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Standard Model III: Higgs and QCD

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:

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Standard Model III: Higgs and QCD

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

  2. Standard model (SU(3)cxSU(2)LxU(1)Y ) passed • all experimental tests! • It is based on three main principles: • Quantum field theory (renormalizability) • Gauge symmetry (fundamental interactions) • 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!

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

  4. [Robert Clare 2003]

  5. [LEPEWWG Summer 2006]

  6. 2006-07-24: Summer 2006 ======================= Contact: Martin.Grunewald@cern.ch 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).

  7. Direct searches for the Higgs SM Higgs branching ratios

  8. Direct searches for the Higgs LEPII

  9. SM Higgs Tevatron production cross section M. Spira hep-ph/9810289

  10. SM Higgs LHC production cross section M. Spira hep-ph/9810289

  11. Luminosity required to find the Higgs Carena & Haber hep-ph/0208209

  12. Significance of the Higgs signal at LHC Gianotti & Mangano hep-ph/0504221

  13. There could be surprises...

  14. 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! • ...

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

  16. Conceptual problems of the SM I. Triviality Running of l: yt yt l l l yt yt for large l:

  17. Running of l: Landau pole: the coupling constant diverges at an energy scale L where:

  18. 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 L. Given a cut-off scale Lthere is an upper bound on the Higgs mass:

  19. II. Stability Higgs boson can’t be too light (small l): Running of l: yt yt l l l yt yt [small l] Vacuum stability (l>0) implies a lower bound:

  20. Triviality and stability bounds on the Higgs mass Riesselmann, hep-ph/9711456 LEPII limit

  21. Triviality and stability bounds on the Higgs mass Kolda&Murayama, hep-ph/0003170

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

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

  24. Fine tuning of the bare Higgs mass is required to keep the Higgs boson light with respect to L: M. Schmaltz hep-ph/0210415 L=10 TeV as an example

  25. 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 MH << MPl?? Roughly we have: Example: Large amount of fine tuning. It is not NATURAL.

  26. 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

  27. 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: s: center-of-mass energy2 Unitarity of S-matrix implies: Hence, there is a unitary limit for the lth partial wave:

  28. The 22 WW scattering amplitude is given by:

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

  30. 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

  31. Quantum Chromo Dynamics • QCD is an unbroken gauge theory based on • the SU(3)cgauge 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.

  32. QCD Lagrangian are the 8 Gell-Mann matrices

  33. In principle, neglecting light quark masses, QCD has only one free parameter: Given as 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

  34. Hadron spectra from lattice QCD CP-PACS Collaboration hep-lat/0206009 quenched fermions!

  35. 1st evidence for gluons 1979

  36. Gluons have self-interactions!

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

  38. 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!

  39. Running of the QCD coupling constant Bethke hep-ex/0606035

  40. 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!

  41. THANKS

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