Leptonic CP Violation in
Neutrino Oscillations
Shun Zhou
KTH Royal Institute of Technology, Stockholm
in collaboration with T. Ohlsson & H. Zhang
Phys. Rev. D 87 (2013) 013012
Phys. Rev. D 87 (2013) 053006
Phys. Rev. D 88 (2013) 013001
Theoretical Physics Division, IHEP, Beijing
2014-03-06
Outline
•
•
•
•
•
Introduction
RG running of Dirac CP-violating phase
Leptonic CP violation in ν oscillations
NSI Effects @ IceCube (DeepCore & PINGU)
Summary
1
Open Questions in ν Physics
• Are neutrinos Dirac or Majorana particles?
Lepton number violation, neutrinoless double beta decays
• What is the neutrino mass hierarchy?
Normal (m1 < m2 < m3 ) or inverted (m3 < m1 < m2)?
• What is the absolute neutrino mass scale?
Is the lightest ν massless? Hierarchical or degenerate?
• What is the origin of neutrino masses and flavor mixing?
Seesaw mechanisms, flavor symmetries, …
• Is there CP violation in the lepton sector?
What is the value of the Dirac CP-violating phase δ?
2
Current Status
Precision measurements of neutrino parameters:
0
0  c13
1


U   0 c23 s23  0
0  s
  s e iδ
c
23
23 
13

Atmospheric /
Accelerator
0 s13e iδ  c12

1
0   s12
0
c13  0
Reactor /
Accelerator
s12
c12
0
0

0
1 
Solar / Reactor
Global-fit analyses:
Forero et al., Phys. Rev. D
86 (2012) 073012
Fogli et al., Phys. Rev. D
86 (2012) 013012
Gonzalez-Garcia et al.,
JHEP 1212 (2012) 123
Pascoli & Schwetz
Adv. HEP, 2013
Octant degeneracy
Leptonic CP violation?
Neutrino mass hierarchy?
3
Neutrino Mass Hierarchy
PINGU
Normal
Hierarchy
ORCA
Inverted
Hierarchy
Akhmedov, Razzaque, Smirnov,
JHEP 1302 (2013) 082
- Medium-baseline reactor experiments:
JUNO, RENO-50
- Long-baseline accelerator experiments:
T2K, NOνA, LBNO, LBNE
- Huge neutrino telescopes:
PINGU, ORCA
4
Leptonic CP Violation
Neutrino oscillations in vacuum:
CP
Aαβ
 P(ν α  ν β )  P(ν α  ν β )
Branco et al., Rev. Mod.
Phys. 84 (2012) 515
2
2
2
m32
L
m31
L
m21
L
 16 s c s c s c sin  sin
sin
sin

4E
4E
4E
J : Jarlskog Invariant
2
12 12 23 23 13 13
Fogli et al.
Gonzalez-Garcia et al.
Forero et al.
- First hint from global fits?
- Predictions from theories
- Compare between theory
& exp. observation of δ:
Radiative corrections
- Optimize the exp. setup:
CP measures, ν-oscillogram
- e.g., NSI effects in the ice
5
RG Running of Neutrino Parameters
Why is RG running important?
- Grand Unified Theories: SU(5), SO(10), …
Predictions from
high-energy theories
- Extra–dimensional models: ADD, UED, …
- Flavor symmetry models: A4, S4, …
RG running
Measurements in
low-energy experiments
6
RG Running of Neutrino Parameters
The SM as an effective theory: dimension-5 operator
Weinberg, Phys. Rev. Lett.
43 (1979) 1566
Majorana neutrino mass matrix:
[]-1 : high energy scale 
Masses, mixing angles, and
leptonic CP-violating phases
Renormalization Group Equation:
Babu et al., Phys. Lett. B
319 (1993) 191;
Chankowski & Pluciennik,
ibid., 316 (1993) 312
Antusch et al., Phys. Lett.
B 519 (2001) 238
- Realized in various seesaw models
  

t  ln 
  EW 
C  
3
2
   3g 22    2tr 3YuYu   3YdYd   YlYl  
- Running of masses is dominated by the
flavor-diagonal term (gauge, quark Yuk.)
- RG running of mixing angles and CPviolating phases is dominated by
charged-lepton Yukawa couplings
7
MSSM and 5D-UED
Extensions of the SM: supersymmetry and extra dimensions
1
L  LH u    LH u
2
1
L  LH  ˆ  LH
2
ν mass matrix:
ν mass matrix:
M    (v sin  ) 2
M  ˆv 2 /(R)
RGE coefficients:
RGE coefficients:
MSSM
C
1
Tau Yukawa coupling
dominated:
y2  m2 (1  tan 2  ) / v 2
radius of the
extra spatial
dimension
CUED  CSM (1  s)
number of
excited KK
modes
Coefficient becomes

larger at highers 
 0 
energy scales:
8
RG Running of Dirac CP-violating Phase
In the standard parametrization:
enhanced if neutrino
masses are nearly
degenerate
Antusch et al., Nucl. Phys. B 674 (2003) 401;
S. Luo and Z.Z. Xing, Phys. Rev. D 86 (2013) 073003;
T. Ohlsson, H. Zhang and S.Z., Phys. Rev. D 87 (2013) 013012
the same order of
magnitude according to
the latest global-fit
results
• Keep all contributions of the same order.
• RG running depends crucially on the Majorana CP-violating phases;
insignificant running for ρ=σ.
• RG running is in the opposite direction for the MSSM, compared to
the SM and 5D-UED.
9
significant running for large tanβ
MSSM
UEDM
cutoff energy scale around 3 × 104 GeV
because of the Landau pole
10
Fogli et al.
Gonzalez-Garcia et al.
tanβ = 50
tanβ = 30
tanβ = 10
11
Summary for RG Running of δ
 The RGE of the leptonic Dirac CP-violating phase is derived, and
small contributions of the same order are included.
 Very tiny RG running effects in the SM, even for nearly-degenerate
neutrino masses
 No significant RG running also in the MSSM and 5-UED, except for a
very large tanβ in the former case; however, note the dependence
on the Majorana phases
 Non-zero δ can be radiatively generated at the low-energy scale
even if δ = 0 holds at a high-energy scale.
 For Dirac neutrinos, RG running is even smaller because of the
absence of Majorana CP-violating phases.
 Constraints on δ from neutrino oscillation experiments can be
directly applied to theory at a superhigh-energy scale.
12
CP Violation and Matter Effects
Neutrino oscillations in matter:
 0

1

 


1  
2
H eff 
U
m21
U  2 2GF N e E  0


2E 
2 


 
m31
0



Oscillation probabilities:
Kimura et al., Phys. Lett.
B 537 (2012) 86
Pμe (δ )  P(ν μ  ν e )  a cos δ  b sin δ  c 

CP

A

μe (δ )  Δa cos δ  Δb sin δ  Δc
Pμe (δ )  P(ν μ  ν e )  a cos δ  b sin δ  c 

 Fake CP violation is induced by matter effects:
- obscuring the intrinsic CP-violating effects by δ
 How to describe leptonic CP violation?
- working observables based on oscillation probabilities
13
Working Observables
Series expansions of the probabilities in terms of α = Δm221 / Δm231 and s13:
sin AΔ sin ( A  1)Δ
cos Δ
A
A 1
sin AΔ sin ( A  1)Δ
b  8αJ r
sin Δ
A
A 1
2
2 sin ( A  1)Δ
c  4 s132 s23
( A  1) 2
T. Ohlsson, H. Zhang and S.Z.,
J r  s12c12 s23c23s13c132
Phys. Rev. D 87 (2013) 053006
a  8αJ r
sin AΔ
Δa  8αJ r Θ 
cos Δ
A
sin AΔ
Δb  8αJ r Θ 
sin Δ
A
2 2
Δc  4s13s23Θ  Θ 
Θ 
sin ( A  1)Δ sin ( A  1)Δ

A 1
A 1
Here Δ = Δm231L/4E and A = VL/2Δ, with V being the matter potential, Δ the oscillation
phase, and L the distance between the source and the detector.
ΔPμeCP (δ ) & ΔPμem
CP
m
ΔAμe
(δ ) & ΔAμe
Definitions:
Definitions:
ΔPμeCP (δ )  Pμe (δ )  Pμe (δ  0)



ΔPμem  max Pμe (δ )  min Pμe (δ )

CP
CP
CP
ΔAμe
(δ )  Aμe
(δ )  Aμe
(δ  0)



m
CP
CP
ΔAμe
 max Aμe
(δ )  min Aμe
(δ )

14
Neutrino Oscillograms of the Earth
h - nadir angle
PREM model
θ - zenith angle
Fe
h=π-θ
h=
inner
core
33o
core-crossing
trajectory
core
outer
core
RE = 6371 km
Si
transition
zone
lower
mantle
upper
mantle
mantle
© A.Yu. Smirnov
15
Oscillograms for CP Violation
Conventional CP asymmetry
CP
Aμe
(δ )
Akhmedov, Maltoni, & Smirnov,
JHEP 05 (2007) 077; 06 (2008) 072
Working observable
CP
ΔAμe
(δ )
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 87 (2013) 053006
16
Oscillograms for CP Violation
Working observable
m
ΔAμe
Locating future experiments
m
ΔAμe
: Zoom - in Plot
LBNO
LBNE
NOvA
T2K
ESS
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 87 (2013) 053006
17
Non-Standard Neutrino Interactions
Neutrino oscillations in matter with NSIs:
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 88 (2013) 013001
 0
 1

   ee
 
  *

1  
2
H eff 
m21
U 
U  2 2GF N e E  0     e
2E  
2 

  *


m
0
31 
  e

 
Oscillation probability with NSIs:
 e  e  
 
     
*
 
  

 Deviation from the std. probability; only mu-tau flavors are involved
 Not suppressed by mixing angle θ13 or the mass ratio Δm221 / Δm231
18
Neutrino Parameter Mappings
Leptonic mixing matrix elements in matter:
Modified NSI parameters:
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 88 (2013) 013001
Modified mixing angle:
Cˆ  cos 213  A
ˆ
sin 13 
2Cˆ
2
Cˆ 
cos 213  A2  sin 2 213
19
Oscillation Probabilities with NSIs
Significant deviation in the high-energy range:
SD
P
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 88 (2013) 013001
SD
P  PNSI  P
20
IceCube (DeepCore and PINGU)
(PINGU, 12/2012)
21
Number of Events @ PINGU
Compare between
standard and NSIs
NH
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 88 (2013) 013001
A
N SD  N NSI
NH (left)
N SD
IH (right)
22
Sensitivity @ IceCube (DeepCore)
Esmaili & Smirnov, arXiv:1304.1042
εττ - εμμ
εττ - εμμ
Higher resonance
energy for smaller εαβ
εμτ
εμτ
23
CP Violation with NSIs
SD
PeSD
(

)

P

e (0)

NH (left)

2
IH (right)
T. Ohlsson, H. Zhang and S.Z.,
Phys. Rev. D 88 (2013) 013001
NSI
PeNSI
(

)

P

e (0)


2
24
Summary
 Future neutrino oscillation experiments aim to determine the
neutrino mass ordering and measure the Dirac CP-violating phase.
 Usually theoretical prediction for the CP phase is given at a
super-high energy scale, which should be compared with low-energy
measurements. So, RG running has to be taken into account.
 Two new working observables have been introduced to describe
intrinsic leptonic CP violation, disentangle the fake CP-violating
effects, and optimize the experimental setup.
 The possibility to constrain NSIs has been investigated at IceCube
(DeepCore and PINGU).
25
Thanks a lot
for your attention!
26