Hadronic Interaction Modelling in MINOS

0.16 MB·English

by  Michael Kordosky

Hadronic Interaction Modelling in MINOS
Michael Kordosky
For the MINOS collaboration
DepartmentofPhysicsandAstronomy
UniversityCollegeLondon
7 GowerStreet
0 LondonWC1E6BT
0 UnitedKingdom
2

n
Abstract.
a
TheMainInjectorNeutrinoOscillationsearch(MINOS)usestwodetectorsseparatedby735km
J
to measure a beam of neutrinos created by the Neutrinos at the Main Injector (NuMI) facility at
9
Fermi National Accelerator Laboratory. The experiment has recently reported an observation [1]

1 of n m disappearance consistent with neutrino oscillations. We describe the manner in which the
experiment’sresultsdependonthecorrectunderstandingandmodelingofhadronicsystems.
v
9 Keywords: hadroncalorimeter,finalstateinteractions,neutrinobeam
0
PACS: 13.75.-n,13.85.-t,24.10.Lx,29.40.Vj,29.25.-t
0
1
0
INTRODUCTION
7
0
/
x TheMainInjectorNeutrinoOscillationSearch(MINOS)isalongbaseline,two-detector
e neutrino oscillation experiment that will use a muon neutrino beam produced by the
-
p NeutrinosattheMainInjector(NuMI)facilityatFermiNationalAcceleratorLaboratory
e
(FNAL) [2, 3]. The measurement is conducted by two functionally identical detectors,
h
: located at two sites, the Near Detector (ND) at FNAL and the Far Detector (FD) in the
v
Soudan Underground Laboratory in Minnesota. The experiment began collecting beam
i
X data in March 2005 and has recently reported n m disappearance consistent with quasi-
ar two-neutrinooscillationsaccording to D m2 =2.74+0.44 10 3eV2/c4 and sin22q >
| 32| 0.26× −
0.87at 68% CL [1]. −
TheMINOSdetectorsaretracking-samplingcalorimeters,optimisedtomeasureneu-
trino interactions in the energy range 1.En .50GeV. The active medium comprises
4.1cm-wide, 1.0cm-thick plastic scintillator strips arranged side by side into planes.
Each scintillator plane is encased within aluminum sheets to form a light-tight module
and then mounted on a steel absorber plate. The detectors are composed of a series of
these steel-scintillator planes hung vertically at a 5.94cm pitch with successive planes
rotated by 90 to measure the three dimensional event topology. Wavelength-shifting
◦
andclear opticalfibers transportscintillationlightfrom each striptoHamamatsumulti-
anode photomultipliertubes that reside in light-tightboxes alongsidethedetector. Both
detectors aremagnetized so as to measuremuon charge-sign and momentumvia curva-
ture.
The n m disappearance measurement is done by using the event topology to identify
interactionsasn m CC,ratherthanNC/n e CC,thenreconstructingtheneutrinoenergy
− −
Y View Y View
20 20
15 15
p p
ri ri
St10 St10
5 5
0 0
0 Plane 20 0 Plane 20
X View X View
20 20
15 15
p p
ri ri
St10 St10
5 5
0 0
0 Plane 20 0 Plane 20
FIGURE 1. p + events measured in the MINOS calibration detector. The pionsare incidentfrom the
leftandtwo(orthogonal)viewsoftheeventareshown.Cellsdemarcatethedetector’sscintillatorstrips,
withshading/colorindicatingthepulse-heightofhits.Theeventontheleftwascollectedat1GeV/cbeam
momentumwhiletheoneontherightisfroma2GeV/crun.Toremovehitsduetoopticalcross-talkinthe
multi-anodePMTs,onlystripsregisteringapulse-heightlargerthan1.5PE(photoelectrons)areshown.
as the sum of the muon energy and the energy transferred to the nucleus : En =Em +n
wherenu=y En .Theoscillationhypothesisistestedbycomparingthemeasuredneu-
×
trinoenergyspectrumtothespectrumexpectedintheabsenceofoscillations.Thelatter
spectrum is anchored to observations made with the Near Detector. MINOS endeavors
to measure D m2 and sin22q with an accuracy of better than 10%. The results depend
upon a reliable knowledge of the event selection efficiency and the energy scale, both
of which are affected by the modeling of the hadronization process and the detector’s
signal and topological response to those hadrons. We will discuss the way that MINOS
hasdealtwiththeseissues.In addition,uncertaintiesintheproductionofhadronsinthe
NuMI target result in uncertainties in the neutrino flux and poor agreement with data.
We close by describing the manner in which data from the Near Detector was used to
constrainthesimulationoftheNuMIbeam.
p
10 data 0.6 GeV/c
data 1.6 GeV/c
data 3.0 GeV/c
5 MC
n
i
b
0

/

s
t 15
n
e e
v
e

%
10
5
0
0 100 200
calorimeter signal (a.u.)
FIGURE2. Pion andelectronline shapesasmeasuredin the MINOScalibrationdetector[4, 5].The
MonteCarlocalculationisthatoftheexperiment’sGEANT3/GCALORsimulation.Thesameprogramis
usedtomodelneutrinoinducedinteractionsintheMINOSNearandFarDetectors.
HADRONIC ENERGY SCALE
MINOS data suggests that (assuming quasi-two-neutrino oscillations) the largest sup-
pression of n m occurs for 1 < En < 2GeV and that the suppression slowly shrinks as
the energy increases to about 10GeV. This is a relativelylow energy range, but not low
enough to make the experiment dominated by quasi-elastic n m CC for which En may
−
+ polarity - polarity
55 55
)
V
e
G
s/
P 50 50
MI
(
e
s
n
o 45 Data 45
p
s
e GCALOR
R
SLAC-GHEISHA
40 40
0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Pion Energy (GeV)
FIGURE3. MINOSdetectorresponsetop inducedshowers[4].DatameasuredintheMINOScali-
±
brationdetectorarecomparedwiththeresultofGEANT3/GCALORandGEANT3GHEISHAsimulations.
Thep +/p responseasymmetryisabsentabove4GeV.
−
be reconstructed from only the muon energy and scattering angle. Instead, events with
1<En <10GeVhave,afterexperimentalcuts,anaverageinelasticityof 0.3.Weare
≈
therefore interested in hadronic showers in the few GeV range and in which the energy
iscarried byarelativelyfewparticles.Theresponseofcalorimeterstotheselowenergy
showers is notoriously difficult to model. Experiments generally remedy this by mea-
suringthe responseto single-particles,either to perform a direct calibrationor as away
of constraining/tuningthe showermodel. Since theMINOS Near and Far Detectors are
largeandhavebeenconstructedunderground,directexposuretoacalibrationbeamwas
notpossible.InsteadadedicatedCalibrationDetector(CalDet)wasbuilttoestablishthe
energy scaleand developthecalibrationtechnique.
The CalDet, a scaled-down but functionally equivalentmodel of the MINOS Far and
Near detectors, was exposedto test beams in the CERN PS East Area during 2001–3to
establishtheresponseoftheMINOScalorimeterstohadrons,electronsandmuonsinthe
momentumrange0.2–10GeV/c.Thedetectorconsistedofsixty2.5cm 1m 1msteel
× ×
plates each of which supported a plane of twenty-four 100cm-long scintillator strips.
Alternating planes were rotated 90 as in the larger MINOS detectors. The sampling
◦
fraction is 6.4% and the detecto±r has a longitudinal (transverse) granularity of 0.15l
I
(0.25l ).Identificationofp +m ,eand pwasaccomplishedusingatimeofflightsystem
I
andseveralthresholdCˇerenkovcounters.Pionsandmuonswerediscriminatedusingthe
event topology. Fig. 1 shows two pion induced showers measured in the detector. Data
were collected in 200MeV/c steps (1GeV/c for p >4GeV/c) in both positiveand
beam
negativebeam polarityandin twobeamlines(T11 andT7).
The detector was calibrated using a procedure similar to that employed in the Near
and Far detectors [6]. Gain and light-output non-uniformities were corrected using an
LED based light injection system [7] and through-going cosmic-ray muons [8]. The
absolute scale, in “muon equivalent units”, was defined as the average signal per-
plane induced by muons with momenta between 0.5–1.1GeV/c at the time of plane
crossing [9]. The momentum was determined by requiring that the muons stop in the
detector(pm .2.2GeV/c),thenworkingbackwardalongthetrack,invertingtherange-
energy relation[10].
Figure 2 shows p + and electron line-shapes measured in the calibration detector
and compared to the GEANT3/GCALOR [11, 12, 13] Monte Carlo. The simulated re-
sponse to electrons was in good agreement with the data after upstream energy loss
(e.g., via bremsstrahlung and ionization) was included in the simulation. The e/p re-
sponse ratio is energy dependent but always > 1 and 1.27 for momenta above a
≈
few GeV. The line-shapes display an asymmetric, high-side tail characteristic of non-
compensatingcalorimeters.TheagreementbetweenthedataandtheMCissurprisingly
good, even at the lowest momentum settings. The energy resolution may be parame-
terisedas 56%/√E 2% forp showersand 21.4%/√E 4%/E forelectrons.
±
The detector’s res⊕ponse to p is shown as a function o⊕f energy in Fig. 3. The data
±
areinsomewhatbetteragreementwiththeGCALORbasedsimulationthantheyarewith
the GHEISHA [14, 15] based one. The agreement is excellent for p + induced showers
butpoorerforp showers.Thisreflectsameasuredasymmetry,asmuchas6%forfew-
−
GeV energies, in the detector’s response to p + and p . This asymettry was not present
−
in the response to e± nor in the range of m ± and vanishes for Ep & 3GeV. Its origin
may lie in differences, between p ++N and p +N, in the multiplicity of secondaries
−
producedin inelasticinteractionsat theselowenergies [16].
Hadronicshowersproducedinneutrinointeractionsaresimulatedwiththeversionof
GEANT/GCALOR shown here. Because these showers consist of multiple particles, and
becausetheresponsetoe,p and palldiffer(thelattertwobelow 1GeVwhereprotons
∼
tendtorangeoutbeforeinteractinghadronically)wecannotderivetherelationbetween
detectorsignalandenergycarriedbytheshowerparticlesdirectlyfromtheCalDetdata.
Instead we derive the relationship from the MC but assign a somewhat pessimistic 6%
systematicerrorontheresponse.Thiserrorissmallenoughtohaveanegligibleeffecton
theprecisionofresultsfromthelow-statisticsfirstyearMINOSdataset.Theuncertainty
may be reduced by introducing data based correction factors into the relation or, more
ideally, by improving the hadronic shower model. Over the long term MINOS plans to
transitiontoaGEANT4basedsimulationinthehopesofimprovingthehadronicshower
treatment.
FINAL STATE INTERACTIONS
Test beam measurements, such as the one discussed above, are used to determine a de-
tector’s hadronic and electromagnetic response to single particle induced showers. The
singleparticlebasedcalibrationmaybeusedforenergymeasurementsofmulti-particle
showers(e.g., “jets”)if theenergy response is sufficientlylinear and if theparticlecon-
tentoftheshoweris wellknownor, especially,ifthecalorimeter’sresponseto different
particles of the same energy is identical (e.g.,a compensating calorimeter) [17]. These
concerns apply to neutrino induced showers (which bear some similarity to jets) but
there is an additional complication owing to the fact that the neutrino interacts in the
dense nuclear medium of the target nucleus. Hadrons produced by the neutrino must
· 103
1.8 30
rescattering
1.6 D m2 = 2.47e-3 eV2 OFF
20 Full p absorption
1.4 t =0.342 fm/c
eV1.2 D m2 = 2.72e-3 eV2 %) 10 t00=0.801 fm/c
0.5 G1.0 D m2 = 3.12e-3 eV2 nse (
nts / 0.8 espo 0
e R
v0.6 -10
e
D
0.4
-20
0.2
0.0 -30
0 2 4 6 8 10 00 22 44 66 88 1100
visible neutrino energy (GeV) ttrruuee nn ((GGeeVV))
FIGURE 4. Left: Energy distribution of simulated n m CC events at the MINOS Far Detector. The
−
effectof neutrinooscillationsis includedfor D m2=2.47,2.72and 3.12 10 3eV2 (68%CL limits of
−
Ref.[1])andsin22q =1.Individualcurvescorrespondtouncorrelated ×1s variationsintheformation
time,pionabsorptioncross-sectionandtheneutrinoinduced2p productio±ncross-section.TheMCsample
correspondsto the “high-statistics limit”, approximately 10 of the planned MINOS exposure. Right:
The variation in the calorimeter’s response as a function×of the energy transfer n and under different
final state interaction scenarios. Zero on the vertical scale correspondsto the p npnp modelof pion
absorptionandt =0.52fm/c. →
0
escapethenucleustocreateasignalinthedetectorbut,atMINOSenergies,oftensuffer
a hadronic interaction before doing so. It is important to account for these “final state
interactions” because neutrino oscillation experiments seek to measure the energy, n ,
transferred bytheneutrinotothetarget,soas toreconstructEn =Em +n .Thepresence
offinalstateinteractionscausesn =E ,wherethelatteristhevisibleenergyofshower
vis
6
particles exiting the nucleus. We will describe the way in which final state interaction
aremodelledand howuncertaintiesareaccounted for.
Neutrino interactions in MINOS are modelled by NEUGEN-v3 [18]. NEUGEN in-
cludesafinal stateinteractions(alsoreferred toas “intranuclearre-scattering”)package
known as INTRANUKE. The code is anchored to a comparison of final states in n +d
andn +NeinteractionsasmeasuredintheBEBCandANL–12ftbubblechambers[19].
The library includes a treatment of pion elastic and inelastic scattering, single charge
exchange and absorption in a cascade simulation of the final state. The relative proba-
bilities for these processes are approximately 35:50:10:5 (40:30:7:23) at a pion kinetic
energy of 1GeV (250MeV). The formation zone concept is included by suppressing
interactionsthatwouldhaveoccurredbeforethepionhastravelledadistancel =t p/m
0
t = 0.52fm/c [20]. The simulation includes a treatment of pion absorption inspired
0
by[21].Absorbedpionstransfertheirenergytoanpnpclusterandtheindividualnucle-
onsare thentracked inGEANT.A morecomprehensivedescriptionoftheINTRANUKE
codeandit’seffect in MINOSisgivenin Ref. [22].
We derive the effect that parametric uncertainties in the final state interaction model
have on the oscillation result as follows. First, the model contains a number of param-
eters for which the uncertainty may be estimated, however roughly, based on external
data.Thedependenceofthereconstructedshowerenergyonn wasstudiedasafunction
ofthesemodelparametersandthemostinfluentialwereidentified.Theparameterswere
then varied in an uncorrelated way over multiple trials and the visible n m CC energy
−
spectra were constructed, accounting for the detector energy smearing. This was done
withoutoscillationssoastorepresentmeasurementsmadeintheNearDetectorandwith
oscillations at varying D m2 and sin22q to represent measurements at the Far Detector.
An example of simulated Far Detector spectra is shown on the left in Fig. 4. The D m2
valueswerechosenaccordingtothebest-fitand 1s uncertaintiesontheinitialMINOS
result [1]. For each trial a fit was performed to±extract D m2 and sin22q and the differ-
ences with respect to the input values were histogrammed. The mean and width of the
distributionsisanestimateoftheuncertaintyattributedtotheparameteruncertaintiesin
thefinalstateinteractionmodel.Wefindd D m2 3 10 5eV2/c4 andd sin22q 0.01.
−
≈ × ≈
These errors are small compared to the overall uncertainty as may be noticed from the
fact thatthecurvesfordifferent valuesofD m2 inFig. 4 areeasily distinguished.
A much larger uncertainty occurs as a consequence of the rather simple way in
which the final state interaction code simulates pion absorption and inelastic collisions.
Absorption is modelled, by default, as solely due to p npnp but we know that
processes such as p npp and p nnp may also occu→r and that the nucleons are
→ →
themselves attenuated inside the nuclear medium (this effect is not accounted for).
In addition, p +N inelastic collisions are modelled but the energy lost by the p is
discarded and secondary p are not created. These model based deficiencies result in
alargeuncertaintyon theamountofvisibleenergy emittedfromthenucleus.
The model based uncertainties cannot be accounted for by the parametric variation
techniquedescribedabove.Instead,westudysimulationsdone(a)withoutre-scattering,
(b)withpionabsorptionaccordingtop npnp(thedefault)and(c)inwhichtheenergy
→
of absorbed pions is discarded. The differences a b and c b in the reconstructed
shower energy are shown as a function of n on the r−ight-hand−side of Fig. 4. The curve
labelled “OFF” corresponds to a c and represents the change in visible energy due to
inelastic pion interactions. The cu−rve labelled “Full p absorption” corresponds to c b
−
and represents the change in visible energy due to pion absorption. For comparison the
(muchsmaller)effectof 1s variationsintheformationtimeisalsoshown.Toestimate
the uncertainty on the ±oscillation parameters, the n E relation is modified
shower
↔
according to Fig. 4 and the analysis is repeated. We find that the parameters shift by
d D m2 6 10 5eV2/c4 and d sin22q 0.05.When drawingthe oscillationcontours,
−
≈ × ≈
uncertainties in both the single particle energy scale and final state interactions are
includedasan 11% penaltyterm (“nuisanceparameter”)on thehadronicenergy scale.
The experiment is currently working on improvements in the final state interaction
model [23] to remedy the deficiencies mentioned above. In addition, the model is
beingre-implementedtofacilitatere-weightingofMCevents.Are-weightablemodelis
extraordinarily important because it vastly reduces the number of MC events needed
to estimate systematic uncertainties. Re-weighting machinery would also allow the
parametric variation technique described above to be used directly in the oscillation fit
by including the final state interaction model parameters as nuisances. The importance
of event by event re-weighting is one reason that experiments may prefer homegrown
codes,forwhichthemodelparameterscanbealteredanduncertaintiesunderstood,over
moresophisticatedbut alsomoreopaquegeneral purposecodes.
40
T 80 80
O
P
6 30 a b c
1 60
0 60
1
V / Data
Ge20 Fluka05 MC 40 40
s / Full MC Tuning
nt10 20 20
e
v
E
1.5 1.5 1.5
o
ati
R 1 1 1
0 5 10 15 0 5 10 15 0 5 10 15
Reconstructed E (GeV)
n
FIGURE 5. The reconstructed energy distribution of n m CC events observed in MINOS. The data
−
werecollectedin the(a) low(b)mediumand(c)highenergybeamconfigurationsandare comparedto
thepredictionsoftheneutrinobeamMonteCarlo,usingFLUKA05tosimulatehadronproductioninthe
NuMItarget.WeshowtheMCpredictionbeforeandafterthetuningproceduredescribedinthetext.
ESTIMATION OF THE NEUTRINO FLUX
Theneutrinobeamlinemodelisseparatedintothreeparts:(a)asimulationofthehadrons
produced by 120GeV/c protons incident on the NuMI target and (b) the propagation
of those hadrons and their progeny through the magnetic focusing elements, along the
677m decay pipe, and intothe primary beam absorber and (c) decay of themesons and
calculationoftheprobabilitythatanyneutrinoprogenytraversestheNearandFardetec-
tors.Hadronicproductionissimulatedusingadetailedmodelofthetargetgeometryand
materialcomposition.Bydefault,interactionsaregeneratedwithFLUKA05[24,25,26]
but output from the MARS-v15 [27, 28, 29] and GEANT-FLUKA [30] codes, as well
as calculations based on the parameterisations of BMPT [31] and Malensek [32], are
usedas cross-checks. Theproduced hadronsare propagatedinaGEANT3simulationof
theNuMIbeamline.Decays in whichaneutrinoisproduced aresavedand laterusedas
inputforneutrinoeventsimulationintheNearand FarDetectors.
The neutrino fluxes predicted by the different models vary by 10-20%. This is un-
suprising given the relatively paucity of hadron production data in the x ,p region
F T
interesting to NuMI, not to mention at 120GeV/c and on a thick Carbon target [33].
Therefore, the rather good agreement between the n m CC energy spectrum measured
−
in the Near Detector and the MC prediction based on FLUKA05 (Fig. 5), comes as a
pleasant suprise. The data/MC agreement is, however, not perfect and can be improved
bytakingadvantageoftheflexibilityoftheNuMIbeamline.TheNuMItargetmaybere-
motelymovedalongthebeamaxis,changingthex ,p regionfocusedbythemagnetic
F T
horns, and thereby the beam energy. Figure 5 shows data taken in three target postions:
z = 10cm,100cm and 250cm where z=0cm is the locatio of the target when fully in-
serted into the first horn. These data, along with data taken at z=10cm with the horns
offandwiththehorncurrentmodifiedby 8%,areusedinaparametericfittoconstrain
±
thebeam model.
Thefitisbased onaparametricmodel[34],similarto thatofBMPT,whichisableto
describethed2N/dx dp distributionpredictedbyFLUKA.Themodelparameterswere
F T
allowedto float inafit to then m CC energy spectra. Thefit also includednuisancepa-
−
rameterstoaccount foruncertaintiesinbeamfocusing,intensity,and detectorresponse.
Themean transversemomentumofpions, p was constrained to theFLUKA05value
T
h i
of 364MeV/c, with a penalty term of 15MeV/c, obtained from the variation of hadron
production models. The results of the fit are shown as the “Full MC Tuning” curve in
Fig.5.Thefittingproceduredramaticallyimprovesthedata/MCagreement,particularly
inthelowestenergyconfigurationinwhichmostoftheoscillationdatasetwasrecorded.
Theoscillationanalysesusetheseresultsasthefirststepinthepredictionoftheneutrino
spectrumat theFarDetector.
SUMMARY
We have attempted to highlight some of the ways in which MINOS depends upon the
correct understanding and modelling of hadronic interactions from 120GeV (hadron
production)toafewtensofMeVandless(calorimetry).Hadronicinteractionsarediffi-
cult to model correctly and whenever possible we have attempted to benchmark and/or
constrain simulations using internal or external datasets. One expects that models will
never completely agree with the data so much effort is concerned with quantifying the
effect that disagreements have upon the oscillation results. Uncertainties are generally
included as nuisance parameters and fitting is greatly facilitated by the ability to re-
weighteventsformodel changes. Finally,in theinterest ofbrevitywe havebeen forced
toomitsomeimportanttopics,suchastheeffectofshowermodelinguncertaintiesonthe
NCbackgroundestimatedinthereconstructedn m CC sampleaswellasthesensitivity
ofthen CC eventselectiontothefragmentation−/hadronisationtreatment.
e
−
The author would like to thank J. Morfin, H. Gallagher, R. Ransome and S. Dytman
foradviceandcommentsregardingfinalstateinteractionsandN.Mokhovforcomments
about low energy pion nucleus interactions. The hadron production fitting is due to
S. Kopp,Ž. Pavlovic´ and P. Vahle.
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