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Summary. Standard Model of Particles (SM) Symmetries, Gauge theories, Higgs,. syn-: together metron : measure. Symmetries. What does it mean being "symmetric". … 6 equivalent positions for the observer. What does it mean being "symmetric" .2. the number of possibilities is .

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  1. Summary Standard Model of Particles (SM) Symmetries, Gauge theories, Higgs, ... A. Bay Beijng October 2005

  2. syn-: together metron : measure Symmetries A. Bay Beijng October 2005

  3. What does it mean being "symmetric" … 6 equivalent positions for the observer A. Bay Beijng October 2005

  4. What does it mean being "symmetric" .2 the number of possibilities is  A. Bay Beijng October 2005

  5. http://www.emmynoether.com Emmy Noether Today theories are based on the work of E. Noether. She studies the dynamic consequences of symmetries of a system. In 1915-1917 she shows that every symmetry of nature yields a conservation law, and reciprocally. The Noether theorem: SYMMETRIES  CONSERVATION LAW A. Bay Beijng October 2005

  6. SYMMETRIES  CONSERVATION LAW Examples of continuous symmetries: Symmetry Conservation law Translation in time  Energy Translation in space  Momentum Rotation  Angular momentum Gauge transformation  Charge d is a displacement Ex.: translation in space r r + d if the observer cannot do any measurement on a system which can detect the "absolute position" then p is conserved. A. Bay Beijng October 2005

  7. Non-observables symmetry transformations conservation law / selection rules difference between permutation B.E. / F.D. statis. identical particles absolute position rr +dp conserved absolute time t  r + t E conserved absolute spatial direction rotation rr'J conserved absolute velocity Lorentz transf. generators L. group absolute right (or left) r-r Parity sign of electric charge q -q Charge conjugation relative phase between states with different charge q y eiqqy charge conserved different baryon nbr B y eiBqy B conserved different lepton nbr L y eiLqy L conserved difference between coherent mixture of (p,n) isospin Symmetries in particle physics A. Bay Beijng October 2005

  8. An introduction to gauge theories Some history. We observe that the total electric charge of a system is conserved. Wigner demonstrated that if one assumes conservation of Energy the "gauge" invariance of the electric potential V => than the electric charge must be conserved Point 2) means that the absolute value of V is not important, any system is invariant under the "gauge" change V  V+v (in other terms only differences of potential matter) A. Bay Beijng October 2005

  9. V2 V1 Wigner conservation of e.m. charge Suppose that we can build a machine to create and destroy charges. Let's operate that machine in a region with an electric field: creation of q needs work W move charge to V2 1 2 3 V2 V2 V2 V1 V1 V1 destroy q, regain W here we gain q(V2-V1) 4 regaining W cannot depend on the particular value of V (inv. gauge) E conservation is violated ! A. Bay Beijng October 2005

  10. Maxwell and the local charge conservation Differential equations in 1868: Taking the divergence of the last equation: • if the charge density is not constant in time in the element of volume considered, this violates the continuity equation: To restore local charge conservation Maxwell introduces in the equation a link to the field E: The concept of global charge conservation has been transformed into a local one. We had to introduce a link between the two fields. A. Bay Beijng October 2005

  11. Gauge in Maxwell theory Introduce scalar and potential vectors: V, and A We have the freedom to change the "gauge": for instance we can do where c is an arbitrary function. To leave E (and B) unchanged, we need to change also A: In conclusion: E and B still satisfy Maxwell eqs, hence charge conservation, but we had to act simultaneously on V and A. * Note that we can rebuild Maxwell eqs, starting from A,V, requiring gauge invariance, and adding some relativity: A,V  add gauge invariance  Maxwell eqs A. Bay Beijng October 2005

  12. Gauge in QM In QM a particle are described by wave function. Take y(r,t) solution of the Schreodinger eq. for a free particle. We have the freedom to change the global phase : independent on r and t still satisfy to the Schroedinger equation for the free particle. We can rewrite the phase introducing the charge q of the particle We cannot measure the absolute global phase: this is a symmetry of the system. One can show that this brings to the conservation of the charge q: it is an instance of the Noether theorem. y assume global gauge invariance  charge conservation A. Bay Beijng October 2005

  13. Gauge in QM .2 If now we try a localphasechange: we obtain a y which does not satisfy the free Schroedinger eq. If we insist on this local gauge, the only way out is to introduce a new field ("gauge field") to compensate the bad behaviour. This compensating field corresponds to an interaction => the Schrödinger eq. is no more free ! y add local gauge invariance  interaction field This is a powerful program to determine the dynamics of a system of particles starting from some hypothesis on its symmetries. A. Bay Beijng October 2005

  14. QED from the gauge invariance • The electron of charge q is represented by the wavefunction y, • satisfying the free Schroedinger eq. (or Dirac, or...) The symmetry is U(1) : multiplication of y by a phase eiqq • * Requiring global gauge symmetry we get conservation of charge: • we recover a continuity equation • * Requiring local gauge symmetry we have to introduce the • massless field (the photon), i.e. the potentials (A,V), and the way it • couples with the electron: the Schroedinger eq. with e.m. interaction ! Adding artificially a mass to the photon destroys the procedure ! A. Bay Beijng October 2005

  15. EW theory from gauge invariance • Particles: the set of leptons and quarks of the SM. The symmetry is SU(2)U(1) U(1) multiplication by a phase eiqq • SU(2) similar: multiplication by exp(igqT) but T are three 22 • matrices and q is a vector with three components. This is an instance of a Yang and Mills theory. • Applying gauge invariance brings to a dynamics with • 4 massless fields (called "gauge" fields). • Fine for the photon, but how to explain that W+ W- and Z have a mass ~ 100 GeV ? • Need to introduce the Higgs mechanism. A. Bay Beijng October 2005

  16. f f A Higgs mechanism Analogy: interaction of the e.m. field with the Cooper pairs in a superconductor. For a T below some critical value Tc the material becomes superconductor and "slow down" the penetration of the e.m. field. This looks like if the photon has acquired a mass. Suppose that an e.m. wave A induces a current J close to the surface of the material, J A. Let's write J = -M2A. In the Lorentz gauge: A = J Replacing: A = -M2A or A + M2A = 0 This is a massive wave equation: the photon, interacting with the (bosonic) Cooper pairs field f has acquired a "mass" M A. Bay Beijng October 2005

  17. f f W Higgs mechanism in EW We apply the same principle to the gauge fields of the EW theory. We have to postulated the existence of a new field, the Higgs field, which is present everywhere (or at least in the proximity of particles). The Higgs generates the mass of the W and Z. The algebra of the theory allows to keep the photon mass-less, and we obtain the correct relations between couplings and masses: On the other hand, the model does not predict the values of the masses and couplings: only the relations between them. A. Bay Beijng October 2005

  18. v A new boson is created by quantum fluctuation of vacuum: the Higgs. Consider a complex field and its potential Higgs mechanism in EW .2 normal vacuum V is minimal on the circle of radius while f = 0 is a local max ! Nature has also to choose Any point on the circle is equivalent... Let's choose an easy one: A fluctuation around this point is given by: H is the bosonic field A. Bay Beijng October 2005

  19. Spontaneous Symmetry Breaking Nature has to choose the phase of f. All the choices are equivalent. Continue analogy with superconductor: superconductivity appears when T becomes lower than Tc. It is a phase transition. Assume that the Higgs potential V(f ) at high temperature (early BigBang) is more parabolic. The phase transition appears when the Universe has a temperature corresponding to E ~ 0.5-1 TeV Nature has to make a choice for f. Maybe different choices in different parts of the Universe. Are there "domains" with different phases ? High T Low T A. Bay Beijng October 2005

  20. The gauge symmetry allows to build the dynamics of the EW theory. In order to give masse to W and Z we use the Higgs mechanism, obtaining as a by-product a new neutral boson: the Higgs. Bounds on its mass: 60 < MH < 700 GeV Summary of EW with Higgs mechanism The search for the Higgs particle is one of the most important of today research projects, at the LHC in particular. Because its mass is not known, it is a difficult search. Moreover there are alternative theories with more than 1 Higgs, or even with no Higgs at all ! I'll give a short description of past, present and future searches for the Standard Model Higgs. A. Bay Beijng October 2005

  21. Higgs, Peter W. P.W. Higgs, Phys. Lett. 12 (1964) 132 A. Bay Beijng October 2005

  22. Higgs searches. The possible decays Decay channels depends on M BR * Low mass: H  gg, e+e-, m+m- * For M~1- 4 GeV: H  gg then gluons hadronize to pp, KK,... * For M 2mb: H  t+t- and cc * For M  2mb up to 1000 GeV/c2: discovery channels - A. Bay Beijng October 2005

  23. TEVATRON/LEP/SLD: indirect bounds Tevatron measurement of the top mass (LP 2005): m(top) =174.3 ± 3.4 GeV with this constraint: MH = 98 +52-36 GeV or MH < 208 GeV at 95%CL A. Bay Beijng October 2005

  24. muon jet 1 muon jet 2 b Example of Higgs searches at LEP .3 Simulated Higgs event in the DELPHI detector m+ m- Z e+ e- Z* H b A. Bay Beijng October 2005

  25. m+ e+ e- m- Example of Higgs searches at LEP .4 A closer look to the interaction region. The initial b quarks are found in b hadrons, a B0 for instance. A B0 has an average lifetime of 1.536 ps. Its velocity is not far from c, with a Lorentz boost g~5 the B0 travels an average distance cgt ~ 2 mm before decaying. We can tag such events by verifying that some tracks point at displaced vertices. A. Bay Beijng October 2005

  26. b tagging with vertex detector example of event with displaced vertices vertices Solid state DELPHI vertex detector A. Bay Beijng October 2005

  27. Higgs searches at LEP ~ 6 events A few events at MH ~ 115 GeV significance 1.7s A. Bay Beijng October 2005

  28. The Large Hadron Collider The LHC is a pp collider built in the LEP tunnel. Ebeam = 7 GeV. Because the p is a composite particle the total beam E cannot be completely exploited. The elementary collisions are between quarks or gluons which pick up only a fraction x of the momentum: quarks spectators proton momentum available is only x1p1+ x2p2 p2 x2p2 x1p1 p1 proton quarks spectators A. Bay Beijng October 2005

  29. LHC is a factory for W, Z, top, Higgs,... Even running at L~1033 cm-2s-1, during 1 year (107s), integrated luminosity of 10fb-1, the following yields are expected: LHC physics Process Events/s Events World statistics (2007) W e 30108 104 LEP / 107 Tevatron Z ee 3107 106 LEP Top 2 107104 Tevatron Beauty 106 1012 – 1013109 Belle/BaBar H (130 GeV) 0.04 105 In one year an LHC experiment can get 10 times the number of Z produced at LEP in 10 years. A. Bay Beijng October 2005

  30. you wish to extract this Higgs 4m ... LHC environment We have to cope with a huge number of particles A. Bay Beijng October 2005 tot (pp) and inel = tot- el - diff

  31. ATLAS CMS LHC experiments ALICE LHCb A. Bay Beijng October 2005

  32. s (pb) SM Higgs production at LHC A. Bay Beijng October 2005

  33. Higgs searches. The possible decays BR - discovery channels A. Bay Beijng October 2005

  34. Higgs discovery MH> 130 GeV gold-plated H  ZZ  4 MH< 130 GeV H   ttH  ttbb LEP A. Bay Beijng October 2005

  35. Example: Hgg Measure the 2 photons 4-momenta (E,p) Combine them and compute the invariant mass of the parent * need to identify the photons * detectors must have the best resolution both in E and position e.m. calorimeters E resolution: CMS crystals: ATLAS liquid Ar Pb sampling A. Bay Beijng October 2005

  36. 1 2 3 4 5 6 Example: Hgg, the background From photons qqgg and gg gg Also from many p0gg : random combinations will produce a large "combinatorial" background. In the figure, we must take all the possible combinations: (1,2), (1,3),..., (5,6). Some of these combinations can mimic the H decay. Because p0 are mostly found in jets, a powerful selection strategy is to require that the photons are far from the jets: they must be isolated. A. Bay Beijng October 2005

  37. ~ 1000 events in the peak ATLAS 100 fb-1 CMS 100 fb-1 K=1.6 Example: Hgg discovery A. Bay Beijng October 2005

  38. b b W q, l q, n b More complex: ttH production, H  bb gluons from beam protons Final state with 4 jets with b hadrons, plus the decay products of the two W: W2 jets or Wlepton and neutrino Backgrounds: combinatorial from signal itself : with 4 b jets => 6 combinations W+jets, WWbbjj, etc. t t j j ~ 60% of the total A. Bay Beijng October 2005

  39. More complex: ttH production, H  bb .2 ATLAS 100 fb-1 mH=120 GeV A. Bay Beijng October 2005

  40. beam jet 1 lepton p neutrino W q b q' H p jet b b beam jet 2 jet b Higgs in LHCb lepton b jets • Process is • b-quarks will hadronize jets of particles beam jets A. Bay Beijng October 2005

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