Exploring the Potential of Short-Baseline Physics at Fermilab Pedro - - PowerPoint PPT Presentation
Exploring the Potential of Short-Baseline Physics at Fermilab Pedro S. Pasquini O. G. Miranda, M. T ortola and J. W. F. Valle 08/16/2018 NuFact 2018 Phys.Rev. D97 (2018) no.9, 095026 Arxiv: hep-pheno/1802.02133 1 / 24 Short-Baseline may
Pedro S. Pasquini
08/16/2018 NuFact 2018 Phys.Rev. D97 (2018) no.9, 095026 Arxiv: hep-pheno/1802.02133
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The Fermilab short-baseline program:
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The Fermilab short-baseline program: (1) Running/Under Construction
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The Fermilab short-baseline program: (1) Running/Under Construction (2) Future/To be designed
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed Source
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed Source ⌫
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed Source ⌫ SBND 100 m
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed Source ⌫ SBND 100 m µBooNe 470 m
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) (2) Future/To be designed Source ⌫ SBND 100 m µBooNe 470 m ICARUS 600 m
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) Detector Active Size Distance SBND 112 t 110 m MicroBooNE 89 t 470 m ICARUS 476 t 600 m (2) Future/To be designed
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) Detector Active Size Distance SBND 112 t 110 m MicroBooNE 89 t 470 m ICARUS 476 t 600 m (2) Future/To be designed DUNE/LBNF near detector arXiv:1512.06148
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) Detector Active Size Distance SBND 112 t 110 m MicroBooNE 89 t 470 m ICARUS 476 t 600 m (2) Future/To be designed DUNE/LBNF near detector arXiv:1512.06148 Detector Active Size Distance ND ? ?
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The Fermilab short-baseline program: (1) Running/Under Construction Short Beseline Neutrino (SBN) Experiment (arxiv:1503.01520) Detector Active Size Distance SBND 112 t 110 m MicroBooNE 89 t 470 m ICARUS 476 t 600 m (2) Future/To be designed DUNE/LBNF near detector arXiv:1512.06148 Detector Active Size Distance ND ? ? around ⇠ 500 t ⇠ 600m
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Near Detec- tor Physics
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Near Detec- tor Physics
Non-Unitarity
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
4 / 24
Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
4 / 24
Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
If number of ⌫ > 3
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
If number of ⌫ > 3 The (unitary) mixing matrix Nn⇥n is Nn⇥n = B B B @ N11 N12 N13 N14 ... N21 N22 N23 N24 ... N31 N32 N33 N34 ... . . . . . . . . . . . . 1 C C C A
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
If number of ⌫ > 3 The (unitary) mixing matrix Nn⇥n is Nn⇥n = B B B @ N11 N12 N13 N14 ... N21 N22 N23 N24 ... N31 N32 N33 N34 ... . . . . . . . . . . . . 1 C C C A Unitary
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
If number of ⌫ > 3 The (unitary) mixing matrix Nn⇥n is Nn⇥n = B B B @ N11 N12 N13 N14 ... N21 N22 N23 N24 ... N31 N32 N33 N34 ... . . . . . . . . . . . . 1 C C C A Unitary Not accessible if Eexp < Mνi
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
If number of ⌫ > 3 The (unitary) mixing matrix Nn⇥n is Nn⇥n = B B B @ N11 N12 N13 N14 ... N21 N22 N23 N24 ... N31 N32 N33 N34 ... . . . . . . . . . . . . 1 C C C A Unitary Not accessible if Eexp < Mνi Not Unitary
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
N3⇥3 = @ ↵11 ↵21 ↵22 ↵31 ↵32 ↵33 1 A .UPMNS
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
N3⇥3 = @ ↵11 ↵21 ↵22 ↵31 ↵32 ↵33 1 A .UPMNS Unitary
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
N3⇥3 = @ ↵11 ↵21 ↵22 ↵31 ↵32 ↵33 1 A .UPMNS Regulates ⌫µ ! ⌫e transitions
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Near Detec- tor Physics
Non-Unitarity
e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 Zero Distance / |↵21|2
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
0.001 0.010 0.100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 L/E [A.U.] Survival Probability
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
0.001 0.010 0.100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 L/E [A.U.] Survival Probability
∆m2
31
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
0.001 0.010 0.100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 L/E [A.U.] Survival Probability
∆m2
31
∆m2
21
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
0.001 0.010 0.100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 L/E [A.U.] Survival Probability
∆m2
31
∆m2
21
∆m2
4i
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879
Near Detec- tor Physics
Light Sterile Neutrino Non-Unitarity
21
32
43
4i ⇡ 1 eV2
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 ⌫4 ⌫3 ⌫2 ⌫1 ∆m2
21
∆m2
32
∆m2
43
arxiv:1507.08204
Near Detec- tor Physics
Light Sterile Neutrino Non- Standard Interaction Non-Unitarity
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 ⌫4 ⌫3 ⌫2 ⌫1 ∆m2
21
∆m2
32
∆m2
43
arxiv:1507.08204
Near Detec- tor Physics
Light Sterile Neutrino Non- Standard Interaction Non-Unitarity
Detector
⌫i ⌫j , Z0..
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 ⌫4 ⌫3 ⌫2 ⌫1 ∆m2
21
∆m2
32
∆m2
43
arxiv:1507.08204
Near Detec- tor Physics
Light Sterile Neutrino Non- Standard Interaction Non-Unitarity
Detector
⌫i ⌫j , Z0.. arxiv:1710.09360
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W
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production: Decay Propagation: Matter Detection: Charge Current Standard Non-Standard P W lα ⌫α P , W 0 lα ⌫β ⌫α W ⌫α , W 0 ⌫α lα W ⌫α lβ , W 0
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 ⌫4 ⌫3 ⌫2 ⌫1 ∆m2
21
∆m2
32
∆m2
43
arxiv:1507.08204
Near Detec- tor Physics
Light Sterile Neutrino Non- Standard Interaction Non-Unitarity
Detector
⌫i ⌫j , Z0.. arxiv:1710.09360
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e2
Uµ1U∗
µ2
τ2
Uµ1U∗
µ2
arxiv:1503.08879 ⌫4 ⌫3 ⌫2 ⌫1 ∆m2
21
∆m2
32
∆m2
43
arxiv:1507.08204
Near Detec- tor Physics
Light Sterile Neutrino Non- Standard Interaction Non-Unitarity
Detector
⌫i ⌫j , Z0.. arxiv:1710.09360 Source/Detec. NSI only
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Why are those (short-baseline) experiments interesting?
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Why are those (short-baseline) experiments interesting? These new physics contain a short-distance (non-Standard) ⌫µ ! ⌫µ
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Why are those (short-baseline) experiments interesting? These new physics contain a short-distance (non-Standard) ⌫µ ! ⌫µ Non-Unitarity NSI Sterile Neutrino P NU
µe
⇠ |↵21|2 P NSI
µe
⇠ |✏d
eµ + ✏s eµ|2
P 3+1
µe
⇠ sin2 2✓µe
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Why are those (short-baseline) experiments interesting? These new physics contain a short-distance (non-Standard) ⌫µ ! ⌫µ Non-Unitarity NSI Sterile Neutrino P NU
µe
⇠ |↵21|2 P NSI
µe
⇠ |✏d
eµ + ✏s eµ|2
P 3+1
µe
⇠ sin2 2✓µe Thus, Ne ⇠ e + P NEW
µe
µ
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Why are those (short-baseline) experiments interesting? These new physics contain a short-distance (non-Standard) ⌫µ ! ⌫µ Non-Unitarity NSI Sterile Neutrino P NU
µe
⇠ |↵21|2 P NSI
µe
⇠ |✏d
eµ + ✏s eµ|2
P 3+1
µe
⇠ sin2 2✓µe Thus, Ne ⇠ e + P NEW
µe
µ
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Normalized Flux
LBNF LBNF e BNB BNB e
1 2 3 4 5 50 100 150 200 250 Energy [GeV] /e 9 / 24
Why are those (short-baseline) experiments interesting? These new physics contain a short-distance (non-Standard) ⌫µ ! ⌫µ Non-Unitarity NSI Sterile Neutrino P NU
µe
⇠ |↵21|2 P NSI
µe
⇠ |✏d
eµ + ✏s eµ|2
P 3+1
µe
⇠ sin2 2✓µe Thus, Ne ⇠ e + P NEW
µe
µ
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Normalized Flux
LBNF LBNF e BNB BNB e
1 2 3 4 5 50 100 150 200 250 Energy [GeV] /e
O(102)
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We simulated:
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We simulated: SBNE = SBND + µBooNE + ICARUS
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We simulated: SBNE = SBND + µBooNE + ICARUS LBNF beam with: protoDUNE and ICARUS as ND
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10-6 10-5 10-4 10-3 5 10 15 10-6 10-5 10-4 10-3 |21
2 or |e d+e s 2
2
SBNE ICARUS at LBNF protoDUNE-SP
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10-6 10-5 10-4 10-3 5 10 15 10-6 10-5 10-4 10-3 |21
2 or |e d+e s 2
2
SBNE ICARUS at LBNF protoDUNE-SP
SBNE: |↵21|2 < 2 ⇥ 104
10 / 24
10-6 10-5 10-4 10-3 5 10 15 10-6 10-5 10-4 10-3 |21
2 or |e d+e s 2
2
SBNE ICARUS at LBNF protoDUNE-SP
SBNE: |↵21|2 < 2 ⇥ 104 LBNF: |↵21|2 < 2.5 ⇥ 105
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10-6 10-5 10-4 10-3 5 10 15 10-6 10-5 10-4 10-3 |21
2 or |e d+e s 2
2
SBNE ICARUS at LBNF protoDUNE-SP
SBNE: |↵21|2 < 2 ⇥ 104 LBNF: |↵21|2 < 2.5 ⇥ 105 Current: |↵21|2 < 7 ⇥ 104
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10-6 10-5 10-4 10-3 5 10 15 10-6 10-5 10-4 10-3 |21
2 or |e d+e s 2
2
SBNE ICARUS at LBNF protoDUNE-SP
LBNF: |↵21|2 < 2.5 ⇥ 105 Can we really reach this level?
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This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
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This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors:
11 / 24
This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors: Source ⌫
11 / 24
This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors: Source ⌫ Near Detector
11 / 24
This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors: Source ⌫ Near Detector Far Detector
11 / 24
This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors: Source ⌫ Near Detector Far Detector
11 / 24
This New Physics changes ⌫ spectrum, Nνe / νe + |↵21|2νµ and P(⌫µ ! ⌫e) = 1 sin2 2✓µe sin ∆m41L
4E
Traditionally, neutrino oscillation experiments uses (at least) two detectors: Source ⌫ Near Detector Far Detector Extrapolation
11 / 24
But we want to measure zero distance effects!
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025)
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam (2) Measuring the muon flux in the decay pipeline and relate it to the ⌫ flux
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam (2) Measuring the muon flux in the decay pipeline and relate it to the ⌫ flux (3) Measuring the low energy transfer events (low-⌫)
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam (2) Measuring the muon flux in the decay pipeline and relate it to the ⌫ flux (3) Measuring the low energy transfer events (low-⌫) May be affected by new physics
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam (2) Measuring the muon flux in the decay pipeline and relate it to the ⌫ flux (3) Measuring the low energy transfer events (low-⌫) May be affected by new physics Need to know production differential cross section and the horn magnetic field
12 / 24
But we want to measure zero distance effects! We need to rely on other types of measurements (see hep-ex/arxiv:1201.3025) (1) Modeling the distribution of ⇡ and K produced by the proton beam (2) Measuring the muon flux in the decay pipeline and relate it to the ⌫ flux (3) Measuring the low energy transfer events (low-⌫) May be affected by new physics Need to know production differential cross section and the horn magnetic field Need to understand detector very well and is hard to measure E dependency
12 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.]
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Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Normalization: N0(1 + a)
13 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Normalization: N0(1 + a) a = 0
13 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Normalization: N0(1 + a) a = 0 a = 5%
13 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Normalization: N0(1 + a) a = 0 a = 5% a = 5%
13 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.]
14 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Shape: N0
i (1 + ai), bin i = 1, 2, ...
14 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Shape: N0
i (1 + ai), bin i = 1, 2, ...
ai = 0
14 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Shape: N0
i (1 + ai), bin i = 1, 2, ...
ai = 0 ai 6= 0
14 / 24
Let’s parametrize our lack of knowledge to see its impact: Eν [a.u.] # of Events [a.u.] Shape: N0
i (1 + ai), bin i = 1, 2, ...
ai = 0 ai 6= 0
14 / 24
A bit of math....
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
2
SYS =
✓ a a ◆2 + ✓ b b ◆2 +
Nbin
X
i=1
✓ ai sa ◆2 + ✓ bi sb ◆2 ,
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
2
SYS =
✓ a a ◆2 + ✓ b b ◆2 +
Nbin
X
i=1
✓ ai sa ◆2 + ✓ bi sb ◆2 , We minimize over a, b, ai, bi
15 / 24
A bit of math.... 2 =
Nbin
X
i=1
Nexp
i
(1 a ai)Nth
i
(1 b bi)Nbg
i
p Nexp
i
!2 + 2
SYS ,
2
SYS =
✓ a a ◆2 + ✓ b b ◆2 +
Nbin
X
i=1
✓ ai sa ◆2 + ✓ bi sb ◆2 , We minimize over a, b, ai, bi sa = sb = s Spectrum error
15 / 24
Usual histogram comparisson (Pearson’s 2) gives
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
Statistical Uncertainty
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
Statistical Uncertainty Adding the ai uncertainty:
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
Statistical Uncertainty Adding the ai uncertainty: 2 = X
i
@Ndata
i
(1 ai)Ntheo
i
q Ndata
i
1 A
2
+ ✓ai i ◆2
X
i
@ Ndata
i
Ntheo
i
q Ndata
i
+ 2
i (Ntheo i
)2 1 A
2
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
Statistical Uncertainty Adding the ai uncertainty: 2 = X
i
@Ndata
i
(1 ai)Ntheo
i
q Ndata
i
1 A
2
+ ✓ai i ◆2
X
i
@ Ndata
i
Ntheo
i
q Ndata
i
+ 2
i (Ntheo i
)2 1 A
2
16 / 24
Usual histogram comparisson (Pearson’s 2) gives 2 = X
i
@Ndata
i
Ntheo
i
q Ndata
i
1 A
2
Statistical Uncertainty Adding the ai uncertainty: 2 = X
i
@Ndata
i
(1 ai)Ntheo
i
q Ndata
i
1 A
2
+ ✓ai i ◆2
X
i
@ Ndata
i
Ntheo
i
q Ndata
i
+ 2
i (Ntheo i
)2 1 A
2
Notice, if i ! 1 one looses sensitivity (2 ! 0)
16 / 24
What we got (for |↵21|2):
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s)
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline not too far
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline not too far
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline not too far s ⇠ O(1)%
17 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
18 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
18 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
18 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
18 / 24
What we got (for |↵21|2):
0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) Spectrum Error [%] ICARUS and ICARUS+ at LBNF
5×10-
5
4×10-
5
2×10-
5
1×10-
5
*
1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Distance (km) protoDUNE-SP ar LBNF Spectrum Error [%]
5×10
4×10-5 2 × 1
1 × 1
*
Spectrum error (s) Baseline
18 / 24
1 2 3 4 5 100 101 Distance [km] Active Mass [kt]
Spectrum Error =1% ProtoDUNE-SP
|21
2=5×10
|
2
= 4 × 1
|21
2=3×10
|21
2=2.5×10
19 / 24
similar for sterile neutrino!
20 / 24
similar for sterile neutrino!
10-3 10-2 10-1 10-1 1 10 10 10 10 sin214 m41
2 [eV2] error=5% error=1% error=9%
10-3 10-2 10-1 sin224
error=1% error=5% error=9%
10-5 10-4 10-3 10-2 10-1 10-2 10-1 1 10 sin22e
error=1% error=5% error=9% 20 / 24
The sensitivity is reasonable good if L ⇠ 1km
10-3 10-2 10-1 10-1 1 10 sin214 m41
2 [eV2] L=0.6 km L=1.5 km L=2.4 km
10-3 10-2 10-1 sin224
L=0.6 km L=1.5 km L=2.4 km
10-5 10-4 10-3 10-2 10-1 10-2 10-1 1 10 sin22e
L=0.6 km L=1.5 km L=2.4 km 21 / 24
If it is possible to use two near detectors, we gain a very good improvement!
22 / 24
If it is possible to use two near detectors, we gain a very good improvement!
10-3 10-2 10-1 10-1 1 10 sin214 m41
2 [eV2]
protoDUNE (2.4 km) protoDUNE (0.6 km) ICARUS+ (2.4 km)
10-3 10-2 10-1 sin224 10-5 10-4 10-3 10-2 10-1 10-2 10-1 1 10 sin22e
22 / 24
Conclusion:
23 / 24
Conclusion: SBN can slightly improve NSI/Non-unitarity
23 / 24
Conclusion: SBN can slightly improve NSI/Non-unitarity LBNF We can probe NSI/Non-unitarity if ⇠ O(1)%
23 / 24
Conclusion: SBN can slightly improve NSI/Non-unitarity LBNF We can probe NSI/Non-unitarity if ⇠ O(1)% (depending on detector size/location)
23 / 24
Conclusion: SBN can slightly improve NSI/Non-unitarity LBNF We can probe NSI/Non-unitarity if ⇠ O(1)% (depending on detector size/location) Similar for sterile neutrino
23 / 24
Thanks
Generalitat Valenciana Ram´
CONACyT and SNI (Mexico).
24 / 24
#