Pion decay

The techniques of u.SR and p-LCR are based on the fact that parity is violated in weak interactions. Consequently, when a positive muon is created from stationary pion decay its spin is directed opposite to its momentum. This makes it possible to form a beam of low energy (4 MeV) positive muons with nearly 100% spin polarization at high intensity particle accelerators such as TRIUMF in Canada, the PSI in Switzerland, LAMPF and BNL in the USA, KEK in Japan, and RAL in England. Furthermore the direction of position emission from muon decay is positively correlated with the muon spin polarization direction at the time of decay. This allows the time evolution of the muon spin polarization vector in a sample to be monitored with a sensitivity unparalleled in conventional magnetic resonance. For example, only about 101 7 muon decay events are necessary to obtain a reasonable signal. Another important point is that //.SR is conventionally done such that only one muon is in the sample at a time, and for p,LCR, even with the highest available incident muon rates, the 2.2 fis mean lifetime of the muon implies that only a few muons are present at a given time. Consequently, muonium centers are inherently isolated from one another. 

We have shown that the vector mesons in the CFL phase have masses of the order of the color superconductive gap, A. On the other hand the solitons have masses proportional to F%/A and hence should play no role for the physics of the CFL phase at large chemical potential. We have noted that the product of the soliton mass and the vector meson mass is independent of the gap. This behavior reflects a form of electromagnetic duality in the sense of Montonen and Olive [29], We have predicted that the nucleon mass times the vector meson mass scales as the square of the pion decay constant at any nonzero chemical potential. In the presence of two or more scales provided by the underlying theory the spectrum of massive states shows very different behaviors which cannot be obtained by assuming a naive dimensional analysis. 

Then it resides on the chiral circle with modulus p and phase , , any point on which is equivalent with each other in the chiral limit, mc = 0, and moved to another point by a chiral transformation. We conventionally choose a definite point, (vac p vac) = /,T (Jn the pion decay constant) and (vac Oi vac) = 0, for the vacuum, which is flavor singlet and parity eigenstate. In the following we shall see that the phase degree of freedom is related to spin polarization that is, the phase condensation with a non-vanishing value of Oi leads to FM [20]. 

The muon g — 2 value has been determined in a series of experiments at CERN [45,46]. The primary purpose of the new muon g — 2 experiment at Brookhaven National Laboratory is to improve the precision of the experiment by about a factor 20 and verify the presence of the electroweak effect which has been evaluated to two loop orders in the Standard Model. In this experiment, polarized muons from pion decays are captured in a storage ring with a uniform magnetic field and a weak-focusing electric quadrupole field. For a muon momentum of 3.09 GeV/c and 7 = 29.3 the muon spin motion is unaffected by the electric quadrupole field and the difference frequency uia is given by... 

At the ttE5 beam of the Paul-Scherrer-Institut (PSI), about 2% of the incoming pions (> 109/s) are stopped in the gas cell with a degrader set-up optimized for pionic atoms. Muons originating from pions decaying shortly before capture are slow enough to be stopped in the gas cell as well. With a set-up optimized for muons, the count rate for muonic atoms is about 4% of the one for pions. 

In this scenario only high energy neutrinos, produced in cosmic sources by charged pion decay, offer the possibility to directly observe TeVTPeV radiation emitted by far cosmic objects and to disentangle between the occurrence of purely electromagnetic or hadronic processes. Thus, the observation of cosmic HE neutrinos can probe hadronic processes and hopefully extend our horizon in the far Universe. 

Nuclear and pion related 7-rays provide important information about the spectra of protons and ions accelerated in solar flares [e.g. Hua and Lingen-felter, 1987 Murphy et al., 1987 Lockwood et al., 1997 Hua et al., 2002], However, nuclear 7-ray lines probe the proton spectrum only up to 40 MeV, while 7-rays from pion decays are only observed in the most intense flares. In addition, any spectral break in the proton spectrum is likely to he below the pion production threshold. Neutrons produced at the solar surface over a wide range of energies may provide important information from the 50-300 MeV regime, complementing 7-ray observations. Due to the long neutron thermal-ization time ( 100 s) the 2.223 MeV neutron capture line is only a limited measure of neutron production. The spectrum of accelerated and interacting protons can be deduced more reliably from direct neutron measurements. 

Muonium is formed when a positive muon thermalizes in a target and picks up an electron from the stopping medium into a bound state. Muons, both high energy (28 MeV) and low energy (4.1 MeV), are the product of positive pion decay, in flight or at rest, respectively. 

M. Daum, R. Frosch, D. Heter, M. Janousch, P.-R. Kettle, New precision measurement of the muon momentum in pion decay at rest, Phys. Lett. B 265 (1991) 425-429. 

The positive pion decays with a mean lifetime of 26 ns to give a muon and a neutrino ... 

Pion decay is mediated by the weak interaction and firll parity violation comes into play. In particular, the neutrino (here v ) always has left-handed chiral symmetry, meaning that its spin Sv (being h/2 like that of the muon) is oriented in the opposite direction to its linear momentum (pv)- The pion has spin zero. Conservation of momentum in its decay (eq. 2) requires that the neutrino (v ) and the muon (p,+) are ejected 180 apart in the rest frame of the pion. Since the orientation of is fixed to (Sy "T J. / v), the same must hold for the muon ( n i p - We thus get perfectly spin polarized muons with their spin directed opposite to their line of flight. The situation is illustrated in fig. 2. Under certain circumstances (to be discussed in the next section) the pion rest frame is identical with the laboratory fi-ame ( surface muon beam). The linear momentum given to the muon firom pion decay at rest is 29.8 MeV/c which corresponds to a kinetic energy of 4.1 MeV... 

In summary, parity violation in weak interactions provides an easy means to obtain a beam of perfectly polarized muons via pion decay and thus fixes initial muon spin orientation. In the decay of muons, parity violation comes into action for a second time in allowing the determination of the final muon spin orientation by a fairly simple counting experiment. 

The conclusion of these works is that the parity (P) invariance and, separately, the charge conjugation (C) invariance are violated in P decay, while the time reversal (T) or combined CP invariance is not. The parity non-invariance (i.e., non-invariance of the Hamiltonian of the weak interaction under space reflection) can be expressed alternativelyby saying that the parity is not conserved. This formulation is a consequence of the fact that the parity P is an observable quantity. The presence of two-pion decay mode in the K° kaon decay implies, however, that even the CP invariance is violated in the weak interaction (Christenson et al. 1964). 

Recently, these findings have been combined with the results of the so-called atmospheric neutrino anomaly, where p-neutrinos generated in pion decays oscillate over into, mainly, r-neutrinos. In addition, terrestrial experiments performed with neutrino fluxes (produced either at nuclear power plants or with accelerators) provide substantial information on the mixing pattern among the different neutrino species. Searches for possible oscillations into further light neutrino flavors, which would be of clear cosmological significance, have not yet provided a clear answer to the question of their existence. (See Sect. 10.8.2 in Chap. 10, Vol. 1)... 

The ECAL barrel has a volume of 8.14 m and its front face is at a radial distance of 1.29 m from the interaction point. It has a 360-fold azimuthal segmentation and two times 85-fold segmentation in pseudorapidity. The endcap has a coverage of 1.479 < 7l < 3 and is situated at a longitudinal distance of 3.15 m from the interaction point. A preshower detector with a thickness of 3 Xq is placed in front of the endcaps (1.653 < rj < 2.6) to guarantee a reliable discrimination of single photons and photons produced in pairs in neutral pion decays. 

Another method of orientating an emitter in its initial state and then observing the angular correlation of the subsequent radiation is used in /tSR spectroscopy. First a pion decays into a muon and a mesonic neutrino. This process determines the spin polarisation of the muon at the time of its creation. Subsequently after a mean lifetime of approximately 2.2 x 10 s the muon decays into a positron, a leptonic neutrino and a mesonic antineutrino. 

Muons are produced artificially from pions formed by the collision of energetic protons with low-Z targets. The pions decay with a lifetime of 26 ns ... 

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