Standard Model III: Higgs and QCD Rogério Rosenfeld Instituto de Física Teórica UNESP Physics Beyond SM – 06/12/2006 UFRJ

Standard model (SU(3) c xSU(2) L xU(1) Y ) passed all experimental tests! It is based on three main principles: 1. Quantum field theory (renormalizability) 2. Gauge symmetry (fundamental interactions) 3. Spontaneous symmetry breaking (mass generation) Precision measurements at the 0.1% level allowed to test the model at the quantum level (radiative corrections). Top quark mass was predicted before its actual detection!

However, symmetry breaking mechanism has not yet been directly tested. direct 95% CL - indirect searches

[Robert Clare 2003]

[LEPEWWG Summer 2006]

: Summer 2006 ======================= Contact: Summer 2006: Changes in experimental inputs w.r.t. winter 2006 * New Tevatron Mtop * New LEP-2 MW and GW combination (ADLO final, but combination preliminary) Hence new world averages for MW and GW Blue-band studies: ================== For ZFITTER 6.41 and later (currently 6.42), and flag AMT4=6 fixed, two flags govern the theory uncertainties in the complete two-loop calculations of MW (DMWW=+-1: +-4 MeV) and fermionic two-loop calculations of sin2teff (DSWW=+-1: +-4.9D-5). The theory uncertainty for the Higgs-mass prediction is dominated by DSWW. The blue band will be the area enclosed by the two ZFITTER DSWW=+-1 \Delta\chi^2 curves. The one-sided 95%CL (90% two-sided) upper limit on MH is given by ZFITTER's DSWW=-1 curve: MH <= 166 GeV (one-sided 95%CL incl. TU) (increasing to 199 GeV when including the LEP-2 direct search limit). (increasing to 199 GeV when including the LEP-2 direct search limit).

Direct searches for the Higgs SM Higgs branching ratios

Direct searches for the Higgs LEPII

M. Spira hep-ph/ SM Higgs Tevatron production cross section

SM Higgs LHC production cross section M. Spira hep-ph/

Luminosity required to find the Higgs Carena & Haber hep-ph/

Significance of the Higgs signal at LHC Gianotti & Mangano hep-ph/

There could be surprises...

Is this the end of particle theory? Program: find the Higgs, study its properties (mass, couplings, widths) and go home?? NO! Standard Model is incomplete: fermion masses (Yukawas, see-saw) fermion mixings (CKM and the like) dark matter (new physics) dark energy (new physics) grand unification (SUSY-GUT?) gravity!...

Furthermore, the SM has conceptual problems related to the scalar sector: Triviality Stability Hierarchy and Naturalness Unitarity

Conceptual problems of the SM I. Triviality Running of : for large : ytytytyt ytytytyt ytytytyt ytytytyt

Running of : Landau pole: the coupling constant diverges at an energy scale  where:

The only way to have a theory defined at all energy scales without divergences is to have zero coupling: theory is trivial! Lesson to be learned: Higgs sector is an effective theory, valid only up to a certain energy scale . Given a cut-off scale  there is an upper bound on the Higgs mass:

II. Stability Running of : [small ] ytytytyt ytytytyt ytytytyt ytytytyt Higgs boson can’t be too light (small ): Vacuum stability (  ) implies a lower bound:

LEPII limit Riesselmann, hep-ph/ Triviality and stability bounds on the Higgs mass

Kolda&Murayama, hep-ph/

III. Hierarchy and naturalness Higgs boson mass (Higgs two-point function) receives quantum corrections: g ytytytyt ytytytyt

Quantum corrections to Higgs boson mass depend quadratically on a cut-off energy scale  :  =10 TeV as an example

Fine tuning of the bare Higgs mass is required to keep the Higgs boson light with respect to  :  =10 TeV as an example M. Schmaltz hep-ph/

Hierarchy problem: in the SM there is no symmetry that protects the Higgs boson to pick up mass of the order of the cut-off! If we want the SM to be valid up to Planck scale, how can one generate the hierarchy M H << M Pl ?? Roughly we have: Example: Large amount of fine tuning. It is not NATURAL.

IV. Unitarity The Higgs boson has another important role in the SM: it makes the scattering of gauge bosons to have a good high energy behaviour. Scattering matrix Conservation of probability: S matrix is unitary S-matrix can be written in terms of scattering amplitudes

The 2  2 scattering amplitude can be expanded in terms of Legendre polynomials of the scattering angle. This is called the partial wave expansion: Partial waves: Unitarity of S-matrix implies: Hence, there is a unitary limit for the l th partial wave: s: center-of-mass energy 2

The 2  2 WW scattering amplitude is given by:

For example, the WW  ZZ l=0 partial wave is: Unitarity of l=0 partial wave for coupled channel VV  VV scattering implies: Low energy theorem

Higgs summary Higgs potential is responsible for electroweak symmetry breaking Higgs couplings and vacuum expectation value generates masses for fermions and EW gauge bosons Higgs restores partial wave unitarity in WW scattering SM is an effective theory: either the SM Higgs boson or new physics will be found at the LHC

Quantum Chromo Dynamics QCD is an unbroken gauge theory based on the SU(3) c gauge group. Quarks come in 3 colors and transform as the fundamental representation of SU(3) c. There are 8 gluons that transform as the adjoint representation of SU(3) c.

QCD Lagrangian are the 8 Gell-Mann matrices

In principle, neglecting light quark masses, QCD has only one free parameter: Given  s one should be able to compute everything in QCD (like hadron spectrum and form factors)! However, at low energies the coupling is large and perturbative methods can’t be used... Lattice QCD

Hadron spectra from lattice QCD CP-PACS Collaboration hep-lat/ quenched fermions!

1 st evidence for gluons 1979

Gluons have self-interactions!

QCD has the property of asymptotic freedom: its coupling becomes weak at large energies. We define an effective energy dependent coupling constant  s (q) : virtual corrections

The lowest order result for the running of the QCD effective coupling is: asymptotic freedom Today the so-called QCD beta function is known up to 4 loops!

Running of the QCD coupling constant Bethke hep-ex/

QCD summary QCD at high energies can be treated perturbatively; many calculations (NLO,NNLO,...) have been done. Low energy QCD is much harder: recent progress with dynamical fermions. Hadron spectra (pentaquarks??). QCD is essential for the calculation of high energy cross sections: Particle Distribution Functions (PDF). QCD at finite temperature and chemical potential is being actively studied: new states of matter (QGP,CGC) Careful with pentaquarks!

THANKS