any light, the pion trajectories are straight lines with a sharp “kink” in the middlewith a sharp “kink” in the middle

To improve the reconstruction of these tracks, a kinked track To improve the reconstruction of these tracks, a kinked track fitter is neededfitter is needed

electron tracks

muon tracks pion tracks

Creating a Kinked FitterCreating a Kinked Fitter The default track hypotheses assume that tracks start at one energy and finish with zero The default track hypotheses assume that tracks start at one energy and finish with zero

energyenergy

For a kinked track likelihood function, the predicted charges are calculated for an For a kinked track likelihood function, the predicted charges are calculated for an unkinked “base track” at the desired energyunkinked “base track” at the desired energy

An “anti-track” is then created collinear with the base track and downstream of the An “anti-track” is then created collinear with the base track and downstream of the original vertex (with proportionately less energy)original vertex (with proportionately less energy)

The predicted charges for the anti-track are subtracted from the base trackThe predicted charges for the anti-track are subtracted from the base track

Finally, a “downstream track” is created at the vertex of the anti-track but with even less Finally, a “downstream track” is created at the vertex of the anti-track but with even less energy (due to energy (due to ΔΔEEkinkkink) and pointing in a new direction) and pointing in a new direction

Kink point

base track

anti-track

downstream track

4 new track parameters:•distance to kink point•kink energy loss•downstream direction(θ and φ)

Energy Reconstruction:Energy Reconstruction:Monte Carlo simulation of single pion eventsMonte Carlo simulation of single pion events

The peak The peak from the from the kinked fit is kinked fit is centered on centered on zero (straight zero (straight track peak is track peak is ~10% low)~10% low)

Kinked peak Kinked peak is narroweris narrower

Low ELow Efitfit

“shoulder” “shoulder” from high from high energy pions energy pions is much is much smaller in smaller in kinked fitkinked fit

(E(Efitfit-E-Etruetrue)/E)/Etruetrue (E(Efitfit-E-Etruetrue)/E)/Etruetrue

Straight

Pion

Fit

Kinked

Pion

Fit

Angle ReconstructionAngle Reconstruction The plot shows the The plot shows the

reconstructed reconstructed μμ//ππ angle versus the angle versus the WORSE of the two WORSE of the two true/reconstructed true/reconstructed anglesangles

At low reconstructedAt low reconstructedμμ//ππ angle, the fitter is angle, the fitter is slightly less accurateslightly less accurate

When one track is When one track is below Cherenkov below Cherenkov threshold, the fitter threshold, the fitter tends to place it on tends to place it on top of the other tracktop of the other track

The bins on the The bins on the diagonal are events diagonal are events where the where the μμ is is misidentified as the misidentified as the ππ (and vice versa)(and vice versa)

true π

true μ

fit μfit π

θ_XθY

θ_X: Max Fit/True Angle (μ or π)

θ_Y

: R

eco

nst

ruct

ed π

μ

Angle

Neutrino Energy Neutrino Energy ReconstructionReconstruction

Since both the muon and pion are reconstructed, the event Since both the muon and pion are reconstructed, the event kinematics are fully specified assumingkinematics are fully specified assuming

Target nucleon is at restTarget nucleon is at rest

Neutrino direction is knownNeutrino direction is known

Recoiling nucleon mass is knownRecoiling nucleon mass is known

Unlike previous analyses that have only reconstructed the muon, no Unlike previous analyses that have only reconstructed the muon, no assumption is needed about the mass of the recoiling assumption is needed about the mass of the recoiling ΔΔ particle particle created in the interactioncreated in the interaction

Fairly insensitive to misidentifying the muon and pion since both Fairly insensitive to misidentifying the muon and pion since both particles have similar massparticles have similar mass

Neutrino Neutrino Energy Energy

ResolutionResolution The reconstructed The reconstructed

neutrino energy is neutrino energy is centered on the true centered on the true energyenergy

The resolution is The resolution is ~13.5% over most ~13.5% over most of the measured of the measured energy range: (0.5 - energy range: (0.5 - 2.0 GeV)2.0 GeV)

(Fit

- T

rue)/

Tru

eEnerg

y R

eso

luti

on

True (MeV)

True (MeV)

ππ+++N Mass+N Mass Since we make no assumptions about the delta mass, we can Since we make no assumptions about the delta mass, we can

reconstruct itreconstruct it The CCQE background piles up at low delta massThe CCQE background piles up at low delta mass

π+N Mass (MeV)

MC Background PredictionData / MC

Relatively normalized

ππ+++N Mass Cut+N Mass Cut The plot shows the The plot shows the

reconstructed reconstructed ππ+++N mass vs the +N mass vs the generated value for generated value for Monte Carlo eventsMonte Carlo events

At low masses, there is At low masses, there is a correlation between a correlation between these quantities, as these quantities, as expectedexpected

Events in which a high energy muon is Events in which a high energy muon is mis-reconstructed as a pion tend to mis-reconstructed as a pion tend to accumulate at high reconstructed massaccumulate at high reconstructed mass

A cut has been placed at 1350 MeV to A cut has been placed at 1350 MeV to removed these mis-reconstructed eventsremoved these mis-reconstructed events

Rejected

Accepted

Selection Cut SummarySelection Cut Summary 3 subevents3 subevents

Subevent 1:Subevent 1: thits > 175thits > 175 vhits < 6vhits < 6

Subevents 2 and 3:Subevents 2 and 3: 20 < thits < 20020 < thits < 200 vhits < 6vhits < 6

Fiducial volume cutFiducial volume cut

Reconstructed Reconstructed ππ+++N mass < 1350 MeV+N mass < 1350 MeV

These cuts result in 48,000 events with a 90% purity, and a These cuts result in 48,000 events with a 90% purity, and a correct muon/pion identification rate of 88%correct muon/pion identification rate of 88%

beam

Observed CCObserved CCππ+ + Cross Cross SectionSection

Neutrino interactions are often modeled in terms of single Neutrino interactions are often modeled in terms of single nucleon cross sections plus additional nuclear processes that nucleon cross sections plus additional nuclear processes that alter the composition of the final statealter the composition of the final state

Since the details of intra-nuclear processes are not accessible Since the details of intra-nuclear processes are not accessible to experiment, we do not attempt to extrapolate our to experiment, we do not attempt to extrapolate our observations to the single nucleon cross sectionobservations to the single nucleon cross section

greatly reduces model dependencegreatly reduces model dependence

Instead, we define an observed CCInstead, we define an observed CCππ++ event to be any event to be any interaction that produces the following final state:interaction that produces the following final state:

one and only one muonone and only one muon one and only one pionone and only one pion any number of photons and baryons from the breakup of the nucleusany number of photons and baryons from the breakup of the nucleus

Measuring the Cross SectionMeasuring the Cross Section

Cross sections are calculated as a function of any variable(s) in Cross sections are calculated as a function of any variable(s) in the interactionthe interaction

The calculation uses the above formula (i = reconstructed bin; j = The calculation uses the above formula (i = reconstructed bin; j = true bin)true bin) vvii: any 1D or 2D distribution: any 1D or 2D distribution DDii: reconstructed data distribution of v: reconstructed data distribution of v BBii: background prediction of v: background prediction of v MMijij: unfolding matrix (see next slide): unfolding matrix (see next slide) εεjj: MC efficiency in unfolded bins: MC efficiency in unfolded bins φφ(j)(j): integrated flux (or flux histogram in the case of E: integrated flux (or flux histogram in the case of Eνν)) POT: protons on targetPOT: protons on target NNtargtarg: number of targets = volume*density*N: number of targets = volume*density*NAA/(target molecular /(target molecular

weight)weight)

Unfolding MatrixUnfolding Matrix Top: the reconstructed Top: the reconstructed

vs true muon kinetic vs true muon kinetic energy histogramenergy histogram

Bottom: each row has Bottom: each row has been normalized to one been normalized to one to produce the unfolding to produce the unfolding matrix, Mmatrix, Mijij

Each row of the matrix Each row of the matrix gives the probability that gives the probability that an event reconstructed an event reconstructed in bin i should be placed in bin i should be placed in true bin jin true bin j

Systematic ErrorsSystematic Errors For each error source, all parameters are varied according For each error source, all parameters are varied according

to a full covariance matrixto a full covariance matrix

For each new set of parameters, a new set of For each new set of parameters, a new set of systematically varied events, or “multisim”, is producedsystematically varied events, or “multisim”, is produced

To determine the systematic errors on each cross section To determine the systematic errors on each cross section measurement, the cross section calculation is repeated measurement, the cross section calculation is repeated using the multisim as though it were the central value using the multisim as though it were the central value Monte Carlo simulationMonte Carlo simulation

For the absolute For the absolute CCCCππ+ + cross section measurements, the cross section measurements, the dominant systematic uncertainties are:dominant systematic uncertainties are: flux predictionflux prediction modeling of pion absorption and charge exchange modeling of pion absorption and charge exchange

interactions in the tankinteractions in the tank

Cross Section Cross Section MeasurementsMeasurements

One-Dimensional MeasurementsOne-Dimensional Measurements σσ(E(Eνν): ): neutrino energyneutrino energy ddσσ/d(Q/d(Q22): ): momentum transfermomentum transfer ddσσ/d(KE/d(KEμμ): ): muon kinetic energymuon kinetic energy ddσσ/d(cos /d(cos θθμνμν): ): muon/neutrino anglemuon/neutrino angle ddσσ/d(KE/d(KEππ): ): pion kinetic energypion kinetic energy ddσσ/d(cos /d(cos θθπνπν): ): pion/neutrino anglepion/neutrino angle

Double Differential Cross SectionsDouble Differential Cross Sections dd22σσ/d(KE/d(KEμμ)d(cos )d(cos θθμνμν): ): muon kinetic energy vs anglemuon kinetic energy vs angle dd22σσ/d(KE/d(KEππ)d(cos )d(cos θθπνπν): ): pion kinetic energy vs anglepion kinetic energy vs angle (emphasize not FSI corrected)(emphasize not FSI corrected)

Each of the Single Differential Cross Sections has also been measured in two-dimensions as a function of neutrino energy

Results in gold will be shown

on the following slides

Absolute CCAbsolute CCππ+ + Cross Section Cross Section in Neutrino Energyin Neutrino Energy

The measured cross section is The measured cross section is shown in red, and the total shown in red, and the total uncertainty is given by the green uncertainty is given by the green error banderror band

The lower plot gives the fractional The lower plot gives the fractional error and the ratio of the Monte error and the ratio of the Monte Carlo prediction to the measured Carlo prediction to the measured cross sectioncross section

The Monte Carlo prediction is The Monte Carlo prediction is shown in black for comparisonshown in black for comparison

In addition to the diagonal errors In addition to the diagonal errors shown, full correlated error shown, full correlated error matrices have been produced for matrices have been produced for all measurementsall measurements

CH2 Target

Absolute CCAbsolute CCππ+ + Cross Section in Cross Section in QQ22

Top: measured cross section Top: measured cross section with error bands (with Monte with error bands (with Monte Carlo prediction for Carlo prediction for comparison)comparison)

Bottom: fractional Bottom: fractional uncertainties in each bin (with uncertainties in each bin (with MC prediction ratio)MC prediction ratio)

Just like CCQE, the data turn Just like CCQE, the data turn over faster relative to Monte over faster relative to Monte Carlo at low QCarlo at low Q22

This measurement is flux This measurement is flux averaged, so each bin has a averaged, so each bin has a minimum uncertainty of 12%minimum uncertainty of 12%

CH2 Target

Double Differential Cross Double Differential Cross Section in Pion Energy and Section in Pion Energy and

AngleAngle Top: measured double Top: measured double

differential cross section in differential cross section in pion kinetic energy and pion kinetic energy and cos(θcos(θπ,νπ,ν))

Bottom: fractional Bottom: fractional measurement uncertainty measurement uncertainty in each binin each bin

A full correlated error A full correlated error matrix has been calculated matrix has been calculated that includes each that includes each measured 2D binmeasured 2D bin

CH2 Target

SummarySummary

MiniBooNE recently submitted a measurement of theMiniBooNE recently submitted a measurement of theCCCCππ++/CCQE/CCQE cross section ratio to PRL cross section ratio to PRL

By exploiting the hadronic interactions of charged pions, we By exploiting the hadronic interactions of charged pions, we can now reconstruct both the pion and the muoncan now reconstruct both the pion and the muon

With a few simple cuts, we can achieve an event purity of 90%, With a few simple cuts, we can achieve an event purity of 90%, while correctly identifying muon & pion tracks with an 88% while correctly identifying muon & pion tracks with an 88% success ratesuccess rate

Using this new fit technique, we have produced the first ever Using this new fit technique, we have produced the first ever differential and double-differential differential and double-differential CCCCππ++ cross section cross section measurements in both muon and pion final state kinematic measurements in both muon and pion final state kinematic variablesvariables

We plan to publish these results this summerWe plan to publish these results this summer

BackupsBackups

Multisim ProductionMultisim Production For systematic uncertainties that only affect the probability For systematic uncertainties that only affect the probability

of an event occurring (e.g. flux & cross sections), multisims of an event occurring (e.g. flux & cross sections), multisims can be created via reweightingcan be created via reweighting

For the optical model, 67 unisims were generated from For the optical model, 67 unisims were generated from scratchscratch

Below are multisim error examples for a single Below are multisim error examples for a single reconstructed neutrino energy bin (1000 < Ereconstructed neutrino energy bin (1000 < Eνν < 1050 MeV) < 1050 MeV)

Central Value MC

100 π+ reweighting multisims

67 Optical Model multisims

Central Value MC

Energy Energy ShoulderShoulder

The low fit energy The low fit energy shoulder inshoulder in(E(Efitfit-E-Etruetrue)/E)/Etruetrue comes comes from higher energy from higher energy eventsevents

more energy lost in more energy lost in kinkskinks

more kinksmore kinksEtrue

(Efit-E

tru

e)/

Etr

ue

From a Monte Carlo simulation ofsingle pion events generated uniformly

between 50 and 450 MeV

Detector Simulation Detector Simulation UncertaintiesUncertainties

The optical model contains 35 The optical model contains 35 parameters that control a variety parameters that control a variety of different phenomena, such asof different phenomena, such as scatteringscattering extinction lengthextinction length reflectionsreflections PMT quantum efficiencyPMT quantum efficiency

Each parameter is simultaneously Each parameter is simultaneously varied within its measured error varied within its measured error in an attempt to ascertain in an attempt to ascertain information about parameter information about parameter correlationscorrelations

The default GFLUKA model has The default GFLUKA model has been replaced by GCALOR, which been replaced by GCALOR, which more accurately represents pion more accurately represents pion absorption and charge exchange absorption and charge exchange datadata The residual discrepancy is taken The residual discrepancy is taken

as a systematic uncertaintyas a systematic uncertainty

Beryllium/Aluminum Cross Beryllium/Aluminum Cross SectionsSections

Nucleon and pion cross sections have several Nucleon and pion cross sections have several components related by:components related by:

σσTOTTOT==σσELAELA++σσINEINE==σσELAELA+(+(σσQEQE++σσREAREA))

σσTOTTOT: total interaction cross section: total interaction cross section σσELAELA: elastic scattering cross section: elastic scattering cross section σσINEINE: inelastic scattering cross section: inelastic scattering cross section σσQEQE: quasi-elastic scattering: quasi-elastic scattering

(target breakup; incident particle intact)(target breakup; incident particle intact) σσREAREA: “reaction” cross section: “reaction” cross section

(all non-QE inelastic scattering)(all non-QE inelastic scattering)

Custom models have been built for the total, Custom models have been built for the total, quasi-elastic, and inelastic cross sectionsquasi-elastic, and inelastic cross sections

σσTOTTOT: Glauber model for elastic scattering : Glauber model for elastic scattering (coherent nucleon sum) + optical theorem(coherent nucleon sum) + optical theorem

σσQEQE: incoherent nucleon sum + shadowed : incoherent nucleon sum + shadowed multiple scattering expansionmultiple scattering expansion

σσINEINE: Regge model parametrization; fit to data: Regge model parametrization; fit to data

Nucleon Inelastic Cross Sections

Pion Inelastic Cross Sections

Be

AlBe

Al

Pion Production Pion Production UncertaintiesUncertainties

The Sanford-Wang function fit to the The Sanford-Wang function fit to the HARP data produces a HARP data produces a χχ22/dof of 1.8/dof of 1.8

To account for this discrepancy, the To account for this discrepancy, the normalization uncertainty has normalization uncertainty has effectively been inflated to 18%effectively been inflated to 18%

The intrinsic HARP uncertainties are an The intrinsic HARP uncertainties are an uncorrelated 7%uncorrelated 7%

Rather than artificially inflate the Rather than artificially inflate the normalization to cover an normalization to cover an incompatibility in the shape of the incompatibility in the shape of the parametrization, the HARP data is fit parametrization, the HARP data is fit to a spline functionto a spline function

The spline function passes through The spline function passes through the data points and the uncertainties the data points and the uncertainties blow up in regions with no datablow up in regions with no data

The SW function is still used to The SW function is still used to generate Monte Carlogenerate Monte Carlo

the uncertainties are given by the the uncertainties are given by the distance between each spline variation distance between each spline variation and the SW central valueand the SW central value

this inflates the error in regions where this inflates the error in regions where the SW and spline central values the SW and spline central values disagreedisagree

pion cross section vs momentum in bins of pion

angle

Flux UncertaintiesFlux Uncertainties Several components of the Several components of the

simulation have been varied to simulation have been varied to assess the effect they have on the assess the effect they have on the ννμμ flux (called “unisims”) flux (called “unisims”)

horn currenthorn current horn current skin depth in the inner horn current skin depth in the inner

conductorconductor all measured (or calculated) all measured (or calculated)

components of the p,n,components of the p,n,ππ-Be,Al cross -Be,Al cross sections (while holding the other sections (while holding the other components fixedcomponents fixed

σσTOTTOT==σσELAELA++σσINEINE==σσELAELA+(+(σσQEQE++σσREAREA))

The plot shows the variations that The plot shows the variations that produce an effect larger than 2%produce an effect larger than 2%

The skin depth produces a large The skin depth produces a large effect at high energieseffect at high energies

The quasi-elastic cross section The quasi-elastic cross section calculations are the least calculations are the least constrained by data constrained by data → largest error→ largest error

ππ++ production uncertainties are given by the spline fit covariance matrix (taken about production uncertainties are given by the spline fit covariance matrix (taken about the SW central value)the SW central value)

KK++ uncertainties are given by the Feynman Scaling fit covariance matrix uncertainties are given by the Feynman Scaling fit covariance matrix

Nuance Nuance UncertaintiesUncertainties

Several parameters of the cross section Several parameters of the cross section model are varied; the most important model are varied; the most important are as followsare as follows

Each of the background processes are Each of the background processes are variedvaried CCQE: CCQE: M MAA = 1.234 ± 0.077 GeV = 1.234 ± 0.077 GeV

(6.2%)(6.2%) CC multi CC multi ππ: M: MAA = 1.30 ± 0.52 GeV (40%) = 1.30 ± 0.52 GeV (40%) DIS: DIS: normalization varied by 25% normalization varied by 25%

Several important nuclear model Several important nuclear model parameters are varied as wellparameters are varied as well binding energy: binding energy: 34 ± 9 MeV 34 ± 9 MeV

(26%)(26%) Fermi momentum: 220 ± 30 MeV/c Fermi momentum: 220 ± 30 MeV/c

(14%)(14%) pion absorption: pion absorption: 25% 25% pion charge exchange: 30%pion charge exchange: 30% ΔΔ+ N + N → N + N:→ N + N: 100% 100%

How Do Pions Behave in the How Do Pions Behave in the Oil?Oil? The top plots show the vertices of every emitted photon that The top plots show the vertices of every emitted photon that

hits a phototube for a typical 300 MeV pionhits a phototube for a typical 300 MeV pion The bottom plots show the Monte Carlo truth informationThe bottom plots show the Monte Carlo truth information

X vs Z Y vs Z

Sample FitSample FitTop plot fit Top plot fit

result result legend:legend:

Black line = pion OneTrack fitBlack line = pion OneTrack fit Red line = muon OneTrack fitRed line = muon OneTrack fit Magenta line = pion Magenta line = pion

OneTrackKinked fitOneTrackKinked fit

X vs Z Y vs Z