Inparticle physics, ameson (/ˈmiːzɒn,ˈmɛzɒn/) is a type ofhadronicsubatomic particle composed of an equal number ofquarks andantiquarks, usually one of each, bound together by thestrong interaction. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly onefemtometre (10−15 m),[1] which is about 0.6 times the size of aproton orneutron. All mesons are unstable, with the longest-lived lasting for only a few tenths of a nanosecond. Heavier mesons decay to lighter mesons and ultimately to stableelectrons,neutrinos andphotons.
Outside the nucleus, mesons appear in nature only as short-lived products of very high-energy collisions between particles made of quarks, such ascosmic rays (high-energy protons and neutrons) andbaryonic matter. Mesons are routinely produced artificially incyclotrons or otherparticle accelerators in the collisions of protons,antiprotons, or other particles.
Higher-energy (more massive) mesons were created momentarily in theBig Bang, but are not thought to play a role in nature today. However, such heavy mesons are regularly created in particle accelerator experiments that explore the nature of the heavier quarks that compose the heavier mesons.
Mesons are part of thehadron particle family, which are defined simply as particles composed of two or more quarks. The other members of the hadron family are thebaryons: subatomic particles composed of odd numbers of valence quarks (at least three), and some experiments show evidence ofexotic mesons, which do not have the conventional valence quark content of two quarks (one quark and one antiquark), but four or more.
Because quarks have a spin1/2, the difference in quark number between mesons and baryons results in conventional two-quark mesons beingbosons, whereas baryons arefermions.
Each type of meson has a correspondingantiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice versa. For example, a positivepion (π+ ) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π− ), is made of one up antiquark and one down quark.
Because mesons are composed of quarks, they participate in both theweak interaction andstrong interaction. Mesons with netelectric charge also participate in theelectromagnetic interaction. Mesons are classified according to their quark content,total angular momentum,parity and various other properties, such asC-parity andG-parity. Although no meson is stable, those of lowermass are nonetheless more stable than the more massive, and hence are easier to observe and study inparticle accelerators or incosmic ray experiments. The lightest group of mesons is less massive than the lightest group of baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher-energy phenomena more readily than do baryons. But mesons can be quite massive: for example, theJ/Psi meson (J/ψ) containing thecharm quark, first seen 1974,[2][3] is about three times as massive as a proton, and theupsilon meson (ϒ) containing thebottom quark, first seen in 1977,[4] is about ten times as massive as a proton.
From theoretical considerations, in 1934Hideki Yukawa[5][6] predicted the existence and the approximate mass of the "meson" as the carrier of thenuclear force that holdsatomic nuclei together.[7] If there were no nuclear force, all nuclei with two or moreprotons would fly apart due toelectromagnetic repulsion.Yukawa called his carrier particle the meson, from μέσοςmesos, theGreek word for "intermediate", because its predicted mass was between that of the electron and that of the proton, which has about 1,836 times the mass of the electron.Yukawa orCarl David Anderson, who discovered themuon, had originally named the particle the "mesotron", but he was corrected by the physicistWerner Heisenberg (whose father was a professor of Greek atLMU Munich). Heisenberg pointed out that there is no "tr" in the Greek word "mesos".[8]
The first candidate for Yukawa's meson, in modern terminology known as themuon, was discovered in 1936 byCarl David Anderson and others in thedecay products of cosmic ray interactions. The"mu meson" had about the right mass to be Yukawa's carrier of the strong nuclear force, but over the course of the next decade, it became evident that it was not the right particle. It was eventually found that the"mu meson" did not participate in the strong nuclear interaction at all, but rather behaved like a heavy version of theelectron, and was eventually classed as alepton like the electron, rather than a meson. In making this choice, physicists decided that properties other than particle mass should control their classification.
There were years of delays in the subatomic particle research duringWorld War II (1939–1945), with most physicists working in applied projects for wartime necessities. When the war ended in August 1945, many physicists gradually returned to peacetime research. The first true meson to be discovered was what would later be called the"pi meson" (or pion). During 1939–1942,Debendra Mohan Bose andBibha Chowdhuri exposedIlfordhalf-tone photographic plates in the high altitude mountainous regions ofDarjeeling, and observed long curved ionizing tracks that appeared to be different from the tracks of alpha particles or protons. In a series of articles published inNature, they identified a cosmic particle having an average mass close to 200 times the mass of electron.[9] This discovery was made in 1947 with improved full-tone photographic emulsion plates, byCecil Powell,Hugh Muirhead,César Lattes, andGiuseppe Occhialini, who were investigating cosmic ray products at theUniversity of Bristol inEngland, based on photographic films placed in the Andes mountains.[10] Some of those mesons had about the same mass as the already-known mu "meson", yet seemed to decay into it, leading physicistRobert Marshak to hypothesize in 1947 that it was actually a new and different meson. Over the next few years, more experiments showed that the pion was indeed involved in strong interactions. The pion (as avirtual particle) is also used as force carrier to model thenuclear force inatomic nuclei (betweenprotons andneutrons). This is an approximation, as the actual carrier of the strong force is believed to be thegluon, which is explicitly used to model strong interaction between quarks. Other mesons, such as the virtualrho mesons are used to model this force as well, but to a lesser extent. Following the discovery of the pion, Yukawa was awarded the 1949Nobel Prize in Physics for his predictions.
For a while in the past, the wordmeson was sometimes used to meanany force carrier, such as"the Z0 meson", which is involved in mediating theweak interaction.[11] However, this use has fallen out of favor, and mesons are now defined as particles composed of pairs of quarks and antiquarks.
Spin (quantum numberS) is avector quantity that represents the "intrinsic"angular momentum of a particle. It comes in increments of1/2ħ.[A]
Quarks arefermions—specifically in this case, particles having spin1/2(S =1/2). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length1/2, and has two spin projections, either(Sz = +1/2 orSz =−+1/2). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of lengthS = 1, with three possible spin projections(Sz = +1,Sz = 0, andSz = −1), and their combination is called avector meson orspin-1 triplet. If two quarks have oppositely aligned spins, the spin vectors add up to make a vector of lengthS = 0, and only one spin projection(Sz = 0), called ascalar meson orspin-0 singlet. Because mesons are made of one quark and one antiquark, they are found in triplet and singlet spin states. The latter are calledscalar mesons orpseudoscalar mesons, depending on their parity (see below).
There is another quantity of quantizedangular momentum, called theorbital angular momentum (quantum numberL), that is the angular momentum due to quarks orbiting each other, and also comes in increments of 1 ħ. The total angular momentum (quantum numberJ) of a particle is the combination of the two intrinsic angular momentums (spin) and the orbital angular momentum. It can take any value fromJ = |L −S| up toJ = |L +S|, in increments of 1.
Particle physicists are most interested in mesons with no orbital angular momentum (L = 0), therefore the two groups of mesons most studied are theS = 1;L = 0 andS = 0;L = 0, which corresponds toJ = 1 andJ = 0, although they are not the only ones. It is also possible to obtainJ = 1 particles fromS = 0 andL = 1. How to distinguish between theS = 1,L = 0 andS = 0,L = 1 mesons is an active area of research inmeson spectroscopy.[12]
P-parity is left-right parity, or spatial parity, and was the first of several "parities" discovered, and so is often called just"parity". If the universe were reflected in a mirror, most laws of physics would be identical—things would behave the same way regardless of what we call "left" and what we call "right". This concept of mirror reflection is calledparity (P).Gravity, theelectromagnetic force, and thestrong interaction all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said toconserve parity (P-symmetry). However, theweak interaction doesdistinguish "left" from "right", a phenomenon calledparity violation (P-violation).
Based on this, one might think that, if thewavefunction for each particle (more precisely, thequantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: In order for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to havenegative orodd parity (P = −1, or alternativelyP = −), whereas the other particles are said to havepositive oreven parity (P = +1, or alternativelyP = +).
For mesons, parity is related to the orbital angular momentum by the relation:[13][14]
where theL is a result of the parity of the correspondingspherical harmonic of thewavefunction. The "+1" comes from the fact that, according to theDirac equation, a quark and an antiquark have opposite intrinsic parities. Therefore, the intrinsic parity of a meson is the product of the intrinsic parities of the quark (+1) and antiquark (−1). As these are different, their product is −1, and so it contributes the "+1" that appears in the exponent.
As a consequence, all mesons with no orbital angular momentum (L = 0) have odd parity (P = −1).
C-parity is only defined for mesons that are their own antiparticle (i.e. flavourless mesons). It represents whether or not the wavefunction of the meson remains the same under the interchange of their quark with their antiquark.[15] If
then, the meson is "C even" (C = +1). On the other hand, if
then the meson is "C odd" (C = −1).
C-parity rarely is studied on its own, but more commonly in combination with P-parity intoCP-parity.CP-parity was originally thought to be conserved, but was later found to be violated on rare occasions inweak interactions.[16][17][18]
G-parity is a generalization of theC-parity. Instead of simply comparing the wavefunction after exchanging quarks and antiquarks, it compares the wavefunction after exchanging the meson for the corresponding antimeson, regardless of quark content.[19]
If
then, the meson is "G even" (G = +1). On the other hand, if
Combinations of oneu,d, ors quark and oneu,d, ors antiquark inJP = 0− configuration form anonet. Combinations of oneu,d, ors quark and oneu,d, ors antiquark inJP = 1− configuration also form a nonet.
The concept of isospin was first proposed byWerner Heisenberg in 1932 to explain the similarities between protons and neutrons under thestrong interaction.[20] Although they had different electric charges, their masses were so similar that physicists believed that they were actually the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbedisospin byEugene Wigner in 1937.[21]
When the first mesons were discovered, they too were seen through the eyes of isospin and so the three pions were believed to be the same particle, but in different isospin states.
The mathematics of isospin was modeled after the mathematics ofspin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a "charged state". Because the "pion particle" had three "charged states", it was said to be of isospinI = 1 . Its "charged states"π+ ,π0 , andπ− , corresponded to the isospin projectionsI3 = +1 ,I3 = 0 , andI3 = −1 respectively. Another example is the "rho particle", also with three charged states. Its "charged states"ρ+ ,ρ0 , andρ− , corresponded to the isospin projectionsI3 = +1 ,I3 = 0 , andI3 = −1 respectively.
This belief lasted untilMurray Gell-Mann proposed thequark model in 1964 (containing originally only theu,d, ands quarks).[22] The success of the isospin model is now understood to be an artifact of the similar masses of theu andd quarks. Because theu andd quarks have similar masses, particles made of the same number of them also have similar masses.
The exactu andd quark composition determines the charge, becauseu quarks carry charge++2/3e whereasd quarks carry charge−+1/3e. For example, the three pions all have different charges
After thequark model was adopted, physicists noted that the isospin projections were related to the up and down quark content of particles by the relation
where then-symbols are the count of up and down quarks and antiquarks.
In the "isospin picture", the three pions and three rhos were thought to be the different states of two particles. However, in the quark model, the rhos are excited states of pions. Isospin, although conveying an inaccurate picture of things, is still used to classify hadrons, leading to unnatural and often confusing nomenclature.
Because mesons are hadrons, the isospin classification is also used for them all, with the quantum number calculated by addingI3 = +1/2 for each positively charged up-or-down quark-or-antiquark (up quarks and down antiquarks), andI3 = −1/2 for each negatively charged up-or-down quark-or-antiquark (up antiquarks and down quarks).
Thestrangenessquantum numberS (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower (more negative) the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds nonet figures). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb nonets. Because only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers only works well for the nonets made of one u, one d and one other quark and breaks down for the other nonets (for example ucb nonet). If the quarks all had the same mass, their behaviour would be calledsymmetric, because they would all behave in exactly the same way with respect to the strong interaction. However, as quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to bebroken.
whereS,C,B′, andT represent thestrangeness,charm,bottomness andtopness flavour quantum numbers respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
meaning that the Gell-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:
Mesons are classified into groups according to theirisospin (I),total angular momentum (J),parity (P),G-parity (G) orC-parity (C) when applicable, andquark (q) content. The rules for classification are defined by theParticle Data Group, and are rather convoluted.[24] The rules are presented below, in table form for simplicity.
Mesons are classified into types according to their spin configurations. Some specific configurations are given special names based on the mathematical properties of their spin configuration.
Flavourless mesons are mesons made of pair of quark and antiquarks of the same flavour (all theirflavour quantum numbers are zero:S = 0,C = 0,B′ = 0,T = 0).[i] The rules for flavourless mesons are:[24]
^For the purpose of nomenclature, the isospin projectionI3 is treated as if it werenot a flavour quantum number. This means that the charged pion-like mesons (π±,a±,b±, andρ± mesons) follow the rules of flavourless mesons, even if they aren't truly "flavourless".
Flavoured mesons are mesons made of pair of quark and antiquarks of different flavours. The rules are simpler in this case: The main symbol depends on the heavier quark, the superscript depends on the charge, and the subscript (if any) depends on the lighter quark. In table form, they are:[24]
^abFor the purpose of nomenclature, the isospin projectionI3 is treated as if it werenot a flavour quantum number. This means that the charged pion-like mesons (π±,a±,b±, andρ± mesons) follow the rules of flavourless mesons, even if they aren't truly "flavourless".
In addition
IfJP is in the "normal series" (i.e.,JP = 0+, 1−, 2+, 3−, ...), a superscript ∗ is added.
If the meson is not pseudoscalar (JP = 0−) or vector (JP = 1−),J is added as a subscript.
When thespectroscopic state of the meson is known, it is added in parentheses.
When the spectroscopic state is unknown, mass (inMeV/c2) is added in parentheses.
When the meson is in itsground state, nothing is added in parentheses.
There is experimental evidence for particles that arehadrons (i.e., are composed of quarks) and are color-neutral with zero baryon number, and thus by conventional definition are mesons. Yet, these particles do not consist of a single quark/antiquark pair, as all the other conventional mesons discussed above do. A tentative category for these particles isexotic mesons.
There are at least five exotic meson resonances that have been experimentally confirmed to exist by two or more independent experiments. The most statistically significant of these is theZ(4430), discovered by theBelle experiment in 2007 and confirmed byLHCb in 2014. It is a candidate for being atetraquark: a particle composed of two quarks and two antiquarks.[26] See the main article above for other particle resonances that are candidates for being exotic mesons.
[a]^ Makeup inexact due to non-zero quark masses. [b]^ PDG reports theresonance width (Γ). Here the conversionτ = ħ/Γ is given instead. [c]^Strongeigenstate. No definite lifetime (seekaon notes below) [d]^ The mass of theK0 L andK0 S are given as that of theK0 . However, it is known that a difference between the masses of theK0 L andK0 S on the order of2.2×10−11 MeV/c2 exists.[36] [e]^Weakeigenstate. Makeup is missing smallCP–violating term (seenotes on neutral kaons below).
[f]^ PDG reports theresonance width (Γ). Here the conversionτ = ħ/Γ is given instead. [g]^ The exact value depends on the method used. See the given reference for detail.
Note that these issues also exist in principle for other neutral,flavored mesons; however, the weak eigenstates are considered separate particles only for kaons because of their dramatically different lifetimes.[55]
^Theħ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ħ". In some systems ofnatural units,ħ is chosen to be 1, and therefore drops out of equations. The remainder of this article uses the "assumeħ units" convention for all types of spin.
