Pion

This article explains the Pion particle. The artillery gun is explained under 2S7 .

Pion (π + )
classification
Boson Hadron Meson
properties
electric charge	1  e (+1.602 10 −19  C )
Resting energy	(139.57039 ± 0.00018)  MeV
Spin parity	0 -
Isospin	1 (z component +1)
average lifespan	(2.6033 ± 0.0005) · 10 −8  s
Quark composition	1 up and 1 anti-down

π 0
classification
Boson Hadron Meson
properties
electric charge	neutral
Resting energy	(134.9768 ± 0.0005)  MeV
Spin parity	0 -
Isospin	1 (z component 0)
average lifespan	(8.52 ± 0.18) 10 −17  s
Quark composition	Superposition of u u and d d

Pions or mesons (formerly also known as Yukawa particles , as predicted by Hideki Yukawa ) are the lightest mesons . According to the standard model of particle physics, they contain two valence quarks and are therefore usually no longer regarded as elementary particles today. Like all mesons, they are bosons , so they have an integral spin . Their parity is negative. ${\displaystyle \pi }$

There is a neutral pion and two charged pions: and its antiparticle . All three are unstable and disintegrate due to weak or electromagnetic interaction . ${\displaystyle \pi ^{0}}$ ${\displaystyle \pi ^{+}}$ ${\displaystyle \pi ^{-}}$

construction

This is a combination of an up quark and an anti-down quark (antiquarks are indicated by an overline): ${\displaystyle \pi ^{+}}$ ${\displaystyle u}$ ${\displaystyle {\bar {d}}}$

${\displaystyle |\pi ^{+}\rangle =|u{\bar {d}}\rangle }$,

its antiparticle is a combination of a down quark and an anti-up quark : ${\displaystyle \pi ^{-}}$ ${\displaystyle d}$ ${\displaystyle {\bar {u}}}$

${\displaystyle |\pi ^{-}\rangle =|d{\bar {u}}\rangle }$.

Both have a mass of 139.6 MeV / c². The current genauesten measurements of its mass based on X-ray transitions in exotic atoms that take an electron one possess. The service life of the is 2.6 · 10 ⁻⁸  s. ${\displaystyle \pi ^{-}}$ ${\displaystyle \pi ^{\pm }}$

This is a quantum mechanical superposition of a - and a - combination, i.e. H. two quarkonia . The following applies: ${\displaystyle \pi ^{0}}$ ${\displaystyle u{\bar {u}}}$ ${\displaystyle d{\bar {d}}}$

${\displaystyle |\pi ^{0}\rangle ={\frac {1}{\sqrt {2}}}{\Big [}|u{\bar {u}}\rangle -|d{\bar {d}}\rangle {\Big ]}}$

while the orthogonal state ,, is mixed with the eta-mesons . ${\displaystyle {\frac {1}{\sqrt {2}}}{\Big [}|u{\bar {u}}\rangle +|d{\bar {d}}\rangle {\Big ]}}$ ${\displaystyle |s{\bar {s}}\rangle }$

At 135.0 MeV / c², its mass is only slightly smaller than that of the charged pions. Since it decays through the much stronger electromagnetic interaction, its service life of 8.5 · 10 ⁻¹⁷  s is about 10 orders of magnitude shorter.

Due to a freely selectable phase, the three wave functions can also be written in the seldom used form , and . This then corresponds to the Condon-Shortley Convention. ${\displaystyle |\pi ^{+}\rangle =|u{\bar {d}}\rangle }$ ${\displaystyle |\pi ^{-}\rangle =-|{\bar {u}}d\rangle }$ ${\displaystyle |\pi ^{0}\rangle ={\frac {1}{\sqrt {2}}}{\Big [}|d{\bar {d}}\rangle -|u{\bar {u}}\rangle {\Big ]}}$

Decays

The different lifetimes are due to the different decay channels:

the charged pions decay to 99.98770 (4)% due to the weak interaction into a muon and a muon neutrino :

${\displaystyle \,\pi ^{+}\to \mu ^{+}+\nu _{\mu }}$

${\displaystyle \,\pi ^{-}\to \mu ^{-}+{\overline {\nu }}_{\mu }}$

The actually energetically more favorable decay into an electron and the associated electron neutrino is strongly suppressed for reasons of helicity .

In contrast, the decay of the neutral pion takes place by means of the stronger and therefore faster electromagnetic interaction. The end products here are usually two photons ${\displaystyle \gamma }$

${\displaystyle \pi ^{0}\to 2\gamma }$

with a probability of 98.823 (32)% or one positron e ⁺ , one electron e ^- and one photon

${\displaystyle \pi ^{0}\to e^{+}+e^{-}+\gamma }$

with a probability of 1.174 (35)%.

Because of its short lifetime of 8.5 · 10 ⁻¹⁷  s, the neutral pion is detected in experiments by observing the two decay photons in coincidence .

Research history

Hideki Yukawa (1949)

The pion was predicted as an exchange particle of nuclear power in 1934/35 by Hideki Yukawa in Japan, who was awarded the Nobel Prize for it in 1949. The first 'meson', initially mistaken for the Yukawa particle and later referred to as the muon , was found by Carl D. Anderson and Seth Neddermeyer in cosmic radiation in 1936 (“meson” was then the name for any charged particle heavier than an electron, but lighter as a proton ). The demarcation to the pion only emerged in the 1940s (first postulated by Y. Tanikawa and Shoichi Sakata in Japan in 1942). Cecil Powell , Giuseppe Occhialini and César Lattes at the H. H. Wills Physical Laboratory in Bristol discovered pions in the cosmic radiation next to muons and investigated their properties. Powell received the Nobel Prize in Physics for this in 1950. This was, however, as only later became known in 1947 earlier something about Donald H. Perkins discovered in cosmic rays. In 1948, pions were artificially detected in accelerators for the first time (Lattes). ${\displaystyle \pi ^{-}}$

Mass comparison with nucleons

When comparing the masses of the pions, which each consist of two quarks (mesons), with the masses of the proton and the neutron (the nucleons ), which both consist of three quarks ( baryons ), it is noticeable that the proton and neutron are each far are over 50% heavier than the pions; the proton mass is almost seven times that of the pion mass. The mass of a proton or a neutron is not obtained by simply adding the masses of their three current quarks, but also by the presence of the gluons responsible for binding the quarks and the so-called sea ​​quarks . These virtual quark-antiquark pairs arise and disappear in the nucleon within the limits of Heisenberg's uncertainty relation and contribute to the observed constituent quark mass .

The Goldstone theorem provides an explanation for the much lower mass : The pions are the quasi-Goldstone bosons of the spontaneously (and moreover explicitly) broken chiral symmetry in quantum chromodynamics .

The pion exchange model

The pions can take on the role of the exchange particles in an effective theory of the strong interaction ( Sigma model ), which describes the binding of nucleons in the atomic nucleus . (This is analogous to the van der Waals forces , which act between neutral molecules, but are not themselves an elementary force; they are based on the electromagnetic interaction .)

This theory, first proposed by Hideki Yukawa and Ernst Stueckelberg , is only valid within a limited energy range, but allows simpler calculations and clearer representations. For example, the nuclear forces mediated by the pions can be represented in compact form using the Yukawa potential : this potential has a repulsive character at small distances (mainly mediated via ω mesons ), at medium distances it has a strongly attractive effect (due to 2-meson exchange, analogous to the 2-photon exchange of the Van der Waals forces), and at large distances it shows an exponentially decaying character (exchange of individual mesons).

Range

In this exchange model, the finite range of the interaction between the nucleons follows from the non-zero mass of the pions. The maximum range of the interaction can be estimated via ${\displaystyle r_{0}}$

• the relationship , ${\displaystyle r_{0}=c\cdot t}$
• the energy-time uncertainty relation , ${\displaystyle \Delta t\Delta E\geq {\frac {\hbar }{2}}\quad \Leftrightarrow \quad \Delta t\geq {\frac {\hbar }{2\Delta E}}\quad \left(\Rightarrow r_{0}=c\cdot {\frac {\hbar }{2E}}\right)}$
• Einstein's equivalence of energy and mass , to: ${\displaystyle E=mc^{2}\quad \Leftrightarrow \quad {\frac {c}{E}}={\frac {1}{mc}}}$

${\displaystyle r_{0}={\frac {\hbar }{2mc}}}$

It is of the order of magnitude of the Compton wavelength of the exchange particle. In the case of the pions, values ​​of a few Fermi (10 ⁻¹⁵  m) are obtained. This range, which is short compared to the size of the nucleus, is reflected in the constant binding energy per nucleon, which in turn forms the basis for the droplet model.

Sample process

Exchange of a virtual pion between proton and neutron

The exchange of a charged pion between a proton and a neutron will be described as an example:

1. A u-quark dissolves from the proton.
2. Because of the confinement , no free quarks can exist. Therefore, a d- d pair is formed.
3. The d-quark remains in the former proton and turns it into a neutron. The u quark and the d quark form a free π ⁺ meson.
4. This meson meets a neutron. A d quark of the neutron annihilates with the d quark of the π ⁺ meson.
5. The initial situation is restored, one proton and one neutron remain.

literature

• WM Yao et al. a: Review of Particle Physics. In: Journal of Physics G: Nuclear and Particle Physics. 33, 2006, pp. 1–1232, doi : 10.1088 / 0954-3899 / 33/1/001 .
• J. Steinberger, W. Panofsky, J. Steller: Evidence for the Production of Neutral Mesons by Photons. In: Physical Review. 78, 1950, pp. 802-805, doi : 10.1103 / PhysRev . 78.802 . (Proof of the neutral pion).

See also

• List of mesons

Individual evidence

1. ↑ ^{a b} The information on the particle properties (info box) are, unless otherwise stated, taken from: PAZyla et al. ( Particle Data Group ): 2020 Review of Particle Physics. In: Prog.Theor.Exp.Phys.2020,083C01 (2020). Particle Data Group, accessed July 26, 2020 . 
2. ↑ D. Perkins: High Energy Physics. Addison-Wesley, 1991.
3. ^ Yukawa: On the interaction of elementary particles I. In: Proceedings of the Physico-Mathematical Society of Japan. 3rd Series, Volume 17, 1935, pp. 48-57.
4. ^ CMG Lattes, H. Muirhead, GPS Occhialini, CF Powell: Processes involving charged mesons. In: Nature. 159 (1947) 694-697.
5. ↑ CMG Lattes, GPS Occhialini, CF Powell: A determination of the ratio of the masses of pi-meson and mu-meson by the method of grain-counting. In: Proceedings of the Physical Society. 61 (1948) pp. 173-183.