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Global Fits in the Neutrino Sector Mona Dentler Workshop Fit(s) for - - PowerPoint PPT Presentation

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Global Fits in the Neutrino Sector Mona Dentler Workshop Fit(s) for the LHC run-2 11 October 2016 General Remark LHC is not a neutrino experiment neutrinos are not detected directly @ LHC But neutrinos are interesting for the physics

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SLIDE 1

Global Fits in the Neutrino Sector

Mona Dentler Workshop ”Fit(s) for the LHC run-2“ 11 October 2016

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SLIDE 2

General Remark

LHC is not a neutrino experiment → neutrinos are not detected directly @ LHC But neutrinos are interesting for the physics (SM @ high energies, BSM) we want to study @ LHC:

  • neutrino mass
  • sterile neutrino
  • CP-violation
  • non standard interactions

⇒ understanding neutrino physics can ”make fit for the LHC run-2“!

2 / 25

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SLIDE 3

Introduction

“We are entering the precision era of neutrino physics”

3 / 25

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SLIDE 4

Introduction

“We are entering the precision era of neutrino physics” Experiments can agree – or disagree – more “subtly”

3 / 25

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SLIDE 5

Introduction

“We are entering the precision era of neutrino physics” Experiments can agree – or disagree – more “subtly”

  • experiments have rarely exactly the same layout
  • ⇒ different systematics, parameter spaces, etc...

3 / 25

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SLIDE 6

Introduction

“We are entering the precision era of neutrino physics” Experiments can agree – or disagree – more “subtly”

  • experiments have rarely exactly the same layout
  • ⇒ different systematics, parameter spaces, etc...

starting point for global fits!

3 / 25

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SLIDE 7

Neutrino Fit Parameters

4 / 25

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SLIDE 8

Neutrino Fit Parameters

In the SM, there are seven free parameters for the neutrino, e.g.:

  • Three masses mi, i = e, µ, τ
  • Three mixing angles θij, i, j = e, µ, τ
  • One CP phase δCP

5 / 25

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SLIDE 9

Neutrino Fit Parameters

In the SM, there are seven free parameters for the neutrino, e.g.:

  • Three masses mi, i = e, µ, τ
  • Three mixing angles θij, i, j = e, µ, τ
  • One CP phase δCP

Most precise parameter values (not bounds) come from

  • scillation experiments

Oscillation experiments are only sensitive to ∆m2

ij ≡ m2 i − m2 j

⇒ one parameter principally not accessible

5 / 25

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SLIDE 10

Neutrino Fit Parameters

In the SM, there are seven free parameters for the neutrino, e.g.:

  • Three masses mi, i = e, µ, τ
  • Three mixing angles θij, i, j = e, µ, τ
  • One CP phase δCP

Most precise parameter values (not bounds) come from

  • scillation experiments

Oscillation experiments are only sensitive to ∆m2

ij ≡ m2 i − m2 j

⇒ one parameter principally not accessible Nevertheless, in this talk concentrate on oscillation experiments

5 / 25

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SLIDE 11

Neutrino Oscillation Parameters

  • Neutrino flavor eigenstate |να and mass eigenstate |νk

not aligned: |να =

N

  • k=1

U∗

αk|νk

  • Neutrino propagates as mass eigenstate. Time evolution:

|νk(t) = exp(−iEkt)|νk

  • Transition probability Pαβ = | νβ|να |2

Pαβ =

N

  • k,j=1

U∗

αkUβkUαjU∗ βj exp(−i(Ek − Ej)t)

  • In the ultrarelativistic limit, using Jαβ

kj ≡ U∗ αkUβkUαjU∗ βj:

Pαβ = δαβ−4

  • k>j

Re(Jαβ

kj ) sin2 (∆ij)+2

  • k>j

Im(Jαβ

kj ) sin (∆ij)

6 / 25

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SLIDE 12

Neutrino Oscillation Parameters

  • Neutrino flavor eigenstate |να and mass eigenstate |νk

not aligned: |να =

N

  • k=1

U∗

αk|νk

  • Neutrino propagates as mass eigenstate. Time evolution:

|νk(t) = exp(−iEkt)|νk

  • Transition probability Pαβ = | νβ|να |2

Pαβ =

N

  • k,j=1

U∗

αkUβkUαjU∗ βj exp(−i(Ek − Ej)t)

  • In the ultrarelativistic limit, using Jαβ

kj ≡ U∗ αkUβkUαjU∗ βj:

Pαβ = δαβ−4

  • k>j

Re(Jαβ

kj ) sin2 (∆ij)+2

  • k>j

Im(Jαβ

kj ) sin (∆ij)

∼ Jarlskog invariant: measures CP violation

6 / 25

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SLIDE 13

Neutrino Oscillation Parameters

  • Neutrino flavor eigenstate |να and mass eigenstate |νk

not aligned: |να =

N

  • k=1

U∗

αk|νk

  • Neutrino propagates as mass eigenstate. Time evolution:

|νk(t) = exp(−iEkt)|νk

  • Transition probability Pαβ = | νβ|να |2

Pαβ =

N

  • k,j=1

U∗

αkUβkUαjU∗ βj exp(−i(Ek − Ej)t)

  • In the ultrarelativistic limit, using Jαβ

kj ≡ U∗ αkUβkUαjU∗ βj:

Pαβ = δαβ−4

  • k>j

Re(Jαβ

kj ) sin2 (∆ij)+2

  • k>j

Im(Jαβ

kj ) sin (∆ij)

with frequency parameter ∆ij ≡ ∆m2

ijL/(4E)

6 / 25

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SLIDE 14

Neutrino Oscillation Parameters

Not all experiments are equally sensitive to all six parameters. ⇒ derive effective transition probability For example: “atmospheric frequency”

  • θ31 ≈ 0

⇒ Im(Pαβ) = 0 (δCP attached to θ31)

  • ∆m2

31 ≈ ∆m2 32,

|∆m2

32| ≫ |∆m2 21|

⇒ Pαβ ≈ δαβ − 4(Jαβ

31 + Jαβ 32 ) sin2 (∆31) − 4Jαβ 21 sin (∆21)

  • frequency such that ∆31 ≈ 1,

⇒ ∆21 ≪ 1 ⇒Pαβ ≈ δαβ − 4(Jαβ

31 + Jαβ 32 ) sin2 (∆31)

⇒Pee ≈ 1, Pµe ≈ Peµ ≈ 0 Pµµ ≈ 1 − sin2 2θ23 sin2 (∆31)

7 / 25

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SLIDE 15

Neutrino Oscillation Parameters

Not all experiments are equally sensitive to all six parameters. ⇒ derive effective transition probability For example: “atmospheric frequency”

  • θ31 ≈ 0

⇒ Im(Pαβ) = 0 (δCP attached to θ31)

  • ∆m2

31 ≈ ∆m2 32,

|∆m2

32| ≫ |∆m2 21|

⇒ Pαβ ≈ δαβ − 4(Jαβ

31 + Jαβ 32 ) sin2 (∆31) − 4Jαβ 21 sin (∆21)

  • frequency such that ∆31 ≈ 1,

⇒ ∆21 ≪ 1 ⇒Pαβ ≈ δαβ − 4(Jαβ

31 + Jαβ 32 ) sin2 (∆31)

⇒Pee ≈ 1, Pµe ≈ Peµ ≈ 0 Pµµ ≈ 1 − sin2 2θ23 sin2 (∆31) “Octant Degeneracy”: cannot distinguish sin2 θ23 from 1 − sin2 θ23

7 / 25

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SLIDE 16

Neutrino Oscillation Parameters

Not all experiments are equally sensitive to all six parameters. ⇒ derive effective transition probability “Eight-fold” Degeneracy

  • ctant degeneracy, (δCP, θ13),(δCP, mass-hierarchy (sgn∆m2

31))

Use global fits to resolve degeneracies

  • combining information from detectors at different baselines
  • using additional oscillation channels
  • spectral information (wide band beam)
  • adding information on θ13 from a reactor experiment
  • adding information from (Mt scale) atmospheric neutrino

experiments

7 / 25

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SLIDE 17

Global Fit to 3-Flavor Oscillations

Gonzalez-Garcia, Maltoni, Schwetz, 1409.5439

8 / 25

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SLIDE 18

Global Fit to 3-Flavor Oscillations

Gonzalez-Garcia, Maltoni, Salvado, Schwetz, 2012 Gonzalez-Garcia, Maltoni, Schwetz, 1409.5439

8 / 25

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SLIDE 19

How to perform a global fit on ν-oscillations

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SLIDE 20

How to perform a global fit on ν-oscillations

The goal

  • build a χ2-function including all relevant systematics for

each experiment

  • find the global minimum of this χ2-function

The challenges

  • high-dimensional parameter space (6 + systematics)
  • event spectra depend non-trivially on pull parameters

(systematics)

  • calculating expected spectra is computationally costly cf.

full 3-flavor probability Pαβ

10 / 25

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SLIDE 21

How to perform a global fit on ν-oscillations

The strategy I: simple + fast algorithm Start from Powell’s algorithm to find minimum

http://mathfaculty.fullerton.edu 11 / 25

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SLIDE 22

How to perform a global fit on ν-oscillations

The strategy I: simple + fast algorithm Start from Powell’s algorithm to find minimum Modify search strategy:

  • divide search direction into

true parameters: computationally expensive pull parameters (systematics): not so expensive

  • in each step, go exclusively in one direction (true/ pull)

11 / 25

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SLIDE 23

How to perform a global fit on ν-oscillations

The strategy I: simple + fast algorithm Start from Powell’s algorithm to find minimum Modify search strategy:

  • divide search direction into

true parameters: computationally expensive pull parameters (systematics): not so expensive

  • in each step, go exclusively in one direction (true/ pull)

The Drawback Powell’s algorithm will only find local minimum

11 / 25

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SLIDE 24

How to perform a global fit on ν-oscillations

The strategy I: simple + fast algorithm Start from Powell’s algorithm to find minimum Modify search strategy:

  • divide search direction into

true parameters: computationally expensive pull parameters (systematics): not so expensive

  • in each step, go exclusively in one direction (true/ pull)

The strategy II: optimal starting position

  • use pre-scans in some plane, e.g. systematics turned off ⇒

use outcome as start value for proper fit

  • use knowledge about degeneracies (e.g. octant) to find

the respective degenerate solution

  • when doing a parameter-scan: use outcome @ previous grid

point as starting position

11 / 25

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SLIDE 25

How to perform a global fit on ν-oscillations

The strategy III: even faster Use highly optimized algorithms for manipulating 3 × 3 matrices, e.g. Cardano’s (analytical) formula to calculate eigenvalues

  • J. Kopp, arXiv:physics/0610206

12 / 25

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SLIDE 26

How to perform a global fit on ν-oscillations

The strategy III: even faster Use highly optimized algorithms for manipulating 3 × 3 matrices, e.g. Cardano’s (analytical) formula to calculate eigenvalues

  • J. Kopp, arXiv:physics/0610206

The software GLoBES General Long Baseline Experiment Simulator

https://www.mpi-hd.mpg.de/personalhomes/globes/ Huber, Kopp, Lindner, Rolinec, Winter, hep-ph/0701187

12 / 25

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SLIDE 27

Global Fits on Sterile Neutrinos

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SLIDE 28

Global Fits on Sterile Neutrinos

Sterile neutrino 101

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SLIDE 29

Global Fits on Sterile Neutrinos

Sterile neutrino 101 What are sterile neutrinos?

  • Leptons
  • Singlets under all gauge groups (of the SM)

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SLIDE 30

Global Fits on Sterile Neutrinos

Sterile neutrino 101 What are sterile neutrinos?

  • Leptons
  • Singlets under all gauge groups (of the SM)

What are they good for?

  • Explanation of neutrino masses → Seesaw mechanism
  • DM/ dark radiation
  • Explain anomalies in oscillation experiments

14 / 25

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SLIDE 31

Global Fits on (Light) Sterile Neutrinos

Sterile neutrino 101 What are sterile neutrinos?

  • Leptons
  • Singlets under all gauge groups (of the SM)

What are they good for?

  • Explanation of neutrino masses → Seesaw mechanism
  • DM/ dark radiation
  • Explain anomalies in oscillation experiments ⇒ light sterile

neutrinos

14 / 25

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SLIDE 32

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Appearance Signals LSND: short-baseline (SBL) experiment: ¯ νµ → ¯ νe MiniBooNE: SBL ¯ νµ → ¯ νe and νµ → νe

Kopp, Machado, Maltoni, Schwetz, 1303.3011

15 / 25

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SLIDE 33

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Appearance Signals LSND: short-baseline (SBL) experiment: ¯ νµ → ¯ νe MiniBooNE: SBL ¯ νµ → ¯ νe and νµ → νe KARMEN: SBL ¯ νµ → ¯ νe NOMAD: SBL νµ → νe ICARUS: long-baseline (LBL) νµ → νe and others

15 / 25

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SLIDE 34

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Disappearance Signals

( )

ν e Reactors: SBL, LBL ¯ νe → ¯ νe

10 100 distance from reactor [m] 0.7 0.8 0.9 1 1.1

  • bserved / no osc. expected

∆m

2 = 0.44 eV 2, sin 22θ14 = 0.13

∆m

2 = 1.75 eV 2, sin 22θ14 = 0.10

∆m

2 = 0.9 eV 2, sin 22θ14 = 0.057

ILL Bugey3,4 Rovno, SRP SRP Rovno Krasn Bugey3 Gosgen Krasn Gosgen Krasn Gosgen Bugey3

Kopp, Machado, Maltoni, Schwetz, 1303.3011

15 / 25

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SLIDE 35

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Disappearance Signals

( )

ν e Reactors: SBL, LBL ¯ νe → ¯ νe Gallium (GALLEX, SAGE): SBL νe → νe

15 / 25

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SLIDE 36

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Disappearance Signals

( )

ν e Reactors: SBL, LBL ¯ νe → ¯ νe Gallium (GALLEX, SAGE): SBL νe → νe Disappearance Signals

( )

ν µ MiniBooNE: SBL ¯ νµ → ¯ νµ and νµ → νµ MINOS: LBL νµ → νµ Charged Current (CC) LBL νµ → νs Neutral Current (NC) and others

15 / 25

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SLIDE 37

Global Fits on (Light) Sterile Neutrinos

Anomalies in Oscillation Experiments Disappearance Signals

( )

ν e Reactors: SBL, LBL ¯ νe → ¯ νe Gallium (GALLEX, SAGE): SBL νe → νe Disappearance Signals

( )

ν µ MiniBooNE: SBL ¯ νµ → ¯ νµ and νµ → νµ MINOS: LBL νµ → νµ Charged Current (CC) LBL νµ → νs Neutral Current (NC) and others New data IceCube: LBL

( )

ν µ →

( )

ν µ+ NC matter effects NEW FEATURE

15 / 25

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SLIDE 38

Global Fits on (Light) Sterile Neutrinos

How many sterile neutrinos should be added?

  • 1 sterile neutrino: hierarchy “3+1”
  • 2 sterile neutrinos: hierarchy either “3+2” or 1+3+1“

⇒ advantage of a CP-phase @ SBL

  • adding more sterile neutrinos introduces no new physical

effects

16 / 25

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SLIDE 39

Global Fits on (Light) Sterile Neutrinos

Global fit on

( )

ν e disappearance

Kopp, Machado, Maltoni, Schwetz, 1303.3011

10 3 10 2 101 101 100 101 Ue4

2

m 41

2 eV2

  • 95 CL

Gallium SBL reactors All Νe disapp LBL reactors C 12 Solar KamL

χ2

min/ dof (GOF)

∆χ2

no osc/ dof (CL)

3+1 SBL + Gallium 64.0/ 78 (87%) 14.0/ 2 (99.9%) global

( )

ν e disapp. 403.3/ 427 (79%) 12.6/ 2 (99.8%) 3+2 SBL + Gallium 60.2/(80-4) (90%) 17.8/ 4 (99.9%)

17 / 25

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SLIDE 40

Global Fits on (Light) Sterile Neutrinos

Global fit on

( )

ν e appearance

Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof (GOF)

global

( )

ν e app. 3+1 87.9/ (68-2) (3.7%) 3+2 72.7/ (68-5) (19%) 1+3+1 74.6/ (68-5) (15%)

18 / 25

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SLIDE 41

Global Fits on (Light) Sterile Neutrinos

Result of separate fits (3+1) channel effective parameter (SBL-approx.) value

( )

ν e →

( )

ν e sin2 2˜ θee ≡ 4|Ue4|2(1 − |Ue4|2) 0.09

( )

ν µ →

( )

ν e sin2 2˜ θµe ≡ 4|Uµ4Ue4|2) 0.013

( )

ν µ →

( )

ν µ sin2 2˜ θµµ ≡ 4|Uµ4|2(1 − |Uµ4|2) no evid. Combination of different channels channels are not independent: sin2 2˜ θµe ≈ 1/4 sin2 2˜ θee sin2 2˜ θµµ Severe tension between different data sets

19 / 25

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SLIDE 42

Global Fits on (Light) Sterile Neutrinos

Severe tension between different data sets

Kopp, Machado, Maltoni, Schwetz, 1303.3011

102 101 101 100 101 UΜ4 2 m41

2 eV2

CDHS atm MINOS 2011 MB disapp LSND MB app reactorsGa Null results combined

  • 99 CL

19 / 25

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SLIDE 43

Global Fits on (Light) Sterile Neutrinos

Severe tension between different data sets

Kopp, Machado, Maltoni, Schwetz, 1303.3011

102 101 101 100 101 UΜ4 2 m41

2 eV2

CDHS atm MINOS 2011 MB disapp LSND MB app reactorsGa Null results combined

  • 99 CL

Need more data to constrain sterile hypothesis ⇒ include e.g. new IceCube data

19 / 25

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SLIDE 44

Global Fits on Sterile Neutrinos

Including the IceCube 2015 data

20 / 25

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SLIDE 45

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data

http://icecube.wisc.edu/science/icecube/detector

Cherenkov detector in the Antarctic ice Measurement of (mostly) atmospheric muon neutrinos from the other hemisphere

21 / 25

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SLIDE 46

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data

IceCube arXiv:1605.01990

Cherenkov detector in the Antarctic ice Measurement of (mostly) atmospheric muon neutrinos from the other hemisphere Unique spectral feature: due to MSW-effect (matter effect) resonance in the disappearance probability

21 / 25

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SLIDE 47

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step I: reproduce the official limits

10-2 10-1 10-2 10-1 100 101 sin2θ24 Δm41

2 [eV2]

solid: official 99% CL 90% CL

solid contours from IceCube arXiv:1605.01990

Quite extensive systematics we currently include

  • seven different ν flux

models

  • four different DOM

efficiency models

  • uncertainty on ν/¯

ν-ratio

  • uncertainty on π/K-ratio

in cosmic flux

22 / 25

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SLIDE 48

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step II: incorporate into global fit

10-2 10-1 10-1 100 101 sin2θ24 Δm41

2 [eV2]

CDHS atm MINOS (2011) M B d i s a p p LSND MB app reactors+Ga Null results combined IC86 (2015) ★

Preliminary

99% CL

MD, Kopp, Machado, Maltoni, Martinez, Schwetz, in preperation

22 / 25

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SLIDE 49

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step III: statistics Global fit 2013 Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof

GOF 3+1 712/(689 − 9) 19% 3+2 701/(689 − 14) 23% 1+3+1 694/(689 − 14) 30% strong tension in data sets not reflected by GOF parameter, because a large number of data points is not sensitive to tension ⇒ ”dilution“ of GOF

22 / 25

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SLIDE 50

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step III: statistics Global fit 2013 Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof

GOF 3+1 712/(689 − 9) 19% 3+2 701/(689 − 14) 23% 1+3+1 694/(689 − 14) 30% strong tension in data sets not reflected by GOF parameter, because a large number of data points is not sensitive to tension ⇒ ”dilution“ of GOF introduce parameter goodness of fit (PG) test: χ2

PG ≡ χ2 min,glob − χ2 min,app − χ2 min,dis

Maltoni Schwetz hep-ph/0304176

22 / 25

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SLIDE 51

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step III: statistics Global fit 2013 Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof

GOF χ2

PG/ dof

PG 3+1 712/(689 − 9) 19% 18.0/ 2 1.2 × 10−4 3+2 701/(689 − 14) 23% 25.8/ 4 3.4 × 10−5 1+3+1 694/(689 − 14) 30% 16.8/ 4 2.1 × 10−3 introduce parameter goodness of fit (PG) test: χ2

PG ≡ χ2 min,glob − χ2 min,app − χ2 min,dis

Maltoni Schwetz hep-ph/0304176

22 / 25

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SLIDE 52

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step III: statistics Global fit 2013 Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof

GOF χ2

PG/ dof

PG 3+1 712/(689 − 9) 19% 18.0/ 2 1.2 × 10−4 3+2 701/(689 − 14) 23% 25.8/ 4 3.4 × 10−5 1+3+1 694/(689 − 14) 30% 16.8/ 4 2.1 × 10−3 Global fit 3+1 + IceCube: 0.4 × 10−4

22 / 25

slide-53
SLIDE 53

Global Fits on (Light) Sterile Neutrinos

Including the IceCube 2015 data Step III: statistics Global fit 2013 Kopp, Machado, Maltoni, Schwetz, 1303.3011 χ2

min/ dof

GOF χ2

PG/ dof

PG 3+1 712/(689 − 9) 19% 18.0/ 2 1.2 × 10−4 3+2 701/(689 − 14) 23% 25.8/ 4 3.4 × 10−5 1+3+1 694/(689 − 14) 30% 16.8/ 4 2.1 × 10−3 Global fit 3+1 + IceCube: 0.4 × 10−4 ”improves“ limit by factor 3

22 / 25

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SLIDE 54

Global Fits on (Light) Sterile Neutrinos

Summary anomalies in (SBL) oscillation experiments

  • found in different channels
  • using different experimental techniques
  • might be due to a common origin ⇒ interesting physics
  • some of the experiments are quite old
  • background might not be fully understood
  • severe tension between different data sets

Outlook update of global fit

  • using new data
  • comparing different subsets of experiments
  • possibly include limits from cosmology

23 / 25

slide-55
SLIDE 55

Summary

Global fits in the neutrino sector are...

  • ...necessary: not all neutrino experiments are equally

sensitive to all parameters ⇒ inevitable tool to analyze data

  • ...computationally challenging: need sophisticated ideas

to speed up computations

  • ...illuminative: give limits on (new) physics phenomena,

which cannot be measured directly (yet)

24 / 25

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SLIDE 56

Thank you for your Attention!

picture penguin: Wikipedia Commons: Liam Quinn - King Penguin

25 / 25