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Scalar quantity, changing sign in mirrored coordinates
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does
Pseudoscalar
Meson with total spin 0 and odd parity
high-energy physics, a pseudoscalar meson is a meson with total spin 0 and odd parity (usually notated as JP = 0− ). Pseudoscalar mesons are commonly seen
Pseudoscalar_meson
Boson with spin equal to zero
scalar under Lorentz transformation (i.e. are Lorentz invariant). A pseudoscalar boson is a scalar boson that has odd parity, whereas "regular" scalar
Scalar_boson
This list is of all known and predicted scalar, pseudoscalar and vector mesons. See list of particles for a more detailed list of particles found in particle
List_of_mesons
Scalar–fermion interaction
the Yukawa potential. Specifically, it is between a scalar field (or pseudoscalar field) ϕ {\displaystyle \phi } and a Dirac field ψ {\displaystyle \psi
Yukawa_coupling
One-dimensional physical quantity
, proper time and proper length), and invariant mass. In physics, a pseudoscalar denotes a physical quantity analogous to a scalar. Both are physical
Scalar_(physics)
Subatomic particle; made of equal numbers of quarks and antiquarks
triplet and singlet spin states. The latter are called scalar mesons or pseudoscalar mesons, depending on their parity (see below). There is another quantity
Meson
Algebraic structure designed for geometry
≥ 4 {\displaystyle n\geq 4} . Unit pseudoscalars are blades that play important roles in GA. A unit pseudoscalar for a non-degenerate subspace W {\displaystyle
Geometric_algebra
Classification in abstract algebra
C. When n is odd, the center includes not only the scalars but the pseudoscalars (degree n elements) as well. After rescaling the volume element by a
Classification of Clifford algebras
Classification_of_Clifford_algebras
Calculus of vector-valued functions
advanced treatments, one further distinguishes pseudovector fields and pseudoscalar fields, which are identical to vector fields and scalar fields, except
Vector_calculus
Theory of the strong nuclear interactions
generating masses for hadrons far above the masses of the quarks, and making pseudoscalar mesons exceptionally light. Yoichiro Nambu was awarded the 2008 Nobel
Quantum_chromodynamics
Capture of a negative muon by a proton
muon capture on the proton is its connection to the proton's induced pseudoscalar form factor gp [1]' The most precise measurement of the muon capture
Muon_capture
American theoretical physicist
in 1975, completing his senior thesis, titled "Broken symmetry of the Pseudoscalar Yukawa theory", under the supervision of Arthur S. Wightman. Preskill
John_Preskill
Assignment of numbers to points in space
[citation needed] More subtly, scalar fields are often contrasted with pseudoscalar fields. In physics, scalar fields often describe the potential energy
Scalar_field
(r = 2). One may generate a finite-dimensional GA by choosing a unit pseudoscalar (I). The set of all vectors that satisfy a ∧ I = 0 {\displaystyle a\wedge
Universal_geometric_algebra
Phenomenon in particle physics
0^{-}} pseudoscalar mesons (such as the pion) are much lighter than any of the other particles in the spectrum. The low masses of the pseudoscalar mesons
Chiral_symmetry_breaking
Physical quantity
second squared (rad⋅s−2). In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise
Angular_acceleration
Non-conservation of chiral current in physics
one-loop Feynman diagram. The π 0 {\displaystyle \pi ^{0}} coupling is a pseudoscalar coupling; the two photons couple as vectors. The triangle sums over all
Chiral_anomaly
Question of why quantum chromodynamics does seem to not break CP-symmetry
CP problem. The most well-known is Peccei–Quinn theory, involving new pseudoscalar particles called axions. CP-symmetry states that physics should be unchanged
Strong_CP_problem
Topics referred to by the same term
theory of relativity which is invariant under a Lorentz transformation Pseudoscalar, a quantity that behaves like a scalar, except that it changes sign under
Scalar
Field theory of scalar fields
many physical phenomena. An example is the pion, which is actually a pseudoscalar. Since they do not involve polarization complications, scalar fields
Scalar_field_theory
British physicist (1902–1984)
given explicit expressions for the scalar meson field (spin zero pion or pseudoscalar meson), the vector meson field (spin one rho meson), and the electromagnetic
Paul_Dirac
Setting of relativistic physics in geometric algebra
{\displaystyle \{I\gamma _{0},I\gamma _{1},I\gamma _{2},I\gamma _{3}\}} and one pseudoscalar { I } {\displaystyle \{I\}} with I = γ 0 γ 1 γ 2 γ 3 {\displaystyle
Spacetime_algebra
Physical quantity that changes sign with improper rotation
written ⋀n−1Rn. The label "pseudo-" can be further generalized to pseudoscalars and pseudotensors, both of which gain an extra sign-flip under improper
Pseudovector
Exterior product of vectors
pseudovector or an antivector. The highest grade element in a space is called a pseudoscalar, and in a space of dimension n is an n-blade. In a vector space of dimension
Blade_(geometry)
Symmetry of spatially mirrored systems
can be extended, for example, into notions of scalars ( P = +1 ) and pseudoscalars ( P = −1 ) which are rotationally invariant. vectors ( P = −1 ) and
Parity_(physics)
Elementary particle involved with rest mass
Strassler highlighted "considerable" evidence that the new particle is not a pseudoscalar negative parity particle (consistent with this required finding for a
Higgs_boson
Meson whose constituents are a quark and its own antiquark of the same flavor
larger than 5 σ. The excess is compatible with a quasi-bound top-antitop pseudoscalar meson known as toponium. The computation of the properties of mesons
Quarkonium
Lowest energy state in quantum chromodynamics
coupling alone, but not the pseudoscalar coupling, at least not by itself. The way nature fixes this in the pseudoscalar model is by simultaneous rotation
QCD_vacuum
Particle physics plot of relative frequency
similar) three-body decays may move apart. The phase-space of a decay of a pseudoscalar into three spin-0 particles can be completely described using two variables
Dalitz_plot
Ternary operation on vectors
scalar, it could be called a "pseudoscalar" by this broader definition. However, the triple product is not a "pseudoscalar density". When a transformation
Triple_product
Geometric object that has length and direction
does, whose result is a bivector. In two dimensions this is simply a pseudoscalar ( a 1 e 1 + a 2 e 2 ) ∧ ( b 1 e 1 + b 2 e 2 ) = ( a 1 b 2 − a 2 b 1 )
Euclidean_vector
Conserved physical quantity; rotational analogue of linear momentum
nature of angular momentum, and treat it as a scalar (more precisely, a pseudoscalar). Angular momentum can be considered a rotational analog of linear momentum
Angular_momentum
Phenomenon in particle physics
named after Henry Primakoff, is the resonant production of neutral pseudoscalar mesons by high-energy photons interacting with an atomic nucleus. It
Primakoff_effect
Hypothetical particle composed of gluons
range of about 1000–1700 MeV/c2. Lattice predictions for scalar and pseudoscalar glueballs, including their excitations, were confirmed by
Glueball
Sum of a scalar and vector in Clifford algebra
{B} ^{\dagger }=\mathbf {B} } and i {\displaystyle i} represents the pseudoscalar volume element. Another example of biparavector is the representation
Paravector
Subatomic particle; lightest meson
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
Pion
Meson with total spin 1 and odd parity
states characteristic of the vector mesons are not at all evident in the pseudoscalar meson or scalar meson multiplets, and may be only slightly realized among
Vector_meson
Classification scheme of hadrons
Figure 1: The pseudoscalar meson nonet. Members of the original meson "octet" are shown in green, the singlet in magenta. Although these mesons are now
Quark_model
Matrices important in quantum mechanics and the study of spin
dot product and cross product results in If i is identified with the pseudoscalar σx σy σz then the right hand side becomes a ⋅ b + a ∧ b , {\displaystyle
Pauli_matrices
Sum of directed areas in exterior algebra
of e12. As the highest grade element of the algebra e12 is also the pseudoscalar which is given the symbol i. With the properties of negative square and
Bivector
Circulation density in a vector field
pseudovector field (2-form); div takes a pseudovector field (2-form) to a pseudoscalar field (3-form) On the other hand, the fact that d2 = 0 corresponds to
Curl_(mathematics)
State of matter
BCS theory of superconductivity. The Cooper pairs are analogous to the pseudoscalar mesons. However, the vacuum carries no charge. Hence all the gauge symmetries
Fermionic_condensate
Type of conserved current
because pions are pseudoscalar particles and, to produce amplitudes (scalar quantities), a pion must couple to another pseudoscalar object like the axial
Axial_current
American theoretical physicist (1929–2019)
system Gell-Mann amnesia effect Kaon Non-linear sigma model Omega baryon Pseudoscalar meson Random phase approximation List of Jewish Nobel laureates In 1954
Murray_Gell-Mann
Hypothetical subatomic particle
phenomenological models have proposed the X17 as a vector, axial-vector, or pseudoscalar particle in order to remain consistent with both the observed kinematic
X17_particle
Meson with total spin 0 and even parity
total spin 0 and even parity (usually noted as JP=0+). In contrast, pseudoscalar mesons have odd parity. The first known scalar mesons have been observed
Scalar_meson
Property of particles related to spin
T-non-invariant chirality. Effects related to chirality are described using pseudoscalar or axial vector physical quantities in general, and particularly, in
Chirality_(physics)
Mathematical description of fermions
spinor. The flagpole, flag-dipole and Weyl spinors all have null mass and pseudoscalar fields; the flagpole additionally has a null pseudovector field, whereas
Dirac_spinor
Mathematical description of spacetime used in relativity
moment, which change their direction with a change of orientation. A pseudoscalar i is introduced, which also changes sign with a change of orientation
Minkowski_spacetime
Application of Clifford algebra
x\star } is the right complement of x {\displaystyle x} with the pseudoscalar (the pseudoscalar is the dimension-dependent wedge product of all basis 1-vectors)
Plane-based_geometric_algebra
Direction and rate of rotation
counter-clockwise, and negative if clockwise. Angular velocity then may be termed a pseudoscalar, a numerical quantity which changes sign under a parity inversion, such
Angular_velocity
Description of the orientation of a rigid body
angle of rotation, u is the rotation axis (unitary vector), and I is the pseudoscalar (trivector in ℝ3). It is possible to define parameters analogous to the
Euler_angles
Mathematical algorithm for calculating area of a simple polygon
v_{2},v_{3}} and ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} . The sign of the pseudoscalar value v 1 ∧ v 2 ∧ v 3 {\displaystyle v_{1}\wedge v_{2}\wedge v_{3}} represents
Shoelace_formula
Branch of mathematics
product Outer product Kronecker delta Levi-Civita symbol Multilinear form Pseudoscalar Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor contraction
Multilinear_algebra
Exterior algebraic map taking tensors from p forms to n-p forms
the tilde denotes the reverse operation, and I is the volume element (pseudoscalar) in the contravariant basis ( d x μ {\displaystyle dx^{\mu }} relating
Hodge_star_operator
Hypothetical bosons and fermions Name Spin Notes axion 0 A pseudoscalar particle introduced in Peccei–Quinn theory to solve the strong-CP problem. curvaton
List of hypothetical particles
List_of_hypothetical_particles
Effective field theory of nucleons
spontaneously broken. The broken symmetries lead to (nearly) massless pseudoscalar bosons, e.g. pions. See Goldstone boson. As mentioned, this model is
Nambu–Jona-Lasinio_model
Infinitesimal calculus on functions defined on a geometric algebra
-dimensional vector space. From geometric algebra, we interpret the pseudoscalar e 1 ∧ e 2 ∧ ⋯ ∧ e n {\displaystyle e_{1}\wedge e_{2}\wedge \cdots \wedge
Geometric_calculus
American particle physicist
lifetime, its anomalous magnetic moment, and its measurement by the pseudoscalar coupling constant." In 1980 he married Nancy Beitman. At the University
David_W._Hertzog
American physicist
photomeson production near threshold and the suppression of pairs in pseudoscalar meson theory". Physical Review. 93 (1): 233–238. Bibcode:1954PhRv...93
Norman_Myles_Kroll
Greek physicist
Laboratory, University of Rochester Thesis Coherent production of light pseudoscalars (axions) inside a magnetic field with a polarized laser beam (1989)
Yannis_K._Semertzidis
Model of mesons in the massless quark limit
current algebra calculations in the early 1970s. At the level of hadrons, pseudoscalar mesons, the ambit of the chiral model, the chiral SU ( 2 ) L × SU (
Chiral_model
Extension of the Standard Model of particle physics
bosons h and H (where H is heavier than h by convention), the CP odd pseudoscalar A and two charged Higgs bosons H±. The discovered Higgs boson is measured
Two-Higgs-doublet_model
Model of the strong nuclear force
inhomogeneous Bethe-Salpeter equation, for the elastic form factors of pseudoscalar mesons, and for the radiative transitions of mesons. Meanwhile the mass
Maris–Tandy_model
Sammarinese physicist
lattice QCD and this led to the first prediction of the decay constant of pseudoscalar charmed mesons and of B mesons. A proponent of supersymmetry, Maiani
Luciano_Maiani
Effort to prove or disprove the existence of particle
Strassler highlighted "considerable" evidence that the new particle is not a pseudoscalar negative parity particle (a required finding for a Higgs boson), "evaporation"
Search_for_the_Higgs_boson
Classification scheme for hadrons
The pseudoscalar meson octet. Particles along the same horizontal line share the same strangeness, s, while those on the same left-leaning diagonals share
Eightfold_way_(physics)
Geometric symmetry operation
involution or grade involution. Reflection through the identity lifts to a pseudoscalar. Affine involution Circle inversion Clifford algebra Congruence (geometry)
Point_reflection
experimental physics in 1959. Her doctoral thesis demonstrated that a pseudoscalar component was not involved in parity nonconservation in beta decay. Chien-Shiung
Renate_Chasman
Malagasy physicist
S2CID 5146465. Narison, Stephan (2014). "Improved light quark masses from pseudoscalar sum rules". Physics Letters B. 738. Elsevier BV: 346–360. arXiv:1401
Stephan_Narison
List with diagrams of common Feynman diagrams
quarks and W or Z bosons Primakoff effect Other production of neutral pseudoscalar mesons by photons interacting with an atomic nucleus Delbrück scattering
List_of_Feynman_diagrams
Representation of the symmetry group of spacetime in special relativity
spaces of a scalar irreducible representation (irrep), the (0, 0), a pseudoscalar irrep, also the (0, 0), but with parity inversion eigenvalue −1, see
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Formulations of electromagnetism
basis { σ k } {\displaystyle \{\sigma _{k}\}} . Similarly, the unit pseudoscalar is I = σ 1 σ 2 σ 3 {\displaystyle I=\sigma _{1}\sigma _{2}\sigma _{3}}
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Physical constant
ISBN 978-0-471-60386-3. Particle Data Group: Decay constants of charged pseudoscalar mesons Particle Data Group & WWW edition of Review of Particle Physics
Pion_decay_constant
Rotation composed with a reflection
distinguish between vectors and pseudovectors (as well as scalars and pseudoscalars, and in general between tensors and pseudotensors), since the latter
Improper_rotation
American theoretical physicist
describes the physics of the chiral anomaly in Lagrangians, including pseudoscalars, spin-1 vector mesons, and the W ± {\displaystyle W^{\pm }} and Z 0
Christopher_T._Hill
Element of an exterior algebra
n-vectors are pseudoscalars. In the presence of a volume form (such as given an inner product and an orientation), pseudovectors and pseudoscalars can be identified
Multivector
Algebra of 4D spacetime
{\displaystyle i=\mathbf {e} _{1}\mathbf {e} _{2}\mathbf {e} _{3}} is the unit pseudoscalar. In the standard Pauli matrix representation, the electromagnetic field
Algebra_of_physical_space
Hypothetical form of quarkonium
1007/s100520050144. S2CID 17321939. CMS Collaboration (2025). "Observation of a pseudoscalar excess at the top quark pair production threshold". Reports on Progress
Theta_meson
Provides integral formulas for all derivatives of a holomorphic function
{\displaystyle i_{n}} is that algebra's unit n {\displaystyle n} -vector, the pseudoscalar. The result is f ( r ) = − 1 i n ∮ ∂ V G ( r , r ′ ) d S f ( r ′ ) =
Cauchy's_integral_formula
Concept in physics
Berry curvature only has the component out of the plane and behaves as a pseudoscalar. It is because there only exists in-plane translational symmetry when
Berry connection and curvature
Berry_connection_and_curvature
Non-tensorial representation of the spin group
unit scalar, 1, two orthogonal unit vectors, σ1 and σ2, and one unit pseudoscalar i = σ1σ2. From the definitions above, it is evident that (σ1)2 = (σ2)2
Spinor
Particle detector at Cornell University
states. Highlights include confirmation of ηc', confirmation of Y(4260), pseudoscalar-vector decays of ψ(2S), ψ(2S)→J/ψ decays, observation of thirteen new
CLEO_(particle_detector)
Mathematical object that describes the electromagnetic field in spacetime
this number does not change from one frame of reference to another. Pseudoscalar invariant: The product of the tensor F μ ν {\displaystyle F^{\mu \nu
Electromagnetic_tensor
Type of geometric algebra
* Circle e 1 e 2 e 3 = I 3 {\displaystyle e_{1}e_{2}e_{3}=I_{3}} 3D pseudoscalar e i j n 0 {\displaystyle e_{ij}n_{0}} Tangent bivector e i j n ∞ {\displaystyle
Conformal_geometric_algebra
Ways to represent 3D rotations
}}\,,} where i = x̂ŷẑ is the unit volume element, the only trivector (pseudoscalar) in three-dimensional space. The result is B ^ = 1 3 ( y ^ z ^ + z ^
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Mathematical concept
three dimensions, up to a scale factor there is only one trivector, the pseudoscalar of the space, and a product of the above bivector and one of the two
Seven-dimensional cross product
Seven-dimensional_cross_product
Type of supersymmetric quantum field theory
The matter content is a real scalar field S {\displaystyle S} , a real pseudoscalar field P {\displaystyle P} , and a real (Majorana) spinor field ψ {\displaystyle
Wess–Zumino_model
and the highest grade (3 in the 3D case) is traditionally called the pseudoscalar and designated I {\displaystyle I} . The ungeneralized 3D vector form
Comparison of vector algebra and geometric algebra
Comparison_of_vector_algebra_and_geometric_algebra
Pseudophakic photic phenomena Pseudopotential Pseudorapidity Pseudoscalar Pseudoscalar meson Pseudotensor Pseudovector Pseudovector meson Psi meson Psychic
Index_of_physics_articles_(P)
Mass formula for hadrons
masses was found in the context of chiral perturbation theory, just for pseudoscalar mesons, since these are the pseudogoldstone bosons of dynamically broken
Gell-Mann–Okubo_mass_formula
Theory of molecular orbitals by Erich Hückel
its chiral characteristics. However, for achiral molecules applying pseudoscalars to simplify the calculations of optical activity cannot be achieved
Hückel_method
Special low-energy state in quantum mechanics
broader use of singlet-style terminology is the nine-member "nonet" of the pseudoscalar mesons. The simplest possible angular momentum singlet is a set (bound
Singlet_state
charge-parity symmetry. It is very light, electrically neutral, and pseudoscalar. azimuthal quantum number A quantum number for an atomic orbital that
Glossary_of_physics
Pakistani theoretical physicist (1930–2013)
Nucleon-nucleon dispersion relation to discriminate proton-proton scattering in pseudoscalar mesons. In 1965, Riazuddin carried out the pioneering work on vector
Riazuddin_(physicist)
Quantization procedure in quantum field theory
(1999). "Mixing angles and electromagnetic properties of ground state pseudoscalar and vector meson nonets in the light cone quark model". Physical Review
Light-front quantization applications
Light-front_quantization_applications
French theoretical physicist
(2016). "Primordial gravitational waves for universality classes of pseudoscalar inflation". Journal of Cosmology and Astroparticle Physics. 2016 (6):
Pierre_Binétruy
French theoretical physicist
champs de Yang-Mills et la diffusion des mésons pseudoscalaires" [Yang-Mills fields and the diffusion of pseudoscalar mesons] (in French). Homepage v t e
Jean-Bernard_Zuber
American-Canadian theoretical physicist
original on 2006-06-27. Retrieved 2006-04-09. Isgur, N. (1975). "Why the pseudoscalar-meson mixing angle is -10 degrees". Phys. Rev. D. 12 (11): 3770–3774
Nathan_Isgur
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