Studia symulacyjne
Rekonstrukcja energii, Q2, przypadki
wielopionowe
Paweł Przewłocki
Warszawska Grupa Neutrinowa
Pomiary związane z ND280

Spektrum energetyczne


Metody rekonstrukcji energii neutrina
Badanie tła pochodzącego od
produkcji pizer w oddziaływaniach
NC


Szacowanie przekrojów czynnych
NCpizero na podstawie CCpi+ (łatwiej
rekonstruowalne)
Tło pizerowe w SuperK – przypadki
wielopionowe
Generator and statistics




Generator: Nuance 3.006
Medium: water
With and without nuclear
reinteractions (FSIs)
500,000 evts generated




210873 cc and 83378 nc events – QE
112776 cc and 42856 nc events – RES
27187 cc and 9250 nc events – DIS
And others, more exotic (diffractive,
coherent, elastic on electrons)
Beam structure (after interactions)
All
QE
All
DIS
Neutrino energy reconstruction

Via total momentum
ν


Outgoing particles)
Sum of outgoing particles’ momenta should give us momentum of
the neutrino (assuming the nucleon is at rest – no fermi
momentum)
For QE we’ve got another formula
μ
θ
ν
p

We also assume no fermi momentum
here and a clean QE event – muon
and proton only
Advantages and drawbacks





QE formula needs only observables associated
with muon track – but it is in principle valid only
for QE interactions
QE formula is therefore senseless for NC events –
no muon
Total momentum formula suffers from the fact
that not all the final states are visible in the
detector
Both methods are impaired by neglecting the
fermi motion of the target nucleon (this results in
some smearing of the reconstructed energy)
What particles are visible – first guess: muons,
electrons, protons, pizeros, pi charged
True (MC) vs total mom (no FSI)

All particles visible – just to show that it works
(smearing due to Fermi motion)
Ereco [GeV]
Solid – MC Energy
Dashed - reconstructed
[GeV]
E MC [GeV]
True (MC) vs total mom vis(no FSI)
Visibility as described before
Ereco [GeV]
Solid – MC Energy
Dashed - reconstructed
[GeV]
Totally invisible events (NC of course, CC have at least a muon)
E MC [GeV]
True (MC) vs QE formula (no FSI)
CC events only
Ereco [GeV]
Solid – MC Energy
Dashed - reconstructed
E MC [GeV]
Wondering which are QEs and which
nonQEs on the scatterplot?
Orange dots denote ideal reconstruction
QEs
nonQEs
The large smearing here is because of Fermi motion (apart from the fact that
Nuance includes deexcitation particles in the final state but this is negligible)
Quality of reconstruction plots
Total mom vis
All evts
QE formula CC
Ereco - EMC
Quality of reconstruction comparison
Solid – QE formula, Dashed – Total visible momentum
CC, all channels
CC QE
QE formula works better for QE, total momentum is better for others
The problem

Sometimes the reconstruction error is REALLY
huge:
the difference
diff: 167.7042
enu (reco): 170.1219
cos: -0.8033161
pmu: 0.5125948
14
0.1056796E-06 0.000000
2.417668
2112 -0.9664943E-02 -0.1033968
-0.1701247
13
0.7104180E-01 -0.2968962
-0.4117757
2212 -0.8070657E-01 0.1934993
2.659319
22
-0.4696306E-02 0.1602426E-03 -0.4013904E-02
id
px
py
pz
2.417668
0.9334740
0.5233710
2.827771
0.6180000E-02
E
0.1993157
0.5125948
2.667571
0.6180000E-02
p
Surprisingly large error in comparison with the Fermi motion distorsion (max. ~250MeV)
Investigation



Simple QE simulator with and without
Fermi motion
Fermi motion in [0, 250MeV]
Incoming neutrino energy in [0, 5GeV]
CMS
Neutrino plus proton
E 
E 2  m2  m 2p
2E
Muon and proton
Muon cosine vs muon momentum
cos
cos
No fermi
smearing
Fermi max 250MeV
P [GeV]
P [GeV]
Muon pz vs muon momentum
smearing
No fermi
Fermi max 250MeV
No doubts where the smearing comes
from
Fermi max 1GeV
Does this cause the errors?

Average error as a function of total muon momentum, in
the region denoted on slide 6
Error in %
Error (forget the bars)
Multiplicity in the same bins
Does this cause the errors?

Average error as a function of sine of ‘angle’ on pz vs p plot
Error in %
Error (forget the bars)
sine
Multiplicity in the same bins
sine
Rozwiązanie


1
0,8
0,6
0,4
muon cosine
Wyjście poza obszar
dozwolony powoduje
niekontrolowane
zachowanie się
mianownika we wzorze
rekonstrukcyjnym
Powinniśmy brać pod
uwagę te przypadki,
które znajdują się w
obszarze dozwolonym
Dla naszej próbki błąd
powyżej +50% ma
0.6% przypadków
0,2
0
-0,2 0
1
2
3
4
5
4
5
-0,4
-0,6
-0,8
-1
muon momentum
QE formula infinity curve
5
4
3
pz

QE formula infinity curve
2
1
0
0
1
2
3
-1
ptot
Rekonstrukcja Q2

Badanie tła pochodzącego od
produkcji pizer w oddziaływaniach
NC


Szacowanie przekrojów czynnych
NCpizero na podstawie CCpi+ (łatwiej
rekonstruowalne)
Źródła różnic w rozkładach qsq dla
przypadków pizerowych i pi+
Różnice teoretyczne
 Różnice wynikające z pędu Fermiego i FSI

Qsquare considerations
Outgoing lepton
Neutrino
Qsq = four-momentum transfer
Nucleon
Hadrons



Ideal qsquare – from lepton vertex
Observable qsquare – from hadron vertex, assuming nucleon
doesn’t have a fermi momentum
We have to take into account additional nucleons in the hadron
vertex (calculating it in a real detector environment is a totally
different issue:-)
Qsquare – true and observable


Zakładamy
rekonstruowalność
wszystkich cząstek
Odpowiednia liczba
nukleonów w stanie
początkowym
All events

Widać rozmycie
spowodowane pedem
Fermiego (co powoduje
wejście Qsquare w
wartości ujemne)
Qsq [GeV^2]
Solid – lepton qsq, dashed – hadron qsq
Qsquare – true and observable
NC 1pizero
CC 1piplus
Qsq [GeV^2]
Solid – lepton qsq, dashed – hadron qsq
Qsq [GeV^2]
Let’s include FSIs


Solid – no FSIs, Dashed
– FSIs included (hadron
qsq)
FSIs smear qsq
distribution a little, but
nothing unexpected
All
Qsq [GeV^2]
FSIs: single pi production evts
Solid – no FSIs, Dashed – FSIs included
NC 1pizero
noFSI: 28685evts,
FSI: 21484evts
CC 1piplus,
noFSI: 109421evts,
FSI: 86276evts
Qsq [GeV^2]
Turning on FSIs means that some pis are absorbed, that’s why the number of evts gets smaller
Co dalej?


Uwzględnienie efektów
detektorowych – widzialność
cząstek (PID, cięcia na energię)
Liczymy na dalsza współpracę z
wrocławianami:-)
Tło wielopionowe




Single pi zero NC production
is the main background to
CC nu_e interactions
producing electrons
When we see a single pi
zero it doesn’t have to be a
single pion event; it can also
be a multipion event
(π0+nπ+/-), with other
(charged) pions being lowenergetic and this way
invisible to us in water
Čerenkov detector like SK
Let’s estimate how much we
miss by taking into account
only single pion events
In other words – how many
multipion events look like a
single pizero?
No FSI
FSI
NC1pizero
total
33632
26377
NC1pizero
0 pichrgd
28378
(84%)
20841
(79%)
NC1pizero
1 pichrgd
3100 (9%)
3218 (12%)
NC1pizero
2 pichrgd
1652 (5%)
1723 (7%)
Total: 500000 evts
Čerenkov visibility criteria



To see a charged particle
in a Čerenkov detector
such as SuperK, it has to
have energy of at least 1.5
times its mass
When there are other rings
in the vicinity, the realistic
threshold is something
about 1.5*m+50MeV (we
need a distinguishable
ring)
Pi zero is always visible by
its decay into two gammas
Results – visibility applied
noFSI
All events
visible as
single
pizero
Events that
fake single
pizero (being
in fact a
multipi)
28536
158(0.5%)
FSI, +50MeV
noFSI,
+50MeV
28797
419(1.5%)
FSI
21232
391(1.8%)
Single visible pizeros
Multi pi background
FSI,
+50MeV
21649
808(3.7%)
Pizero momentum [MeV]
Conclusion



4% is not a large contribution, at
least in the first phase of the
experiment
But in the phase of precise
measurements even 4% may be
significant
Measurements in ND280, perhaps in
future 2km LAr detector?