Monday, February 2, 2015

Reviewing the Basics: Pions

The lightest hadrons in the universe, and indeed, the lightest free particles containing quarks in the universe, are the humble pions.  As noted in previous posts, their masses are far lower than a naive study of meson and hadron masses uninformed by the unique properties of QCD would expect.  A quick review of their core properties follows.  An overview of the particle from Wikipedia explains that:
The exchange of virtual pions, along with the vector, rho and omega mesons, provides an explanation for the residual strong force between nucleons. Pions are not produced in radioactive decay, but are produced commonly in high energy accelerators in collisions between hadrons. All types of pions are also produced in natural processes when high energy cosmic ray protons and other hadronic cosmic ray components interact with matter in the Earth's atmosphere. Recently, detection of characteristic gamma rays originating from decay of neutral pions in two supernova remnant stars has shown that pions are produced copiously in supernovas, most probably in conjunction with production of high energy protons that are detected on Earth as cosmic rays.

The concept of mesons as the carrier particles of the nuclear force was first proposed in 1935 by Hideki Yukawa. While the muon was first proposed to be this particle after its discovery in 1936, later work found that it did not participate in the strong nuclear interaction. The pions, which turned out to be examples of Yukawa's proposed mesons, were discovered later: the charged pions in 1947, and the neutral pion in 1950. . . .

The pion also plays a crucial role in cosmology, by imposing an upper limit on the energies of cosmic rays surviving collisions with the cosmic microwave background, through the Greisen–Zatsepin–Kuzmin limit.

In the standard understanding of the strong force interaction (called QCD, "quantum chromodynamics"), pions are understood to be the pseudo-Nambu-Goldstone bosons of spontaneously broken chiral symmetry. This explains why the three kinds of pions' masses are considerably less than the masses of the other mesons, such as the scalar or vector mesons. If their current quarks were massless particles, hypothetically, making the chiral symmetry exact, then the Goldstone theorem would dictate that all pions have zero masses. In reality, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero rest masses, albeit almost an order of magnitude smaller than that of the nucleons, roughly mπ ≈ √v mq / fπ ≈ √mq 45 MeV, where m are the relevant current quark masses in MeV, 5−10 MeVs.
Neutral Pions

Neutral pions are pseudoscalar mesons that are normally considered to be linear combinations of up-antiup quark mesons and down-antidown quark mesons.

The mass of the neutral pion is 134.9766 +/- 0.0006 MeV,   Measurements of the difference between the neutral and charged pion mass, without regard to absolute masses, indicate that it is 4.5936 +/- 0.0005 MeV (a slight improvement in margin of error from the difference obtained from the independent measurements).

All of their decays are to photons and/or leptons. About 98.823 +/- 0.034% of the time, they decay to two photons. About 1.174 +/- 0.035% of the time, they decay to an electron, a positron and a photon.  Nine other rare decay modes take place 0.06% of the time or less have been observed.

The neutral pion's mean lifetime is (8.52 +/- 0.18)*10^-17 seconds, indicating that they decay predominantly via electromagnetic matter-antimatter annihilation, rather than weak force decay.

Charged Pions

Charged pions are pseudoscalar mesons made up of an up quark and an anti-down quark, or an anti-up quark and a down quark.

The mass of the charged pion is 139.57018 +/- 0.00035 MeV.

The dominant decay for a negatively charged pion is via the muon and an antimuon neutrino, 99.877% of the time. A muon, antimuon neutrino and photon are present in the decay 0.02% of the time. An electron and antielectron neutrino are present 0.0123% of the time. Three other leptonic decay modes less common than 0.0005% of decays are observed.

And, a decay mode involving an electron, antielectron neutrino, and a neutral pion (the sole hadronic decay mode observed) occurs 0.000001036% of the time.  This rare process is also called "pion beta decay."

Functionally, the ratio of the electron decay fraction to the muon decay fraction is given by:

R_pi = (m_e/m_mu)^2 *((m_pi^2-m_e^2)/(m_pi^2-m_mu^2))^2 = 1.283356*10^-4

This is only a leading order estimate, however,  It is off by 4.3% from the experimentally measured value, a 9.4 sigma difference given the margins of error in the measurements of the two decay fractions.

Positively charged pions decay in the same way (and have the same mass and mean lifetime) but with the CP of the products flipped.

They have a mean lifetime of 2.6*10^-8, which is typical of a particle that decays via the weak force and just a little shorter than the lifetime of the muon.

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