Setting limits on a new parameter outside of Standard Model muon decay.

1
Setting limits on a new parameter outside of
Standard Model muon decay.
Kristen Williams Jacksonville State
University Dr. Carl Gagliardi Cyclotron
Institute Texas AM
University
WHAT IS THE STANDARD MODEL?
CURRENT KNOWLEDGE AND LIMITS
EXAMINING THIS THEORY

• Standard Model (SM) is the name given to the
  current theory of elementary particles and how
  they interact.
• These particles are classified as fermions
  (leptons and quarks) or bosons.

• The simplified differential decay probability
  (shown below) is parameterized by the four Michel
  parameters ?, ?, ?, d.
• New measurements of all four parameters have been
  published in the past year. As shown in the
  table, the current values seem to agree nicely
  with the SM.
• 90 confidence levels have also been set for 10
  of the 12 coupling constants yielded from the
  decay matrix element.

• We began the fits by assuming that each parameter
  in the SM spectrum would change by some small
  amount, with each extra piece being a function of
  kappa SM ??(?) ??(?) ??d(?)

• The SM describes nature on atomic and subatomic
  scales where interactions are governed not by
  gravity, but by the other 3 forces
• Electromagnetic force - acts on charged
  particles
• force carrier - photon
• Strong force - binds the components of the
  nucleus
• force carrier - gluon
• Weak force - describes particle decay
• force carriers - Z and W bosons

• To quantify ??(?), ??(?), and ??d(?) we performed
  ?2 minimizations of the isotropic piece and the
  decay asymmetry over a given range of ? values

• RR and LL tensor couplings do not occur when the
  decay is localized at a point.
• Thus, these two constants are assumed to be
  identically zero.

• We fit each graph to a polynomial trendline and
  found that the quadratic pieces are unaffected by
  the minimum energy.
• Only the linear pieces change when the energy
  range is adjusted.
• This confirms our hypothesis that the linear
  contribution from ? is sensitive to the energy
  range of the fit.

• When the theory was developed in the 1970s, it
  incorporated all knowledge of particle physics at
  that time.
• Since then, it has continued to successfully
  predict the outcomes of a number of experiments.
• Thus, the goal of much of current particle
  physics research is to test the SMs limits.
• In each realm of particle physics, we ask, How
  adequate is the SM?
• One test of the SM is a rigorous study of one
  well-known weak interaction - muon decay.
• Since the SM specifies exactly how this decay
  should occur, any unexpected observations would
  be of great interest.
• Searching for such deviations is the goal of
  TWIST (TRIUMF Weak Interaction Symmetry Test).

Simplified differential probability spectrum
Matrix element

• In order to better quantify the linear
  variations, we replaced the Michel parameters
  with their SM values.

These graphs show how the functions shift when
the minimum energy of the fit range is changed
from 10 to 20 MeV.

• From these graphs, we can see how the
  coefficients of the linear pieces change for
  different minimum energies. We can then redefine
  the coefficients (below) and use the TWIST
  experimental values to set limits on ?.

INTRO TO MUON DECAY
Current limits set in 2005.3

• The muon (a lepton) has a mass over 200 times the
  electron
• 105.7 MeV.
• Thus, it will decay after a mean life of only
  2.2 µs.
• While the muon can decay via 3 different modes,
  the primary mode (100) produces an electron and
  two neutrinos

NEW THEORY TO TEST THE SM
These graphs show the shifts in the linear
pieces at 10, 15, and 20 MeV.

• M.V. Chizhov, a theorist at CERN, proposes
  inclusion of a new, non-local tensor interaction
  when describing muon decay.
• This would predict a non-zero value for .
• Chizhov presents this value as a new variable, ?,
  and calculates
• ? 0.013.5

• Direct muon decay is governed by the weak
  interaction as described by the SM.
• This interaction
• is CPT invariant
• involves the W boson

• Chizhovs ? affects both the isotropic and
  anisotropic terms of the decay spectrum by
  addition of an extra linear term and predicts new
  values for each of the Michel parameters.5

• Due to its large mass, the W boson will
  propagate a finite, statistically insignificant
  distance 0.0025 fm.
• Thus, the decay can be localized at a point.

• Combined, these two ranges set a final, 90
  confidence level limit on the possible value of
  ?.

Chizhovs simplified differential probability
spectrum
Setting limits on ? from TWIST values.

• While theory assumes 0, experiment has
  only been successful at narrowing the value
  lt 0.024.2
• Within this limit, Chizhovs value, 0.013, is
  certainly plausible.
• Our goal set limits on the value of and
  determine if the existence of ? will alter the SM
  view of muon decay.

• This value range for ? is based on an analysis
  with the momentum range of past TWIST
  measurements 19ltpelt50 MeV/c.
• In the future, TWIST hopes to extend to 51.5
  MeV/c.
• Since minimum energy affects the fit
  coefficientswhich factor into the effective
  parameter calculationsother, more precise limits
  for ? could be achieved.

• Many of the current muon decay measurements and
  fits have been conducted by TWIST.
• TWIST performs its fits within a specific
  fiducial region in accordance with the
  capabilities of the TRIUMF detector.
• Previous TWIST fits have not included Chizhovs
  linear terms.
• Thus, our approach was to perform a similar fit
  for ? and set a limit on how sensitive the linear
  pieces are to the chosen energy range.

Feynman diagrams for muon decay

• References
• TWIST Collaboration, J.R. Musser et al., Phys.
  Rev. Lett. PRL 94, 101805 (2005).
• TWIST Collaboration, A. Gaponenko et al., Phys.
  Rev. D 71, 071101(R) (2005).
• C. A. Gagliardi, R.E. Tribble, and N.J. Williams,
  Phys. Rev. D 72, 073002 (2005).
• TWIST Collaboration, B. Jamieson et al.,
  submitted to Phys. Rev. D hep-ex/0605100.
• M.V. Chizhov, hep-ph/0405073.