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The decay rate

The decay rate. The decay rate. The decay rate. Lorentz Invariant Phase Space. The decay rate. The decay rate. Decay amplitude. Describes the interactions during the decay. The Feynman diagrams. The Feynman diagrams. Gluons are massless. They don’t interact with the Higgs!.

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The decay rate

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  1. The decay rate

  2. The decay rate

  3. The decay rate Lorentz Invariant Phase Space

  4. The decay rate

  5. The decay rate Decay amplitude. Describes the interactions during the decay.

  6. The Feynman diagrams

  7. The Feynman diagrams Gluons are massless. They don’t interact with the Higgs!

  8. The Feynman diagrams Interaction occurs through a fermion (quark) loop

  9. From the Feynman diagram to the decay amplitude

  10. From the Feynman diagram to the decay amplitude

  11. l + p From the Feynman diagram to the decay amplitude l l - k

  12. l + p From the Feynman diagram to the decay amplitude l l - k

  13. l + p From the Feynman diagram to the decay amplitude l l - k

  14. l + p From the Feynman diagram to the decay amplitude l l - k

  15. l + p From the Feynman diagram to the decay amplitude l l - k

  16. l + p From the Feynman diagram to the decay amplitude l l - k

  17. l + p From the Feynman diagram to the decay amplitude l l - k

  18. l + p From the Feynman diagram to the decay amplitude l l - k

  19. l + p From the Feynman diagram to the decay amplitude l l - k

  20. Calculating the decay amplitude The numerator:

  21. Calculating the decay amplitude The numerator: Contains terms

  22. Calculating the decay amplitude The numerator: Numerator algebra (trace technology) • Tr[] = 0 • +

  23. The denominator: Calculating the decay amplitude

  24. The denominator: Calculating the decay amplitude

  25. The denominator: Calculating the decay amplitude We would like it to be in the form

  26. Feynman Parameterization observe that: This generalizes to:

  27. Feynman Parameterization

  28. Feynman Parameterization The loop integral becomes: }

  29. Feynman Parameterization The loop integral becomes: }

  30. Dimensional Regularization The loop integral becomes:

  31. Dimensional Regularization The loop integral becomes: Wick Rotation :

  32. Dimensional Regularization The loop integral becomes: Wick Rotation :

  33. Dimensional Regularization The loop integral becomes: Wick Rotation :

  34. Calculation of M The loop integral : }

  35. Calculation of M The loop integral : } Is part of M:

  36. Calculation of M The loop integral : } Is part of M:

  37. Calculation of M The loop integral : } Is part of M:

  38. Calculation of M The loop integral : } Is part of M: and Many terms vanish!

  39. Calculation of M The loop integral : } Is part of M: Many terms vanish!

  40. Calculation of M The loop integral : } Is part of M: Many terms vanish!

  41. Final expression for M

  42. Final expression for M • For a specific polarization of the k gluon and of the p gluon

  43. Final expression for M • For a specific polarization of the k gluon and of the p gluon • For specific gluon colors a and b

  44. Final expression for M • For a specific polarization of the k gluon and of the p gluon • For specific gluon colors aandb • For a specific quark q

  45. For the decay rate Remembering the decay rate: We need to sum over all different polarizations , over all different colors and over different quark species!

  46. For the decay rate

  47. For the decay rate Useful identity:

  48. For the decay rate Useful identity:

  49. For the decay rate Useful identity:

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