decoding neutrino masses and mixing from symmetry to anarchynuhorizons/nuhri6/talks/kpatel.pdf ·...

Ketan Patel 1

Decoding Neutrino Masses and Mixing From Symmetry to Anarchy

Ketan Patel (IISER Mohali)

Nu HoRIzons VI, HRI, AllahabadMarch 17-19, 2016

Current status of neutrino masses and mixing

Decoding neutrino masses and mixing: From Symmetry to AnarchyKetan Patel 2

[M. C. Gonzalez-Garcia et al. (2014)]

[F. Capozzi et al. (2014)]

[D. Forero et al. (2014)]

[…see S. Goswami’s Talk]

Current status of neutrino masses and mixing


• Neutrinos have tiny mass.

• Can have normal or inverted ordering, can be quasidegenerate in masses.

• The mass hierarchy is weaker.

• Two of the three mixing angles are large.

• One is small but not zero.

• Weak indication of maximal Dirac CP phase.

The SM Flavour Puzzle


Neutrinos with respect to charged fermions…

|UPMNS| ⇡

0

@0.8 0.5 0.20.5 0.6 0.60.3 0.6 0.7

1

A

|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

A

� ⇡ 0.23

Approaches to the Flavour Puzzle




Largely responsible for smallness of neutrino masses



Largely responsible for smallness of neutrino massesMainly responsible for

flavour structure




flavour structure

Two well-known approaches:

Symmetry

Y are deduced from first principle

Symmetry and/or dynamical principle determines Yukawas in a fundamental

theory




flavour structure

Two well-known approaches:

Symmetry

Y are deduced from first principle

Symmetry and/or dynamical principle determines Yukawas in a fundamental

theory

Anarchy

Y are due to chance

Observed Yukawas are environmental selection and cannot be fully predicted


Symmetry Approaches

Exploring Residual symmetries of Leptons through Neutrino data

Symmetry behind neutrinos


Tracing the symmetry of Lagrangian



[…see S. Pramanick’s Talk]



• Generalisation of symmetries predicting [A.S.Joshipura, KMP (2015)]

can arise from the DSG of O(3)



Discrete Symmetries Beyond the Neutrino Mixing Angles Predictions

• Let S is the symmetry of Majorana neutrino mass matrix

at least one of the neutrinos is massless if Symmetry is DSG of U(3) and not SU(3)

[A.S.Joshipura, KMP (2013)]







• Scan over various DSG of U(3) is performed and mixing pattern is analysed [A.S.Joshipura, KMP (2014)]








• Idea is extended for (at least two) degenerate neutrinos [A.S.Joshipura, KMP (2014), D.Hernandez, A.Smirnov (2014)]








• Idea is extended for (at least two) degenerate neutrinos [A.S.Joshipura, KMP (2014), D.Hernandez, A.Smirnov (2014)]

• Neutrino Anti-symmetry [A.S.Joshipura (2015)]

[… See N. Nath’s Talk]

Lessons from symmetries


• No (simple) symmetry predicting the observed values of all three mixing angles.

• Perturbations of the order of Cabibbo angle are needed.




• Symmetries not predicting reactor angle but predicting maximal atmospheric angle and maximal Dirac CP violation are of current interests.







• New approaches based on mass dependent mixing patterns






• New approaches based on mass dependent mixing patterns

• No clear and elegant picture of “Theory of Flavour” so far!


Anarchy approaches to Neutrino data

Structureless natural couplings of order unity

Anarchy and Neutrino data


Empirical evidence of symmetry from a quark sector:

|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1




|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1

Can easily be produced using Froggatt-Nielsen symmetry [Froggatt and Nielsen (1979)]




|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1

Can easily be produced using Froggatt-Nielsen symmetry [Froggatt and Nielsen (1979)]

Order unity numbers, No structure !!




|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1




|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1

Leads to observed form of CKM mixings




|VCKM| ⇡

0

@1 � �3

� 1 �2

�3 �2 1

1

Amu : mc : mt ⇡ �8 : �4 : 1

md : ms : mb ⇡ �5 : �3 : 1

Leads to observed form of CKM mixings

Leads to viable mass ratios in quark sector (with a moderate tuning in O(1) parameters)



Extension to the Lepton Sector

Hierarchy only in the charged lepton masses

Viable for both Dirac and Majorana neutrinos






An Extreme Possibility [Hall, Murayama, Weiner (1999); De Gouvea, Murayama (2012)]






An Extreme Possibility [Hall, Murayama, Weiner (1999); De Gouvea, Murayama (2012)]

supported by nonzero reactor angle and non-maximal atmospheric angle

Neutrino mass ratios and mixing angles are O(1) numbers

consistent with current data!



Other variants of Anarchy in Lepton sector[Buchmuller, Domcke, Schmitz (2011); Altarelli, Feruglio, Masina, Merlo (2012); Bergstrom, Meloni, Merlo (2014)]



Other variants of Anarchy in Lepton sector[Buchmuller, Domcke, Schmitz (2011); Altarelli, Feruglio, Masina, Merlo (2012); Bergstrom, Meloni, Merlo (2014)]

Difficult to go beyond order of magnitude predictions!



Is symmetry necessary to support Anarchy?



Is symmetry necessary to support Anarchy?Flavour Hierarchies from Extra-dimensions

φ=0φ=+π

φ=−π Identify+φ with −φ

(i.e. x5 with −x5)

φ=0 φ=π

φ=0

x5=0

φ=π

x5=πR

Figure 10: Orbifolding the circle to an interval

interval as an “orbifold” of the circle. This is illustrated in Fig. 10, where thepoints on the two hemispheres of the circle are identified. Mathematically,we identify the points at φ or x5 with −φ or −x5. In this way the physicalinterval extends a length πR, half the circumference of our original circle.This identification is possible if we also assign a “parity” transformation toall the fields, which is respected by the dynamics (i.e. the action). The actionwe have considered above has such a parity, given by

P ( x5) = −x5 P (Aµ) = +Aµ P (A(0)5 ) = −A(0)

5

P (ΨL) = +ΨL P (ΨR) = −ΨR ,(5.1)

precisely when the 5D fermion mass vanishes, m = 0. We consider this casefor now.

Ex. Check that the action is invariant under this parity transformation.With such a parity transformation we continue to pretend to live on a

circle, but with all fields satisfying

Φ(xµ,−x5) = P (Φ)(xµ, x5) . (5.2)

That is, the degrees of freedom for x5 < 0 are merely a reflection of degreesof freedom for x5 > 0, they have no independent existence. Of course we alsorequire circular periodicity,

Φ(xµ, φ + 2π) = Φ(xµ, φ) . (5.3)

These conditions specify “orbifold boundary conditions” on the interval, de-rived from the the circle, which of course has no boundary.

17

xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)

Figure 11: Orbifolded higher dimensional spacetime (with boundaries)

which live in the “bulk” of the 5D spacetime, there is a 4D Weyl fermion pre-cisely confined to one of the 4D boundaries of the 5D spacetime, say φ = π.It can couple to the gauge field evaluated at the boundary if it carries somenon-trivial representation, say triplet. This represents a second way in whichthe chirality problem can be solved, localization to a physical 4D subspaceor “3-brane” (a “p”-brane has p spatial dimensions plus time), in this casethe boundary of our 5D spacetime. The new fermion has action,

Sχ =

!d4x χ

Li(x)

"i∂µδ

ij + gA ijµ (x, φ = π)

#χ

Lj(x) . (5.12)

At low energies, E ≪ 1/R, this fermion will have identical gauge coupling asthe Ψ(0) triplet, but it will have no Yukawa coupling, thereby giving a cruderepresentation of a light fermion of the standard model.

Well, there are other tricks that one can add to get closer and closer tothe real world. Ref. [14] gives a nice account of many model-building issuesand further references. I want to move in a new direction.

20

[N. Arkani-Hamed, M. Schmaltz (2000), D. Kaplan,T. Tait (2001)]




L = f(x5) �L(xµ) + f

1(x5) �1L(xµ) + ...

Flavour Hierarchies from Extra-dimensions

φ=0φ=+π



φ=0 φ=π

φ=0

x5=0

φ=π

x5=πR



P ( x5) = −x5 P (Aµ) = +Aµ P (A(0)5 ) = −A(0)

5

P (ΨL) = +ΨL P (ΨR) = −ΨR ,(5.1)




Φ(xµ,−x5) = P (Φ)(xµ, x5) . (5.2)


Φ(xµ, φ + 2π) = Φ(xµ, φ) . (5.3)


17

xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20





L = f(x5) �L(xµ) + f

1(x5) �1L(xµ) + ...

H(x)Solving E.O.M. and performing dimension reduction..

f(x5) ⇠pM exp(�Mx5)


φ=0φ=+π



φ=0 φ=π

φ=0

x5=0

φ=π

x5=πR



P ( x5) = −x5 P (Aµ) = +Aµ P (A(0)5 ) = −A(0)

5

P (ΨL) = +ΨL P (ΨR) = −ΨR ,(5.1)




Φ(xµ,−x5) = P (Φ)(xµ, x5) . (5.2)


Φ(xµ, φ + 2π) = Φ(xµ, φ) . (5.3)


17

xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20





L = f(x5) �L(xµ) + f

1(x5) �1L(xµ) + ...

H(x)Solving E.O.M. and performing dimension reduction..

f(x5) ⇠pM exp(�Mx5)

i jH(x) ! fi(⇡R) fj(⇡R) �i(x)�j(x)H(x)

pMiMj exp(�|Mj +Mi|⇡R)

M1 > M2 > 0 > M3 generates appropriate hierarchy


φ=0φ=+π



φ=0 φ=π

φ=0

x5=0

φ=π

x5=πR



P ( x5) = −x5 P (Aµ) = +Aµ P (A(0)5 ) = −A(0)

5

P (ΨL) = +ΨL P (ΨR) = −ΨR ,(5.1)




Φ(xµ,−x5) = P (Φ)(xµ, x5) . (5.2)


Φ(xµ, φ + 2π) = Φ(xµ, φ) . (5.3)


17

xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20





• No symmetry, Hierarchy is produced by geometry.

• Generalisation of FN charges.

• Unlike FN symmetry, idea of generating hierarchies through extra-dimension is compatible with Quark-Lepton Unification.




• No symmetry, Hierarchy is produced by geometry.

• Generalisation of FN charges.

• Unlike FN symmetry, idea of generating hierarchies through extra-dimension is compatible with Quark-Lepton Unification.

for example, in SO(10) unification

leads to universal hierarchy in quarks and leptons




xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20

H(x)

In SO(10) common profiles for all fermions…

f16(x5) ⇠p

M16 exp(�M16x5)

f16

[F. Feruglio, KMP, D. Vicino (2014,15)]




xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20

H(x)


f16(x5) ⇠p

M16 exp(�M16x5)

However, if in the bulk SO(10) �! SU(5)⇥ U(1)X

M16 �! M16 +QXh45�i

16 = 10�1 + 53 + 1�5(Q, uc, ec) (dc, L) (N c)

f16





xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20

H(x)


f16(x5) ⇠p

M16 exp(�M16x5)


M16 �! M16 +QXh45�i

16 = 10�1 + 53 + 1�5(Q, uc, ec) (dc, L) (N c)





xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20

H(x)


f16(x5) ⇠p

M16 exp(�M16x5)


M16 �! M16 +QXh45�i

16 = 10�1 + 53 + 1�5(Q, uc, ec) (dc, L) (N c)

f16 �! {f10, f5, f1}

f10

f5 f1





xµ

φ = 0x5 = 0

φ = πx5 = πR

AM , Ψ

χL(x)



Sχ =

!d4x χ

Li(x)

"i∂µδ


#χ

Lj(x) . (5.12)



20

H(x)


f16(x5) ⇠p

M16 exp(�M16x5)


M16 �! M16 +QXh45�i

16 = 10�1 + 53 + 1�5(Q, uc, ec) (dc, L) (N c)

f16 �! {f10, f5, f1}

f10

f5 f1

Only 4 parameters create 9 different profiles; Differences are created by only one parameter!

SO(10) in 5D creates SU(5) with U(1) FN like structure




Some Results [F. Feruglio, KMP, D. Vicino (2014,15)]

Normal ordering Inverted ordering

Observable Fitted value Pull Fitted value Pull

yt 0.51 0 0.54 1.00

yb 0.37 0 0.37 0

y⌧ 0.51 0 0.47 -1.00

mu/mc 0.0027 0 0.0031 0.67

md/ms 0.051 0 0.045 -0.86

me/mµ 0.0048 0 0.0048 0

mc/mt 0.0023 0 0.0023 0

ms/mb 0.016 0 0.015 -0.50

mµ/m⌧ 0.050 0 0.049 -0.50

|Vus| 0.227 0 0.227 0

|Vcb| 0.037 0 0.038 1.00

|Vub| 0.0033 0 0.0030 -0.50

JCP 0.000023 0 0.000021 -0.51

�S/�A 0.0309 0 0.0320 0.73

sin

2 ✓12 0.308 0 0.309 0.06

sin

2 ✓23 0.425 0 0.435 -0.07

sin

2 ✓13 0.0234 0 0.0237 -0.10

�2min ⇡ 0 ⇡ 5.75

Predicted value Predicted valuem⌫lightest [meV] 0.08 2.15|m�� | [meV] 1.63 30.4

sin �lCP 0.265 0.510

MN1 [GeV] 3.85⇥ 10

61.13⇥ 10

4

MN2 [GeV] 9.31⇥ 10

73.06⇥ 10

6

MN3 [GeV] 2.19⇥ 10

142.02⇥ 10

13

�R [GeV] 0.05⇥ 10

160.18⇥ 10

16




F10 = �0.7

0

@�3.9 0 00 �2.2 00 0 1

1

A

F5 = �0.4

0

@�0.8 0 00 �0.4 00 0 1

1

A

F1 = �1.5

0

@�7.4 0 00 �5.5 00 0 1

1

A

F10 = �0.3

0

@�3.7 0 00 �2.4 00 0 1

1

A

F5 = �0.3

0

@�1.5 0 00 �0.9 00 0 1

1

A

F1 = �0.4

0

@�6.2 0 00 �4.8 00 0 1

1

A

Normal Ordering

Inverted Ordering

Fitted ProfilesNormal ordering Inverted ordering

Observable Fitted value Pull Fitted value Pull

yt 0.51 0 0.54 1.00

yb 0.37 0 0.37 0

y⌧ 0.51 0 0.47 -1.00

mu/mc 0.0027 0 0.0031 0.67

md/ms 0.051 0 0.045 -0.86

me/mµ 0.0048 0 0.0048 0

mc/mt 0.0023 0 0.0023 0

ms/mb 0.016 0 0.015 -0.50

mµ/m⌧ 0.050 0 0.049 -0.50

|Vus| 0.227 0 0.227 0

|Vcb| 0.037 0 0.038 1.00

|Vub| 0.0033 0 0.0030 -0.50

JCP 0.000023 0 0.000021 -0.51

�S/�A 0.0309 0 0.0320 0.73

sin

2 ✓12 0.308 0 0.309 0.06

sin

2 ✓23 0.425 0 0.435 -0.07

sin

2 ✓13 0.0234 0 0.0237 -0.10

�2min ⇡ 0 ⇡ 5.75

Predicted value Predicted valuem⌫lightest [meV] 0.08 2.15|m�� | [meV] 1.63 30.4

sin �lCP 0.265 0.510

MN1 [GeV] 3.85⇥ 10

61.13⇥ 10

4

MN2 [GeV] 9.31⇥ 10

73.06⇥ 10

6

MN3 [GeV] 2.19⇥ 10

142.02⇥ 10

13

�R [GeV] 0.05⇥ 10

160.18⇥ 10

16




0 2 4 6 80.0

0.1

0.2

0.3

0.4

m n1 @meV DProbability

0 2 4 6 80.00

0.05

0.10

0.15

0.20

»m bb » @meV D

Probability

-1.0 -0.5 0.0 0.5 1.00.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

dCPêp

Probability




NOIO

0.1 1. 10. 100. 1000. 10 000.0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

cmin2 ê n

Probability

0 2 4 6 80.0

0.1

0.2

0.3

0.4


0 2 4 6 80.00

0.05

0.10

0.15

0.20

»m bb » @meV D

Probability

-1.0 -0.5 0.0 0.5 1.00.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

dCPêp

Probability




NOIO

0.1 1. 10. 100. 1000. 10 000.0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

cmin2 ê n

Probability

0 2 4 6 80.0

0.1

0.2

0.3

0.4


0 2 4 6 80.00

0.05

0.10

0.15

0.20

»m bb » @meV D

Probability

MN1

MN 2

MN 3

4 6 8 10 12 140.0

0.1

0.2

0.3

0.4

0.5

0.6

Log10 HMNi ê GeVL

Probability

-1.0 -0.5 0.0 0.5 1.00.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

dCPêp

Probability

Conclusions


• Flavour Symmetry is quite a predictive and elegant tool in our quest for a theory of Flavour. But no clear compelling picture seems to be emerging so far. Present data can be described by varieties of idea and frameworks based on symmetries

• Anarchy: Simple schemes with minimal structures can well reproduce the flavour in both the quark and lepton sector.

Consistent with complete Quark-Lepton unification. Major drawback: No sharp predictions. No precision test is allowed.

• If special features (like maximal atmospheric mixing angle, maximal Dirac CP phase, inverted hierarchy in neutrino masses,…) survive experimental refinements then they can guide us in the search of first principles.

decoding neutrino masses and mixing from symmetry to anarchynuhorizons/nuhri6/talks/kpatel.pdf ·...

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