2 B C f c ( 0 E ) = 1 + 2 A + ..... 0 0 A E E 1 - - PDF document

SLIDE 1

Relative Flux, FD/ND, using Low-ν Technique: Part-I

• H. ¡Duyang, ¡ ¡Sanjib ¡R. ¡Mishra, ¡& ¡Xinchun ¡Tian ¡

with ¡contributions ¡from ¡ ¡ Maxim Gonchar & Roberto Petti 01

SLIDE 2

Low-ν Idea ¡➾

SRM, Wold.Sci. 84(1990), Ed.Geesman

3 Determination of Relative Neutrino Flux

The dynamics of neutrino-nucleon scattering implies that the number of events in a given energy bin with Ehad < ν0 is proportional to the neutrino (antineutrino) flux in that energy bin up to corrections O(ν0/Eν) and O(ν0/Eν)2. The method follows from the general expression

• f the ν-nucleon differential cross section. By invoking the assumptions of locality, Lorentz

invariance, CP-invariance, and the V-A current structure of the lepton vertex, the expression

• f the differential cross section is:

dσν(ν) dxdy = G2

FME

π

• (1 − y − Mxy

2E )F ν(ν)

2

+ y2 2 2xF ν(ν)

1

± y

• 1 − y

2

• xF ν(ν)

3

• (2)

The symbols have their usual meanings; the structure functions Fi are functions of x and

• Q2. It should be noted that the above expression is independent of the specifics of nucleon

composition; in particular no assumption about quark/partons as nucleon constituents need be invoked. Using ν = Eν × y, and integrating the ν-N differential cross section with respect to x (from 0 to 1) and ν (from 0 to ν0), we get: N(ν < ν0) = Φ(Eν). ν0 1 dσ dxdν dxdν = C.Φ(Eν).

• (ν0 − ν2

0/2Eν)F2 + ν3

6E2

ν

F1 ± ( ν2 2Eν − ν3 6E2

ν

)F3

• (3)

where Fi = 1 ν0

0 Fi(x)dxdν, N(ν < ν0) is the number of events in a given energy bin (Eν)

with hadronic energy less than ν0, C is a constant, and the term Mxy

2Eν has been suppressed for

• simplicity. It should be noted that the integrals Fi contain the appropriate factors of x in the

integrand for the structure functions xF3 and 2xF1. By rearranging terms as coefficients of (ν0/Eν) and its powers we arrive at the more amenable form: N(ν < ν0) = C.Φ(Eν).ν0

• F2 − ν0

2Eν (F2 ∓ F3) + ν2 6E2

ν

(F2 ∓ F3)

• =

C.Φ(Eν).ν0

• A + ( ν0

Eν )B + ( ν0 Eν )2C + O( ν0 Eν )3

• 19

N(ν<ν0) α φ(Eν) up to (ν0/E), (ν0/E) 2

02

SLIDE 3

RELATIVE FLUX WITH LOW-ν METHOD

✦ Relative νµ, ¯ νµ flux vs. energy from low-ν0 method: N(Eν, EHad < ν0) = kΦ(Eν)fc( ν0

Eν )

the correction factor fc(ν0/Eν) → 1 for ν0 → 0: fc( ν0

Eν ) = 1 +

• ν0

Eν

• B

A −

• ν0

Eν

2

C 2A + .....

where A = G2

FM/π

1

0 F2(x)dx, B = −G2 FM/π

1

0 (F2(x) ∓ xF3(x)) dx and

C = B − G2

FM/π

1

0 F2(x) [(1 + 2Mx/ν)/(1 + R(x, Q2)) − Mx/ν − 1] dx

✦ In practice use MC to calculate the correction factor normalized at high Eν: fc(Eν) =

σ(Eν, EHad<ν0) σ(Eν→∞, EHad<ν0)

where the denominator is evaluated at the highest energy accessible in the spectrum. = ⇒ Need precise muon energy scale and good resolution at low ν values = ⇒ Reliable flux predictions for Eν 2ν0 − → DUNE spectra require ν0 ≃ 0.25 ÷ 0.50 GeV

etti

(S. R. Mishra, Wold. Sci. 84 (1990), Ed. Geesm

➳

⇐

03

SLIDE 4

Enu

10 20 30 40 50 60

correction

0.5 0.6 0.7 0.8 0.9 1 1.1

neutrino anti−neutrino

correction ν

Figure 1: ν0 correction for ν0 = 1.0 GeV as a function of Eν for νµ and νµ

5 Empirical Parametrization of π+, K+, π−, and K− using the Low-ν Events in ND

Our analysis entails an empirical prarametrization (EP) of the secondary π± and K± pro- duction in 120 GeV p-NuMI target as a function of xF and pT using the relative flux determined by the low-ν events in the ND. The analysis should be contrasted with the ‘traditional’ method of using the low-ν events, as in CCFR/NuTEV and in the MINOS- ND: start with data CC events with EHad ≤ ν0 correct for acceptance and smearing; apply the low-ν correction to obtain the relative ν-flux at ND. (The analysis of the in- clusive νµ-cross section by Debdatta and Donna [2] essentially use this method.) The advantage of the EP analysis is as follows:

• ND and FD Flux: The EP constraints of pions and kaons allows us to accurately predict

the FD flux predicated on the ND low-ν events.

• The νe and νe Flux: Constraining the normalization and energy dependence of π+,

and, hence, of µ+, and K+ allows us to predict the νe/νµ ratio at the ND and the FD [3]. 19

*(B/A), ¡(C/A) ¡➾ ¡Low-­‑ν ¡Processes ¡ ¡

Figure ¡of ¡Merit ¡for ¡(B/A): ¡ ¡ν ¡~ ¡-0.3; ¡ ¡ν ¡~ ¡-1.5 (NOMAD spectrum) ¡

*Error ¡on ¡(B/A) ¡ ¡⇔ ¡Err. ¡in ¡Low-­‑ν ¡Interactions

_

04

SLIDE 5

(MINOS)( (MINOS)(

E (GeV)

• 2

10 × 5

• 1

10

• 1

10 × 2 1 2 3 4 5 6 78 10 20 30 40 )

2

cm

• 38

(10 σ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 <0.25 ν GENIE MC <0.5 ν GENIE MC <1.0 ν GENIE MC <2.0 ν GENIE MC <5.0 ν GENIE MC

<1 ν MINOS <2 ν MINOS <5 ν MINOS Cut for Neutrino on Carbon Fraction of Events with

E (GeV)

• 1

10 × 2 1 2 3 4 5 6 7 8 910 20 30 40 50 )

2

cm

• 38

(10 σ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

<0.25 ν GENIE MC <0.5 ν GENIE MC <1.0 ν GENIE MC <2.0 ν GENIE MC <5.0 ν GENIE MC <1 ν MINOS <2 ν MINOS <5 ν MINOS

MINOS Coll., PRD 81 (2010) 072002

• A. Bodek et al., EPJC 72 (2012) 1973

*(B/A), ¡(C/A) ¡➾ ¡Low-­‑ν ¡Processes ¡ ¡

Figure ¡of ¡Merit ¡for ¡(B/A): ¡ ¡ν ¡~ ¡-0.3; ¡ ¡ν ¡~ ¡-1.5 (for ¡NOMAD) ¡

*Error ¡on ¡(B/A) ¡⇔ ¡Err. ¡in ¡Low-­‑ν ¡Interactions

_

⟸

05

SLIDE 6

✦ Low-ν technique only provides RELATIVE BIN-TO-BIN flux as a function of Eν, NOT ABSOLUTE flux = ⇒ Implicit constraint of fixed flux integral (introduces correlation among bins) ✦ Freedom to chose the energy range used to impose the normalization constraint = ⇒ E.g. Eν bins with higher statistics / smaller systematic uncertainties ✦ The correction factor fc(Eν) can be affected by model uncertainties on (anti)neutrino-nucleus cross-sections (QE, RES, DIS)

• Typically keep fc(Eν) at the level of few percent or below (small ν0/Eν)

to minimize model uncertainties (correction to correction);

• For ν0 = 0.25 ÷ 0.50 GeV samples almost entirely QE (99 ÷ 75%) and RES;
• Low-ν sensitive only to model uncertainties modifying the total cross-section vs. Eν

(integrated over Q2 and other kinematic variebles) = ⇒ Shape of σ(Eν) intrinsically more stable

06

SLIDE 7

☙ ~3.5m ¡x ¡3.5m ¡x ¡6.5m ¡STT ¡(ρ≃0.1gm/cm3) ¡ ☙ 4π-­‑ECAL ¡in ¡a ¡Dipole-­‑B-­‑Field ¡(0.4T) ☙ 4π-­‑μ-­‑Detector ¡(RPC) ¡in ¡Dipole ¡and ¡ Downstream ☙Pressurized ¡Ar-­‑target ¡(≃x5 ¡FD-­‑Stat) ➾ LAr- FD

High-­‑Resolu,on ¡Fine ¡Grain ¡Tracker: ¡ ¡ Reference ¡ND ¡of ¡DUNE ¡

¡ ¡ ¡ ¡ ¡STT ¡& ¡

Ar-­‑Target

μ ¡Detector ¡

Dipole-­‑B ECAL ¡

ν

Transition ¡Radiation ➳ e+/-­‑ ¡ID ¡⇒ γ dE/dx ¡ ➳ Proton, ¡π+/-­‑, ¡K+/-­‑ ¡ ¡ Magnet/Muon ¡Detector ➳ μ+/- e+/- (⇒ Absolute ¡Flux ¡measurement) 1X0 ¡~ ¡600 ¡cm ¡/ ¡1λ ¡~ ¡1200 ¡cm

07

SLIDE 8

Composition ¡of ¡the ¡Neutrino ¡Beam ¡

(1) νμ ¡ ¡⇒ π+ ⊕ K+ ➾ ID’d by 𝜈- (2) νμ ¡ ¡⇒ π- ⊕ K- ⊕ 𝜈+(⇐π+) ➾ ID’d by 𝜈+ (3) νe ¡ ¡⇒ K+ ⊕ 𝜈+(⇐π+) ⊕ K0L ➾ ID’d by e- (4) νe ¡ ¡⇒ K0L ⊕ K- ⊕ 𝜈-(⇐π-) ⊕ Charm ➾ ID’d by e+

Need: Accurate identification & measurement of each specie: ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡Required ¡for ¡the ¡need ¡redundancy! ¡ ¡

_ _

08

SLIDE 9

NOMAD ¡Experience ¡

E(GeV) 10 10 2 10 3 10 4 100 200 300 E(GeV) 10

• 1

1 10 10 2 10 3 100 200 300

νμ ¡ ¡⇒ π+ ⊕ K+

νμ ¡ ¡⇒ π- ⊕ K- ⊕ 𝜈+(⇐π+)

E(GeV) 10

• 1

1 10 50 100 150 200

νe ¡ ¡⇒ K0L ⊕ K- ⊕ 𝜈-(⇐π-)

⊕ Charm

E(GeV) 10

• 2

10

• 1

1 10 10 2 100 200 300

νe ¡ ¡⇒ K+ ⊕ 𝜈+(⇐π+)

⊕ K0L

_ _

09

SLIDE 10

Evis(GeV)

10 20 30 40 50 60

Events/GeV

2

10

3

10

4

10

5

10

Data Total π K

L

K µ

signal background Example of Low-ν EP fit to the MINOS low energy (LE) data (J. Ling and S.R. Mishra)

MINOS ¡Experience ¡

10

SLIDE 11

Salient Considerations in Low-ν Flux Analysis:

✴Measurement and in situ calibration of Leptons: 𝜈 & e ✴Calibration of ECAL: Response to π+/-, Proton, n, π0 in a dedicated Test-beam ! ✴Differential Cross-sections of Low-ν Processes: Measure ➳ QE, ¡ ¡Resonance, ¡& ¡DIS ¡ ✴ Theoretical Errors in estimation of fc(E): ✴ Constraining Non-Prompt Background ✴ Empirical-Parametrization of π/K Diff-Xsec ✴ Constraints from external Hadro-Production Experiments ✴ Beam Transport Errors in MC: Affects the acceptance ✴ Experimental Errors 11

SLIDE 12

Roberto Petti South Carolina Group

A νµ CC candidate in NOMAD

μ

• ­‑

Observation ➾ (1) Hadrons are tracks, enabling the momentum vector measurement (2) μ is kinematically separated from Hardon-vector ⇒ Miss-PT Measurement (3) FGT offers ~x5 higher tracking-points for hadronic tracks

μ ¡ ¡Measurement

12

SLIDE 13

Roberto Petti USC

THE MUON DETECTOR

✦ Glo-Sci-51 measure absolute and relative νµ and ¯ νµ spectra separately. Glo-Sci-52 measure NC and CC cross-sections separately vs. hadronic energy = ⇒ identify muons exiting the tracking volume NDC-L2-34,35 = ⇒ 4π muon detector with < 1 mm space resolution ✦ Instrument magnet yoke (3 planes), and downstream (5 planes) and upstream (3 planes) stations ✦ Bakelite RPC chambers 2m × 1m (432 in total) with 7.65 (7.5) mm X (Y) strips in avalanche or streamer mode

16

✴ 166k Channels

13

SLIDE 14

Roberto Petti USC

4.04m 5m 1.8m 2.25m FGT UA1

THE DIPOLE MAGNET

✦ Design based on established UA1/NOMAD/T2K magnet ✦ Magnetic volume 4.5m × 4.5m × 8.1m, nominal B=0.4 T ✦ Return yoke with 8+8 ”C” sections: 6 × 100 mm steel plates, 50 mm gaps (960 tons) ✦ 4 vertical Cu coils (150 tons) made of 8 double pancake ✦ Power requirement for nominal field 2.43 MW, water flow for coil cooling 20 l/s

14

Design by BARC: Sanjay Malhotra & team

14

SLIDE 15

Muon Momentum Reconstruction using Curvature in the B-Field ✴Need a uniform B-Field with Good ¡design ¡uniformity (~1% variation over the volume of 3.5m x 3.5m x 6.5m) ✴Detailed B-Field map-varations measured with ≤10% precision ⇒ B-Field known to ~0.1% precision ✴Continual monitoring of the B-Field during operation ⇒ Built in instrumentation in the field volume, especially the edges & yokes

✦ B uniformity in 3.5m × 3.5m × 7m tracking volume better than 2% (field simulations) ✦ Maximal deformation of C yoke 1.16 mm, maximal buckling of bobbin 1 mm ✦ Glo-Sci-51,23 measure absolute and relative νµ, νe and ¯ νµ, ¯ νe spectra separately. = ⇒ Low-ν technique for relative fluxes requires muon energy scale to < 0.2% = ⇒ B field mapping to better than 1% matches the requirement

0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9"

• 3250"
• 2750"
• 2250"
• 1750"
• 1250"
• 750"
• 250"

0" 250" 750" 1250" 1750" 2250" 2750" 3250"

RELATIVE(VARIATION(IN(MAGNETIC(FIELD((%)( Z4(AXIS(IN(MM((LONGITUDINAL)(

B"rela've"varia'on"in"X-Y"plane" B"rela've"varia'on"along"Z"(beam)"axis"

1% 0.5%

• 0.5%
• 1%

0.0% 1.37%

• 1.26%

15 BARC, India

15

SLIDE 16

µ

/p

µ

p δ

• 0.2 -0.15 -0.1 -0.05

0.05 0.1 0.15 0.2 Events 1 2 3 4 5 6

3

10 ×

/ ndf

2

χ 8357 / 197 Constant 16.4 ± 5806 Mean 6.7e-05 ±

• 8.2e-05

Sigma 0.00006 ± 0.03287 µ

/p

µ

p δ

• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2

Events

1 2 3 4 5 6 7 8

3

10 ×

/ ndf

2

χ 7145 / 197 Constant 17.5 ± 7064 Mean 0.0000618 ± 0.0005378 Sigma 0.00006 ± 0.03358

Muon Momentum Resolution in FGT

FGT

NOMAD

Mean -0.004912 RMS 0.008866

(Rad.)

reco µ

θ

• true

µ

θ

• 0.04
• 0.02

0.02 0.04 50 100 150 200 250 300 350 400

3

10 ×

Mean -0.004912 RMS 0.008866

𝜺θ~1 ¡mRad

Muon Efficiency in FGT (Prelim.) Efficiencies from Fast-MC; cross-checked against NOMAD Purity, in P<1 GeV , estimated from Fast-MC (prelim.) Includes backward going Muon. ✴ P > 1 GeV: Efficiency ~ ~95%; Purity >99% ✴ P ∈ [0.6, 1] GeV: Efficiency ~ ~80%; Purity ~80% ✴ P ∈ [0.3, 0.6] GeV: Efficiency ~ ~60%; Purity ~70%

16

SLIDE 17

2/17/16 MINERvA Low ν, Nelson/W&M MINERvA 
 Preliminary MINERvA 
 Preliminary

Comparison ¡with ¡Minerva ¡ ¡➾

⟸

17

SLIDE 18

Mass-K0s

✴

Measurement of the Mass-­‑K0s ⇒ in situ constraint on the Energy-­‑scale

✴

NOMAD, 32k K0s ⇒ error on the |p|-scale < 0.2%

in situ Constraint on the Eμ-scale ! ✴Measure K0s produced in the ν-interactions Expect > 750,000 reconstructed K0s ✴Constrain the error on the |p|-from-curvature Expect an error <0.1% on the momentum energy scale

18

SLIDE 19

in situ Constraint on the Eμ-efficiency ! ✴Measure the beam Muons (1) Using the Up-stream Mu-ID module & Up-Stream ECAL module with Barrel, or Down-stream ECAL -&- RPC-in-Yoke or RPC-in-Down-stream ⇒ Define the muon entering the detector (Denominator) (2) Reconstruct these muons using STT and mu-ID (Numerator) (3) Compute the Efficiency = Numerator/Denominator as a function of Eμ (4) Repeat this with the corresponding MC-Simulation (5) Compare (3) with (4) : Check on the absolute Eμ-efficiency

Run Number 20 40 60 80 100 120 140 160 180 Efficiency 0.997 0.9975 0.998 0.9985 0.999 0.9995 1 1.0005 1.001 1.0015 1.002

<Data ¡μ-­‑Eff> ¡= 0.99963 <MC ¡ ¡ ¡μ-­‑Eff> ¡ ¡= ¡0.99961

4 ≤Eμ ¡≤ 40 GeV

19

SLIDE 20

Plan for 𝜈-Measurement (1) Measure Eμ ¡with ~ 3.5% resolution (2) 100% distinction between μ- .vs. μ+ in ~0.3 - 50 GeV (3) B-field design allows the |Eμ|-scale to be measured to ~ 0.1% precision (4) in situ measurement of 0.75M K0s checks the |Eμ|-scale to ~ 0.1% precision (5) Absolute efficiency of the μ-reconstruction will be checked using the Beam-μ using the built-in redundancy offered by the 4π coverage by ECAL & RPC with < 0.1% precision (6) Measure large-angle muons, e.g. 𝛊 > 600, without loss of efficiency/bias compared to low-angle muons ⟸ Important for the 2nd oscillation maximum

20

SLIDE 21

Roberto Petti South Carolina Group

A ¯ νe CC candidate in NOMAD

e-/e+ ID using TRD, ECAL

Conclusion ➾ (1) e⇐νe ¡ ↔ μ⇐ νμ ¡ are Tracks: Curvature & Direction with very high precision (2) Universality equivalence: μ-νμ ¡ ↔ e -νe ¡

e+

➾ Most difficult to measure among the 4 ν-species

In FGT, ~x5 higher track-points

e ¡ ¡Measurement

21

SLIDE 22

Electron/Positron Measurement in FGT

✴ νe ¡↔ ¡e-­‑; anti-­‑νe ¡↔ ¡e+;

✴ e- Momentum Vector Measurement: Track-reconstruction in STT: Curvature ⇒ |p| & “-” or “+” Direction-cosines ⇒ STT Track-fit, including dE/dx Energy ⇒ Cluster & Brem-Strip in the ECAL: A more precise measure of |pe| ✴ e-ID Measurement: 1st: Transition Radiation (TR) measurement in the STT 2nd: Energy-profile, Transverse ¡and ¡Longitudinal ¡energy-­‑deposition ¡pattern, in the ECAL (match the STT-Track with the ECAL-Track) Note: ECAL ¡has ¡a ¡4π-­‑coverage ¡⇒ ¡Wide-­‑angle ¡e-­‑/e+ ¡acceptance ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡➾ ¡ ¡π/𝜈 ¡ ¡reduced ¡by ¡~10-4 ¡ ¡while ¡Electron-­‑Eff ¡> ¡90% ¡ 3rd: Pattern of energy loss (Helical track-fit) in STT

22

SLIDE 23

Roberto Petti South Carolina Group

110 The NoMilD CollaborationJNucl.

• Instr. md Meth. in Ph.v.s. Rex A 404 (199X) 96-128

angular distribution

• f emitted

photons peaks around the initial particle direction (the mean angle

• f emission

is about l/y). The algorithm developed for electron identifica- tion [21] is based on a likelihood ratio method and relies on test beam measurements and detector simulation. The TRD simulation has been exten- sively tested in situ using the muons (5 GeV/c < pi, < 50 GeV/c) crossing the detector during the flat top between the two neutrino

• spills. Fig. 13

shows a comparison between the experimental and simulated distributions

• f the energy deposited

in straw tubes by 5 GeV/c muons (ionization losses

• nly)

and by &ray electrons with a mean mo- mentum

• f about 2 GeV/c, emitted

by muons (sum

• f ionization

losses and detected transition radi- ation photons). A pion rejection factor greater than 1000 is ob- tained with the 9 TRD modules in the momentum range from 1 to 50 GeV/c, while retaining an elec- tron efficiency of 90% (see Section 3.4). 2.7. Preshower detector The preshower (PRS), which is located just in front of the electromagnetic calorimeter, is com- posed

• f two planes
• f proportional

tubes (286 horizontal and 288 vertical tubes) preceded by a 9 mm (1.6X,) lead-antimony (96%4%) conver- ter, see Fig. 14. The proportional tubes are made from extruded aluminium profiles and are glued to two aluminium end plates

• f 0.5 mm thickness.

Each tube has a square cross-section

• f 9 x 9 mm2 and the walls

are 1 mm thick. The 30 urn gold-plated tungsten anode is strung with a tension

• f 50 g and secured

at each end in hollow copper pins. In order to avoid wire vibrations, the anodes are also glued in the middle

• f the preshower
• n small resofil spacers.

The proportional tubes

• perate

at a voltage

• f

1500 V, with a mixture

• f (80: 20) Ar :

CO,. Signals from each tube are fed into charge pre- amplifiers; at the output

• f the preamplifier,

two

5 GeV/c muons

• Fig. 13. Comparison
• f experimental

(points with error bars) and simulated (solid lines) distributions

• f the energy deposited

in TRD straw tubes by 5 GeV/c muons (open circles) and 2 GeV/c electrons (closed circles).

2 GeV/c electrons

NOMAD TRD reaches a 0.1% pion contamination for isolated tracks

• f momenta 1-50 GeV/c with 90% electron efficiency

126

The NOMAD CoNahorationiNucl.

• Instr. md M&h. in Ph_v,.p.
• Res. A 404 (IYY8) Y6-128

Y 2 0.035 s ti I? 2 0.03 a d > 0.025 a

/?

Pions 90% electron cut 1

• Fig. 31.

The likelihood ratio distributions for pions and electrons with track momenta 10 GeV/c crossing nine TRD modules (Monte-Carlo simulation). Pion rejection is better than 1OOO:l at 90% electron efficiency.

combinations were properly identified, which is in agreement with the 75% expected. The NOMAD TRD reaches a lo3 pion rejection factor for isolated tracks in the l-50 GeV/c momentum range with a 90% electron detection

• efficiency. The algorithm

developed for the identi- fication of non-isolated tracks allows the number

• f

misidentified particles to be reduced, particularly in large multiplicity events. 3.4..?. Using the preshower and the electromagnetic calorimeter A PRS prototype consisting

• f two layers of 10

tubes each was exposed to beams of electrons and 7c mesons at the CERN PS and SPS accelerators. Based on the data obtained, a procedure was de- veloped for electron identification. The PRS pulse- height (measured in m.i.p.) was required to be larger than: 0.836 + 6.86111(E) - 0.22(ln(E))2, where E is the energy of the particle in GeV, correc- ted for linearity and for the energy loss in the PS, as explained in Ref. [24]. For energies greater than 4 GeV this yields an efficiency of 90% with a residual 7~ contamination smaller than 10%. The x/e separation is substantially improved when ECAL is used in association with the PRS. Using a test-beam setup comprising PRS and ECAL prototypes, the response to both electrons and pions was measured.

• Fig. 32 shows the scatter

plots

• f PRS

vs ECAL pulse-height for 5 GeV electrons and pions. The rectangular regions in the figure correspond to events in which the energy deposited by electrons is consistent with the beam energy within the resolution

• f ECAL, and the PRS

pulse height satisfies the condition described above. A rejection factor against pions

• f about

lo3 is

• btained

in the energy range 2-10 GeV, while re- taining an overall efficiency of 90% to detect elec-

• trons. An additional

rejection factor of about 2-3

10 GeV/c pions/electrons

Analog readout: pulse height

✺Atlas-­‑TRT’s-­‑simulation ¡conducted ¡for ¡the ¡ FGT ¡con8ig. ¡veri8ies ¡the ¡e/μ-­‑π ¡separation ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ➣(See P.Nevski LBNE-DocDB#432-V1)

Electron TR-Eff as a function

• f Pe for 10-3 rejection of π/μ

Electron ID: ¡ ¡TR ¡-­‑ ¡The ¡most ¡ ¡potent ¡ ¡discriminant ¡ 23

SLIDE 24

Electron ID: ¡ ¡ECAL ¡-­‑ ¡Energy, ¡Longitudinal ¡and ¡ Transverse ¡ProPiles ¡as ¡discriminants ¡

Measure ➳ e, γ, & ¡ ¡n/K0s

✴ Scintillator-Pb calorimeter: Motivated by the T2K-ECAL design

Alternating planes of X/Y planes 2.5cm Sci-slats read on both ends (SiPM) ✴ Downstream (Forward) ECAL: 60 Layers with 1.75mm Pb-sheets: 20X0 Single electron ⇒ ~6%/√ E ✴ Barrel ECAL: 18 Layers with 3.5mm Pb-sheets: 10X0 ✴ Upstream ECAL: 18 Layers with 3.5mm Pb-sheets: 10X0 24

SLIDE 25

Electron Efficiency in FGT (Prelim.) Efficiencies/Purity from Fast-MC. (TR cut: 40-planes of ST) Cross-checked against NOMAD Data -vs- MC ✴ P > 0.5 GeV: Efficiency ~ ~58%; Purity >90%

✴ Efficiency & Purity largely energy independent ✴ Fast-MC of NOMAD yeilds : Efficiency ~ ~38%; Purity ~82%

NOMAD Geant-MC (Data-driven): Efficiency ~ ~40%; Purity ~79%

Electron Energy Resolution in FGT (Prelim.) ✴ 𝜺|P| ~ 10% (@FWHM) ✴ 𝜺|E| (ECAL) ~ 3.6% ( consistent with 6%/ √E) ✴ NOMAD Geant-MC (Data-driven): 𝜺|P| ~ 13% (@FWHM) 𝜺|E| (ECAL) ~ 2.0% ( ~ 3%/ √E)

Will ¡be ¡updated: ¡More ¡details ¡(plots/#s) ¡later

25

SLIDE 26

Test-Beam Calibration ¡of ¡ ¡STT ¡(TR) ¡and ¡ECAL ¡(Shape) ¡ ¡ ✴Measurement of the STT prototype in a Test-Beam ⇒ Check/obtain calibration ⇒ dE/dx, TR: e vs 𝜈 vs π vs …. in momentum bins ⇒ Essential before full-scale fabrication ✴Measurement of the STT and ECAL prototypes in a Test-Beam ⇒ Obtain energy (ADC ⇒ GeV) calibration ⇒ Measure the energy-dependent non-Gaussian tails ⇒ Particle ID: e vs 𝜈 vs π shower-shape discriminant in momentum bins ⇒ Essential before full-scale fabrication

26

SLIDE 27

in situ Constraint on ¡ ¡the ¡ Electron-ef,iciency ¡ ¡ ✴Measure the TR and ECAL Efficiencies using source of pure e+e- (1) Select γ➳ e+e- conversions using track reconstruction & kinematics ⇒ A V0 separated from the vertex (>1cm) ⇒ The opening angle in X-Z plane is <5 mrad ⇒ Mee < 30 MeV (consistent with a Photon) ⇒ ~ 5. 107 reconstructed Photons with Purity > 99% Sanity-Check: Apply the analysis to, and learn from, the NOMAD data (see fig.) Estimates of the parametrized calculation, Purity & Eff, agree within 15%. (2) On the e-/+ tracks, impose the TR-cuts (Data & MC) ⇒ Evaluate the TR efficiency in Data and MC (3) On the e-/+ tracks, impose the ECAL Shower-Shape cuts (Data & MC) ⇒ Evaluate the ECAL-Id efficiency in Data and MC

γ➳ e+e-

27

SLIDE 28

e-­‑/e+ ¡TR-­‑Ef*iciency ¡in ¡Data ¡.vs. ¡MC ¡Using γ ¡➳ e+e- sample (γ’s come from π0➳γγ)

Conclusion ➾ Data-­‑Eff ¡-­‑ ¡e- = MC-­‑Eff - e- at << 1%

(E-averaged)

28

SLIDE 29

NOvA experience: ¡ EM-­‑Shower-­‑ID ¡ ¡ ✴NOvA is a tracking calorimeter ⇒ Cell: 4cm(X) * 15.6m(Y) * 6.6cm(Z) [ ND: 4.2m(Y) ] ⇒ Longitudinal Sampling: 0.17X0 along the beam-direction (6.6cm) ⇒ Transverse Sampling: ~4cm alternating X/Y planes ⇒ Timing: 500 ns window in 10 𝜈s spill versus ✴FGT-ECAL ⇒ Cell: 2.5cm(X) * 4m(Y) * 20cm(Z) ⇒ Longitudinal Sampling: 0.3X0 along the beam-direction (0.55X0 for Barrel) ⇒ Transverse Sampling: ~2.5cm alternating X/Y planes ⇒ Timing: ~1 ns Ecal-Cluster time-resolution in 10 𝜈s spill

29

SLIDE 30

in situ Constraint on the Em-Shower reconstruction in NOvA

✴Use the 𝜈-Removed Cosmic-Brem in FD

𝜈-Rm ➾

νe El-ID ➾

30

SLIDE 31

in situ Constraint on ¡ ¡the ¡ Electron/ECal ¡Energy ¡Scale ¡ ¡ ! ✴Measure π0 produced in the ν-interactions Expect ~ O(10M) reconstructed π0 using γ-conv. & γ-clus. Use π0 mass, constrain the ECAL energy scale (…see Figs.) ✴Measure K0 produced in the ν-interactions Expect ~ O(200k) reconstructed K0 ➳ π0 π0 using γ-conv. & γ-clust. Use sharp K0 mass, constrain the ECAL energy scale ✴Measure η ➳ γ γ produced in the ν-interactions (…see Fig.) Expect ~ O(0.4M) reconstructed η using γ-conv. and γ-clus. Use sharp η mass, constrain the ECAL energy scale

31

SLIDE 32

1000 2000 3000 4000 5000 6000 7000 8000 9000 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3 500 1000 1500 2000 2500 3000 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3 100 200 300 400 500 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

Mγγ ➳ Mγγ ➳ Mγγ ➳

Cluster-­‑Cluster ¡ 71,595 ¡π0

Conv.-­‑Cluster ¡ 25,172 π0

Conv.-­‑Conv. ¡ 4,142 π0

π0 Reconstruction ¡using ¡NOMAD ¡Data ¡(νμ-­‑CC ¡Sample) ¡ ¡(background: ¡Rit ¡data ¡excluding ¡80< ¡Mγγ ¡<170 ¡MeV)

32

SLIDE 33

π0 Reconstruction ¡in ¡NOvA ¡ ¡(NC⇔no-­‑𝜈 ¡Sample) ¡ Constraint ¡on ¡the ¡EM-­‑energy ¡Scale ¡

33

SLIDE 34

Dt Ph2 M!0 Cl/v0

25 50 75 100 125 150 175 200 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

Dt Ph2 M!0 v0/v0

• 5

5 10 15 20 25 30 35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

Dt Ph2 M!0 Cl/Cl

100 200 300 400 500 600 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

Cluster-­‑Cluster ¡ 12,660.1 ¡η

Conv.-­‑Cluster ¡ 3,960.7 η

Conv.-­‑Conv. ¡ 672.2 η

η Reconstruction ¡using ¡NOMAD ¡Data ¡(νμ-­‑CC ¡Sample) ¡ ¡(background: ¡Rit ¡data ¡excluding ¡475< ¡Mγγ ¡<625 ¡MeV)

34

SLIDE 35

e ¡ ¡Measurement

A final separation of νe ¡⇒ e from the non-prompt π0/π+-⇒ e/e-­‑like ✴Use the Lepton-Hadron kinematic isolation to reduce the impurity (…later)

35

SLIDE 36

Plan: Electron/Positron ¡Measurement ¡in ¡FGT ¡… ¡in ¡progress ¡ (1) 100% distinction between e- .vs. e+ in ~0.3 - 50 GeV (3) Measure Pe in STT ⇒ Direction-cosines using the track-fit ⇒ Resolution of |Pe| ~ 12% using curvature ⇒ Resolution of |Ee| ~ 6%/√Ee ⇒ Resolution of θe ~ 3 mrad (3 GeV e-) (4) Electron-ID measurement via ⇒ TR (Transition Radiation) in STT ⇒ Shower-shape in ECAL ⇒ Patter of Energy-Loss (track-fit) in STT (5) in situ constraints on the electron-ID efficiency using e+/e- tracks

• riginating from the reconstructed γ➳ e+e-

(6) in situ constraints on the electron-energy using reconstructed ⇒ ~O(10M) π0 using γ-conversion and γ-clusters ⇒ ~O(200k) K0 ➳ π0 π0 & ~O(400k) η ➳ γ γ

36

SLIDE 37

(1) Select -CC with Ehad<ν0, ν0~0.3 ( 0.5) GeV (2) Sample (entirely) dominated by QE and Res (3) Apply the ν0-correction ⇒ Model errors (Fig.) (4) Experimental Errors: ⇒ Eμ reconstruction is the key! ⇒ ν0 (scale, smearing) (Discussion later..) (5) Beam transport errors (7) No variable cuts (introduces systematics at ~5% level)

Extracting ¡the ¡Low-­‑ν ¡ ¡Flux ¡ ¡of ¡ ¡νμ ¡& ¡ ¡νμ ¡using ¡the ¡ND ¡Data _

37

SLIDE 38

E (GeV)

• 1

10 × 6 1 2 3 4 5 6 7 8

C

Error in f

• 0.07
• 0.06
• 0.05
• 0.04
• 0.03
• 0.02
• 0.01

0.01 Error

C

Transverse High f Error

C

Transverse Low f (Transverse)

C

=1.3) - f

A

(M

C

f (Transverse)

C

=1.014) - f

A

(M

C

f

<0.25) ν for Neutrino (

C

Error in f <0.25) for Antineutrino ( Error in f

E (GeV) E (GeV)

• 1

10 × 6 1 2 3 4 5 6 7 8

C

Error in f

• 0.01

0.01 0.02 0.03 0.04 0.05 Error

C

Transverse High f Error

C

Transverse Low f (Transverse)

C

=1.3) - f

A

(M

C

f (Transverse)

C

=1.014) - f

A

(M

C

f

<0.25) ν for Antineutrino (

C

Error in f

✦ Bodek at al. [EPJC 72 (2012) 1973] showed low-ν works well down to very low values ν0 = 0.25 GeV and ν0 = 0.5 GeV and estimated model uncertainties:

• Averaging different models gives uncertainty < 1.9% for νµ at Eν > 0.7 GeV;
• Averaging different models gives uncertainty < 2.5% for ¯

νµ at Eν > 1.0 GeV.

✦ Stringent constraints on QE models will be available in DUNE ND from in-situ precision measurements of double differential cross-section = ⇒ Substantial reduction of model dependence expected

Theoretical Errors in estimation of fc(E): Low-­‑ν ¡ ¡Flux ¡ ¡of ¡ ¡νμ ¡& ¡ ¡νμ _

➾Model ¡error ¡in ¡Low-­‑Nu ¡Flux ¡is ¡small ¡

38

SLIDE 39

ν < 3 GeV Variable ν cut

✦ Gonchar and Petti (docdb #9275) showed with NOMAD analysis that a variable ν0 cut as a function of Eν dramatically enhances effect of cross-section uncertainties

• Fixed ν0 cut provides reduced dependence upon cross-section models;
• Variable ν0 cut alters event composition (QE/RES/DIS) and corresponding Eν dependence.

= ⇒ Must keep the lowest fixed ν0 cut allowed by experimental resolution / statistics Effect of cross-section variation: QE, RES +- 15% DIS +- 2.1%

➾Variable ¡ν0-­‑cut ¡introduces ¡systematic ¡error ¡~5% ¡level ¡

39

SLIDE 40

MINOS low-nu relative flux uncertainties

0.02 0.04 0.06 0.08 0.1 0.12 0.14 5 10 15 20 25 30 35 40 45 50 Energy (GeV) Relative uncertainty (stat.+syst.)

NOMAD low-nu relative flux uncertainties

0.005 0.01 0.015 0.02 0.025 0.03 20 40 60 80 100 120 140 160 Energy (GeV) Relative uncertainty (stat.+syst.)

Error ¡on ¡the ¡Low-­‑ν ¡ ¡Flux: ¡MINOS ¡.vs. ¡NOMAD

➾Precision ¡on ¡the ¡Eμ ¡scale ¡& ¡resolution, ¡followed ¡by ¡that ¡on ¡

ν0, ¡ ¡are ¡the ¡driving ¡systematics ¡

40

SLIDE 41

41

SLIDE 42

Goal: Predict FD/ND (Eν) with 1-2% precision in Eν-bins

❧ Use the ND Low-ν ¡flux to obtain an Empirical Parametrization of the

π+/K+ differential cross-section

❧ Impose constraints from the hydro-production experiments

⇒ Data driven rays capable of producing FD & ND flux with complete

correlation

Empirical ¡Parametrization ¡of ¡π+/K+ (π-/K-) ¡ ¡ using ¡the ¡Low-­‑ν ¡ ¡Flux ¡ ¡of ¡ ¡νμ ¡& ¡ ¡νμ ¡using ¡the ¡ND ¡Data

✦ Fit Near Detector νµ, ¯ νµ (νe, ¯ νe) spectra in 4-5 (x,y) radial bins:

• Trace secondaries through beam-elements, decay;
• Predict (anti)neutrino fluxes by folding experiental acceptance;
• Compare predicted to measured spectra =

⇒ χ2 minimization: d2σ dxF dP 2

T

= f(xF )g(PT )h(xF , PT )

• Functional form constraint allows flux prediction close to Eν ∼ ν0.

✦ Add measurements of π+/K+ and π−/K−ratios from hadro-production experiments to the empirical fit of the neutrino spectra in the Near Detector

42

SLIDE 43

43

SLIDE 44

5.2 Functional Form

The following functional forms are used to fit the meson cross-sections: F = BxF(1 − x)A(1 + Ce−Dx) (5) Here x = PMeson/PProton in the lab frame. PT = e−GP 2

T

(1 + P 2

T/M 2)R

(6) G = e−SPT (1 + T log(1 + x))eUx (7) The central functional form of the EP for π+, π−, and K0

L is:

F × PT (8) The central functional form of the EP for the K+ and K− is: F × PT × G (9) Other functional forms were tried. The functional forms that did not succeed in fitting the control samples were rejected. The few successful ones had forms as shown below. H = e−SPT xTPT (1 − x)UPT (10) I = 1 + SPT xT + UPT x (11) J = 1 + SPT x + TP 2

T

xU (12)

Empirical ¡Parametrization ¡#1

44

SLIDE 45

• E × d3σ

dp3

• =

A (1 − xR)α (1 + BxR)x−β

R ×

• 1 + a′(xR)pT + b′(xR)p2

T

• e−a′(xR)pT

(4) where a′(xR) = a/xγ

R and b′(xR) = a2/2xδ

• R. The scaling variable xR = E∗/E∗

max is

defined as the ratio of the energy of the meson in the centre-of-momentum frame and the maximum kinematically available energy. Positive and negative mesons are assumed to have the same pT distribtuions. The ratio r of positive to negative meson (π+/π− or K+/K−) is parameterized using the formulae: r(π) = r0 · (1 + xR)r1 (5) r(K) = r0 · (1 − xR)r1 (6)

Empirical ¡Parametrization ¡#2

45

SLIDE 46

Steps:

❧ Conduct the fit in Radial-bins ❧ Calibrated the non-prompt background ❧ Constraints from hydro-production data ❧ Fold the Low-Nu and acceptance into MC ❧ For each systematic variation, repeat the entire chain

y x

Drift Chamber: 300 x 300 cm

120-130 cm 0-30 30-60 60-95 95-120

46

SLIDE 47

EP ¡Analysis: ¡NOMAD

Data 000-130 Final Foc+ No Kin.Cut NuMu Flux-Data(Sym) -vs- EP-NB612(Hist) 10 10 2 10 3 10 4 100 200

Central Variance A 3.6122 0.000062 C 14.3937 0.011 D 12.9231 0.036 F 0.8801 0.000028 G

• 0.1625

0.054 M2 3.3439 0.62 R

• 2.4197

0.69 S 1.5901 0.022 T 136.9179 61.2 U

• 1.4274

0.0052 Table 6: Fitted K+ parrameters Central Variance A 5.1198 0.00074 C 4.1214 0.0075 D 19.3258 0.18 F 1.1086 0.000018 G 1.2286 0.034 M2 0.8004 0.0129 R 2.2437 0.039 Table 5: Fitted π+ parrameters

SPY K+/Pi+ ¡ Constraint ¡

➾ *Fitted ¡Pi+ ¡& ¡K+ ¡induced ¡NuMu ¡

¡ ¡ ¡ ¡ ¡ ¡ ¡*Inclusion ¡of ¡SPY ¡(K+/Pi+) ¡constraint

π+

K+

47

SLIDE 48

Data 000-130 Final 10000 20000 30000 40000 25 50 75 100

➾ Good ¡Uit ¡quality ¡

48

SLIDE 49

Data 000-030 Final Foc+ No Kin.Cut NuMu Rad.Bins Flux-Data(Sym) -vs- EP-NB612(Hist) 1 10 2 10 3 200 Data 030-065 Final 10 10 4 200 Data 065-090 Final 10 10 4 200 Data 090-120 Final 10 10 4 200 Data 120-130 Final 1 10 2 10 3 200 Data 000-120 Final 10 10 4 200

➾Good ¡Uit ¡in ¡Radial ¡bins ¡ ¡⇔ ¡

Better ¡constraint ¡on ¡the ¡Beam-­‑Divergence

49

SLIDE 50

Constraints from the SPY (Hadro-Production) Experiment 50

SLIDE 51

Data F 000-130 Dis Foc+ No Kin.Cut NuMu DIS-Data(Sym) -vs- EP-NB612(Hist) 10 2 10 3 10 4 10 5 100 200 300

Comparison of Data-vs-MC(EP-ReWt) for Ehad>ν0

0.8 1 1.2

➾Good ¡agreement ¡in ¡High-­‑Nu ¡Region

51

SLIDE 52

Data 000-130 Final Foc+ No Kin.Cut NuMuBar Flux-Data(Sym) -vs- EP-NB612(Hist) 500 1000 1500 25 50 75 100 Entries Mean RMS 13977 26.97 27.18

EP fit to the NuMuBar Low-ν0 Data

SPY ¡ ¡K-­‑/Pi-­‑ Constraint ¡

52

SLIDE 53

Constraints from the SPY (Hadro-Production) Experiment 53

SLIDE 54

❧ Emu scale and resolution ❧ Variation in Nu0-Cut & Correction

❧ Variation in the functional form ❧ Variation QE, Resonance, DIS

❧ Error in K/Pi (SPY) constraint ❧ Error in Beam Trasport

⇒Secondary & tertiary interactions ⇒Inert Material ⇒Horn current ⇒B-Field modeling in the horn ⇒Alignment (Horn, Collimator, Detector)

⇒ Repeat the entire EP-analysis for each variation

Systematic Errors in the NOMAD Low-Nu EP Analysis 54

SLIDE 55

EP ¡Analysis: ¡MINOS ¡Experience

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

50 100 150 200 250 300

3

10 ×

Mock data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

1000 2000 3000 4000 5000 6000 7000 8000

Mock data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 3: Mockdata Test: Combined νµ and νµ EP fits to the mockdata and comparison

• f the deduced flux.

pz(GeV)

10 20 30 40 50 60 70 80 90 100

pt(GeV)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1 1.2 1.4

reweight

+

π

pz(GeV)

10 20 30 40 50 60 70 80 90 100

pt(GeV)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.6 0.8 1 1.2

reweight

+

K

Systematic Errors ✴EP Functional forms ✴Low-Nu0 correction ✴QE variation ✴Resonance variation ✴Reconstruction errors in (Emu, ThMu, Ehad) ✴Beam transport errors

55

SLIDE 56

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

50 100 150 200 250 300 350

3

10 ×

data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

1000 2000 3000 4000 5000 6000 7000 8000 9000

data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 16: The EP fit to LE RunI Data: The EP fits to the νµ and νµ LE-Run1 data with EHad ≤ 1 GeV in the Eν ≤ 20 GeV range are shown. The ratio of Data/Fit is shown below.

EP ¡Analysis: ¡MINOS ¡LE ¡Data ¡

56

SLIDE 57

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

20 40 60 80 100 120 140 160 180 200 220

3

10 ×

data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

1000 2000 3000 4000 5000 6000 7000

data untuned MC tuned MC

CC LE010z185i, Eshw<1.0GeV

µ

ν

2 4 6 8 10 12 14 16 18 20

data/MC ratio

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Figure 27: The EP fit to LE RunIII Data using Helium MC: The EP fits to the νµ and νµ LE-RunIII data with EHad ≤ 1 GeV in the Eν ≤ 20 GeV range are shown. The ratio of Data/Fit is presented below.

EP ¡Analysis: ¡MINOS ¡LE ¡Data ¡(w. ¡He ¡in ¡Beam-­‑pipe)

57

SLIDE 58

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ratio, pt[0, 0.2]GeV

+

π /

−

π

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ratio, pt[0.2, 0.4]GeV

+

π /

−

π

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ratio, pt[0.4, 0.6]GeV

+

π /

−

π

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fluka05 tuned MC BMPT MIPP NuMI Target

ratio, pt[0.6, 1.0]GeV

+

π /

−

π

Figure 33: Comparision of Ratio of π−/π+ as a Function of Energy in pT-bins: The EP-fits are compared to the available data and other parametrizations.

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ratio, , pt[0, 0.2]GeV

+

π /

+

K

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ratio, , pt[0.2, 0.4]GeV

+

π /

+

K

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ratio, , pt[0.4, 0.6]GeV

+

π /

+

K

pz(GeV)

10 20 30 40 50 60 70 80 90 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Fluka05 tuned MC BMPT MIPP NuMI Target

ratio, , pt[0.6, 1.0]GeV

+

π /

+

K

Figure 34: Comparision of Ratio of K+/π+ as a Function of Energy in pT-bins: The EP-fits are compared to the available data and other parametrizations.

MIPP ¡constraints ¡in ¡the ¡MINOS ¡EP ¡Analysis:

58

SLIDE 59

Evis(GeV)

10 20 30 40 50 60

Events/GeV

2

10

3

10

4

10

5

10 Data Total π K

L

K µ signal background

LE010z185i, Eshw<1GeV

µ

ν

Figure 43: RunI low-ν data sample composition for νµ in log scale.

Evis(GeV)

2 4 6 8 10 12 14 16 18 20

Events/GeV

1000 2000 3000 4000 5000 6000 7000 8000 9000 Data Total π K

L

K µ signal background

LE010z185i, Eshw<1GeV

µ

ν

Figure 44: RunI low-ν data sample composition for νµ

NuMi ¡(MINOS) ¡Beam ¡Composition

Enu(GeV)

2 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 70

Total µ K

L

K

LE010z185i flux

e

ν

Figure 46: RunI low-ν data sample composition for νe

➾NuE ¡Prediction ¡

59

SLIDE 60

Enu(GeV)

2 4 6 8 10 12 14 16 18 20 1000 2000 3000 4000 5000 6000 7000 8000

Default Ehad −12.5% Ehad +12.5%

flux LE010z185i, Near

µ

ν

0 2 4 6 8 10 12 14 16 18 20 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Eh ¡Scale ¡12.5% Enu(GeV)

2 4 6 8 10 12 14 16 18 20 1000 2000 3000 4000 5000 6000 7000 8000

Default Emu −5% Emu +5% flux LE010z185i, Near

µ

ν

0 2 4 6 8 10 12 14 16 18 20 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Emu ¡Scale ¡5% EP-­‑MINOS Enu(GeV)

2 4 6 8 10 12 14 16 18 20 50 100 150 200 250 300 350

Default Emu −5% Emu +5% flux LE010z185i, Near

µ

ν

0 2 4 6 8 10 12 14 16 18 20 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

60

SLIDE 61

Low-ν E.P. Flux Analysis in DUNE-ND: Part2

✴Low-Nu NuMu & NuMuBar Flux in the DUNE-ND ✴Empirical parametrization of π/K Diff-Xsec ✴Prediction of FD/ND ✴Error analysis of the FD/ND prediction ✴νe ¡& anti-νe ¡sample ✴Calibration of the Non-Prompt background ✴Prediction of νe ¡wrt νμ ¡ ✴Prediction of anti-νe ¡wrt anti-νμ ¡ ✴Plans for further studies 61

SLIDE 62