The SM Flavour Puzzle and accidental Symmetries

38 Pages·2007·3.33 MB·English

The flavour puzzle and
accidental symmetries
Andrea Romanino
SISSA
based on: Ferretti, King, R hep-ph/0609047
Outline
The flavour puzzle in the SM
Approaches to the flavour puzzle
A new approach
• Basic idea
• Vus and LR symmetry
• s/b vs c/t and Pati-Salam
• Neutrinos
• A model
2
The flavour puzzle in the SM
3 families, or U(3)5 symmetry of the fermion gauge lagrangian
family number
1 2 3 (horizontal)
not understood
l l l l
1 2 3
ec (ec) (ec) (ec)
1 2 3
q q q q
1 2 3
uc (uc) (uc) (uc)
1 2 3
dc (dc) (dc) (dc)
1 2 3
gauge irreps
(vertical)
well understood
3
The flavour puzzle in the SM
3 families, or U(3)5 symmetry of the fermion gauge lagrangian
Pattern of U(3)5 breaking from Yukawa sector (most SM pars)
flavor E c D c U c
= λ e L H + λ d Q H + λ u Q H + h.c.
SM ij i j † ij i j † ij i j
L
3
The flavour puzzle in the SM
3 families, or U(3)5 symmetry of the fermion gauge lagrangian
Pattern of U(3)5 breaking from Yukawa sector (most SM pars)
• (horizontal) hierarchy of fermion± masses: 1 « 2 « 3
TeV
• CKM mixing angles « 1 t
b
Τ
c
GeV
Μ
s
d
u
MeV e
keV
Q = m
t
eV
Ν
3
The flavour puzzle in the SM
3 families, or U(3)5 symmetry of the fermion gauge lagrangian
Pattern of U(3)5 breaking from Yukawa sector (most SM pars)
• (horizontal) hierarchy of fermion± masses: 1 « 2 « 3
TeV
• CKM mixing angles « 1 t
• U vs D vs E
b Τ
GeV
c
Μ
- different hierarchies: U » D, E
s
d
- m ≈ m , 3m ≈ m , m ≈ 3m @ M MeV u
b τ s μ d e G e
• mass hierarchy vs mixing hierarchy
keV
- |V | ~ m /m , |V | ≈ (m /m )1/2
cb s b us d s Q = M
G
(MSSM)
• neutrino sector
eV
Ν
- 2 PMNS mixing angles O(π/4), 1 small
- θ = O(π/4) & |∆m2| « |∆m2| , θ ≠ π/4
23 12 23 12
3
The flavour puzzle in SM extensions
The peculiar SM flavour structure (m , m « <H>, |V |,|V | « 1) allows the
1 2 td ts
SM to pass the FCNC test
s¯ds¯d 1 1
(Q H ) ,
L ! " # ⊃ Λ2 Λ2 ∼ (103 TeV)2
f f
1 g4 m2 m2 1
u u
(V V )(V V )f i , j
Λ2 ∼ (4π)2 × s†ui uid s†uj ujd M2 M2 × M2
SM
f W W W
! " ! "
The unknown physics at the SM cutoff should not provide new generic
flavour structure
1 1
?
Λ2 ∼ × Λ2
NP
f NP
! "
• e.g. in the MSSM δ « 1, or (m˜2 -m˜2 )/m˜2 and |W |,|W | « 1
12 d s 31 32
Is the origin of the peculiar structure in SM and the MSSM/NP the same?
4
(Some) approaches to the flavour puzzle
“Flavour symmetries” acting on family indexes (subgroup of U(3)5)
• symmetric limit: only O(1) Yukawas possibly allowed: λ (λ λ )
t b τ
- e.g. tc, q , h neutral under a U(1): Y t c q h is allowed
3 33 3
• spontaneous breaking of U(1) by SM singlets ϕ at high scale
φ φ
- e.g. Q(q ) = 1, Q(ϕ) = -1: t c q h is allowed (cid:15482) Y = ! "
2 2 32
M M
• breaking communicated to SM fermions by heavy messengers (M = mass)
h φ
- at E « M
M φ
c
tc X q2 → t q2 h
M
¯
Q Q
• gauge/global, continuous/discrete, abelian/non-abelian
Extra-dimension mechanisms
• flavour symmetry breaking with boundary conditions
• localized fermions
- e.g. in RS-type models:
(0)
A
µ
H
AdS
5 e(0) t(0)
(1 c c )πkR
H λ e i j
ij − −
UV (M ) IR (TeV) ∝
P
c<1/2 c>1/2
0 y !R
UV (M ) IR (TeV)
P
Figure 1: A slice of AdS : The Randall-Sundrum scenario.
5
m M e πkRFigure 2: The Standaψrd (Myod)el ineth(e1w/a2rpecdi)fikvey-dimensional bulk.
H 5 − i −
∼ ∝
the warped down scale
k = curvature c = bulk mass in k units
requires that lepton number is conserved on the UV brane. Instead in the “reversed”
1 1
M2Ψ¯iΨjΨ¯kΨl → (M escπekRn)a2rΨi¯oiΨojnΨ¯ekcΨaln, place the right((3l)eft) handed neutrino near the IR (UV) brane. In
5 5 −
this case even though lepton number is violated on the UV brane, the neutrinos will
1 1
ννHH stillνoνbHtHain, naturally tiny Dirac m(4a)sses [21].
M → M e πkR
5 5 −
where Ψi is a Standard Model fermion and ν3is.2the nHeuitgrinhoe.rT-hdisimleaedns stoiognene6oripc erators
problemswithprotondecayandFCNCeffects, andalsoneutrinomassesarenolonger
consistent with experiment. Thus, while the hierarchy problem has been addressed
Let us consider the following generic four-fermion operators which are relevant for
in the Higgs sector by a classical rescaling of the Higgs field, this has¯come at the
proton decay and K K mixing
expense of introducing proton decay and FCNC problems from highe−r-dimension op-
erators that were sufficiently suppressed in the Standard Model. 1 1
d4x dy √ g Ψ¯ Ψ Ψ¯ Ψ d4x Ψ¯(0)Ψ(0)Ψ¯(0)Ψ(0) , (38)
− M3 i j k l ≡ M2 i+ j+ k+ l+
Exercise: The classical rescaling Φ edΦπkRΦ whe!re d != 1(3) for sca5lars ! 4
• → Φ 2
(fermions), suffers from a quantum anomalywahnedreletahdesetffoetchteivaed4dDitiomnaossf sthcealeLaM- for 1/2 < c < 1 is approximately given by[11]
4 i
grangian term ∼ ∼
δLanomaly = πkR!i β4(ggi3i)TrFµ2ν,i , M142 %(5)Mk53e(4−ci−cj−ck−cl)πkR . (39)
where β(g ) is the β-function for the corresponding gauge couplings g . Show that this
i If we want the suppriession scale for higher-dimension proton decay operators to be
anomaly implies that quantum mass scales, such as the gauge coupling unification
M M then (39) requires c 1 assuming k M M . Unfortunately for these
scale MGUT, are also redshifted by an amount M4G∼UTe−πPkR. i % ∼ 5 ∼ P
values of c thecorresponding Yukawa couplings would betoosmall. Nevertheless, the
i
values of c needed to explain the Yukawa coupling hierarchies still suppresses proton
Instead in the slice of AdS with the Standard Model fields confined on the IR brane
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decay by a mass scale larger than the TeV scale [11, 22]. Thus there is no need to
one has to resort to discrete symmetries to forbid the offending higher-dimension
operators. Of course it is not adequate just tiomfpoorbseidathdeislceraedtiengsyhmigmheert-rdyimwehnsiciohnforbids very large higher-dimension operators.
On the other hand the suppression scale for FCNC processes only needs to be
M > 1000 TeV. This can easily be achieved for the values of c that are needed
4 4
∼
to explain the Yukawa coupling hierarchies. In fact the FCNC constraints can be
used to obtain a lower bound on the Kaluza-Klein mass scale m . For example
KK
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A new (economical) approach
The knowledge (or existence) of special
1 2 3
horizontal dynamics is not required to explain
the fermion hierarchical pattern
l l l l
1 2 3
nc (nc) (nc) (nc)
1 2 3
The pattern follows from the relative lightness
of one set of heavy fields and is associated to ec (ec) (ec) (ec)
1 2 3
the breaking of the gauge group (Pati-Salam)
q q q q
1 2 3
Chiral symmetries acting on family indexes uc (uc) (uc) (uc)
1 2 3
“protecting” the mass of the lighter families
dc (dc) (dc) (dc)
emerge in this context as accidental symmetries 1 2 3
7