We use experimental limits on the neutrino mass to derive model‐independent upper bounds on various muon decay parameters. We find that the bounds obtained in this way are improved by more than three orders of magnitude over current experimental limits

Erwin, Rebecca J.

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Constraints on Muon Decay Parameters from Neutrino Mass
Rebecca J. Erwin 
 
Citation: AIP Conference Proceedings 842, 903 (2006); doi: 10.1063/1.2220417 
View online: http://dx.doi.org/10.1063/1.2220417 
View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/842?ver=pdfcov 
Published by the AIP Publishing 
 
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Constraints on Muon Decay Parameters
from Neutrino Mass1
Rebecca J. Erwin
Department of Physics, California Institute of Technology,
Pasadena, CA 91125
Abstract. We use experimental limits on the neutrino mass to derive model-independent upper
bounds on various muon decay parameters. We find that the bounds obtained in this way are
improved by more than three orders of magnitude over current experimental limits.
Keywords: muon decay, michel parameters, neutrino mass
PACS: 13.15.+g, 13.35.Bv, 14.60.Lm
INTRODUCTION
The discovery of neutrino mass has led to new connections between Standard Model
(SM) and non-SM phenomena (for example, see Refs. [1] and [4]). One of these connec-
tions is between neutrino mass and muon decay. By analyzing the mixing of chirality-
changing operators that contribute to both processes, we can use upper bounds on the
neutrino mass to place upper bounds on some ju-decay parameters.
MICHEL PARAMETERS
The Michel parameters are a way of parameterizing contributions to jU-decay from
physics beyond the SM. Depending on the details of the process being examined there
can be as many as ten parameters (excluding radiative decay) describing muon decay.
Physically, they represent the energy and angular distributions and the longitudinal and
transverse polarizations of the outgoing electrons in |U-decay.
Muon decay can be described with the four-fermion interaction [2],
*
=W X iaf
a,p=R,L
where GF is the Fermi coupling constant, fixed by the muon lifetime, and in the coupling
constants g* , y = S, V, T indicates scalar, vector, and tensor interactions and a,fi=R,L
are the chiralities of the charged leptons. The chiralities n and m of the neutrinos are
determined by the values of y, a, and /3. In the SM, gvLL~ 1, and the remaining gs
1
 Work done in collaboration with Jennifer E. Kile, Michael Ramsey-Musolf, and Peng Wang.
903
ATTACHMENT  
CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE  
OF EACH PAPER  
 
 
 
 
CP842, Particles and Nuclei, 
Seventeenth International Conference on Particles and Nuclei 
 edited by P. D. Barnes, M. D. Cooper, R. A. Eisenstein, H. van Hecke, and G. J. Stephenson 
© 2006 American Institute of Physics 0-7354-0338-4/06/$23.00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Constraints on Muon Decay Parameters
from Neutrino Mass1
Rebecca J. Erwin
Department of Physics, California Institute of Technology,
Pasadena, CA 91125
Abstract. We use experimental limits on the neutrino mass to derive model-independent upper
bounds on various muon decay parameters. We find that the bounds obtained in this way are
improved by more than three orders of magnitude over current experimental limits.
Keywords: muon decay, michel parameters, neutrino mass
PACS: 13.15.+g, 13.35.Bv, 14.60.Lm
INTRODUCTION
The discovery of neutrino mass has led to new connections between Standard Model
(SM) and non-SM phenomena (for example, see Refs. [1] and [4]). One of these connec-
tions is between neutrino mass and muon decay. By analyzing the mixing of chirality-
changing operators that contribute to both processes, we can use upper bounds on the
neutrino mass to place upper bounds on some ju-decay parameters.
MICHEL PARAMETERS
The Michel parameters are a way of parameterizing contributions to jU-decay from
physics beyond the SM. Depending on the details of the process being examined there
can be as many as ten parameters (excluding radiative decay) describing muon decay.
Physically, they represent the energy and angular distributions and the longitudinal and
transverse polarizations of the outgoing electrons in |U-decay.
Muon decay can be described with the four-fermion interaction [2],
*
=W X iaf
a,p=R,L
where GF is the Fermi coupling constant, fixed by the muon lifetime, and in the coupling
constants g* , y = S, V, T indicates scalar, vector, and tensor interactions and a,fi=R,L
are the chiralities of the charged leptons. The chiralities n and m of the neutrinos are
determined by the values of y, a, and /3. In the SM, gvLL~ 1, and the remaining gs
1
 Work done in collaboration with Jennifer E. Kile, Michael Ramsey-Musolf, and Peng Wang.
903
ATTACHMENT  
CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE  
OF EACH PAPER  
 
 
 
 
CP842, Particles and Nuclei, 
Seventeenth International Conference on Particles and Nuclei 
 edited by P. D. Barnes, M. D. Cooper, R. A. Eisenstein, H. van Hecke, and G. J. Stephenson 
© 2006 American Institute of Physics 0-7354-0338-4/06/$23.00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions IP:  131.215.225.131 On: Wed, 20 Apr 2016 20:50:34
are zero. Interestingly, in many extensions to the SM these other coupling constants are
nonzero.
The Michel parameters are bilinear combinations of the |U-decay coupling constants
g7*. Several parameterizations of the Michel parameters exist, and to avoid confusion
we will quote our results in terms of these gs, which can be directly compared with other
studies ([3, 4]).
CONNECTING jU-DECAY AND v MASS
We use the minimally extended SM with gauge-singlet right-handed Dirac neutrinos. A
basis of operators up to dimension six that contribute both to jit-decay and v mass and
are invariant under SU(2)i x U(l)y is:
By using a set of gauge-invariant operators, the contributions to mv from scales lying
between the electroweak scale at v = 246 GeV and the scale of new physics (typically
A w 1 TeV) can be taken into account. While all of the chirality-changing operators
above contribute to neutrino mass, only the operators ff/f, 0y, and ffw contribute
to jU-decay. The remaining dimension-six operators mix with these at one loop under
dimensional regularization and must be taken into account. In addition, there is mixing
of the dimension-six operators ffff and ffy with the dimension-four mass operator G\} .
This contribution is estimated using dimensional analysis.
The various operators above (those contributing to jU-decay) will contribute to differ-
ent coupling constants. For example, the mixing of the operator ffff with the dimension-
( A\ o fi
four mass operator ff]^ gives an estimate of the upper bound on gRLLR, while mixings
among the dimension-six operators (see Fig. 1 for an example) give upper bounds on
SRLLR- Notice that these chirality-changing operators, and hence mv, put no constraints
on the a, j3 = RR, LL coupling constants in gjL.
IMPLICATIONS FOR THE TWIST EXPERIMENT
In Table 1, bounds on g^« obtained from the operator mixing analysis are compared
with bounds from two previous studies: a recent global analysis [3] that includes new
and more precise measurements of six parameters from the TWIST experiment and PSI,
and bounds from the theoretical analysis in [4].
A degenerate neutrino mass spectrum with mv = 1 eV was used in our calculations.
Since the upper limit on the gs is proportional to neutrino mass, a smaller bound on mv
S V T
would result in tighter limits on gRL'LR.
The upper limits on the gs on columns four and five are at least two orders of
magnitude smaller than those in the third column and at least three orders of magnitude
904
are zero. Interestingly, in many extensions to the SM these other coupling constants are
nonzero.
The Michel parameters are bilinear combinations of the |U-decay coupling constants
g7*. Several parameterizations of the Michel parameters exist, and to avoid confusion
we will quote our results in terms of these gs, which can be directly compared with other
studies ([3, 4]).
CONNECTING jU-DECAY AND v MASS
We use the minimally extended SM with gauge-singlet right-handed Dirac neutrinos. A
basis of operators up to dimension six that contribute both to jit-decay and v mass and
are invariant under SU(2)i x U(l)y is:
By using a set of gauge-invariant operators, the contributions to mv from scales lying
between the electroweak scale at v = 246 GeV and the scale of new physics (typically
A w 1 TeV) can be taken into account. While all of the chirality-changing operators
above contribute to neutrino mass, only the operators ff/f, 0y, and ffw contribute
to jU-decay. The remaining dimension-six operators mix with these at one loop under
dimensional regularization and must be taken into account. In addition, there is mixing
of the dimension-six operators ffff and ffy with the dimension-four mass operator G\} .
This contribution is estimated using dimensional analysis.
The various operators above (those contributing to jU-decay) will contribute to differ-
ent coupling constants. For example, the mixing of the operator ffff with the dimension-
( A\ o fi
four mass operator ff]^ gives an estimate of the upper bound on gRLLR, while mixings
among the dimension-six operators (see Fig. 1 for an example) give upper bounds on
SRLLR- Notice that these chirality-changing operators, and hence mv, put no constraints
on the a, j3 = RR, LL coupling constants in gjL.
IMPLICATIONS FOR THE TWIST EXPERIMENT
In Table 1, bounds on g^« obtained from the operator mixing analysis are compared
with bounds from two previous studies: a recent global analysis [3] that includes new
and more precise measurements of six parameters from the TWIST experiment and PSI,
and bounds from the theoretical analysis in [4].
A degenerate neutrino mass spectrum with mv = 1 eV was used in our calculations.
Since the upper limit on the gs is proportional to neutrino mass, a smaller bound on mv
S V T
would result in tighter limits on gRL'LR.
The upper limits on the gs on columns four and five are at least two orders of
magnitude smaller than those in the third column and at least three orders of magnitude
904
 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions IP:  131.215.225.131 On: Wed, 20 Apr 2016 20:50:34
\ /vv\/\/\/?
FIGURE 1. Mixing of 0V into 6$.
TABLE 1. Upper bounds on |U-decay coupling
constants gya» from two recent studies (second
and third columns), and this work (fourth and
fifth columns). A — indicates that this g is not
constrained by a mixing of this dimensionality.
&V,
SLR
SRL
SLR
SRL
SLR
STRL
Global
Analysis[3]
< 0.088
< 0.417
< 0.036
< 0.104
< 0.025
< 0.104
Ref. [4]
io-4
io-2
io-4
io-2
io-4
io-2
4D
io-7
io-5
10~6
10~4
io-7
io-5
6D
-
-
10~6
io-4
-
-
smaller than the bounds from the recent global analysis. One implication of our stronger
constraints on the g coupling constants is that at current experimental sensitivities, any
9 I/ Tdeviation from the SM values of gRL'LR = 0 would have to result from fine-tuning in
order to overcome the limits set by a birac neutrino mass.
CONCLUSIONS
We have presented results from a model-independent analysis connecting upper limits
on the neutrino mass to the Michel parameters, which describe contributions to ]U-
decay from beyond the SM. The resulting constraints are much smaller than current
^ V T
experimental limits. Since the bounds on gRL'LR are directly proportional to the neutrino
mass, smaller limits on mv will decrease these upper bounds.
REFERENCES
1. N. F. Bell, V. Cirigliano, M. J. Ramsey-Musolf, P. Vogel and M. B. Wise, Phys. Rev. Lett. 95,151802
(2005).
2. S. Eidelman et al [Particle Data Group], Phys. Lett. B 592,1 (2004).
3. C. A. Gagliardi, R. E. Tribble and N. J. Williams, arXiv:hep-ph/0509069.
4. G. Prezeau and A. Kurylov, Phys. Rev. Lett. 95,101802 (2005).
905
\ /vv\/\/\/?
FIGURE 1. Mixing of 0V into 6$.
TABLE 1. Upper bounds on |U-decay coupling
constants gya» from two recent studies (second
and third columns), and this work (fourth and
fifth columns). A — indicates that this g is not
constrained by a mixing of this dimensionality.
&V,
SLR
SRL
SLR
SRL
SLR
STRL
Global
Analysis[3]
< 0.088
< 0.417
< 0.036
< 0.104
< 0.025
< 0.104
Ref. [4]
io-4
io-2
io-4
io-2
io-4
io-2
4D
io-7
io-5
10~6
10~4
io-7
io-5
6D
-
-
10~6
io-4
-
-
smaller than the bounds from the recent global analysis. One implication of our stronger
constraints on the g coupling constants is that at current experimental sensitivities, any
9 I/ Tdeviation from the SM values of gRL'LR = 0 would have to result from fine-tuning in
order to overcome the limits set by a birac neutrino mass.
CONCLUSIONS
We have presented results from a model-independent analysis connecting upper limits
on the neutrino mass to the Michel parameters, which describe contributions to ]U-
decay from beyond the SM. The resulting constraints are much smaller than current
^ V T
experimental limits. Since the bounds on gRL'LR are directly proportional to the neutrino
mass, smaller limits on mv will decrease these upper bounds.
REFERENCES
1. N. F. Bell, V. Cirigliano, M. J. Ramsey-Musolf, P. Vogel and M. B. Wise, Phys. Rev. Lett. 95,151802
(2005).
2. S. Eidelman et al [Particle Data Group], Phys. Lett. B 592,1 (2004).
3. C. A. Gagliardi, R. E. Tribble and N. J. Williams, arXiv:hep-ph/0509069.
4. G. Prezeau and A. Kurylov, Phys. Rev. Lett. 95,101802 (2005).
905
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Constraints on Muon Decay Parameters from Neutrino Mass

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Constraints on Muon Decay Parameters from Neutrino Mass

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