158
Relic neutrinos and axions
with the strength g f given in terms of the PQ charges of the right- and left-chiral
components of I by
gf = XfR - x/L.
(5.73)
There is by now overwhelming evidence that the original 'visible' axion,
characterized by
la '" VPQ '" V '" 250 GeV
(5.74)
does not exist [15]. We mention briefly some of the laboratory-based experiments
that lead to this conclusion. The coupling of the light quarks u, d to the axion
may be expressed in terms of isoscalar and isovector combinations in an obvious
way. The isovector part (A I) determines the mixing between the axion and the 1r 0
and, since the decay rate for pion beta-decay
1r+ .... 1r°e+v e
(5.75)
is well known, the rate for the process
1r+ .... ae+v e
(5.76)
can be reliably predicted in terms of the isovector amplitude (AI). Now, if the
mass of the axion satisfies (5.68) it decays rapidly via the process
a .... e+e(5.77)
and a bound on the branching ratio for this process can be inferred from the
measured branching ratio [17] for the process
rr+ .... e+e-e+v e
(5.78)
This requires that the isovector amplitude is small,
lAd :s 2 x 10- 2
(5.79)
and this is sufficient to exclude the 'short-lived visible axion' models satisfying
(5.68), since AI is predicted to be large in such models [15].
However, if the mass of the axion satisfies
ma < 2me
(5.80)
it can only decay slowly, via the process (5.67). In this case, there are strong
experimental bounds deriving from the failure to detect axion production in
various beam dump experiments. In such experiments, many different processes
may produce axions and while it is difficult to calculate individual processes
reliably, they contribute incoherently and cannot all vanish. Thus, the production
cross sections for the processes
pN .... aX
eN .... aX
Relic neutrinos and axions
with the strength g f given in terms of the PQ charges of the right- and left-chiral
components of I by
gf = XfR - x/L.
(5.73)
There is by now overwhelming evidence that the original 'visible' axion,
characterized by
la '" VPQ '" V '" 250 GeV
(5.74)
does not exist [15]. We mention briefly some of the laboratory-based experiments
that lead to this conclusion. The coupling of the light quarks u, d to the axion
may be expressed in terms of isoscalar and isovector combinations in an obvious
way. The isovector part (A I) determines the mixing between the axion and the 1r 0
and, since the decay rate for pion beta-decay
1r+ .... 1r°e+v e
(5.75)
is well known, the rate for the process
1r+ .... ae+v e
(5.76)
can be reliably predicted in terms of the isovector amplitude (AI). Now, if the
mass of the axion satisfies (5.68) it decays rapidly via the process
a .... e+e(5.77)
and a bound on the branching ratio for this process can be inferred from the
measured branching ratio [17] for the process
rr+ .... e+e-e+v e
(5.78)
This requires that the isovector amplitude is small,
lAd :s 2 x 10- 2
(5.79)
and this is sufficient to exclude the 'short-lived visible axion' models satisfying
(5.68), since AI is predicted to be large in such models [15].
However, if the mass of the axion satisfies
ma < 2me
(5.80)
it can only decay slowly, via the process (5.67). In this case, there are strong
experimental bounds deriving from the failure to detect axion production in
various beam dump experiments. In such experiments, many different processes
may produce axions and while it is difficult to calculate individual processes
reliably, they contribute incoherently and cannot all vanish. Thus, the production
cross sections for the processes
pN .... aX
eN .... aX