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Summary

Summary. Standard Model of Particles (SM) Symmetries, Gauge theories, Higgs, LEP, LHC. 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, LEP, LHC A. Bay Beijing October 2005

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

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

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

  5. What does it mean being "symmetric" .3 The concept of symmetry contains the idea of non-measurability and invariance. Of a snow flake or the liquid water, which one is "more symmetric" ? A. Bay Beijing October 2005

  6. Do we always need symmetry ? GD GG DD Not too much symmetry is better for the aesthetics perception A. Bay Beijing October 2005

  7. 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 Beijing October 2005

  8. 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 Beijing October 2005

  9. F1 F2 Translation in space and conservation of p Consider 2 bodies initially at rest, interacting (by gravitation, for instance). Initial total momentum is p = 0. Suppose that there is some kind of non-homogeneity in that region of space and that the interaction strength is not identical at the two positions. Suppose F1 >F2 , then there is a total net force acting on the system. => The total momentum p is not constant with time. A. Bay Beijing October 2005

  10. 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 Beijing October 2005

  11. 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 Beijing October 2005

  12. 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 Beijing October 2005

  13. Maxwell assures 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 Beijing October 2005

  14. 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. We had to act simultaneously on V and A. Note that one can rebuild Maxwell eqs, starting from A,V, requiring gauge invariance, and adding some relativity: A,V  add gauge invariance  Maxwell eqs A. Bay Beijing October 2005

  15. 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 add global gauge invariance  charge conservation A. Bay Beijing October 2005

  16. 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 Beijing October 2005

  17. 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 A. Bay Beijing October 2005

  18. L = - energy of the e.m. field interaction particle-e.m. field free part y A q y QED from the gauge invariance .2 The corresponding relativistic Lagrangian is no mass term for the photon A ! this graph explains the interaction term qyyA A mass term for a boson field looks like this in a Lagrangian: M2A2 A. Bay Beijing October 2005

  19. 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 ? • We introduce now the Higgs mechanism. A. Bay Beijing October 2005

  20. 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 Beijing October 2005

  21. 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 Beijing October 2005

  22. 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 Beijing October 2005

  23. 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 Beijing October 2005

  24. Spontaneous Symmetry Breakingat dinner before dinner once dinner starts A. Bay Beijing October 2005

  25. Higgs mechanism in EW .3 our EW vacuum ! The theory allows to compute v, or m/l: ~ 246 GeV with this we cannot predicts the masses. For the Higgs: there are only (weak) bounds: 60 < M < 700 GeV. The theory predicts the couplings of processes: MW2/v M2/v2 M2/v A. Bay Beijing October 2005

  26. Summary of EW with Higgs mechanism We have exploited a particular symmetry, the gauge symmetry, to construct 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 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 Beijing October 2005

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

  28. 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 Beijing October 2005

  29. Higgs searches before LEP some of the searches of the '80: from pion decay from J/Y and U decays A. Bay Beijing October 2005

  30. Higgs at LEP/SLD: indirect bounds measured with high precision at LEP/SLD correction function of MH correction function of top mass top mass now measured at TEVATRON A. Bay Beijing October 2005

  31. LEP/SLD/TEVATRON: indirect mass determination Tevatron measurement of the top mass (LP 2005): m(top) =174.3 ± 3.4 GeV A. Bay Beijing October 2005

  32. Higgs at LEP/SLD: indirect 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 Beijing October 2005

  33. f f f f Z* Z e+ e+ e- e- Z* Z H H LEP/SLD: direct searches of Higgs At LEP I (~ 100GeV) At LEP II (~ 200GeV) with E > MZ + MH A. Bay Beijing October 2005

  34. b Example of Higgs searches at LEP An example at LEP II. Assume MH > 2 b-quark mass. The 2 fermions from Z decay can be m+ m-, for instance. Procedure: Collect 2 m of opposite sign. Their parent must be a Z: the total invariant mass~91 GeV m+ m- Z e+ The ~rest of the energy of the event goes into the two b quarks. They hadronize into jets with b hadrons. e- Z* H b A. Bay Beijing October 2005

  35. m+ Jet 1 e- e+ Jet 2 m- Example of Higgs searches at LEP .2 Idealized topology of the event: interaction vertex Kinematical constraints: * Total event Energy ~ 2Ebeam * Total momentum ~ 0 * |Pm+ + Pm-| ~ Mass(Z) not completely true: - neutrinos are lost - detector not tight - detector resolutions ... A. Bay Beijing October 2005

  36. Example of Higgs searches at LEP .3 Simulated Higgs event in the DELPHI detector jet 1 muon beam pipe muon jet 2 A. Bay Beijing October 2005

  37. 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 Beijing October 2005

  38. Vertex detector 3 layers Si strips on cylinders r = 63, 89.5, 103 mm plus pixel and ministrips layers on the edges. A. Bay Beijing October 2005

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

  40. b tagging with vertex detector .2 example of event with displaced vertices A. Bay Beijing October 2005

  41. Example of Higgs searches at LEP .3 In conclusion, the search for events requires the precise measurement and identification of the 2 muons the tagging of the 2 b quarks the calculation of the H mass with the best precision In principle MH = |pH| = | pjet1 + pjet2|, where each p represent a 4-vector: (E, p). We can invoke the total event E and p conservations: ptotal = (2Ebeam, 0) => pH = ptotal- pm+- pm- i.e. MH = |pH| = | ptotal- pm1- pm2| with a better resolution A. Bay Beijing October 2005

  42. Higgs searches at LEP ~ 6 events LEP Conclusion: 114.4 < MH < 193 GeV 95% C.L. A few events at MH ~ 115 GeV significance 1.7s A. Bay Beijing October 2005

  43. 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 Beijing October 2005

  44. jet d'eau Alps Pb Pb Geneva Leman lake LHCb point 8 LHCb LHC A. Bay Beijing October 2005

  45. Salève Jet d’eau Genève ALTAS surface buildings CERN viewed from the sky on July 13, 2005 new wood building A. Bay Beijing October 2005

  46. Lowering of 1st dipole into the tunnel (March 2005) Joining things up Cryogenic servicesline • ~1650 main magnets (~1000 produced) + a lot more other magnets • 1232 cryogenic dipole magnets (~800 produced, 70 installed): • each 15-m long, will occupy together ~70% of LHC’s circumference ! LHC magnets B fields of 8.3 T in opposite directions for each proton beam Cold mass (1.9 K) A. Bay Beijing October 2005

  47. LHC schedule • Beam commissioning starting in Summer 2007 • Short very-low luminosity “pilot run” in 2007 used to debug/calibrate detectors, no (significant) physics • First physics run in 2008, at low luminosity (1032–1033 cm–2s–1) • Reaching the design luminosity of 1034 cm–2s–1 will take until 2010 A. Bay Beijing October 2005

  48. detector a 25 ns LHC parameters • Ecm = 14 TeV • Luminosity ~ 3 1034 cm-2 s-1 generated with • 1.7 1011 protons/bunch • Dt = 25 ns bunch crossing • bunch transverse size ~15 mm • bunch longitudinal size ~ 8cm • crossing angle a=200 mrad The proton current is ~1A, ~500 Mjoules/beam (100kg TNT) A. Bay Beijing October 2005

  49. 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 Beijing October 2005

  50. LHC physics .2 The total cross section is not very well known data fitted with stot ~ (log Ecm2) pp total cross section The TOTEM experiment will try to measure stot with ~ 1 %precision tot  100 mb inel  70 mb Ecm (GeV) A. Bay Beijing October 2005 tot (pp) and inel = tot- el - diff

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