1. Higgs physics theory aspects experimental approaches Monika Jurcovicova Department of Nuclear Physics, Comenius University Bratislava H f ~ m f

2. 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 , Z 0 problems with origin of fermion masses

3. 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

4. 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:

5. 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

6. The EW Weinberg-Salam model formulation of Higgs mechanism: –W , Z 0 - 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 , Z 0 masses:

7. Fermion masses the fermion mass term is excluded from the original Lagrangian by gauge invariance the same doublet which generates W , Z 0 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

8. Theory summary the existence of the Higgs field has 3 main consequences: –W , Z 0 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

9. What do we know today about mass not predicted by theory except that m H < 1000 GeV from direct searches at LEP m H > 114.4 GeV indirect limits from fit of SM to data from LEP, Tevatron (m W, m top) Best fit (minimum χ 2 ): m H = 81 + 52 - 33 GeV m H < 193 GeV 95% C.L.

10. Higgs decays m H < 130 GeV: H  dominates m H  130 GeV : H  WW (*), ZZ (*) dominate important: H , H  ZZ  4, H  WW , etc. H f ~ m f

11. H   select events with 2 photons with p T ~50 measure energy and direction of each photon calculate invariant mass of photon pair: m γγ = ((E 1 + E 2 ) 2 -(p 1 + p 2 ) 2 ) 1/2 plot the m γγ spectrum - Higgs should appear as a peak at m H H W*   m H  150 GeV

12. Main backgrounds of H   γγ production: irreducible (i.e. same final state as signal) γ jet + jet jet production where one/two jets fake photons : reducible q q   g g   q g   (s) 00 q ~ 10 8  60 m  ~ 100 GeV

14. H  ZZ (*)  4 “gold-plated” channel for Higgs discovery at LHC select events with 4 high-p T leptons (  excluded): e + e - e + e -,          e + e -     require at least one lepton pair consistent with Z mass plot 4 invariant mass distribution : H Z (*) Z e,  mZmZ 120  m H < 700 GeV Higgs should appear as a peak at m H

15. Backgrounds of H  ZZ (*)  4 irreducible pp  ZZ (*)  4 reducible t, t W b g g b b Z Both reducible rejected by asking : -- m ~ m Z -- leptons are isolated -- leptons come from interaction vertex ( B lifetime : ~ 1.5 ps  leptons from B produced at  1 mm from vertex )

17. How can one claim a discovery Signal significance peak width due to detector resolution m  N S = number of signal events N B = 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 5  is 10 -7  discovery

18. 2 critical parameters to maximize S detector resolution S ~ 1 /  m detector with better resolution has larger probability to find signal ( Note: only valid if  H <<  m. If Higgs is broad, detector resolution is not relevant.) integrated luminosity S ~  L numbers of events increase with luminosity

19. 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

20. What about the Tevatron for m H ~ 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 5σ discovery end 2007-beg 2008 ? Discovery possible up to m H ~120 GeV

21. Conclusions Standard Model Higgs can be discovered: –at the Tevatron up to m H ~120 GeV –at the LHC over the full mass region up to m H ~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