Lecture 18 - Beyond the

Why is the Standard Model incomplete? • Grand Unification • and Number Violation • More Higgs ? • (SUSY) • Experimental signatures for SUSY •

1 Why is the Standard Model incomplete?

The Standard Model does not explain the following: The relationship between different interactions • (strong, electroweak and ) The nature of dark and • The matter- of the • The existence of three generations of and • Conservation of lepton and • and mixing • The pattern of weak couplings (CKM matrix) •

2 Grand Unification

The strong, electromagnetic and weak couplings αs, e and g are 15 running constants. Can they be unified at MX 10 GeV? ≈

We would also like to include gravity at the scale 19 MX 10 GeV. Is theory a candidate for this? ≈

3 SU(5) Grand Unified Theory (GUT)

Simplest theory that unifies strong and electroweak interactions (Georgi & Glashow)

15 Introduces 12 gauge bosons and Y at MX 10 GeV ≈ These are known as . They make charged and neutral couplings between leptons and quarks

Explains why Qν Qe = Qu Qd − − Existence of three colors is related to fractional quark charges Predicts decay p π0e+ →

4 2 of sin θW

Loop diagram with ff¯ pair couples a Z0 to a In electroweak theory the Z0 and γ are orthogonal states The sum of loop diagrams over all pairs must be zero:

2 2 P QI3 X Q(I3 Q sin θW )=0 sin θW = 2 − P Q

In a Grand Unified Theory (GUT) the sum is taken over a fermion supermultiplet [νe,e,dr,dg,db] 2 2 sin θW = 0.375, but at sin θW = 0.22! 2 GUT predicts the running of sin θW from 0.215 at √s = MW to 0.375 at 1015 GeV

5

The couplings in GUTs do not conserve baryon and , only the combination B-L

4 0 + MX 31 Γ(p π e ) = 0 τp 2 5 10 years → 6 ∝ α mp ≈

This is age of universe - not a problem for our existence ≫ Large underground experiments (Kamiokande ...) have looked for 32 proton decays. None seen so τp > 2 10 years. × Minimal SU(5) GUT is ruled out by absence of proton decay signal Non-minimal SO(10) GUT is not ruled out. Predicts different decay modes, e.g. p K+ν¯. →

6 Matter-Antimatter Asymmetry The Sakharov conditions for generating the matter-antimatter asymmetry of the universe: C and CP violation in quark or lepton decays. • Baryon number violation. • Departure from thermal equilibrium during the early universe. •

Baryogenesis: Non-conservation of baryon number in quark decays and CP violation between quark and antiquark decays. Note that CP violation due to CKM matrix is too small by 109 × : Non-conservation of lepton number and CP violation in the lepton sector. This leads to non-conservation of baryon number by conservation of B-L. Could be associated with neutrino masses and mixing

7 Multiple Higgs Doublets The Standard Model only requires one Higgs doublet, and one physical H0 It is straightforward to increase the number of doublets, e.g. A doublet that couples to d-type quarks and charged leptons A doublet that couples to u-type quarks Suppresses Higgs contributions to flavour-changing neutral currents

In a two Higgs doublet model there are eight φ variables of which three get “eaten” during electroweak breaking.

There are two vacuum expectation values v1, v2 with 2 2 2 tan β = v1/v2, and v1 + v2 = v where v = 246 GeV There are five physical Higgs bosons H+, H−, h0, H0, A0 N.B. there are no charged Higgs bosons in the Standard Model!

8 Experimental Signatures for Charged Higgs

For a charged Higgs 100 < MH+ < 170 GeV:

t bH+ H+ W +h0 h0 b¯b → → →

For a light charged Higgs MH+ < 100 GeV:

+ − + − + − − e e H H H c¯b H τ ντ → → → Indirect constraints from + + rare decays B τ ντ → and b sγ. → Expressed as limits in + MH and tan β.

9 Supersymmetry (SUSY)

Every Standard Model (SM) gets a supersymmetric (SUSY) partner:

New S = 1/2 New S = 0 bosons () ( and ) Quarks Squarks ⇔ ⇔ Leptons Sleptons Photon ⇔ ⇔ Sneutrinos W,Z bosons Wino,Zino ⇔ ⇔ Higgs boson ⇔

10 Pros and Cons of SUSY

Solves (GUT Electroweak scale) ≫ Higgs and fermion loop contributions cancel precisely with SUSY partners at all mass scales between 102 and 1014 GeV Suppresses flavour-changing neutral currents The lightest is a candidate

No experimental evidence yet for SUSY SUSY particle masses and mixings are unknown Many new parameters compared to Standard Model

String theories that include gravity are naturally supersymmetric

11 The Minimal Supersymmetric Model (MSSM)

The MSSM requires two Higgs doublets: The masses of the lightest Higgs, h0 and H± are 100 GeV ≈

The MSSM conserves R-: The number of SUSY particles is conserved (can’t change SUSY particles into normal particles)

The MSSM assumes minimal flavour violation (MFV) Flavour couplings of SUSY partners are same as Standard Model All data are consistent with MFV

Indirect constraints on the allowed parameters of the MSSM ⇒

12 SUSY masses from Direct Searches

From not seeing anything at LEP-II: masses > 100GeV sleptonmasses > 100 GeV

From not seeing anything at the : gluino mass > 300 GeV squark masses > 300 GeV ... but a light is still allowed > 100 GeV

From these can infer a lower bound on the lightest SUSY particle neutralino masses > 50GeV (LSP) This still allows the LSP to be the dark matter of the universe!

SUSY Higgs masses:

114 < mh < 150 GeV mH+ > 80 GeV mA > 90 GeV

13 Squarks and at the Large Collider

An example of a signature for SUSY at the LHC:

Cascade from gluino to lightest neutralino (stable) gluino squark(+¯q) neutralino(+q) slepton(+ℓ¯) LSP (+ℓ) → → → → Can reconstruct gluino, squark and neutralino masses from measurements of leptons, quarks and missing energy

14 International Linear Collider (ILC) Reference Design

http://www.linearcollider.org February 2007

500 GeV e+e− collider 30 km long Cost $ 6.9B

e+e− sleptons The next thing after LHC? →

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