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SM contains 19 free parameters (excluding neutrino mass)!

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.

Steve King, Thursday Seminar

Steve King, Thursday Seminar

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

Steve King, Thursday Seminar

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”

Steve King, Thursday Seminar

Technicolour

Bottom-up motivation for new physics BSM

TeV

Supersymmetry

Mz

The Hierarchy Problem

Steve King, Thursday Seminar

Top-down motivation for new physics BSM

String Unification

M*

Supersymmetry

Extra dimensions

New TeV scale physics

Steve King, Thursday Seminar

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”.)

Steve King, Thursday Seminar

A nice feature of MSSM is radiative EWSB Ibanez-Ross

(s)top loops drive negative

MSSM

Two Higgs doublets

Min conds at low energy

Natural expectation is MZ»» mHu» mstop

In fact MZ¿ mstop FINE TUNING

Steve King, Thursday Seminar

- MSSM solves “technical hierarchy problem” (loops)
- But no reason why Higgs/Higgsino mass » msoft the “ problem”.
- In the NMSSM =0 but singlet allows SHuHd <S> Hu Hd where <S>»
- 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 27’s 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

Steve King, Thursday Seminar

Steve King, Thursday Seminar

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

Steve King, Thursday Seminar

Neutrino mass states

Three neutrino mass and mixing

.

. .

.

. .

.

. .

.

. .

Reactor

Solar

Majorana

Atmospheric

3 masses + 3 angles + 1(3) phase(s) = 7(9) new parameters for SM

Oscillation phase

Majorana phases

Steve King, Thursday Seminar

Solar

Latest global fit for atmospheric & solar oscillations

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

Steve King, Thursday Seminar

Neutrino mass squared splittings and angles

3 errors

Valle et al

Normal

Inverted

Absolute neutrino mass scale?

Steve King, Thursday Seminar

Harrison, Perkins, Scott

c.f. data

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

Steve King, Thursday Seminar

Useful to Parametrize lepton mixing matrix in terms of deviations from tri-bimaximal mixing

SFK arXiv:0710.0530

r = reactor

s = solar

a = atmospheric

Present data is consistent with r,s,a=0 tri-bimaximal

Steve King, Thursday Seminar

Steve King, Thursday Seminar

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

Steve King, Thursday Seminar

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)

Steve King, Thursday Seminar

Steve King, Thursday Seminar

Extra U(1)X survives to TeV scale

MPlanck

E6! SU(4)PS£ SU(2)L£ SU(2)R

£ U(1)

MGUT

SU(4)PS£ SU(2)L£ SU(2)R£ U(1)! SM £ U(1)X

M3

RH masses

Quarks, leptons

Triplets and Higgs

Singlet

M2

M1

Three families of 27’s survive to low energy (minus the RH ’s)

TeV

U(1)X broken, Z’ and triplets get mass, term generated

MW

SU(2)L£ U(1)Y broken

Minimal E6SSM: Unification at MP

E6 broken via Pati-Salam chain

Steve King, Thursday Seminar

Unification at MP in Minimal E6SSM

MPlanck

MPlanck

Low energy (below MGUT) three complete families of 27’s 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.

Right handed neutrinos are neutral under:

MGUT

E6! SU(5)£U(1)N

! SM £ U(1)N

M3

RH masses

To achieve GUT scale unification we add non-Higgs

Quarks, leptons

Triplets and Higgs

Singlets and RH s

M2

H’,H’-bar

M1

TeV

U(1)N broken, Z’ and triplets get mass, term generated

MW

SU(2)L£ U(1)Y broken

SFK, Moretti, Nevzorov

E6SSM: Unification at MGUT

Steve King, Thursday Seminar

Unification at MGUT in E6SSM

2 loop, 3(MZ)=0.118

SFK, Moretti, Nevzorov

1.5 TeV

250 GeV

Steve King, Thursday Seminar

Exotic D,D-bar

Three families of Higgs

Singlets

Right-handed neutrinos

Optional non-Higgs from incomplete reps 27’+27’-bar ’ and doublet-triplet problems (absent in minimal E6SSM)

Low energy matter content of E6SSM’s

. .

Steve King, Thursday Seminar

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

Steve King, Thursday Seminar

Two potential problems: rapid proton decay + FCNCs

- FCNC problem may be tamed by introducing a Z2under which third family Higgs and singlet are even all else odd only allows Yukawa couplings involving third family Higgs and singletHu , 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 <10-12 will suppress p decay sufficiently
- but couplings >10-12 will allow D decay with lifetime <0.1 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

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 andsinglet VEV <S>=s 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 <0 (c.f. large ht to drive mH2<0 )

Steve King, Thursday Seminar

Athron, SFK, Miller, Moretti, Nevzorov

P1

Consider a particular EWSB solution P1 with = -0.5

P1

P1

Steve King, Thursday Seminar

Spectrum for P1

Athron, SFK, Miller, Moretti, Nevzorov

non-Higgs

Steve King, Thursday Seminar

Chargino and neutralino production and decay

N.B. Wino productiononly 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

Steve King, Thursday Seminar

e.g. N2N2 production and decay

Three body decays M < MZ

End point gives mass difference

Steve King, Thursday Seminar

Gluinos are light < 1 TeV and easily produced

Steve King, Thursday Seminar

SFK,Moretti,Nevzorov

Total cross section

SFK,Moretti,Nevzorov

Exotic D-quarks in E6SSM

Usual case is of scalar leptoquarks, here we have novel case of D being fermonic leptoquarks or diquarks

Steve King, Thursday Seminar

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 >300 GeV:

Dp or Dn

Clean events with two D-jets containing a pair of stable D-hadrons

p

p

Dp or Dn

Steve King, Thursday Seminar

Steve King, Thursday Seminar

Steve King, Thursday Seminar

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

Steve King, Thursday Seminar

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