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## Higgs physics

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**H**f ~ mf Higgs physics theory aspects experimental approaches Monika Jurcovicova Department of Nuclear Physics, Comenius University Bratislava**Reasons for Higgs**• the presence of mass terms for gauge fields destroys the gauge invariance of Lagrangian • no problem for gluons and photons • serious problem for W, Z0 • problems with origin of fermion masses**Spontaneous Symmetry Breaking**• way to generate particle masses • opposite of putting them by hand into Lagrangian basic idea: -- there is a simple world consisting just of scalar particles described by -- where so not a usual mass term -- ground state (vacuum) is not there are 2 minima**Spontaneous Symmetry Breaking**• perturbative calculations involve expansions around classical minimum or one of them has to be chosen ( ) • then the reflection symmetry of Lagrangian is broken • the mass is revealed:**The Higgs mechanism**• spontaneous breaking of a local gauge symmetry (simplest U(1) gauge symmetry) • procedure: add the Higgs potential to Lagrangian translate the field to a true ground state • obtained particle spectrum: 1 Higgs field with mass 1 massive vector A - desired 1 massless Goldstone boson - unwanted • with a special choice of gauge the unwanted Goldstone boson becomes longitudinal polarization of the massive vector the Higgs mechanism has avoided massless particles**The EW Weinberg-Salam model**• formulation of Higgs mechanism: • W, Z0 - become massive • photon remains massless • SU(2) x U(1) gauge symmetry • must be an isospin doublet • special choice of vacuum • U(1)em symmetry with generator remains unbroken => the photon remains massless • W, Z0 masses:**Fermion masses**• the fermion mass term is excluded from the original Lagrangian by gauge invariance • the same doublet which generates W, Z0 masses is sufficient to give masses to leptons and quarks • however:the value of mass is not predicted - just parameters of the theory • nevertheless: the Higgs coupling to fermions is proportional to their masses this can be tested**Theory summary**• the existence of the Higgs field has 3 main consequences: • W, Z0 acquire masses in the ratio • there are quanta of the Higgs field, called Higgs bosons • fermions acquire masses • deficiencies of the theory • fermion masses are not predicted • the mass of the Higgs boson itself is not predicted either**What do we know today about**• mass not predicted by theory except that mH < 1000 GeV • from direct searches at LEP mH > 114.4 GeV • indirect limits from fit of SM to data from LEP, Tevatron (mW,mtop) • Best fit (minimum χ2): mH=81 +52-33GeV • mH < 193 GeV 95% C.L.**H**f ~ mf Higgs decays • mH < 130 GeV: H dominates • mH 130 GeV : H WW(*), ZZ(*) dominate • important: H , H ZZ 4, HWW , etc.**g**H W* W* W* g H gg mH 150 GeV • select events with 2 photons with pT ~50 • measure energy and direction of each photon • calculate invariant mass of photon pair: mγγ= ((E1+ E2 )2 -(p1+ p2 )2 )1/2 • plot the mγγ spectrum - Higgs should appearas a peak at mH**γγ production: irreducible (i.e. same final state as**signal) γ jet + jet jet production where one/two jets fake photons : reducible q g g q g g g g q g ~ 108 g g (s) q p0 Main backgrounds of H gg 60mgg ~ 100GeV**e, m**Z(*) H e, m Z mZ e, m H ZZ(*) 4 120 mH < 700 GeV • “gold-plated” channelfor Higgs discovery at LHC • select events with 4 high-pT leptons (t excluded): e+e- e+e-, m+m- m+m-, e+e-m+m- • require at least one lepton pair consistent with Z mass • plot 4 invariant mass distribution : Higgs should appear as a peak at mH**irreduciblepp ZZ (*) 4**reducible W t , t n b g b Z g b Backgrounds of H ZZ(*) 4 Both reducible rejected by asking: -- m ~ mZ -- leptons are isolated -- leptons come from interaction vertex ( B lifetime : ~ 1.5 ps leptons from B produced at 1 mm from vertex)**How can one claim a discovery**• Signal significance peak width due to detector resolution NS= number of signal events NB= number of background events in peak region if S > 5 : signal is larger than 5x error of background probability that background fluctuates up by more than 5s is 10-7 discovery mgg**2critical parameters to maximize S**• detector resolutionS ~ 1 /sm detector with better resolution has larger probability to find signal (Note: only valid if GH << sm. If Higgs is broad, detector resolution is not relevant.) • integrated luminosityS ~ L numbers of events increase with luminosity**Summary on Higgs at LHC**• LHC can discover Higgs over full mass range with S > 5 in < 2 years • detector performance is crucial in most cases • discovery faster for larger masses • whole mass range can be excluded at 95% C.L. after 1 month of running**What about the Tevatron**• for mH ~ 115 GeV Tevatron needs: • 2 fb-1 for 95% C.L. in 2003-2004 ? • 5 fb-1 for 3σ observation in 2004-2005 ? • 15 fb-1 for 5σdiscovery end 2007-beg 2008 ? Discovery possible up to mH ~120 GeV**Conclusions**• Standard Model Higgs can be discovered: • at the Tevatron up to mH ~120 GeV • at the LHC over the full mass region up to mH ~1 TeV final word about SM Higgs mechanism • if SM Higgs is not found before/at LHC, then alternative methods for generation of masses will have to be found