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physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): :\mathbf: \beginx\\y\\z\end \mapsto \begin-x\\-y\\-z\end. It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...
s, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions. A matrix representation of P (in any number of dimensions) has
determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if a ...
equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is ''not'' a parity transformation; it is the same as a 180° rotation. In quantum mechanics, wave functions that are unchanged by a parity transformation are described as
even Even may refer to: General * Even (given name), a Norwegian male personal name * Even (surname) * Even (people), an ethnic group from Siberia and Russian Far East **Even language, a language spoken by the Evens * Odd and Even, a solitaire game wh ...
functions, while those that change sign under a parity transformation are odd functions.


Simple symmetry relations

Under rotations, classical geometrical objects can be classified into
scalars Scalar may refer to: * Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...
, vectors, and
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
s of higher rank. In classical physics, physical configurations need to transform under representations of every symmetry group. Quantum theory predicts that states in a
Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...
do not need to transform under representations of the group of rotations, but only under
projective representation In the field of representation theory in mathematics, a projective representation of a group ''G'' on a vector space ''V'' over a field ''F'' is a group homomorphism from ''G'' to the projective linear group \mathrm(V) = \mathrm(V) / F^*, where ...
s. The word ''projective'' refers to the fact that if one projects out the phase of each state, where we recall that the overall phase of a quantum state is not observable, then a projective representation reduces to an ordinary representation. All representations are also projective representations, but the converse is not true, therefore the projective representation condition on quantum states is weaker than the representation condition on classical states. The projective representations of any group are isomorphic to the ordinary representations of a central extension of the group. For example, projective representations of the 3-dimensional rotation group, which is the special orthogonal group SO(3), are ordinary representations of the special unitary group SU(2). Projective representations of the rotation group that are not representations are called spinors and so quantum states may transform not only as tensors but also as spinors. If one adds to this a classification by parity, these can be extended, for example, into notions of *''scalars'' () and '' pseudoscalars'' () which are rotationally invariant. *''vectors'' () and ''axial vectors'' (also called ''
pseudovector In physics and mathematics, a pseudovector (or axial vector) is a quantity that is defined as a function of some vectors or other geometric shapes, that resembles a vector, and behaves like a vector in many situations, but is changed into its ...
s'') () which both transform as vectors under rotation. One can define reflections such as :V_x: \beginx\\y\\z\end \mapsto \begin-x\\y\\z\end, which also have negative determinant and form a valid parity transformation. Then, combining them with rotations (or successively performing ''x''-, ''y''-, and ''z''-reflections) one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In even dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used. Parity forms the
abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...
\mathbb_2 due to the relation \hat^2 = \hat. All Abelian groups have only one-dimensional irreducible representations. For \mathbb_2, there are two irreducible representations: one is even under parity, \hat\phi = +\phi, the other is odd, \hat\phi = -\phi. These are useful in quantum mechanics. However, as is elaborated below, in quantum mechanics states need not transform under actual representations of parity but only under projective representations and so in principle a parity transformation may rotate a state by any phase.


Representations of O(3)

An alternative way to write the above classification of scalars, pseudoscalars, vectors and pseudovectors is in terms of the representation space that each object transforms in. This can be given in terms of the group homomorphism \rho which defines the representation. For a matrix R\in \text(3), * scalars: \rho(R) = 1, the trivial representation * pseudoscalars: \rho(R) = \det(R) * vectors: \rho(R) = R, the fundamental representation * pseudovectors: \rho(R) = \det(R)R. When the representation is restricted to \text(3), scalars and pseudoscalars transform identically, as do vectors and pseudovectors.


Classical mechanics

Newton's equation of motion \mathbf = m\mathbf (if the mass is constant) equates two vectors, and hence is invariant under parity. The law of gravity also involves only vectors and is also, therefore, invariant under parity. However, angular momentum \mathbf is an axial vector, :\begin \mathbf &= \mathbf\times\mathbf \\ \hat\left(\mathbf\right) &= (-\mathbf) \times (-\mathbf) = \mathbf. \end In classical electrodynamics, the charge density \rho is a scalar, the electric field, \mathbf, and current \mathbf are vectors, but the magnetic field, \mathbf is an axial vector. However,
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
are invariant under parity because the curl of an axial vector is a vector.


Effect of spatial inversion on some variables of classical physics

The two major divisions of classical physical variables have either even or odd parity. The way into which particular variables and vectors sort out into either category depends on whether the ''number of dimensions'' of space is either an odd or even number. The categories of ''odd'' or ''even'' given below for the ''parity transformation'' is a different, but intimately related issue. The answers given below are correct for 3 spatial dimensions. In a 2 dimensional space, for example, when constrained to remain on the surface of a planet, some of the variables switch sides.


Odd

Classical variables whose signs flip when inverted in space inversion are predominantly vectors. They include:


Even

Classical variables, predominantly scalar quantities, which do not change upon spatial inversion include:


Quantum mechanics


Possible eigenvalues

In quantum mechanics, spacetime transformations act on
quantum states In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
. The parity transformation, \hat, is a unitary operator, in general acting on a state \psi as follows: \hat\, \psi = e^\psi. One must then have \hat^2\, \psi = e^\psi, since an overall phase is unobservable. The operator \hat^2, which reverses the parity of a state twice, leaves the spacetime invariant, and so is an internal symmetry which rotates its eigenstates by phases e^. If \hat^2 is an element e^ of a continuous U(1) symmetry group of phase rotations, then e^is part of this U(1) and so is also a symmetry. In particular, we can define \hat' \equiv \hat\, e^, which is also a symmetry, and so we can choose to call \hat' our parity operator, instead of \hat. Note that ^2 = 1 and so \hat' has eigenvalues \pm 1. Wave functions with eigenvalue +1 under a parity transformation are even functions, while eigenvalue −1 corresponds to odd functions. However, when no such symmetry group exists, it may be that all parity transformations have some eigenvalues which are phases other than \pm 1. For electronic wavefunctions, even states are usually indicated by a subscript g for ''gerade'' (German: even) and odd states by a subscript u for ''ungerade'' (German: odd). For example, the lowest energy level of the hydrogen molecule ion (H2+) is labelled 1\sigma_g and the next-closest (higher) energy level is labelled 1\sigma_u. The wave functions of a particle moving into an external potential, which is
centrosymmetric In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point gr ...
(potential energy invariant with respect to a space inversion, symmetric to the origin), either remain invariable or change signs: these two possible states are called the even state or odd state of the wave functions. The law of conservation of parity of particles states that, if an isolated ensemble of particles has a definite parity, then the parity remains invariable in the process of ensemble evolution. However this is not true for the
beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...
of nuclei) which is due to the
weak nuclear interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, ...
. The parity of the states of a particle moving in a spherically symmetric external field is determined by the
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
, and the particle state is defined by three quantum numbers: total energy, angular momentum and the projection of angular momentum.


Consequences of parity symmetry

When parity generates the
Abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...
2, one can always take linear combinations of quantum states such that they are either even or odd under parity (see the figure). Thus the parity of such states is ±1. The parity of a multiparticle state is the product of the parities of each state; in other words parity is a multiplicative quantum number. In quantum mechanics, Hamiltonians are invariant (symmetric) under a parity transformation if \hat commutes with the Hamiltonian. In non-relativistic quantum mechanics, this happens for any scalar potential, i.e., V = V, hence the potential is spherically symmetric. The following facts can be easily proven: *If \left, \varphi \right\rangle and \left, \psi \right\rangle have the same parity, then \left\langle \varphi \left, \hat \ \psi \right\rangle = 0 where \hat is the position operator. *For a state \left, \vec, L_z\right\rangle of orbital angular momentum \vec with z-axis projection L_z, then \hat \left, \vec, L_z\right\rangle = \left(-1\right)^ \left, \vec, L_z\right\rangle. *If \left hat,\hat\right= 0 , then atomic dipole transitions only occur between states of opposite parity. *If \left hat, \hat\right= 0, then a non-degenerate eigenstate of \hat is also an eigenstate of the parity operator; i.e., a non-degenerate eigenfunction of \hat is either invariant to \hat or is changed in sign by \hat. Some of the non-degenerate eigenfunctions of \hat are unaffected (invariant) by parity \hat and the others are merely reversed in sign when the Hamiltonian operator and the parity operator commute: :\hat\left, \psi \right\rangle = c \left, \psi \right\rangle, where c is a constant, the
eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denote ...
of \hat, :\hat^2\left, \psi \right\rangle = c\,\hat\left, \psi \right\rangle.


Many-particle systems: atoms, molecules, nuclei

The overall parity of a many-particle system is the product of the parities of the one-particle states. It is −1 if an odd number of particles are in odd-parity states, and +1 otherwise. Different notations are in use to denote the parity of nuclei, atoms, and molecules.


Atoms

Atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any ...
s have parity (−1)''ℓ'', where the exponent ℓ is the azimuthal quantum number. The parity is odd for orbitals p, f, ... with ℓ = 1, 3, ..., and an atomic state has odd parity if an odd number of electrons occupy these orbitals. For example, the ground state of the nitrogen atom has the electron configuration 1s22s22p3, and is identified by the term symbol 4So, where the superscript o denotes odd parity. However the third excited term at about 83,300 cm−1 above the ground state has electron configuration 1s22s22p23s has even parity since there are only two 2p electrons, and its term symbol is 4P (without an o superscript).NIST Atomic Spectrum Database
To read the nitrogen atom energy levels, type "N I" in the Spectrum box and click on Retrieve data.


Molecules

The complete (rotational-vibrational-electronic-nuclear spin) electromagnetic Hamiltonian of any molecule commutes with (or is invariant to) the parity operation P (or E*, in the notation introduced by Longuet-Higgins) and its eigenvalues can be given the parity symmetry label ''+'' or ''-'' as they are even or odd, respectively. The parity operation involves the inversion of electronic and nuclear spatial coordinates at the molecular center of mass. Centrosymmetric molecules at equilibrium have a centre of symmetry at their midpoint (the nuclear center of mass). This includes all homonuclear diatomic molecules as well as certain symmetric molecules such as
ethylene Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds). Ethylene ...
,
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms ...
,
xenon tetrafluoride Xenon tetrafluoride is a chemical compound with chemical formula . It was the first discovered binary compound of a noble gas. It is produced by the chemical reaction of xenon with fluorine: : Xe + 2  → This reaction is exothermic, rel ...
and sulphur hexafluoride. For centrosymmetric molecules, the point group contains the operation ''i'' which is not to be confused with the parity operation. The operation ''i'' involves the inversion of the electronic and vibrational displacement coordinates at the nuclear centre of mass. For centrosymmetric molecules the operation ''i'' commutes with the rovibronic (rotation-vibration-electronic) Hamiltonian and can be used to label such states. Electronic and vibrational states of centrosymmetric molecules are either unchanged by the operation ''i'', or they are changed in sign by ''i''. The former are denoted by the subscript ''g'' and are called ''gerade, ''while the latter are denoted by the subscript ''u'' and are called ''ungerade.'' The complete Hamiltonian of a centrosymmetric molecule does not commute with the point group inversion operation ''i'' because of the effect of the nuclear hyperfine Hamiltonian. The nuclear hyperfine Hamiltonian can mix the rotational levels of ''g'' and ''u'' vibronic states (called ''ortho-para'' mixing) and give rise to ''ortho''-''para'' transitions


Nuclei

In atomic nuclei, the state of each nucleon (proton or neutron) has even or odd parity, and nucleon configurations can be predicted using the
nuclear shell model In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The first shell ...
. As for electrons in atoms, the nucleon state has odd overall parity if and only if the number of nucleons in odd-parity states is odd. The parity is usually written as a + (even) or − (odd) following the nuclear spin value. For example, the isotopes of oxygen include 17O(5/2+), meaning that the spin is 5/2 and the parity is even. The shell model explains this because the first 16 nucleons are paired so that each pair has spin zero and even parity, and the last nucleon is in the 1d5/2 shell, which has even parity since ℓ = 2 for a d orbital.


Quantum field theory

:''The intrinsic parity assignments in this section are true for relativistic quantum mechanics as well as quantum field theory.'' If one can show that the vacuum state is invariant under parity, \hat\left, 0 \right\rangle = \left, 0 \right\rangle, the Hamiltonian is parity invariant \left hat,\hat\right/math> and the quantization conditions remain unchanged under parity, then it follows that every state has good parity, and this parity is conserved in any reaction. To show that quantum electrodynamics is invariant under parity, we have to prove that the action is invariant and the quantization is also invariant. For simplicity we will assume that canonical quantization is used; the vacuum state is then invariant under parity by construction. The invariance of the action follows from the classical invariance of Maxwell's equations. The invariance of the canonical quantization procedure can be worked out, and turns out to depend on the transformation of the annihilation operator: :Pa(p, ±)P+ = −a(−p, ±) where p denotes the momentum of a photon and ± refers to its polarization state. This is equivalent to the statement that the photon has odd intrinsic parity. Similarly all
vector boson In particle physics, a vector boson is a boson whose spin equals one. The vector bosons that are regarded as elementary particles in the Standard Model are the gauge bosons, the force carriers of fundamental interactions: the photon of electromagne ...
s can be shown to have odd intrinsic parity, and all axial-vectors to have even intrinsic parity. A straightforward extension of these arguments to scalar field theories shows that scalars have even parity, since :Pa(p)P+ = a(−p). This is true even for a complex scalar field. (Details of spinors are dealt with in the article on the Dirac equation, where it is shown that fermions and antifermions have opposite intrinsic parity.) With fermions, there is a slight complication because there is more than one
spin group In mathematics the spin group Spin(''n'') page 15 is the double cover of the special orthogonal group , such that there exists a short exact sequence of Lie groups (when ) :1 \to \mathrm_2 \to \operatorname(n) \to \operatorname(n) \to 1. As a ...
.


Parity in the Standard Model


Fixing the global symmetries

Applying the parity operator twice leaves the coordinates unchanged, meaning that must act as one of the internal symmetries of the theory, at most changing the phase of a state. For example, the
Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...
has three global U(1) symmetries with charges equal to the baryon number , the lepton number , and the
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...
. Therefore, the parity operator satisfies for some choice of , , and . This operator is also not unique in that a new parity operator can always be constructed by multiplying it by an internal symmetry such as for some . To see if the parity operator can always be defined to satisfy , consider the general case when for some internal symmetry present in the theory. The desired parity operator would be . If is part of a continuous symmetry group then exists, but if it is part of a discrete symmetry then this element need not exist and such a redefinition may not be possible. The Standard Model exhibits a symmetry, where is the fermion number operator counting how many fermions are in a state. Since all particles in the Standard Model satisfy , the discrete symmetry is also part of the continuous symmetry group. If the parity operator satisfied , then it can be redefined to give a new parity operator satisfying . But if the Standard Model is extended by incorporating Majorana neutrinos, which have and , then the discrete symmetry is no longer part of the continuous symmetry group and the desired redefinition of the parity operator cannot be performed. Instead it satisfies so the Majorana neutrinos would have intrinsic parities of .


Parity of the pion

In 1954, a paper by William Chinowsky and Jack Steinberger demonstrated that the pion has negative parity. They studied the decay of an "atom" made from a deuteron () and a negatively charged pion () in a state with zero orbital
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
~ \mathbf L = \boldsymbol 0 ~ into two
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s (n). Neutrons are fermions and so obey Fermi–Dirac statistics, which implies that the final state is antisymmetric. Using the fact that the deuteron has spin one and the pion spin zero together with the antisymmetry of the final state they concluded that the two neutrons must have orbital angular momentum ~ L = 1 ~. The total parity is the product of the intrinsic parities of the particles and the extrinsic parity of the spherical harmonic function ~ \left( -1 \right)^L ~. Since the orbital momentum changes from zero to one in this process, if the process is to conserve the total parity then the products of the intrinsic parities of the initial and final particles must have opposite sign. A deuteron nucleus is made from a proton and a neutron, and so using the aforementioned convention that protons and neutrons have intrinsic parities equal to ~+1~ they argued that the parity of the pion is equal to minus the product of the parities of the two neutrons divided by that of the proton and neutron in the deuteron, explicitly \frac = -1 ~, from which they concluded that the pion is a pseudoscalar particle.


Parity violation

Although parity is conserved in
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...
and
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
, it is violated in weak interactions, and perhaps to some degree in
strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...
s. The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in charged weak interactions in the Standard Model. This implies that parity is not a symmetry of our universe, unless a hidden mirror sector exists in which parity is violated in the opposite way. An obscure 1928 experiment, done by R. T. Cox, G. C. McIlwraith, and B. Kurrelmeyer, had in effect reported parity violation in
weak decay In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interacti ...
s, but since the appropriate concepts had not yet been developed, those results had no impact. In 1929 Hermann Weyl explored, without any evidence, existence of a two-component massless particle of spin one-half. This idea was rejected by Pauli, because it implied parity violation. By the mid-20th century, it had been suggested by several scientists that parity might not be conserved (in different contexts), but without solid evidence these suggestions were not considered important. Then, in 1956, a careful review and analysis by theoretical physicists
Tsung-Dao Lee Tsung-Dao Lee (; born November 24, 1926) is a Chinese-American physicist, known for his work on parity violation, the Lee–Yang theorem, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons, and soliton stars ...
and Chen-Ning Yang went further, showing that while parity conservation had been verified in decays by the strong or electromagnetic interactions, it was untested in the weak interaction. They proposed several possible direct experimental tests. They were mostly ignored, but Lee was able to convince his Columbia colleague
Chien-Shiung Wu ) , spouse = , residence = , nationality = ChineseAmerican , field = Physics , work_institutions = Institute of Physics, Academia Sinica University of California at Berkeley Smith College Princeton University Columbia UniversityZhejiang ...
to try it. She needed special cryogenic facilities and expertise, so the experiment was done at the National Bureau of Standards. Wu, Ambler, Hayward, Hoppes, and Hudson (1957) found a clear violation of parity conservation in the beta decay of
cobalt-60 Cobalt-60 (60Co) is a synthetic radioactive isotope of cobalt with a half-life of 5.2713 years. It is produced artificially in nuclear reactors. Deliberate industrial production depends on neutron activation of bulk samples of the monoisot ...
. As the experiment was winding down, with double-checking in progress, Wu informed Lee and Yang of their positive results, and saying the results need further examination, she asked them not to publicize the results first. However, Lee revealed the results to his Columbia colleagues on 4 January 1957 at a "Friday Lunch" gathering of the Physics Department of Columbia. Three of them, R.L. Garwin, L.M. Lederman, and R.M. Weinrich modified an existing cyclotron experiment, and they immediately verified the parity violation. They delayed publication of their results until after Wu's group was ready, and the two papers appeared back-to-back in the same physics journal. The discovery of parity violation immediately explained the outstanding puzzle in the physics of kaons. In 2010, it was reported that physicists working with the
Relativistic Heavy Ion Collider The Relativistic Heavy Ion Collider (RHIC ) is the first and one of only two operating heavy-ion colliders, and the only spin-polarized proton collider ever built. Located at Brookhaven National Laboratory (BNL) in Upton, New York, and used by a ...
had created a short-lived parity symmetry-breaking bubble in quark–gluon plasmas. An experiment conducted by several physicists in the STAR collaboration, suggested that parity may also be violated in the strong interaction. It is predicted that this local parity violation, which would be analogous to the effect that is induced by fluctuation of the
axion An axion () is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest ...
field, manifest itself by
chiral magnetic effect Chiral magnetic effect (CME) is the generation of electric current along an external magnetic field induced by chirality imbalance. Fermions are said to be chiral if they keep a definite projection of spin quantum number on momentum. The CME is a ...
.


Intrinsic parity of hadrons

To every particle one can assign an intrinsic parity as long as nature preserves parity. Although weak interactions do not, one can still assign a parity to any
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the ...
by examining the strong interaction reaction that produces it, or through decays not involving the weak interaction, such as rho meson decay to pions.


See also

*
C-symmetry In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
*
CP violation In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be t ...
* Electroweak theory * Mirror matter * Molecular symmetry * T-symmetry


References

Footnotes Citations


Sources

* * * * {{DEFAULTSORT:Parity (Physics) Physical quantities Quantum mechanics Quantum field theory Nuclear physics Conservation laws Quantum numbers Asymmetry