The Standard Model

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The Standard Model
SM contains 19 free parameters (excluding
neutrino mass)!
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Standard Model of particle physics has many
remaining puzzles, in particular   1. The origin
of mass the origin of the weak scale, its
stability under radiative corrections, and the
solution to the hierarchy problem (most urgent
problem may be solved by LHC!)   2. The problem
of flavour the problem of the undetermined
fermion masses and mixing angles (including
neutrino masses and mixing angles) together with
the CP violating phases, in conjunction with the
observed smallness of flavour changing neutral
currents and very small strong CP violation.   3.
The question of unification the question of
whether the three known forces of the standard
model may be related into a grand unified theory,
and whether such a theory could also include a
unification with gravity.
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The Origin of Mass
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Origin of Mass in the SM
SM Higgs doublet
SM Higgs Potential
If (why?) and
(why?) then potential is minimised by
(why this scale?)
WLOG suppose
4 d.o.f.?3 G.B.s
Plus 1 physical Higgs boson
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Hierarchy Problem in SM
Note the (tree-level) min cond
Including rad corr it becomes
Fine-tuning is required if the cut-off

• New physics at TeV scale (still the best
  motivation)
• But no hint in precision LEP measurements LEP
  Paradox

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Bottom-up motivation for new physics BSM
TeV
Supersymmetry
Mz
The Hierarchy Problem
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Top-down motivation for new physics BSM
String Unification
M
Supersymmetry
Extra dimensions
New TeV scale physics
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SPIN ½ FERMIONS
SPIN 0,1 BOSONS
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Stabilising the Hierarchy in SUSY
SUSY implies ?top ?stop leading to cancellation
of the quadratic divergence, leaving only log
divergence which allows ? up to the Planck scale.

SUSY stabilises the hierarchy providing (Also
works for gauge boson loops and applies to all
loop order due to non-renormalization theorem.)
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MSSM
Two Higgs doublets
Min conds at low energy ?
Natural expectation is MZ ? mHu mstop In
fact MZ mstop ? FINE TUNING
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The ? problem

• MSSM solves technical hierarchy problem (loops)
  
• But no reason why Higgs/Higgsino mass ? msoft ?
  the ? problem.
• In the NMSSM ?0 but singlet allows SHuHd ? ltSgt
  Hu Hd where ltSgt ?
• S3 term required to avoid a massless axion due to
  global U(1) PQ symmetry
• S3 breaks PQ to Z3 resulting in cosmo domain
  walls (or tadpoles if broken)

• One solution is to forbid S3 and gauge U(1) PQ
  symmetry so that the dangerous axion is eaten to
  form a massive Z gauge boson ? U(1) model
• Anomaly cancellation in low energy gauged U(1)
  models implies either extra low energy exotic
  matter or family-nonuniversal U(1) charges
• For example can have an E6 model with three
  complete 27s at the TeV scale to cancel
  anomalies with a U(1) broken by singlets which
  solve the ? problem
• This is an example of a model where Higgs
  triplets are not split from doublets

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The Flavour Problem
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Before 1998 the flavour sector contained 13
parameters
Who ordered that ?
6 quark masses, 3 charged lepton masses,
3 quark mixing angles and 1 CP violating
phase
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• Three neutrino mass and mixing

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Reactor
Solar
Majorana
Atmospheric
3 masses 3 angles 1(3) phase(s) 7(9) new
parameters for SM
Oscillation phase
Majorana phases
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Latest global fit for atmospheric solar
oscillations

• Latest version 19th Oct 07
• Latest SSM
• SNO salt data
• K2K
• Latest MINOS results

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• Neutrino mass squared splittings and angles

3 ? errors
Valle et al
Normal
Inverted
Absolute neutrino mass scale?
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Tri-bimaximal mixing (TBM)
Harrison, Perkins, Scott
c.f. data

• Current data is consistent with TBM
• But no convincing reason for exact TBM expect
  deviations

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Useful to Parametrize lepton mixing matrix in
terms of deviations from tri-bimaximal mixing
SFK arXiv0710.0530 
r reactor
s solar
a atmospheric
Present data is consistent with r,s,a0
?tri-bimaximal
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Neutrinos and the Universe
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Neutrino masses and mixing parameters introduces
9 extra flavour parameters
Can the extra parameters help with the creation
of the universe ?
3 neutrino masses, 3 lepton mixing angles and 3
CP violating phases
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• Can neutrino mass help solve some of the problems
  of the Standard Model of Cosmology
• The origin of dark matter and dark energy the
  embarrassing fact that 96 of the mass-energy of
  the Universe is in a form that is presently
  unknown, including 23 dark matter and 73 dark
  energy ? many potential
  solutions involve neutrinos
• 2. The problem of matter-antimatter asymmetry
  the problem of why there is a tiny excess of
  matter over antimatter in the Universe, at a
  level of one part in a billion, without which
  there would be no stars, planets or life ?
  Leptogenesis
•  3. The question of the size, age, flatness and
  smoothness of the Universe the question of why
  the Universe is much larger and older than the
  Planck size and time, and why it has a globally
  flat geometry with a very smooth cosmic microwave
  background radiation containing just enough
  fluctuations to seed the observed galaxy
  structures ? sneutrino inflation
  (chaotic vs. hybrid)

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The Problem of Unification
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Howl, SFK
Minimal E6SSM Unification at MP
E6 broken via Pati-Salam chain
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Howl, SFK
Unification at MP in Minimal E6SSM
MPlanck
MPlanck
Low energy (below MGUT)

three complete families of 27s of E6 High
energy (above MGUT 1016 GeV) this is embedded
into a left-right symmetric Pati-Salam model and
additional heavy Higgs are added.
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SFK, Moretti, Nevzorov
E6SSM Unification at MGUT
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Unification at MGUT in E6SSM
2 loop, ?3(MZ)0.118
SFK, Moretti, Nevzorov
1.5 TeV
250 GeV
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LHC signatures
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Low energy matter content of E6SSMs
. .
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E6SSM couplings
DQQ, DQL allows D decay but also proton decay
Singlet-Higgs-Higgs couplings includes effective
? term
Singlet-D-D couplings includes effective D mass
terms
Yukawa couplings but extra Higgs give FCNCs
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• Two potential problems rapid proton decay
  FCNCs
• FCNC problem may be tamed by introducing a Z2
  under which third family Higgs and singlet are
  even all else odd ? only allows Yukawa couplings
  involving third family Higgs and singlet Hu , Hd
  , S
  
• Z2 also forbids all DFF and hence forbids D
  decay (and p decay)
• ? Z2 cannot be an exact symmetry!
  
  How do we reconcile D decay with p decay?
• Two strategies extra exact discrete symmetries
  or small D Yukawas
• In E6SSM can have extra discrete symmetries, two
  possibilities
• I. Z2L under which L are odd ? forbids DQL,
  allows DQQ ? exotic D are diquarks
• II. Z2B with L D odd ? forbids DQQ, allows
  DQL ? exotic D are leptoquarks
• Small DFF couplings lt10-12 will suppress p
  decay sufficiently
  
• but couplings gt10-12 will allow D decay with
  lifetime lt0.1 s (nucleosynth) N.B. ?D / g2, ?p /
  g4 (this is the only possibility in the minimal
  E6SSM)
• Henceforth assume problems solved by one of these
  approaches

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Athron, SFK, Miller, Moretti, Nevzorov
The Constrained E6SSM
The Z2 allowed couplings
Hu, Hd, S without indices are third family Higgs
and singlet, Hu,?, Hd,?, S? are non-Higgs
Assume universal soft masses m0, A, M1/2 at MGUT
In practice, input SUSY and exotic threshold
scale ?S then select tan ? and singlet VEV ltSgts
and run up third family Yukawas from ?S to MGUT
Then choose m0, A, M1/2 at MGUT and run down
gauge couplings, Yukawas and soft masses to low
energy and minimise Higgs potential for the 3
Higgs fields S, Hu, Hd (even under Z2)
EWSB is not guaranteed, but remarkably there is
always a solution for sufficiently large ? to
drive mS2 lt0 (c.f. large ht to drive mH2lt0 )
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Athron, SFK, Miller, Moretti, Nevzorov
P1
Consider a particular EWSB solution P1 with ?
-0.5
P1
P1
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Spectrum for P1
Athron, SFK, Miller, Moretti, Nevzorov
non-Higgs
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Note the lightest gaugino states easy_at_LHC
Gluino
Wino
Bino
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Chargino and neutralino production and decay
N.B. Wino production only is allowed (no Bino
production via W,Z) ? Expect N2N2 , N2C1 , C1C1
pair production (not involving the N1 Bino )
However the decays must involve N1
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e.g. N2N2 production and decay
Three body decays ? M lt MZ
End point gives mass difference
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Gluinos are light lt 1 TeV and easily produced
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Z lt 5 TeV can be discovered
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Exotic D-quarks in E6SSM
Usual case is of scalar leptoquarks, here we have
novel case of D being fermonic leptoquarks or
diquarks
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Novel signatures of D quarks
In E6SSM it is possible that the D fermions
decay rapidly as leptoquarks or diquarks giving
missing energy in the final state
However it is also possible that DFF couplings
are highly suppressed giving rise to long lived D
quarks giving jets containing heavy long lived
D-hadron
D-hadrons resemble protons or neutrons but with
mass gt300 GeV
Clean events with two D-jets containing a pair of
stable D-hadrons
Dp or Dn
p
p
Dp or Dn
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Unified Flavour Models
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Nothing
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Conclusion

• In 1998 Super-Kamiokande discovered neutrino mass
  and added 9 extra parameters to the SM
• In 2008 the LHC may discover SUSY which may add
  over 100 extra parameters to the SM
• Future high precision neutrino and collider
  experiments such as the Neutrino Factory and
  ILC/CLIC will hopefully enable a unified flavour
  theory to emerge based on a smaller number of
  parameters