Fermion Masses and Unification

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Fermion Masses and Unification

• Lecture I Fermion Masses and Mixings
• Lecture II Unification
• Lecture III Family Symmetry and Unification
• Lecture IV SU(3), GUTs and SUSY Flavour
• Steve King
• University of Southampton

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Lecture IFermion Masses and Mixings

• The Flavour Problem and See-Saw
• From low energy data to high energy data
• Textures in a basis
• Appendix 1 References
• Appendix 2 Basis Changing

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1.The Flavour Problem and See-Saw
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The Flavour Problem1. Why are there three
families of quarks and leptons?
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The Flavour Problem2. Why are quark and charged
lepton masses so peculiar?
t
u
d
c
e
s
b
Family symmetry e.g. SU(3)
GUT symmetry e.g. SO(10)
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The Flavour Problem3. Why is lepton mixing so
large?
e.g.Tri-bimaximal
Harrison, Perkins, Scott
c.f. small quark mixing
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The Flavour Problem4. What is the origin of CP
violation?
a
g
b
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The Flavour Problem5. Why are neutrino masses so
small?
See-saw mechanism is most elegant solution
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The See-Saw Mechanism
Light neutrinos
Heavy particles
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The see-saw mechanism
Type II see-saw mechanism (SUSY)
Type I see-saw mechanism
Lazarides, Magg, Mohapatra, Senjanovic, Shafi,
Wetterich (1981)
P. Minkowski (1977), Gell-Mann, Glashow,
Mohapatra, Ramond, Senjanovic, Slanski, Yanagida
(1979/1980)
Type II
Type I
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See-Saw Standard Model (type I)
Yukawa couplings to 2 Higgs doublets (or one with
)
Insert the vevs
Rewrite in terms of L and R chiral fields, in
matrix notation
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The See-Saw Matrix
Dirac matrix
Type II contribution (ignored here)
Heavy Majorana matrix
Diagonalise to give effective mass
Light Majorana matrix
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Lepton mixing matrix VMNS
Neutrino mass matrix (Majorana)
Defined as
Can be parametrised as
Solar
Reactor
Atmospheric
Oscillation phase
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Quark mixing matrix VCKM
Defined as
Can be parametrised as
Phase convention independent
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From low energy data to high energy data
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(From Particle Data Book)
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Quark data (low energy)
Ross and Serna
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Andre de Gouvea
Neutrino Masses and Mixings
c.f. quark mixing angles
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Renormalisation Group running
SM beta functions
MSSM beta functions
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SM couplings at low energy
Latest coupling constant measurements at
energy scale
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Evolution of SM couplings
Two-loop RGEs for the SM
.
.
.
.
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MSSM
Two-loop RGEs for the MSSM with 1 TeV effective
SUSY threshold
.
.
.
.
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MSSM
Two-loop RGEs for the MSSM with 1 TeV effective
SUSY threshold
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MSSM
Two-loop RGEs for the MSSM with 250 GeV effective
SUSY threshold
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RGEs for t,b,? in the MSSM
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RGEs for Yukawa matrices in MSSM
Wavefunction anomalous dimensions
RGEs (one-loop accuracy)
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Charged fermion data (high energy)
Ross and Serna
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3. Textures in a basis
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Hierarchical Symmetric Textures
Symmetric hierarchical matrices with 11 texture
zero motivated by
Gatto et al
This motivates the symmetric down texture at GUT
scale of form
? ¼ 0.2 is the Wolfenstein Parameter
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Up quarks are more hierarchical than down
quarks This suggests different expansion
parameters for up and down
Detailed fits require numerical (order unity)
coefficients
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Ross and Serna
Detailed fits at the GUT Scale
No SUSY thresholds
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Ross and Serna
With SUSY thresholds
Georgi-Jarlskog
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Final remarks on choice of basis
We have considered a particular choice of quark
texture in a particular basis
But it is shown in the Appendix that all choices
of quark mass matrices that lead to the same
quark masses and mixing angles may be related to
each other under a change of basis. For example
all quark mass matrices are equivalent to the
choice
However this is only true in the Standard Model,
and a given high energy theory of flavour will
select a particular preferred basis. Also in the
see-saw mechanism all choices of see-saw matrices
are NOT equivalent.
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Appendix 1 References

• W. De Boer hep-ph/9402266
• S.Raby ICTP Lectures 1994
• G.G.Ross ICTP Lectures 2001
• J.C. Pati ICTP Lectures 2001
• S. Barr ICTP Lectures 2003
• S. Raby hep-ph/0401115
• S.Raby PDB 2006
• A. Ceccucci et al PDB 2006
• G. Ross and M. Serna 0704.1248
• D. Chung et al hep-ph/0312378
• S.F. King hep-ph/0310204

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Appendix 2 Basis Changing
S.F. King hep-ph/0610239

• 2.1 Quark sector
• 2.2 Effective Majorana sector
• 2.3 See-saw sector

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