1. A. Bay Beijng October 20051 Summary Standard Model of Particles (SM) Symmetries, Gauge theories, Higgs,...

2. A. Bay Beijng October 20052 syn-: together metron : measure Symmetries

3. A. Bay Beijng October 20053 What does it mean being "symmetric" … 6 equivalent positions for the observer

4. A. Bay Beijng October 20054 What does it mean being "symmetric".2 the number of possibilities is 

5. A. Bay Beijng October 20055 Emmy Noether http://www.emmynoether.com 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

6. A. Bay Beijng October 20056 SYMMETRIES  CONSERVATION LAW Examples of continuous symmetries: SymmetryConservation law Translation in time  Energy Translation in space  Momentum Rotation  Angular momentum Gaugetransformation  Charge 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. d is a displacement

7. A. Bay Beijng October 20057 Symmetries in particle physics Non-observablessymmetry transformationsconservation law / selection rules difference between permutationB.E. / F.D. statis. identical particles absolute position r  r +  p conserved absolute time t  r +  E conserved absolute spatial directionrotation r  r' J conserved absolute velocityLorentz transf. generators L. group absolute right (or left)r   r Parity sign of electric chargeq   qCharge conjugation relative phase between states with different charge q   e iq   charge conserved different baryon nbr B   e iB   B conserved different lepton nbr L   e iL   L conserved difference between coherent mixture of (p,n)isospin

8. A. Bay Beijng October 20058 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 1)conservation of Energy 2)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)

9. A. Bay Beijng October 20059 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: V1V1 V2V2 V1V1 V2V2 creation of q needs work W V1V1 V2V2 move charge to V 2 V1V1 V2V2 destroy q, regain W regaining W cannot depend on the particular value of V (inv. gauge) here we gain q(V 2 -V 1 ) 1 23 4 E conservation is violated !

10. A. Bay Beijng October 200510 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.

11. A. Bay Beijng October 200511 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  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

12. A. Bay Beijng October 200512 Gauge in QM In QM a particle are described by wave function. Take  r,t  solution of the Schreodinger eq. for a free particle  We have the freedom to change the global phase : 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.   assume global gauge invariance  charge conservation independent on r and t

13. A. Bay Beijng October 200513 Gauge in QM.2 If now we try a local phase change: we obtain a  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 !   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.

14. A. Bay Beijng October 200514 The electron of charge q is represented by the wavefunction  satisfying the free Schroedinger eq. (or Dirac, or...) The symmetry is U(1) : multiplication of  by a phase e iq   * 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 QED from the gauge invariance ! Adding artificially a mass to the photon destroys the procedure !

15. A. Bay Beijng October 200515 Particles: the set of leptons and quarks of the SM. The symmetry is SU(2)  U(1) U(1) multiplication by a phase e iq   SU(2) similar: multiplication by exp(ig  T) but T are three 2  2  matrices and  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. EW theory from gauge invariance

16. A. Bay Beijng October 200516 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 =  M 2 A. In the Lorentz gauge:  A = J Replacing:  A =  M 2 A or  A + M 2 A = 0 This is a massive wave equation: the photon, interacting with the (bosonic) Cooper pairs field  has acquired a "mass" M   A

17. A. Bay Beijng October 200517 Higgs mechanism in EW   W 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.

18. A. Bay Beijng October 200518 Higgs mechanism in EW.2 A new boson is created by quantum fluctuation of vacuum: the Higgs. Consider a complex field and its potential normal vacuum V is minimal on the circle of radius while  = 0 is a local max ! Any point on the circle is equivalent... v Let's choose an easy one: A fluctuation around this point is given by: H is the bosonic field Nature has also to choose

19. A. Bay Beijng October 200519 Spontaneous Symmetry Breaking Nature has to choose the phase of  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(  ) 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 High T Low T Nature has to make a choice for  Maybe different choices in different parts of the Universe. Are there "domains" with different phases ?

20. A. Bay Beijng October 200520 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. 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 < M H < 700 GeV

21. A. Bay Beijng October 200521 Higgs, Peter W. P.W. Higgs, Phys. Lett. 12 (1964) 132

22. A. Bay Beijng October 200522 Higgs searches. The possible decays * For M~1  4 GeV: H  gg * For M  2m b : H      and cc - * For M  2m b up to 1000 GeV/c 2 : then gluons hadronize to  KK,... Decay channels depends on M BR discovery channels * Low mass: H  , e  e ,    

23. A. Bay Beijng October 200523 TEVATRON/LEP/SLD: indirect bounds Tevatron measurement of the top mass (LP 2005): m(top) =174.3 ± 3.4 GeV with this constraint: M H = 98 +52 -36 GeV or M H < 208 GeV at 95%CL

24. A. Bay Beijng October 200524 Example of Higgs searches at LEP.3 muon jet 1 jet 2 Simulated Higgs event in the DELPHI detector Z* Z H e+e+ ee   b b

25. A. Bay Beijng October 200525 Example of Higgs searches at LEP.4 A closer look to the interaction region. The initial b quarks are found in b hadrons, a B 0 for instance. A B 0 has an average lifetime of 1.536 ps. Its velocity is not far from c, with a Lorentz boost  ~5  e+e+ ee  the B 0 travels an average distance c  ~ 2 mm before decaying. We can tag such events by verifying that some tracks point at displaced vertices.

26. A. Bay Beijng October 200526 b tagging with vertex detector Solid state DELPHI vertex detector vertices example of event with displaced vertices

27. A. Bay Beijng October 200527 Higgs searches at LEP A few events at M H ~ 115 GeV significance 1.7  ~ 6 events

28. A. Bay Beijng October 200528 The Large Hadron Collider The LHC is a pp collider built in the LEP tunnel. E beam = 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: proton quarks spectators quarks spectators p2p2 p1p1 x1p1x1p1 x2p2x2p2 momentum available is only x 1 p 1 + x 2 p 2

29. A. Bay Beijng October 200529 LHC physics LHC is a factory for W, Z, top, Higgs,... Even running at L~10 33 cm -2 s -1, during 1 year (10 7 s), integrated luminosity of 10fb -1, the following yields are expected: Process Events/s Events World statistics (2007) W  e 30 10 8 10 4 LEP / 10 7 Tevatron Z  ee 3 10 7 10 6 LEP Top 2 10 7 10 4 Tevatron Beauty 10 6 10 12 – 10 13 10 9 Belle/BaBar H (130 GeV) 0.04 10 5 In one year an LHC experiment can get 10 times the number of Z produced at LEP in 10 years.

30. A. Bay Beijng October 200530 LHC environment  tot (pp) and  inel =  tot -  el -  diff We have to cope with a huge number of particles you wish to extract this Higgs  4 

31. A. Bay Beijng October 200531 LHC experiments ATLAS CMS LHCb ALICE

32. A. Bay Beijng October 200532 SM Higgs production at LHC  (pb)

33. A. Bay Beijng October 200533 - BR discovery channels Higgs searches. The possible decays

34. A. Bay Beijng October 200534 Higgs discovery M H > 130 GeV gold-plated H  ZZ  4 M H < 130 GeV H   ttH  ttbb LEP

35. A. Bay Beijng October 200535 Example: H  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

36. A. Bay Beijng October 200536 Example: H  the background From photons qq  and gg   Also from many  0   random combinations will produce a large "combinatorial" background. 1 2 3 4 5 6 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  0 are mostly found in jets, a powerful selection strategy is to require that the photons are far from the jets: they must be isolated.

37. A. Bay Beijng October 200537 Example: H  discovery ~ 1000 events in the peak ATLAS 100 fb -1 CMS 100 fb -1 K=1.6

38. A. Bay Beijng October 200538 More complex: ttH production, H  bb Final state with 4 jets with b hadrons, plus the decay products of the two W: W  2 jets or W  lepton and neutrino b b b q, l q, W Backgrounds: combinatorial from signal itself : with 4 b jets => 6 combinations W+jets, WWbbjj, etc. t t j j ~ 60% of the total gluons from beam protons

39. A. Bay Beijng October 200539 More complex: ttH production, H  bb.2 ATLAS 100 fb -1 m H =120 GeV

40. A. Bay Beijng October 200540 Higgs in LHCb p p beam jet 1 beam jet 2 q q' W H b b lepton neutrino jet b Process is b-quarks will hadronize  jets of particles b jets lepton beam jets