CP Violation and the Mass Hierarchy Last lecture: the quest for the two remaining unknowns in our understanding of 3-neutrino mixing

Aside: Other Unknowns Important Neutrino Physics Goals

• Majorana or Dirac nature of neutrinos – double beta decay

•  absolute scale of neutrino mass – direct neutrino mass measurements and cosmology

•  are there only 3 active neutrino states? •  any evidence for sterile neutrinos?

Neutrino CP Violation •  is as “simple” as conducting two experiments and measuring

•  this is a direct test of CP symmetry •  could imagine this starting with electron neutrinos and electron

antineutrinos, but: •  these have to be appearance experiments – survival probabilities for

disappearance experiments don’t depend δCP •  it is possible to make energetic electron neutrino and antineutrino

beams that could then search for muon appearance •  e.g. beta beams

•  but muon neutrino and antineutrino beams are the current leading technology (DAR: LSND, DIF: MINOS, T2K, NOνA, MiniBooNE, CNGS, LBNE)

•  don’t even bother thinking about tau neutrino beams except to entertain yourself with thought experiments

Pνµ→νe– Pνµ→νe

T Violation •  by the way, CP violation for neutrino oscillations was first

discussed in 1978 •  N. Cabibbo, Phys. Lett. B 72, 333-335 (1978)

“Time Reversal Violation in Neutrino Oscillation”

•  short paper pointing out that if you have 3 (or more) neutrino states, non-degenerate masses (e.g. so both Δm2 have to be non-zero), the unitary mixing matrix can be complex and can lead to T (or CP) violation

•  note: CPT tells us that CP violation is the same as T violation •  that’s why a disappearance experiment doesn’t work for CP

Pνe→νe time reversed experiment would be the same

T Violation cont’d •  for appearance experiments, it can work to search for

• mathematically, the same quantities will be involved

•  technical note: Nunokawa, Parke and Valle point out in arXiv:0710.0554 (review published in Prog. Part. Nucl. Phys.) that does contain cosδ and thus by doing a disappearance experiment you can determine sinδ (up to a sign) since the other angles can be determined

Pνµ→νe= Pνe→νu

?

Pνµ→νµ= Pνµ→νµ

this bothers me greatly!

Neutrinos and Antineutrinos

Right-Handed

Giunti

PMNS Neutrino Mixing Matrix ν f = U fi ν ii∑

CP Violation

2Re [Uαk* UβkUα jUβ j

*

k> j∑ −UαkUβk

* Uα j* Uβ j ]exp(−i

Δmkj2L

2E)

= 4Re i Im[Uαk* UβkUα jUβ j

*

k> j∑ ]exp(−i

Δmkj2L

2E)

= 4 Im[Uαk* UβkUα jUβ j

*

k> j∑ ]sin(

Δmkj2L

2E)

Pνµ→νe– Pνµ→νe

=

Jarlskog Invariant •  this quantity is called a Jarlskog invariant, from the quark

CKM unitarity triangle J = c12 s12 c23 s23 c13

2 s13 sin δ =

J = Im[Uαk* UβkUα jUβ j

* ]

= 4 Im[Uαk* UβkUα jUβ j

*

k> j∑ ]sin(

Δmkj2 L

2E)

= sinδ sin2θ12 sin2θ23 sinθ13 cos2θ13 sin(

Δm312 L

2E)

−sinδ sin2θ12 sin2θ23 sinθ13 cos2θ13 sin(

Δm322 L2E

)

−sinδ sin2θ12 sin2θ23 sinθ13 cos2θ13 sin(

Δm212 L

2E)

if any angle is zero, ΔP=0; if any Δm2=0, ΔP=0

18sin2θ12 sin2θ23 sin2θ13 cosθ13 sinδ

Properties of Jarlskog Permutations

AαβCP = 4J sαβ ;kj sin(

Δmkj2 L

2E)

k> j∑

•  s for 31 is –1 •  s for 32 is +1 •  s for 21 is +1

J = c12 s12 c23 s23 c132 s13 sin δ =

e→ µ,µ→τ ,τ → eIs positive and the sign flips if flavours flip

Pνe→νµ− Pνe→νµ

= AµeCP = −Aeµ

CP

18sin2θ12 sin2θ23 sin2θ13 cosθ13 sinδ

Search for CP Violation

•  all angles should be large! •  should place detector at correct L for neutrino beam E • Δm21 solar is small compared to Δm31

•  the mass hierarchy can matter

• NH •  IH

•  |J| ≤ 0.039 from present knowledge of all 3 mixing angles

AαβCP = 4J sαβ ;kj sin(

Δmkj2 L

2E)

k> j∑

Δm312 = Δm21

2 + Δm322

Δm322 = Δm21

2 + Δm312

J = 18sin2θ12 sin2θ23 sin2θ13 cosθ13 sinδ

compare J for CKM quarks = 3 × 10–5

Accelerator Neutrino Beams for CP Violation

figure from H. Ray

T2K as an Example The!T2K!Experiment!

~500 Collaborators / 340 Authors / 59 Institutions / 11 Countries (Canada / France / Germany / Italy / Japan / Poland / Russia / Spain / Switzerland / UK / USA)

30 GeV Tunnel

06/04/2014! Chris!Walter!9!Results!from!T2K!9!Neutrino2014! 2!

T2K slides from C. Walter talk at Neutrino 2014

The T2K Off-Axis Beam

0

50

100

150

200

250

300

350

400

0En (GeV)

at 295 km

2ºAll

1 2 3 4 5

High$energy$$tail$causes$$backgrounds$

At$1$GeV$an$off5axis$$beam$has$a$higher$$and$narrower$flux$peak.$

Super9Kamiokande!Off!Axis!(2.5°)!Neutrino$Source$

π

120m 0m 280m 295 km

on-axis off-axis

monitor

Proton$Beam$ Neutrino$Beam$

The$kinemaQcs$of$pion$decay$allow$$us$to$make$a$narrower$neutrino$$beam.$$

06/04/2014! Chris!Walter!9!Results!from!T2K!9!Neutrino2014!

Epion!(GeV)!

E ν!(G

eV)!

7!

ND280!Near!Detector!

Example Off-axis Spectra

Eν (MeV) (GeV)

your homework: make this plot

Electron Appearance Probability

and then there are matter effects on top of this! in an experiment, DIF beam has some intrinsic νe contamination

•  Comparing!with!the!external!reactor!constraint!the!best!overlap!is!for!the!normal!hierarchy!with!δcp=–π/2.!

•  This!is!a!lucky$point!!•  You!also!need!to!increase!the!θ23!mixing!angle!to!account!for!the!number!of!observed!events.!

06/04/2014! 15!Chris!Walter!9!Results!from!T2K!9!Neutrino2014!

Let’s!think!about!these!regions!!

Note: Marginalized over θ23 and Δm2

32

T2K Recent Results •  narrow band is reactor θ13

measurement •  use theta13 reactor results to

help constrain (break degeneracies)

•  use second expt (e.g. T2K-NOνA) to break degeneracies •  especially different baselines with

both at different oscillation maxima •  must correct for/exploit different

matter effects for different baselines of beam traversing the Earth

Future!SensiQvity!to!CPV!using!T2K!

06/04/2014! Chris!Walter!9!Results!from!T2K!9!Neutrino2014! 23!

No systematics 5% error on signal, 10% on background

T2K!studies!indicate!our!best!sensiQvity!will!be!for!50%!ν/50%!anQ9ν!!running.!AnQ9nu!running!also!opens!a!large!new!physics!program.!!

50%!ν/50%!anQ9ν!(true!NH)!100%!ν!(true!NH)!

50%!ν/50%!anQ9ν!(true!NH)!w/!Reactor!constraint!

100%!ν!(true!NH)!w/!Reactor!constraint!

“Lucky! (+: Sin22θ=0.1, δCP=-90)”

NH$

T2K:!50%!ν/50%!anQ9ν!

Precision Reactor Neutrino Disappearance

•  could break degeneracy with other experiments that can determine the hierarchy •  precision atmospheric neutrino (e.g. PINGU, ICAL) •  in principle could have something to say about δCP (I showed that

yesterday when we looked at recent Super-K atmospheric results)

•  one class of experiments is precision reactor neutrino disappearance (e.g. JUNO, RENO-50)

Future Long Baseline Neutrino Experiments plans for LBNE, Hyper-K feature: -  intense neutrino beams for higher statistics -  ideally both neutrino and antineutrino beams -  large far detectors to accumulate statistics

-  how to break the hierarchy degeneracy? -  exploit matter effects

-  over long baseline, beams traverse greater distance underground -  we know matter effects care about the sign of the hierarchy

Future Long Baseline Neutrino Experiments plans for LBNE, Hyper-K feature: -  intense neutrino beams for higher statistics -  ideally both neutrino and antineutrino beams -  large far detectors to accumulate statistics

-  how to break the hierarchy degeneracy? -  exploit matter effects

-  over long baseline, beams traverse greater distance underground -  we know matter effects care about the sign of the hierarchy

Neutrino Mass Hierarchy • Large T13 open doors to MH

– Utilize matter effects ¾e-Q CC interactions in the earth

modulate the oscillation probability at long baselines (LBNE, LBNO, T2HK)

2

Precision Reactor Neutrino Disappearance

•  could break degeneracy with other experiments that can determine the hierarchy •  precision atmospheric neutrino (e.g. PINGU, ICAL) •  in principle could have something to say about δCP (I showed that

yesterday when we looked at recent Super-K atmospheric results)

•  one class of experiments is precision reactor neutrino disappearance (e.g. JUNO, RENO-50)

JUNO •  Jiangmen Underground Neutrino Observatory •  20 kton liquid scintillator with 3%/√E energy resolution

Daya Bay ~60 km JUNO

JUNO Experiment

5

� Jiangmen Underground Neutrino Observatory (was Daya Bay II) slides from L. Wed talk at Neutrino 2014

Location of JUNO NPP Daya Bay Huizhou Lufeng Yangjiang Taishan Status Operational Planned Planned Under construction Under construction Power 17.4 GW 17.4 GW 17.4 GW 17.4 GW 18.4 GW

Yangjiang NPP

Taishan NPP

Daya Bay NPP

Huizhou NPP

Lufeng NPP

53 km 53 km

Hong Kong

Macau

Guang Zhou

Shen Zhen

Zhu Hai 700 m underground

2.5 h drive

JUNO

6

Previous site candidate

JUNO Detector Concept Challenge: high-precision, giant LS detector

11

20 kt LS

Acrylic tank: )a34.5m Stainless Steel tank: )a39.0m

~1500 20”  VETO PMTs

coverage: ~77% ~18000 20” PMTs

Muon detector

Steel Tank

5m

~6kt MO

~20kt water

JUNO RENO-50

Mass Hierarchy from Precision Reactor Spectrum •  need high statistics and excellent energy resolution

Phys.Rev.D78:111103,2008

Neutrino Mass Hierarchy • Large T13 open doors to MH

– Exploit L/E spectrum with reactors

3

S.T. Petcov et al., PLB533(2002)94 S.Choubey et al., PRD68(2003)113006 J. Learned et al., PRD78, 071302 (2008) L. Zhan, Y. Wang, J. Cao, L. Wen, PRD78:111103, 2008, PRD79:073007, 2009 J. Learned et al., arXiv:0810.2580 … Realistic requirements about determining MH with reactors will be discussed later

Vision&of&the&Future&for&Neutrino&Oscilla3ons&•  from%puzzle%

–  to%discoveries%•  to%complete%determina3on%of%mixing%parameters%in%the%lepton%sector%

– CP%viola3on%(Majorana%nature%of%neutrinos)%

•  probing&neutrino&mass&and&mixing&will&guide&us&to&the&correct&extensions&of&the&Standard&Model&at&higher&energy&scales&