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Standard Model III: Higgs and QCDStandard Model III: Higgs and QCD
Rogério RosenfeldInstituto de Física Teórica UNESP
Physics Beyond SM – 06/12/2006 UFRJ
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• 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!
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• However, symmetry breaking mechanism has not yet been directly tested.
LEPIIGeV4.114HM direct searches
GeV199HM @ 95% CL - indirect searches
ZHee
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[Robert Clare 2003][Robert Clare 2003]
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[LEPEWWG Summer 2006][LEPEWWG Summer 2006]
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2006-07-24: Summer 2006 ======================= Contact: [email protected] 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).
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Direct searches for the HiggsSM Higgs branching ratios
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Direct searches for the Higgs
LEPII
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M. Spirahep-ph/9810289
SM Higgs Tevatron production cross section
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SM Higgs LHC production cross section
M. Spirahep-ph/9810289
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Luminosity required to find the Luminosity required to find the HiggsHiggs
Carena & Haberhep-ph/0208209
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Significance of the Higgs signal Significance of the Higgs signal at LHC at LHC
Gianotti & Manganohep-ph/0504221
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There could be surprises... There could be surprises...
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• 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!• ...
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Furthermore, the SM has conceptualproblems related to the scalar sector:
• Triviality
• Stability
• Hierarchy and Naturalness
• Unitarity
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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
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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
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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:
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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
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LEPII limit
Riesselmann, hep-ph/9711456
Triviality and stability bounds on the Higgs mass
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Triviality and stability bounds on the Higgs mass
Kolda&Murayama, hep-ph/0003170
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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
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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
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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
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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..
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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
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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
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The 2The 22 WW scattering amplitude is given by:2 WW scattering amplitude is given by:
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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
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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
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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 .
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QCD Lagrangian
are the 8 Gell-Mann matrices
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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
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Hadron spectra from lattice QCD
CP-PACS Collaborationhep-lat/0206009quenched fermions!
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1st evidence for gluons 1979
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Gluons have self-interactions!
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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
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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!
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Running of the QCD coupling constant
Bethkehep-ex/0606035
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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!
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THANKS