Studies in Higgs and Z Decays By: Edward Timko Advisor: Dr. James Wells

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Studies in Higgs and Z DecaysBy Edward
TimkoAdvisor Dr. James Wells
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Introduction The Process

• A Higgs boson is produced by some process.
• The Higgs then decays into two Z bosons.
• Each Z bosons then decays into a charged
  lepton-antilepton pair

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Introduction Areas of Interest

• Kinematics
• Transverse Momentum and Pseudorapidity
• Isotropic Decays and Distributions
• Z Decay Amplitudes and Decay Widths

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Introduction Restrictions

• Focus will be on the Z to lepton-antilepon decay
• Details of the complete decay can be discussed if
  time permits.
• Primary goal to introduce concepts

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Kinematics The Masses

• Higgs Mass 182.38 GeV and up
• Z boson Mass 91.19 GeV
• Lepton Mass From 0.511MeV to 1.78 GeV

• This is a heavy Higgs description.
• Other descriptions exist where this decay cannot
  occur.

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Kinematics Mass Comparison

• If an electron were to weigh 1 mg, about as much
  as a mosquito...
• ...then a Z boson would weigh about 178 grams,
  which is a bit heavier than a baseball.

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Kinematics Speeds

• The masses of the leptons in comparison to the Z
  are very small.
• This causes the leptons to behave similar to
  massless particles.
• From the rest frame of the Z
• Speed of the t 0.999240c
• Speed of the µ 0.999996c
• Speed of the e c (to 9 places)?

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Kinematics The Complete Boosts
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Transverse Momentum (pT)?
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Pseudorapidity (?)?
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Basic Decay Features Z to Lepton

• Only the pT and ? distribution of the Z decay
  will be presented for brevity.
• Leptons will be assumed massless.

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Basic Decay Features Z to Lepton

• Isotropic Decays are considered first.
• But this isn't quite right, as will be seen later.

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Isotropic Decays pT Distribution
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Isotropic Decays ? Distribution
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Anistropic Decay of the Z

• A previously said, the decay distribution of the
  Z boson into a lepton is not exactly isotropic.
• Inorder to see the difference, so simple Quantum
  Field Theory calculations need be made.

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Polarizations of the Z

• Since the Z boson is a vector boson, it, like the
  photon, is endowed with polarizations.
• The Transverse Polarizations R(ight) and L(eft).
• The Longitudinal Polarization S(calar)?

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The Decay Matrix

• The decay matrix describes the likelihood of a
  given particle decaying into a particular
  resultant particle.
• This expression can be derived directly from the
  Standard Model Lagrangian.

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The Invariant Amplitude

• In general, it is the absolute square of the
  Decay Matrix
• Used for calculating
• Decay Widths
• Cross Sections
• Decay Distributions
• An invariant amplitude is often summed over the
  final spin states, and averaged over the
  polarizations of the initial state.
• We look at particular polarizations.

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The Invariant Amplitude for a Scalar Z

• Note that the amplitude is a function of ?.
• Here, ? is the angle between the incident
  partical path and the resultant particle path.

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The Decay Width (G)?

• The Decay Width is used to describe transent
  particles like the Z and W bosons.
• The decay width for a particular decay chanel is
  inversely proportional to the lifetime of the
  initial particle.

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The Invariant Amplitude and Decay Distributions

• The Invariant Amplitude proportional to the
  distribution of decays over solid angles in the Z
  rest frame.
• This can be rewritten in terms of ?, averaging
  out the azimuthal angle, as it does not
  contribute.

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Anisotropic Decays pT Distribution(Scalar)?
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Anisotropic Decays ? Distributions(Scalar)?
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...And Much More

• This is only really an introduction to the
  matrial I have been working on.
• I have written various programs in C for
  examinging more complicated cases where the exact
  solution cannot be arrived at.
• I am currently looking to opening angles and the
  fully boosted pT and ? distributions.

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References

• Jackson, John David. Classical Electrodynamics.
  3rd edition. Academic Press, New York, 1998.
  Chapter 11.
• Kaku, Michio. Quantum Field Theory a modern
  introduction. Oxford University Press, New York,
  1993. Chapters 3, 6, and Appendix A.5
• Renton, Peter. Electroweak Interacts An
  introduction to the physics of Quarks and
  Leptons. Cambridge University Press, Cambridge,
  1990. Chapter 8 and 10.
• Wackerly, et al. Mathematical Statistics with
  Applications. 6th edition. Duxbury, US office,
  2002. Chapter 6.

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Programs Used for Presentation

• GIMP Image Editor for the image editing
• Gnuplot for the plots
• GNU Texmacs Editor for the equation editing
• OpenOffice.org Presentation for the slide
  preperation.
• Jaxodraw for the Feynman Diagrams

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Special Thanks To...

• Corky and Randy, for getting me food when I was
  sick.
• Dave, for driving me to the hostpital in the
  middle of the night.
• Dr. Wells for his advise and patience

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• And to xkcd, for this cartoon.
• Irrelevant?
• Perhaps.
• But I like it.
• Questions?