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Why Does the Standard Model Need the Higgs Boson ?

Why Does the Standard Model Need the Higgs Boson ?. II. Augusto Barroso. Sesimbra 2007. Scattering. W -. e -. e +. q. Incoming. W +. Outgoing. W -. e-. W +. e +. Scattering. g and Z s-channel. Both terms grow as s. However, notice the cancelation between gamma and Z.

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Why Does the Standard Model Need the Higgs Boson ?

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  1. Why Does the Standard Model Need the Higgs Boson ? II Augusto Barroso Sesimbra 2007

  2. Scattering W- e- e+ q Incoming W+ Outgoing W- e- W+ e+

  3. Scattering g and Z s-channel Both terms grow as s. However, notice the cancelation between gamma and Z.

  4. t-channel diagram It cancels with the similar contribution from the s-channel, i. e. Conclusion: All contributions that grow with s or cancel

  5. Notice that: The previous results were obtained with m=0. Otherwise there would be an additional contribution to the t-channel diagram, namely:

  6. Again the scalar exchange rescues the theory!

  7. The Standard Model Number of Parameters: SU(3)xSU(2)xU(1) x Gravity 27 parameters. 23 are generated by the Higgs Sector. Another one, the Cosmological Constant, “does not like the Higgs sector”.

  8. The Higgs gives: Cosmology gives: The Higgs Sector and =2x10-52 m-2

  9. The Electroweak Sector

  10. Example: only SU(2) But QFT is more than Lg

  11. Ex: Calculate the Self Energy + + …=finite terms is absorbed in the Wave Function renormalization.

  12. Now, introduce fermions, F We don’t want to decide if F is left, right or whatever. Hence we use the coupling: There is another contribution to the gauge field self-energy. The new singular term requires a mass renormalization.

  13. Renormalization of massless non-Abelian Gauge Theory • Without Fermions • Simply • With massive fermions axial coupled • It requires This implies a mass term for the gauge bosons.

  14. Loop Corrections • Because the W and Z self energies are different we have a correction to r.

  15. Summary: Electron in Dirac Rep. Parity conservation in QED Mass terms are Left-right Parity violation in Weak Int. The weak currents are left Bad behaviour of WW scattering Scalar boson couples to W Scalar is a doublet of SU(2) Bad behaviour of e+e- WW The scalar couples to fermions

  16. Solution with Spontaneous symmetry breaking. Three degrees of freedom become the longitudinal polarizations of W and Z. The remaining is the Higgs Boson.

  17. Higgs Boson From the value of GF one obtains: The parameter l can be traded off with the Higgs mass. Inserting the LEP upper bound: • MH < 144 GeV (95%CL) gives One can safely use perturbation theory.

  18. FAQ • The Higgs mechanism is a “clever trick”. Can we do it without ending up with an Higgs Boson? NO. Cif. the example on WW scattering. Unless …

  19. FAQ • If we are not careful can we also break the electromagnetic gauge group and give the photon a mass? • No, in the minimal model with a single doublet.

  20. Conclusion • LEP results tested the SM in such a way that it is hard to believe that one is not checking the loop expansion of a QFT. • Then, the standard model is a QFT valid at the same level as, for instance, QED. • Hence, the Higgs boson ought to exist.

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