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Pion Decay Kinematics

According to ref.[1], and taking into account the ISIS beam structure, the mean time-of-flight (TOF) for the hypothetical X-particles over a distance of 17.5 m is (3.39 ± 0.25) ms. This together with the pion and muon masses [6] corresponds to a mass of the X-particle of

m_X = (33.905 ± 0.001) MeV,

which is close to the kinematic limit

m_p - m_m = (33.91157 ± 0.00067) MeV.

The small Q-value makes it prohibative to look for such a particle in `heavy neutrino searches' from pions decaying at rest. However, it has certain advantages when looking at decays in flight: firstly, the velocity of the muon is very close to that of the original pion (p_m ~ p_p · m_m / m_p), secondly, the flight direction of the muon differs only slightly from that of the pion, and finally, the specific energy-loss of the muon is almost equal to that of the pion. These factors enable one to use the beam-line itself as a spectrometer to optimally separate muons from the decay (1) from both other beam particles and muons from the normal pion decay p⁺ ® m⁺ n_m. (2)

Figure 1: Pion decay-in-flight kinematics for p_p = 150 MeV/c, showing the difference in available phase space for decay (1) and (2).

An example of the pion decay kinematics in flight for a pion momentum p_p = 150 MeV/c is shown in Fig.1. The momentum for a muon from decay (1) lies between (112.7-114.2) MeV/c and has decay angles up to 5.1 mrad, whereas a muon from decay (2) has momenta between (74-162) MeV/c with decay angles reaching 260 mrad. Thus, in the momentum region of interest for decay (1) the muons from both types of decay are separated in decay angle by at least 255 mrad, and should therefore be separable from the beam-optics point-of-view.

Created by J. Koglin on October-15-1999.