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04/19/23 Steve King, Thursday Seminar

. .STANDARD MODEL

04/19/23

SM contains 19 free parameters SM contains 19 free parameters (excluding neutrino mass)!(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.


0

HH

H

2 42 12HV m H H

If (why?) and (why?) then potential is

minimised by (why this scale?)

2 0Hm 0

2

2 22 246HmH v GeV

Origin of Mass in the SMOrigin of Mass in the SM

SM Higgs doublet

SM Higgs Potential

WLOG suppose 0 246eH v GeV

4 d.o.f.3 G.B.s 0 0 0, , , , cos

2 L L L W Z W

gvH H A mH W W Z M M

Plus 1 physical Higgs boson 0 2 212, hh eH v m v


22 2 246Hm v GeV

Hierarchy Problem in SMHierarchy Problem in SM

Note the (tree-level) min cond

Including rad corr it becomes

22 2 246H Hm m GeV

2

22 2 2

2

3( ) 100

12

H F tm top loop G m GeVTeV

Fine-tuning is required if the cut-off 1 TeV

•New physics at TeV scale (still the best motivation)

•But no hint in precision LEP measurements “LEP Paradox”

H H3LQ

Rt


Supersymmetry

The Hierarchy Problem

Bottom-up motivation for new physics BSM

Extra dimensions

Technicolour

TeV

Mz


String Unification

Supersymmetry

Extra dimensions

New TeV scale physics

Top-down motivation for new physics BSM

M*


SupersymmetrSupersymmetryy

SPIN ½ FERMIONS

SPIN 0,1 BOSONS


Stabilising the Hierarchy in Stabilising the Hierarchy in SUSYSUSY

2 2 22

3( )

8

H tm top

2 2 22

3( )

8

H tm stop

2 2 22

9ln

8

H t tt

m mm

SUSY stabilises the hierarchy providing:

(Also works for gauge boson loops and applies to all loop order due to “non-renormalization theorem”.)

1tm TeV

SUSY implies top =stop leading to cancellation of the quadratic divergence, leaving only log divergence which allows up to the Planck scale.


MSSMMSSM

22 2 2 22 2 2 2 2 '218. .

d uH d H u d u u dV m H m H B H H h c g g H H

2 42 12HV m H H [c.f.

SM ] u dW H H

0

0

u du d

u d

H HH H

H HTwo Higgs doublets

Min conds at low energy 2

2 2 2

2

u u

ZH H

Mm m

A nice feature of MSSM is radiative EWSB Ibanez-Ross

0ZM GUTM

2 2

uHm

(s)top loops drive negative

2

uHm

H H3LQ

Rt

2 2 2 22

3ln ~ (1)

4

u

GUTH t stop stop

Mm m O m

Q

Natural expectation is MZ » » mHu » mstop

In fact MZ ¿ mstop FINE TUNING


•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)

The The problemproblem

•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


Before 1998 the flavour sector contained 13 parameters

6 quark masses, 3 charged lepton masses, 3 quark mixing angles and 1 CP violating phase

Who ordered that ?


e

Le

L

L

Standard Model states

Neutrino mass states

1m2m

3m

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

Atmospheric

Reactor Solar

.

. .

.

. .

.

. .

.

. .

Majorana

Majorana phases1 2,

1

2

/ 213 13 12 12

/ 223 23 12 12

23 23 13 13

1 0 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 0 1 0 0 1

ii

iMNS

i

c s e c s e

U c s s c e

s c s e c

Three neutrino mass and mixing


Latest global fit for atmospheric & solar oscillations

Latest version 19th Oct 07

•Latest SSM

•SNO salt data

• K2K

•Latest MINOS results

Atmospheric

Solar


Normal Inverted

12

23

13

33 5

45 10

13

3 errors

Valle et al

Absolute neutrino mass scale?

Neutrino mass squared splittings and angles


Tri-bimaximal mixing (TBM)

12 23

12 23 13

1333 5 , 45 10 ,

35 , 45 , 0 .

13

Harrison, Perkins, Scott

c.f. data

• Current data is consistent with TBM

• But no convincing reason for exact TBM – expect deviations


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

r = reactor s = solars = solar a = atmospheric

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

SFK arXiv:0710.0530


Neutrino masses and mixing parameters introduces 9 extra flavour parameters

3 neutrino masses, 3 lepton mixing angles and 3 CP violating phases

Can the extra parameters

help with the creation of the

universe ?


Can neutrino mass help solve some of the problems of the Standard Model of Cosmology:

1. 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)


Strong

Weak

Electromagnetic


Minimal EMinimal E66SSM: Unification at SSM: Unification at MMPP

Howl, SFK

(10) (4) (2) (2)PS L RSO SU SU SU6 (10) (1)E SO U

MGUT

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

MPlanck

Quarks, leptons

Triplets and Higgs

Singlet

MW SU(2)L£ U(1)Y broken

E6! SU(4)PS£ SU(2)L £ SU(2)R

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

(4,2,1) (4,1,2) (6,1,1) (1,2,2) (1,1,1) 27

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

£ U(1)

Extra U(1)X survives to TeV scale

RH masses

M1

M2

M3

E6 broken via Pati-Salam chain

Unification at MUnification at MPP in Minimal in Minimal EE66SSMSSM

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.

Howl, SFK

MPlanck MPlanck


EE66SSM: Unification at MSSM: Unification at MGUTGUT

SFK, Moretti, Nevzorov

15 14 4(1) (1) (1) NU U U

(10) (5) (1)SO SU U 6 (10) (1)E SO U

E6 ! SU(5)£U(1)N MGUT

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

27',27'

To achieve GUT scale unification

we add non-Higgs

Quarks, leptons

Triplets and Higgs

Singlets and RH s

H’,H’-bar

MW SU(2)L£ U(1)Y broken

Right handed neutrinos are neutral under:

! SM £ U(1)N

RH masses

M1

M2

M3

E6 broken via SU(5) chain

Unification at MUnification at MGUTGUT in E in E66SSMSSM

3

2

1

250 GeV

1.5 TeV

Blow-up of GUT region2 loop, 3(MZ)=0.118

SFK, Moretti, Nevzorov

162 10

XM

GeV


Low energy matter content of ELow energy matter content of E66SSM’s SSM’s

Exotic D,D-bar

Three families of Higgs

Singlets Right-handed neutrinos

Quarks and Leptons

27i . .

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

H H


EE66SSM couplingsSSM couplings

SDD HSH FF D FH FW

, ,

, , , , ,

i i

c c c ci i i i i i

D D D

F Q L U D E N

,

,

i

u di i

S S

H H H

Singlet-Higgs-Higgs couplings includes effective term

Singlet-D-D couplings includes effective D mass terms

Yukawa couplings but extra Higgs give FCNCs

DQQ, DQL allows D decay but also proton decay

Two potential problems: rapid proton decay + FCNCsTwo 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 <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 approachesHenceforth assume problems solved by one of these approaches


The Constrained EThe Constrained E66SSMSSM

, ,

, ,

i u i d i i i i

j u d u d

t u b d d

W SH H SD D

f S H H h S H H

hQH t h QH b h LH

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 <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 mS

2 <0 (c.f. large ht to drive mH2<0 )

Athron, SFK, Miller, Moretti, Nevzorov

Hu, Hd, S without indices are third family Higgs and singlet, Hu,, Hd,, S are non-Higgs

The Z2 allowed couplings



P1

P1

P1

tan 3, 6 , 0.7s TeV

Consider a particular EWSB solution P1 with = -0.5


Spectrum for Spectrum for P1 P1

12 0700 , 1.6 , 1M GeV m TeV A TeV

1.4TeV

1.8TeV

2.2TeV

03,4 2,

02, ,H h A

0 05,6 3, ,h Z

tan 3, 6 , 0.7, 0.5s TeV

01

02 1, g

97GeV

174GeV

460GeV

01h

120GeV


4.7TeV3D3D5TeV

1,2D1.5TeV

1,2D300GeV

1.4TeV 1t

2, , ,Q t b L 1.8TeV1.7TeV

non-Higgsinos

non-Higgs

??GeV


Note the lightest gaugino states: easy@LHCNote the lightest gaugino states: easy@LHC

01 1N

02 2 1 1,N C

g123 0.7M M

122 0.25M M

121 0.15M M

12

400 1000M GeV

» Wino

» Bino

Gluino


Chargino and neutralino production and decayChargino and neutralino production and decay

2N

1N

ll

1C

1N

l

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


e.g. Ne.g. N22NN22 production and decay production and decay

2N

1N

( )l p

( )l p Three body decays M < MZ

22llm p p

2 1max ll N Nm M M M

End point gives mass difference

Y=N2, N=N1

2 2missTN N l l l l E

2 2pp N N V


g

1N

qq

5

4g

q

m

m

1

,Y g

N N

pp gg V

Gluinos are light < 1 TeV and easily producedGluinos are light < 1 TeV and easily produced

missTgg qqqq E


'1 ZM g S

SFK,Moretti,Nevzorov

Z’ < 5 TeV can be Z’ < 5 TeV can be discovered discovered


Exotic D-quarks in EExotic D-quarks in E66SSMSSM

300Dm GeV

Inv. mass distribution


Total cross section


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


Novel signatures of D quarksNovel 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 >300 GeV:

p p

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

Dp or Dn

Dp or Dn

,p nD Du D Dd


E 6

(5) (1)SU U (3) (3) (3)C L RSU SU SU

(4) (2) (2)PS L RSU SU SU

(3) (2) (2) (1)C L R B LSU SU SU U

(3) (2) (1)C L YSU SU U

(5)SU

(10)SO

GGUT


U(1)

SU(2)

SU(3) SO(3)

S(3)Nothing

(3) (3)L RO O

(3) (3)L RS S 4(27),A

GFamily


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

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