Skip to main content

Particle Physics operators

42 operators in the particle_physics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
HCS48Shannon entropy over 48 particle states for high-energy collision event characterization.H_{CS} = -\sum_{i=1}^{48} p_i \ln p_i
HCS52Shannon entropy over 52 particle states for extended Standard Model event analysis.H_{CS} = -\sum_{i=1}^{52} p_i \ln p_i
HEP1Dirac Lagrangian for a free spin-1/2 fermion field.\mathcal{L} = \bar{\psi}(i\gamma^\mu\partial_\mu - m)\psi
HEP10CKM quark mixing matrix parameterizing flavor-changing weak interactions.V_{CKM} = \begin{pmatrix} V_{ud} & V_{us} & V_{ub} \\ V_{cd} & V_{cs} & V_{cb} \\ V_{td} & V_{ts} & V_{tb} \end{pmatrix}
HEP11Renormalization group equation: running of the coupling constant with energy scale.\mu^2\frac{d\alpha}{d\mu^2} = \beta(\alpha)
HEP12QCD running coupling constant exhibiting asymptotic freedom at high energies.\alpha_s(Q^2) = \frac{12\pi}{(33-2n_f)\ln(Q^2/\Lambda^2)}
HEP13Higgs potential with spontaneous symmetry breaking giving mass to gauge bosons.V(\phi) = \mu^2|\phi|^2 + \lambda|\phi|^4
HEP14Higgs boson mass related to the quartic coupling and vacuum expectation value.m_H = \sqrt{2\lambda}v
HEP15Graviton perturbation: linearized metric perturbation for quantum gravity approaches.g_{\mu\nu} \to g_{\mu\nu} + h_{\mu\nu}
HEP16Planck mass: the mass scale where quantum gravity effects become important.M_P = \sqrt{\frac{\hbar c}{G}}
HEP17Einstein-Hilbert action: the gravitational action principle yielding Einstein's field equations.S = \int d^4x \sqrt{-g}\left(\frac{R}{16\pi G} + \mathcal{L}_m\right)
HEP18Neutrino mass-squared difference governing neutrino oscillation frequencies.\Delta m^2 = m_2^2 - m_1^2
HEP19Neutrino oscillation probability: flavor transition as a function of mixing angle and mass splitting.P(\nu_\alpha \to \nu_\beta) = \sin^2(2\theta)\sin^2\left(\frac{\Delta m^2 L}{4E}\right)
HEP2QED Lagrangian: Dirac field minimally coupled to the electromagnetic field.\mathcal{L}_{QED} = \bar{\psi}(i\gamma^\mu D_\mu - m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}
HEP20Dark energy density parameter: cosmological constant energy density relative to critical density.\Omega_\Lambda = \frac{\rho_\Lambda}{\rho_c}
HEP3Gauge covariant derivative introducing the electromagnetic coupling to charged fermions.D_\mu = \partial_\mu + ieA_\mu
HEP4Yang-Mills Lagrangian for non-abelian gauge fields, the basis of the Standard Model.\mathcal{L}_{YM} = -\frac{1}{4}F^a_{\mu\nu}F^{a\mu\nu}
HEP5Non-abelian field strength tensor with self-interaction terms for gluon and weak boson fields.F^a_{\mu\nu} = \partial_\mu A^a_\nu - \partial_\nu A^a_\mu + gf^{abc}A^b_\mu A^c_\nu
HEP6Mandelstam variables s, t, u parameterizing relativistic scattering kinematics.s = (p_1 + p_2)^2, \quad t = (p_1 - p_3)^2, \quad u = (p_1 - p_4)^2
HEP7Scattering cross-section from the squared matrix element integrated over phase space.\sigma = \frac{1}{F}\int|\mathcal{M}|^2 d\Phi
HEP8Particle decay rate from the squared matrix element and available phase space.\Gamma = \frac{1}{2m}\int|\mathcal{M}|^2 d\Phi
HEP9Fermi coupling constant relating weak interaction strength to the W boson mass.G_F = \frac{g^2}{4\sqrt{2}M_W^2}
PP1Plasma frequency: natural oscillation frequency of electrons in a plasma.\omega_p = \sqrt{\frac{n_e e^2}{m_e \epsilon_0}}
PP10Lawson criterion for fusion ignition: triple product of density, confinement time, and temperature.n\tau_E T > 3 \times 10^{21} \text{ keV s m}^{-3}
PP11Generalized Ohm's law for a magnetized plasma including the Hall term.\vec{E} + \vec{v} \times \vec{B} = \eta\vec{J}
PP12Magnetic Reynolds number: ratio of magnetic advection to diffusion in a conducting fluid.R_m = \frac{\mu_0 \sigma v L}{1}
PP13Ampère's law in the MHD limit: curl of B proportional to current density.\nabla \times \vec{B} = \mu_0 \vec{J}
PP14Magnetic induction equation governing evolution of the magnetic field in a conducting plasma.\frac{\partial \vec{B}}{\partial t} = \nabla \times (\vec{v} \times \vec{B}) + \frac{1}{\mu_0\sigma}\nabla^2\vec{B}
PP15E cross B drift: velocity of charged particles drifting perpendicular to crossed electric and magnetic fields.\vec{v}_E = \frac{\vec{E} \times \vec{B}}{B^2}
PP16Gradient-B drift: particle drift caused by spatial variation in magnetic field strength.\vec{v}_\nabla B = \frac{1}{2}v_\perp r_L \frac{\vec{B} \times \nabla B}{B^2}
PP17Magnetic moment: first adiabatic invariant of a charged particle gyrating in a magnetic field.\mu = \frac{m v_\perp^2}{2B}
PP18Critical density for electromagnetic wave propagation in a plasma.n_c = \frac{\omega^2 m_e \epsilon_0}{e^2}
PP19Alfvén velocity: speed of magnetic disturbances propagating along field lines in a plasma.v_A = \frac{B}{\sqrt{\mu_0 \rho}}
PP2Debye length: characteristic shielding distance in a plasma.\lambda_D = \sqrt{\frac{\epsilon_0 k_B T_e}{n_e e^2}}
PP20Alfvén wave dispersion relation: frequency proportional to wave number times Alfvén speed.\omega^2 = k^2 v_A^2
PP3Larmor radius: radius of a charged particle's circular orbit in a magnetic field.r_L = \frac{m_\perp v_\perp}{|q|B}
PP4Cyclotron frequency: angular frequency of a charged particle gyrating in a magnetic field.\omega_c = \frac{|q|B}{m}
PP5Plasma beta: ratio of thermal pressure to magnetic pressure in a plasma.\beta = \frac{nk_B T}{B^2/2\mu_0}
PP6Plasma continuity equation: conservation of particle number with sources and sinks.\frac{\partial n}{\partial t} + \nabla \cdot (n\vec{v}) = S - L
PP7Boltzmann-Vlasov kinetic equation governing the phase-space distribution of plasma particles.\frac{\partial f}{\partial t} + \vec{v}\cdot\nabla f + \frac{q}{m}(\vec{E}+\vec{v}\times\vec{B})\cdot\nabla_v f = C(f)
PP8Saha ionization criterion: condition for a gas to be considered a plasma.n_e T_e^{3/2} / n_n > 1
PP9Energy confinement time: ratio of stored plasma energy to power loss rate.\tau_E = \frac{W}{P_{loss}}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["HCS48"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​