Pion

(or residual strong force) interaction. The small colored double disks are gluons. For the choice of anticolors, see . for the same process as in the animation, with the individual quark constituents shown, to illustrate how the fundamental strong interaction gives rise to the nuclear force. Straight lines are quarks, while multi-colored loops are gluons (the carriers of the fundamental force). Other gluons, which bind together the proton, neutron, and pion "in-flight", are not shown.The meson contains an anti-quark, shown as travelling in the opposite direction, as per the Feynman–Stueckelberg interpretation. Theoretical work by Hideki Yukawa in 1935 had predicted the existence of mesons as the carrier particles of the strong nuclear force. From the range of the strong nuclear force (inferred from the radius of the atomic nucleus), Yukawa predicted the existence of a particle having a mass of about . Initially after its discovery in 1936, the muon (initially called the "mesotron" or the "mu meson") was thought to be this particle, since it has a mass of . However, later experiments showed that the muon did not participate in the strong nuclear interaction. In 1941–42, Bibha Chowdhuri and Debendra Mohan Bose reported cosmic-ray meson tracks at the Bose Institute that later historians have regarded as early evidence of pions. Although particle accelerators had already been developed by the early 1930s, atmospheric cosmic rays remained the principal source of high-energy subatomic particles until high-energy accelerators became available in the early 1950s. Photographic emulsions were placed for long periods of time in sites located atop Mount Sandakphu in present-day West Bengal and in the higher town of Pharijong in Tibet. The particles recorded at Sandakphu (about []) were lighter than those observed at Pharijong (about []), which led to a tentative conclusion that the lighter ones (the muons) were the decay product of the heavier ones (the pions). However, follow-up studies could not be conducted because only halftone plates were available during World War II. A study in 1947 by the collaboration led by Cecil Powell at the University of Bristol in England obtained more conclusive results with fulltone plates at Pic du Midi de Bigorre in the Pyrenees, and later at Chacaltaya in the Andes Mountains, for which Powell won the 1950 Nobel Prize in Physics. Marietta Kurz was the first person to detect the unusual "double meson" tracks upon inspecting the Powell team's plates, characteristic for a pion decaying into a muon, but they were too close to the edge of the photographic emulsion and deemed incomplete. A few days later, Irene Roberts observed the tracks left by pion decay that appeared in the discovery paper. Both women are credited in the figure captions in the article, and the previous study by Chowdhuri and Bose was credited as well. In 1948, Lattes, Eugene Gardner, and their team first artificially produced pions at the University of California's cyclotron in Berkeley, California, by bombarding carbon atoms with high-speed alpha particles. Further advanced theoretical work was carried out by Riazuddin, who in 1959 used the dispersion relation for Compton scattering of virtual photons on pions to analyze their charge radius. Since the neutral pion is not electrically charged, it is more difficult to detect and observe than the charged pions are. Neutral pions do not leave tracks in photographic emulsions or Wilson cloud chambers. The existence of the neutral pion was inferred from observing its decay products from cosmic rays, a so-called "soft component" of slow electrons with photons. The was identified definitively at the University of California's cyclotron in 1949 by observing its decay into two photons. Later in the same year, they were also observed in cosmic-ray balloon experiments at Bristol University. == Possible applications ==

The use of pions in medical radiation therapy, such as for cancer, was explored at a number of research institutions, including the Los Alamos National Laboratory's Meson Physics Facility, which treated 228 patients between 1974 and 1981 in New Mexico, and the TRIUMF laboratory in Vancouver, British Columbia. == Theoretical overview ==

In the standard understanding of the strong force interaction as defined by quantum chromodynamics, pions are loosely portrayed as Goldstone bosons of spontaneously broken chiral symmetry. That explains why the masses of the three kinds of pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current quarks were massless particles, it could make the chiral symmetry exact and thus the Goldstone theorem would dictate that all pions have a zero mass. In fact, it was shown by Gell-Mann, Oakes and Renner (GMOR) that the square of the pion mass is proportional to the sum of the quark masses times the quark condensate: M^2_\pi = (m_\text{u}+m_\text{d})B+\mathcal{O}(m^2), with the quark condensate: B = \left\vert \frac{\rm \langle 0 \vert \bar{u}u \vert 0 \rangle}{f^2_\pi} \right\vert_{m_\text{q} \to 0} This is often known as the GMOR relation and it explicitly shows that M_\pi=0 in the massless quark limit. The same result also follows from light-front holography. Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero rest masses. However, those masses are almost an order of magnitude smaller than that of the nucleons, roughly \ m_\pi \approx \tfrac{ \sqrt{ v\ m_\text{q}\ } }{\ f_\pi } \approx \sqrt{ m_\text{q}\ }\ 45 MeV, where are the relevant current quark masses, around . The pion is one of the particles that mediate the residual strong interaction between a pair of nucleons. This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the Yukawa potential. The pion, being spinless, has kinematics described by the Klein–Gordon equation. In the terms of quantum field theory, the effective field theory Lagrangian describing the pion-nucleon interaction is called the Yukawa interaction. The nearly identical masses of and indicate that there must be a symmetry at play: this symmetry is called the SU(2) flavour symmetry or isospin. The reason that there are three pions, , and , is that these are understood to belong to the triplet representation or the adjoint representation 3 of SU(2). By contrast, the up and down quarks transform according to the fundamental representation 2 of SU(2), whereas the anti-quarks transform according to the conjugate representation 2*. With the addition of the strange quark, the pions participate in a larger, SU(3), flavour symmetry, in the adjoint representation, 8, of SU(3). The other members of this octet are the four kaons and the eta meson. Pions are pseudoscalars under a parity transformation. Pion currents thus couple to the axial vector current and so participate in the chiral anomaly. == Basic properties ==

Pions, which are mesons with zero spin, are composed of first-generation quarks. In the quark model, an up quark and an anti-down quark make up a , whereas a down quark and an anti-up quark make up the , and these are the antiparticles of one another. The neutral pion is a combination of an up quark with an anti-up quark, or a down quark with an anti-down quark. The two combinations have identical quantum numbers, and hence they are only found in superpositions. The lowest-energy superposition of these is the , which is its own antiparticle. Together, the pions form a triplet of isospin. Each pion has overall isospin () and third-component isospin equal to its charge (). Charged pion decays of the dominant leptonic pion decay. decay in a nuclear emulsion. The positively-charged kaon enters at the top of the image and decays into a meson (a) and two mesons (b and c). The meson interacts with a nucleus in the emulsion at B. The mesons have a mass of and a mean lifetime of . They decay due to the weak interaction. The primary decay mode of a pion, with a branching fraction of 0.999877, is a leptonic decay into a muon and a muon neutrino: \begin{align} \pi^+ &\longrightarrow \mu^+ + \nu_\mu \\[2pt] \pi^- &\longrightarrow \mu^- + \overline\nu_\mu \end{align} The second most common decay mode of a pion, with a branching fraction of 0.000123, is also a leptonic decay into an electron and the corresponding electron antineutrino. This "electronic mode" was discovered at CERN in 1958: \begin{align} \pi^+ &\longrightarrow {\rm e}^+ + \nu_e \\[2pt] \pi^- &\longrightarrow {\rm e}^- + \overline\nu_e \end{align} The suppression of the electronic decay mode with respect to the muonic one is given approximately (up to a few percent effect of the radiative corrections) by the ratio of the half-widths of the pion–electron and the pion–muon decay reactions, R_\pi = \left(\frac{m_e}{m_\mu}\right)^2 \left(\frac{m_\pi^2 - m_e^2}{m_\pi^2 - m_\mu^2}\right)^2 = 1.283 \times 10^{-4} and is a spin effect known as helicity suppression. Its mechanism is as follows: The negative pion has spin zero; therefore the lepton and the antineutrino must be emitted with opposite spins (and opposite linear momenta) to preserve net zero spin (and conserve linear momentum). However, because the weak interaction is sensitive only to the left chirality component of fields, the antineutrino has always left chirality, which means it is right-handed, since for massless anti-particles the helicity is opposite to the chirality. This implies that the lepton must be emitted with spin in the direction of its linear momentum (i.e., also right-handed). If, however, leptons were massless, they would only interact with the pion in the left-handed form (because for massless particles helicity is the same as chirality) and this decay mode would be prohibited. Therefore, suppression of the electron decay channel comes from the fact that the electron's mass is much smaller than the muon's. The electron is relatively massless compared with the muon, and thus the electronic mode is greatly suppressed relative to the muonic one, virtually prohibited. Although this explanation suggests that parity violation is causing the helicity suppression, the fundamental reason lies in the vector-nature of the interaction which dictates a different handedness for the neutrino and the charged lepton. Thus, even a parity conserving interaction would yield the same suppression. Measurements of the above ratio have been considered for decades to be a test of lepton universality. Experimentally, this ratio is . Neutral pion decays The meson has a mass of and a mean lifetime of . == See also ==