Standard Model III: Higgs and QCDStandard Model III: Higgs and QCD

Rogério RosenfeldInstituto de Física Teórica UNESP

Physics Beyond SM – 06/12/2006 UFRJ

• Standard model (SU(3)cxSU(2)LxU(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.

LEPIIGeV4.114HM direct searches

GeV199HM @ 95% CL - indirect searches

ZHee

[Robert Clare 2003][Robert Clare 2003]

[LEPEWWG Summer 2006][LEPEWWG Summer 2006]

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)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 HiggsSM Higgs branching ratios

Direct searches for the Higgs

LEPII

M. Spirahep-ph/9810289

SM Higgs Tevatron production cross section

SM Higgs LHC production cross section

M. Spirahep-ph/9810289

Luminosity required to find the Luminosity required to find the HiggsHiggs

Carena & Haberhep-ph/0208209

Significance of the Higgs signal Significance of the Higgs signal at LHC at LHC

Gianotti & Manganohep-ph/0504221

There could be surprises... 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 conceptualproblems related to the scalar sector:

• Triviality

• Stability

• Hierarchy and Naturalness

• Unitarity

Conceptual problems of the SM Conceptual problems of the SM

I. Triviality

222

2

8

3

ln

d

d

Running of Running of ::

for large for large ::

yytt

yytt yytt

yytt

22

2

2

22

v/ln8

v31

v

Running of Running of ::

Landau pole: the coupling constant Landau pole: the coupling constant divergesdiverges at an at anenergy scale energy scale where: where:

1v/ln8

v3 222

2

The only way to have a theory defined at all energyThe only way to have a theory defined at all energyscales without divergences is to have zero coupling:scales without divergences is to have zero coupling:theory is trivialtheory is trivial!!

Lesson to be learned: Lesson to be learned: Higgs sector is an Higgs sector is an effective theoryeffective theory, valid only up to a , valid only up to a certain energy scale certain energy scale ..

22

22222

222

2

v/ln3

v16vv2

1v/ln8

v3

HM

Given a cut-off scale Given a cut-off scale there is an there is an upper boundupper bound on on the Higgs mass:the Higgs mass:

II. Stability

4

22

2

8

3

ln tyd

d

Running of Running of ::

[small [small ]]

yytt

yytt yytt

yytt

Higgs boson can’t be too light (small Higgs boson can’t be too light (small ):):

222

422 v/ln

8

3v

ty

Vacuum stability (Vacuum stability () ) implies a implies a lower boundlower bound::

2222

42 v/lnv

4

3

t

H

yM

LEPII limit

Riesselmann, hep-ph/9711456

Triviality and stability bounds on the Higgs mass

Triviality and stability bounds on the Higgs mass

Kolda&Murayama, hep-ph/0003170

III. Hierarchy and naturalness

Higgs boson mass (Higgs two-point function) receives Higgs boson mass (Higgs two-point function) receives quantum corrections:quantum corrections:

gg

yytt yytt

Quantum corrections to Higgs boson mass depend Quantum corrections to Higgs boson mass depend quadraticallyquadratically on a cut-off energy scale on a cut-off energy scale ::

=10 TeV as an example=10 TeV as an example

Fine tuningFine tuning of the bare Higgs mass is required to keep of the bare Higgs mass is required to keepthe Higgs boson light with respect to the Higgs boson light with respect to ::

=10 TeV as an example=10 TeV as an example

M. Schmaltzhep-ph/0210415

Hierarchy problem: in the SM there is no Hierarchy problem: in the SM there is no symmetrysymmetry that protects the Higgs boson to pick up mass of thethat protects the Higgs boson to pick up mass of theorder of the cut-off! order of the cut-off!

If we want the SM to be valid up to Planck scale, how If we want the SM to be valid up to Planck scale, how can one generate the hierarchy Mcan one generate the hierarchy MHH << M << MPlPl????

Roughly we have:Roughly we have:

2

bare22bare22phys2 1 H

HH

MMM

Example:Example:

!101

GeV10GeV;100

262

bare2

15phys

H

H

M

M

Large amount of Large amount of fine tuning. It is notfine tuning. It is notNATURALNATURAL..

IV. Unitarity

The Higgs boson has another important role in the SM:The Higgs boson has another important role in the SM:it makes the scattering of gauge bosons to have a goodit makes the scattering of gauge bosons to have a goodhigh energy behaviour.high energy behaviour.

Scattering matrixScattering matrix outin S

Conservation of probability: S matrix is unitaryConservation of probability: S matrix is unitary 1SS

S-matrix can be written in terms of scattering amplitudesS-matrix can be written in terms of scattering amplitudes

fii

if

f ppppS

4421

The 2The 22 scattering amplitude can be expanded in terms2 scattering amplitude can be expanded in termsof Legendre polynomials of the scattering angle.of Legendre polynomials of the scattering angle.This is called the partial wave expansion:This is called the partial wave expansion:

Partial waves: Partial waves:

Unitarity of S-matrix implies: Unitarity of S-matrix implies:

sesasasa lsi

llll sinIm

2

l

ll Psal cos121622

sal

Hence, there is a Hence, there is a unitary limitunitary limit for the l for the lthth partial wave: partial wave:

1sal

s: center-of-mass energys: center-of-mass energy22

2/1Re sal

The 2The 22 WW scattering amplitude is given by:2 WW scattering amplitude is given by:

For example, the WWFor example, the WWZZ l=0 partial wave is:ZZ l=0 partial wave is:

2

2H

22H

220

v32

M

/Mv32v32

2

WMs

Wl sMOs

ssssa

Unitarity of l=0 partial wave for coupled channelUnitarity of l=0 partial wave for coupled channelVVVVVV scattering implies: VV scattering implies:

GeV780HM

Low energy theoremLow 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 andform factors)!

However, at low energies the coupling is largeand perturbative methods can’t be used...Lattice QCD

Hadron spectra from lattice QCD

CP-PACS Collaborationhep-lat/0206009quenched fermions!

1st 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:

0

0 /log2

1 qqq

s

ss

03

2110 fn

00qq

s q asymptotic freedom

Today the so-called QCD beta function is known up to 4 loops!

Running of the QCD coupling constant

Bethkehep-ex/0606035

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