1. WHAT IS THE STANDARD MODEL?
Setting limits on a new parameter outside of Standard Model muon decay.
Kristen Williams – Jacksonville State University
Dr. Carl Gagliardi – Cyclotron Institute
Texas A&M 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: ρ, η, ξ, δ.
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 + Δρ(κ) + Δξ(κ) + Δξδ(κ)
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 Δρ(κ), Δξ(κ), and Δξδ(κ) we performed χ2 minimizations of the isotropic piece and the decay asymmetry over a given range of κ 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. ρ
3/4
± (stat.)
± (syst.) ± δ
± (stat.)
± (syst.)2 η ± ξ 1
N/A
Pμξ
1.0003
± (stat.)
± (syst.)4
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 κ is sensitive to the energy range of the fit.
When the theory was developed in the 1970’s, 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 SM’s 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]
<0.067
<0.088
<0.417
<0.550
<0.034
<0.036
<0.104 1
>0.960
≡ 0
<0.025
<0.104
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 κ.
INTRO TO MUON DECAY
[Current limits set in ]
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, κ, and calculates
κ = ≈
Direct muon decay is governed by the weak interaction as described by the SM.
This interaction:
is CPT invariant
involves the W boson
Chizhov’s κ 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 ~ 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 κ.
[Chizhov’s simplified differential probability spectrum]
Setting limits on κ from
TWIST values.
While theory assumes ≡ 0, experiment has only been successful at narrowing the value: <
Within this limit, Chizhov’s value, 0.013, is certainly plausible.
Our goal: set limits on the value of and determine if the existence of κ will alter the SM view of muon decay.
This value range for κ is based on an analysis with the momentum range of past TWIST measurements: 19<pe<50 MeV/c.
In the future, TWIST hopes to extend to 51.5 MeV/c.
Since minimum energy affects the fit coefficients—which factor into the effective parameter calculations—other, more precise limits for κ 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 Chizhov’s linear terms.
Thus, our approach was to perform a similar fit for κ 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, (2005).
TWIST Collaboration, A. Gaponenko et al., Phys. Rev. D 71, (R) (2005).
C. A. Gagliardi, R.E. Tribble, and N.J. Williams, Phys. Rev. D 72, (2005).
TWIST Collaboration, B. Jamieson et al., submitted to Phys. Rev. D; hep-ex/
M.V. Chizhov, hep-ph/