List of mesons
Encyclopedia
- This list is of all known and predicted scalarScalar mesonIn high energy physics, a scalar meson is a meson with total spin 0 and even parity . Compare to pseudoscalar meson....
, pseudoscalarPseudoscalar mesonIn high energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity . Compare to scalar meson.Pseudoscalar mesons are commonly seen in proton-proton scattering and proton-antiproton annihilation...
and vectorVector mesonIn high energy physics, a vector meson is a meson with total spin 1 and odd parity . Compare to a pseudovector meson, which has a total spin 1 and even parity....
mesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s. See list of particles for a more detailed list of particles found in particle physicsParticle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
.
Mesons are unstable subatomic particle
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...
s composed of one quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
and one antiquark. They are part of the hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
particle family – particles made of quarks. The other members of the hadron family are the baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
s – subatomic particles composed of three quarks. The main difference between mesons and baryons is that mesons have integer spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
(thus are boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s) while baryons are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s (half-integer spin). Because mesons are bosons
Spin-statistics theorem
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum...
, the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
does not apply to them. Because of this, they can act as force mediating particle
Force carrier
In particle physics, quantum field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type...
s on short distances, and thus play a part in processes such as the nuclear interaction.
Since mesons are composed of quarks, they participate in both the weak
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
and strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
s. Mesons with net electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
also participate in the electromagnetic interaction. They are classified according to their quark content, total angular momentum, parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
, and various other properties such as C-parity and G-parity
G-parity
In theoretical physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles....
. While no meson is stable, those of lower mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
s or in cosmic ray
Cosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...
experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and will exhibit higher energy phenomena sooner than baryons would. For example, the charm quark was first seen in the J/Psi meson in 1974, and the bottom quark in the upsilon meson in 1977.
Each meson has a corresponding antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
(antimeson) where quarks are replaced by their corresponding antiquarks and vice-versa. For example, a positive pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion , is made of one up antiquark and one down quark. Some experiments show the evidence of tetraquark
Tetraquark
In particle physics a tetraquark is a hypothetical meson composed of four valence quarks. In principle, a tetraquark state may be allowed in quantum chromodynamics, the modern theory of strong interactions. However, there has been no confirmed report of a tetraquark state to date...
s – "exotic" mesons made of two quarks and two antiquark, but the particle physics community as a whole does not view their existence as likely, although still possible.
Summary table
| LIGHT UNFLAVOURED(S=C=B=0) | STRANGE(S=±1, C=B=0) | CHARMED(C=±1, B=0) | BOTTOM(B=±1) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| IG(JPC) | IG(JPC) | IG(JP) | IG(JP) | IG(JPC) | |||||
| π± | 1−(0−) | π2(1670) | 1−(2−+) | K± | ½(0−) | D± | ½(0−) | B± | ½(0−) |
| π0 | 1−(0−+) | φ(1680) | 0−(1−−) | K0 | ½(0−) | D0 | ½(0−) | B0 | ½(0−) |
| η | 0+(0−+) | ρ3(1690) | 1+(3−−) | K0S | ½(0−) | D*(2007)0 | ½(1−) | B±/B0 Admixture | |
| f0(600) | 0+(0++) | ρ(1700) | 1+(1−−) | K0L | ½(0−) | D*(2010)± | ½(1−) | B±/B0/B0s/b-baryonAdmixture | |
| ρ(770) | 1+(1−−) | a2(1700) | 1−(2++) | K*0(800) | ½(0+) | D*0(2400)0 | ½(0+) | ||
| ω(782) | 0−(1−−) | f0(1710) | 0+(0++) | K*(892) | ½(1−) | D*0(2400)± | ½(0+) | B* | ½(1−) |
| η'(958) | 0+(0−+) | η(1760) | 0+(0−+) | K1(1270) | ½(1+) | D1(2420)0 | ½(1+) | B*J(5732) | ?(??) |
| f0(980) | 0+(0++) | π(1800) | 1−(0−+) | K1(1400) | ½(1+) | D1(2420)± | ½(??) | B1(5721)0 | ½(1+) |
| a0(980) | 1−(0++) | f2(1810) | 0+(2++) | K*(1410) | ½(1−) | D1(2430)0 | ½(1+) | B*2(5747)0 | ½(2+) |
| φ(1020) | 0−(1−−) | X(1835) | ??(?−+) | K*0(1430) | ½(0+) | D*2(2460)0 | ½(2+) | BOTTOM STRANGE | |
| h1(1170) | 0−(1+−) | φ3(1850) | 0−(3−−) | K*2(1430) | ½(2+) | D*2(2460)± | ½(2+) | B0s | 0(0−) |
| b1(1235) | 1+(1+−) | η2(1870) | 0+(2−+) | K(1460) | ½(0−) | D*(2640)± | ½(??) | B*s | 0(1−) |
| a1(1260) | 1−(1++) | π2(1880) | 1−(2−+) | K2(1580) | ½(2−) | CHARMED STRANGE | Bs1(5830)0 | ½(1+) | |
| f2(1270) | 0+(2++) | ρ(1900) | 1+(1−−) | K(1630) | ½(??) | D±s | 0(0−) | B*s2(5840)0 | ½(2+) |
| f1(1285) | 0+(1++) | f2(1910) | 0+(2++) | K1(1650) | ½(1+) | D*±s | 0(??) | B*sJ(5850) | ?(??) |
| η(1295) | 0+(0−+) | f2(1950) | 0+(2++) | K*(1680) | ½(1−) | D*s0(2317)± | 0(0+) | BOTTOM CHARMED | |
| π(1300) | 1−(0−+) | ρ3(1990) | 1+(3−−) | K2(1770) | ½(2−) | Ds1(2460)± | 0(1+) | B±c | 0(0−) |
| a2(1320) | 1−(2++) | f2(2010) | 0+(2++) | K*3(1780) | ½(3−) | Ds1(2536)± | 0(1+) | BOTTOM BOTTOM | |
| f0(1370) | 0+(0++) | f0(2020) | 0+(0++) | K2(1820) | ½(2−) | Ds2(2573) | 0(??) | ηb(1S) | 0+(0−+) |
| h1(1380) | ?−(1+−) | a4(2040) | 1−(4++) | K(1830) | ½(0−) | D*s1(2700)± | 0(1−) | Υ(1S) | 0−(1−−) |
| π1(1400) | 1−(1−+) | f4(2050) | 0+(4++) | K*0(1950) | ½(0+) | D*sJ(2860)± | 0(??) | χb0(1P) | 0+(0++) |
| η(1405) | 0+(0−+) | π2(2100) | 1−(2−+) | K*2(1980) | ½(2+) | DsJ(3040)± | 0(??) | χb1(1P) | 0+(1++) |
| f1(1420) | 0+(1++) | f0(2100) | 0+(0++) | K*4(2045) | ½(4+) | CHARMED CHARMED | χb2(1P) | 0+(2++) | |
| ω(1420) | 0−(1−−) | f2(2150) | 0+(2++) | K2(2250) | ½(2−) | ηc(1S) | 0+(0−+) | Υ(2S) | 0−(1−−) |
| f2(1430) | 0+(2++) | ρ(2150) | 1+(1−−) | K3(2320) | ½(3+) | J/ψ(1S) | 0−(1−−) | Υ(1D) | 0−(2−−) |
| a0(1450) | 1−(0++) | φ(2150) | 0−(1−−) | K*5(2380) | ½(5−) | χc0(1P) | 0+(0++) | χb0(2P) | 0+(0++) |
| ρ(1450) | 1+(1−−) | f0(2200) | 0+(2++or 4++) | K4(2500) | ½(4−) | χc1(1P) | 0+(1++) | χb1(2P) | 0+(1++) |
| η(1450) | 0+(0−+) | K(3100) | ??(???) | hc(1P) | ??(1+−) | χb2(2P) | 0+(2++) | ||
| f0(1500) | 0+(0++) | η(2225) | 0+(0−+) | χc2(1P) | 0+(2++) | Υ(3S) | 0−(1−−) | ||
| f1(1510) | 0+(1++) | ρ3(2250) | 1+(3−−) | ηc(2S) | 0+(0−+) | Υ(4S) | 0−(1−−) | ||
| f'2(1525) | 0+(2++) | f2(2300) | 0+(2++) | ψ(2S) | 0−(1−−) | Υ(10860) | 0−(1−−) | ||
| f2(1565) | 0+(2++) | f4(2300) | 0+(4++) | ψ(3770) | 0−(1−−) | Υ(11020) | 0−(1−−) | ||
| ρ(1570) | 1+(1−−) | f0(2330) | 0+(0++) | X(3872) | 0?(??+) | ||||
| h1(1595) | 0−(1+−) | f2(2340) | 0+(2++) | χc2(2P) | 0+(2++) | ||||
| π1(1600) | 1−(1−+) | ρ5(2350) | 1+(5−−) | X(3940) | ??(???) | ||||
| a1(1640) | 1−(1++) | a6(2450) | 1−(6++) | X(3945) | 0+(??+) | ||||
| f2(1640) | 0+(2++) | f6(2510) | 0+(6++) | ψ(4040) | 0−(1−−) | ||||
| η2(1645) | 0+(2−+) | X(4050)± | ?(??) | ||||||
| ω(1650) | 0−(1−−) | X(4140) | 0+(??+) | ||||||
| ω3(1670) | 0−(3−−) | ψ(4160) | 0−(1−−) | ||||||
| X(4160) | ??(???) | ||||||||
| X(4250)± | ?(??) | ||||||||
| X(4260) | ??(1−−) | ||||||||
| X(4350) | 0+(??+) | ||||||||
| X(4360) | ??(1−−) | ||||||||
| ψ(4415) | 0−(1−−) | ||||||||
| X(4430)± | ?(??) | ||||||||
| X(4660) | ??(1−−) | ||||||||
Because this table was initially derived from published results and many of those results were preliminary, as many as 64 of the mesons in the above table may not exist or have the wrong mass or quantum numbers.
List of mesons
These lists detail all known and predicted pseudoscalar (JPParity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
= 0−) and vector (JP
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
= 1−) mesons.
The symbols encountered in these lists are: I (isospin
Isospin
In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
), J (total angular momentum), P (parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
), C (C-parity), G (G-parity
G-parity
In theoretical physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles....
), u (up quark
Up quark
The up quark or u quark is the lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the down quark, forms the neutrons and protons of atomic nuclei...
), d (down quark
Down quark
The down quark or d quark is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. It, along with the up quark, forms the neutrons and protons of atomic nuclei...
), s (strange quark
Strange quark
The strange quark or s quark is the third-lightest of all quarks, a type of elementary particle. Strange quarks are found in hadrons, which are subatomic particles. Example of hadrons containing strange quarks include kaons , strange D mesons , Sigma baryons , and other strange particles...
), c (charm quark
Charm quark
The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
), b (bottom quark
Bottom quark
The bottom quark, also known as the beauty quark, is a third-generation quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
), Q (charge
Charge (physics)
In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.-Formal definition:...
), B (baryon number), S (strangeness
Strangeness
In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
), C (charm), and B′ (bottomness
Bottomness
In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
), as well as a wide array of subatomic particles (hover for name).
The properties and quark content of the particles are tabulated below; for the corresponding antiparticles, simply change quarks into antiquarks (and vice-versa) and flip the sign of Q, B, S, C, and B′. Particles with † next to their names have been predicted by the standard model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
but not yet observed. Values in red have not been firmly established by experiments, but are predicted by the quark model
Quark model
In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons....
and are consistent with the measurements.
Pseudoscalar mesons
| Particle name | Particle symbol |
Antiparticle symbol |
Quark content |
Rest mass (MeV/c Speed of light The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time... 2) |
I Isospin In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number... G |
JP Parity (physics) In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:... C |
S Strangeness In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time... |
C | B' Bottomness In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a... |
Mean lifetime (s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... ) |
Commonly decays to (>5% of decays) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Pion | 1− | 0− | 0 | 0 | 0 | ||||||
| Pion | Self |  |
1− | 0−+ | 0 | 0 | 0 | ||||
| Eta meson | Self | 0+ | 0−+ | 0 | 0 | 0 | or |
||||
| Eta prime meson | (958) | Self |  |
0+ | 0−+ | 0 | 0 | 0 | |
||
| Charmed eta meson | (1S) | Self | 0+ | 0−+ | 0 | 0 | 0 | See decay modes | |||
| Bottom eta meson | (1S) | Self | 0+ | 0−+ | 0 | 0 | 0 | Unknown | See decay modes | ||
| Kaon | 0− | 1 | 0 | 0 | |
||||||
| Kaon | 0− | 1 | 0 | 0 | |||||||
| K-Short | Self |  |
0− | (*) | 0 | 0 | |
||||
| K-Long | Self |  |
0− | (*) | 0 | 0 | |
||||
| D meson | 0− | 0 | +1 | 0 | See decay modes | ||||||
| D meson | 0− | 0 | +1 | 0 | See decay modes | ||||||
| strange D meson | 0 | 0− | +1 | +1 | 0 | See decay modes | |||||
| B meson | 0− | 0 | 0 | +1 | See decay modes | ||||||
| B meson | 0− | 0 | 0 | +1 | See decay modes | ||||||
| Strange B meson | 0 | 0− | −1 | 0 | +1 | See decay modes | |||||
| Charmed B meson | 0 | 0− | 0 | +1 | +1 | See decay modes |
[a] Makeup inexact due to non-zero quark masses.
[b] PDG reports the resonance width (Γ). Here the conversion τ = is given instead.
[c] Strong eigenstate. No definite lifetime (see kaon notes below)
[d] The mass of the and are given as that of the . However, it is known that a difference between the masses of the and on the order of exists.
[e] Weak eigenstate. Makeup is missing small CP–violating
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
term (see notes on neutral kaons below).
Vector mesons
| Particle name | Particle symbol |
Antiparticle symbol |
Quark content |
Rest mass (MeV/c Speed of light The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time... 2) |
I Isospin In physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number... G |
JP Parity (physics) In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:... C |
S Strangeness In particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time... |
C | B' Bottomness In physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a... |
Mean lifetime (s Second The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock.... ) |
Commonly decays to (>5% of decays) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Charged rho meson | (770) | (770) | 1+ | 1− | 0 | 0 | 0 | ||||
| Neutral rho meson | (770) | Self |  |
1+ | 1−− | 0 | 0 | 0 | |||
| Omega meson | (782) | Self |  |
0− | 1−− | 0 | 0 | 0 | |
||
| Phi meson | (1020) | Self | 0− | 1−− | 0 | 0 | 0 | |
|||
| J/Psi | Self | 0− | 1−− | 0 | 0 | 0 | See (1S) decay modes | ||||
| Upsilon meson | (1S) | Self | 0− | 1−− | 0 | 0 | 0 | See (1S) decay modes | |||
| Kaon | 1− | 1 | 0 | 0 | See (892) decay modes | ||||||
| Kaon | 1− | 1 | 0 | 0 | See (892) decay modes | ||||||
| D meson | (2010) | (2010) | 1− | 0 | +1 | 0 | |
||||
| D meson | (2007) | (2007) | 1− | 0 | +1 | 0 | |
||||
| strange D meson | 0 | 1− | +1 | +1 | 0 | |
|||||
| B meson | 1− | 0 | 0 | +1 | Unknown | ||||||
| B meson | 1− | 0 | 0 | +1 | Unknown | ||||||
| Strange B meson | 0 | 1− | −1 | 0 | +1 | Unknown | |||||
| Charmed B meson† | Unknown | 0 | 1− | 0 | +1 | +1 | Unknown | Unknown | |||
[f] PDG reports the resonance width (Γ). Here the conversion τ = is given instead.
[g] The exact value depends on the method used. See the given reference for detail.
See also
- List of baryons
- List of particles
- Timeline of particle discoveriesTimeline of particle discoveriesThis is a timeline of subatomic particle discoveries, including all particles thus far discovered which appear to be elementary given the best available evidence...
External links
- Particle Data Group – The Review of Particle Physics (2008)
- Mesons made thinkable, an interactive visualisation allowing physical properties to be compared