:orphan:

Examples
========

This gallery walks through ``physicskit.particle``'s worked examples:
radioactivity and decay chains, relativistic kinematics, nuclear physics,
detector signatures, the weak interaction, the neutral kaon system,
electroweak theory, QCD confinement, flavor physics, the collider
pipeline, and resonance discovery.

See also the narrative tutorials:

- :doc:`/tutorials/relativistic_two_body_decay`
- :doc:`/tutorials/nuclear_decay_chains_and_scattering`

Each script in this gallery is self-contained and can be run directly with
``python examples/particle/<section>/<script>.py``. Every script also
carries an RST module docstring as its title/description and uses ``# %%``
markers to split narrative text from code, which is exactly what
Sphinx-Gallery renders into the pages below -- the script *is* the source of
truth for what you see, not a copy of it.

Sections
--------

- **radioactivity** -- the exponential decay law and Bateman's decay chains.
- **kinematics** -- mass-energy equivalence, Compton scattering, and
  Mandelstam variables.
- **nuclear** -- Rutherford scattering, the neutron and the semi-empirical
  mass formula, and fusion/fission energy release.
- **detector_signatures** -- cloud-chamber tracks and cascade showers.
- **weak_interaction** -- two- vs. three-body decay kinematics, inverse
  beta decay, parity violation, and neutrino oscillations.
- **kaon_system** -- the neutral kaon system, from discovery to CP
  violation.
- **electroweak** -- renormalized QED, the Higgs mechanism, and
  electroweak unification.
- **qcd** -- asymptotic freedom and confinement.
- **flavor_physics** -- the CKM quark-mixing matrix.
- **collider_pipeline** -- from collision to detector: the hard 2-to-2
  vertex, its parton shower, and the curved tracks final-state particles
  leave in a schematic detector.
- **resonance_discovery** -- the invariant-mass bump hunt behind the
  J/psi, W/Z, top quark, and Higgs discoveries.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. thumbnail-parent-div-close

.. raw:: html

    </div>

Collider pipeline
--------------------

From a hard 2-to-2 collision through its QCD parton shower to the curved
tracks final-state particles leave in a schematic detector.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A real collider event unfolds in three stages, each with its own physics: a hard 2-to-2 collision fixes the initial parton kinematics from exact relativistic two-body phase space; each outgoing parton then radiates repeatedly (a &quot;shower&quot;) until its energy falls below a hadronization scale, producing a collimated spray of partons -- a jet; and finally every final-state charged particle curves through the detector&#x27;s magnetic field, r = p_T/(qB), while neutral particles fly straight, both depositing their energy once they reach the calorimeter.">

.. only:: html

  .. image:: /api/gallery/particle/collider_pipeline/images/thumb/sphx_glr_plot_collision_to_detector_thumb.gif
    :alt:

  :doc:`/api/gallery/particle/collider_pipeline/plot_collision_to_detector`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">From collision to detector: a hard scatter, its shower, and its tracks</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Detector signatures
----------------------

Curved cloud-chamber tracks and branching cascade showers -- the
signatures that identified the positron, the muon, and cosmic-ray
showers, from :mod:`physicskit.particle.collider`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A charged particle in a magnetic field traces a circular arc of radius r=p_T/(qB). Anderson (1932) used exactly this geometry to identify the positron from a single cloud-chamber photograph: a track curving the &quot;wrong&quot; way for an electron or proton moving in the direction its ionization required. Four years later, Anderson and Neddermeyer (and independently Street and Stevenson) found tracks implying a mass between the electron&#x27;s and the proton&#x27;s -- the muon, identified from the same curvature-plus-ionization method. This example builds both tracks with charged_track_points and animate_detector_event, and shows how the arc radius alone fixes momentum, while momentum together with an independent speed estimate is what actually fixes mass.">

.. only:: html

  .. image:: /api/gallery/particle/detector_signatures/images/thumb/sphx_glr_plot_01_cloud_chamber_tracks_thumb.gif
    :alt:

  :doc:`/api/gallery/particle/detector_signatures/plot_01_cloud_chamber_tracks`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cloud-chamber tracks: the positron and the muon</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Bhabha, Heitler, Carlson, and Oppenheimer (1937) explained the cosmic-ray &quot;transition curve&quot; -- the number of shower particles first growing, then shrinking, with depth -- as a branching cascade: a single high-energy electron, positron, or photon alternately radiates a photon or materializes one into an electron-positron pair, each product repeating the process until individual energies fall low enough for ordinary ionization losses to take over. This example builds exactly this kind of branching cascade with simple_shower, checks that its total four-momentum is conserved from the single primary particle down to every final-state leaf, and shows the exponential growth in particle count with generation that gives the transition curve its characteristic rise.">

.. only:: html

  .. image:: /api/gallery/particle/detector_signatures/images/thumb/sphx_glr_plot_02_cascade_showers_thumb.gif
    :alt:

  :doc:`/api/gallery/particle/detector_signatures/plot_02_cascade_showers`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bhabha and Heitler's cascade theory of cosmic-ray showers</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Electroweak theory
---------------------

Renormalized QED annihilation, the Higgs symmetry-breaking mechanism,
and their unification into a single electroweak theory, from
:mod:`physicskit.particle.electroweak`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Renormalized QED&#x27;s cleanest tree-level prediction is e^+e^-\to\mu^+\mu^-, whose differential cross section in the massless-fermion limit is">

.. only:: html

  .. image:: /api/gallery/particle/electroweak/images/thumb/sphx_glr_plot_01_qed_annihilation_thumb.png
    :alt:

  :doc:`/api/gallery/particle/electroweak/plot_01_qed_annihilation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tomonaga, Schwinger, Feynman, and Dyson: renormalized QED</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In 1964, three independent groups showed how a gauge symmetry can be spontaneously broken while still keeping the theory&#x27;s equations exactly symmetric -- the mechanism that gives the W and Z bosons their mass while leaving the photon massless. The classical, single-field toy version is a real scalar in the double-well potential V(\phi)=-a\phi^2+b\phi^4: the field must &quot;choose&quot; one of two degenerate minima \phi=\pm v, v=\sqrt{a/(2b)}. This example evolves higgs_field_rollover from a tiny perturbation near the unstable symmetric point, watches it settle into one of the two vacua, and shows that a mirrored initial perturbation settles into the other, degenerate vacuum -- spontaneous symmetry breaking captured directly.">

.. only:: html

  .. image:: /api/gallery/particle/electroweak/images/thumb/sphx_glr_plot_02_higgs_mechanism_thumb.png
    :alt:

  :doc:`/api/gallery/particle/electroweak/plot_02_higgs_mechanism`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Higgs, Brout-Englert, and Guralnik-Hagen-Kibble: symmetry breaking</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Glashow (1961), Weinberg (1967), and Salam (1968) showed that the electromagnetic and weak interactions are two faces of a single SU(2)\times U(1) gauge theory, spontaneously broken by the Higgs mechanism into the massless photon (electromagnetism) and the massive W^\pm,Z^0 bosons (the weak force) -- unifying two of nature&#x27;s four fundamental interactions. Gargamelle&#x27;s 1973 discovery of weak neutral currents, mediated by the previously unobserved Z^0, was the theory&#x27;s first direct experimental confirmation. This example puts the theory&#x27;s two already-modeled pieces side by side: qed_dsigma_domega_mumu, the electromagnetic sector reproduced at low energy, and higgs_vev, the symmetry-breaking scale that gives the W/Z their mass while leaving the photon massless -- exactly the two ingredients the unification joins.">

.. only:: html

  .. image:: /api/gallery/particle/electroweak/images/thumb/sphx_glr_plot_03_unification_thumb.png
    :alt:

  :doc:`/api/gallery/particle/electroweak/plot_03_unification`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Glashow, Weinberg, and Salam: electroweak unification</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Flavor physics
-----------------

The CKM quark-mixing matrix and its single, unavoidable CP-violating
phase once three quark generations mix.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Cronin and Fitch&#x27;s CP violation had no accepted explanation until Kobayashi and Maskawa (1973) showed that a third generation of quarks -- at the time, an unconfirmed extrapolation -- forces the resulting three-generation quark-mixing matrix to admit exactly one physical complex phase, making CP violation an unavoidable feature of the weak interaction rather than an ad hoc addition. No dedicated CKM function exists in physicskit.particle (the package&#x27;s other CP-violation model, the neutral-kaon system, is phenomenological rather than built from an underlying mixing matrix); this example builds the standard three-generation unitary mixing matrix directly from Euler-like mixing angles and one phase -- the same parametrization structure as the PMNS lepton-mixing matrix -- checks its unitarity, and shows that the single complex phase is exactly what a two-generation (Cabibbo) matrix cannot admit.">

.. only:: html

  .. image:: /api/gallery/particle/flavor_physics/images/thumb/sphx_glr_plot_01_ckm_matrix_thumb.png
    :alt:

  :doc:`/api/gallery/particle/flavor_physics/plot_01_ckm_matrix`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Kobayashi and Maskawa: the CKM matrix and three quark generations</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

The neutral kaon system
--------------------------

From the discovery of the strange particles to CP violation: the
Wigner-Weisskopf two-state mixing model in
:mod:`physicskit.particle.electroweak`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Rochester and Butler&#x27;s 1947 cloud-chamber photographs of forked &quot;V0&quot; tracks were the first examples of the &quot;strange particles,&quot; among them the neutral kaon -- a genuinely new two-state system whose mixing would, seventeen years later, supply the first evidence for CP violation. By the early 1960s, CP symmetry predicted that the long-lived neutral kaon K_L, being CP-odd, could not decay to two pions; Cronin and Fitch (1964) found that it does, at a rate of about two parts in a thousand. This example models the neutral-kaon system as the Wigner-Weisskopf two-state mixing problem meson_decay_rates_cp_eigenstate implements, and reproduces the decay-rate asymmetry cp_asymmetry that a real measurement of \Delta m and CP violation is built from.">

.. only:: html

  .. image:: /api/gallery/particle/kaon_system/images/thumb/sphx_glr_plot_01_kaon_cp_violation_thumb.png
    :alt:

  :doc:`/api/gallery/particle/kaon_system/plot_01_kaon_cp_violation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The neutral kaon system: from discovery to CP violation</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Relativistic kinematics
--------------------------

Mass-energy equivalence, Compton scattering, and Mandelstam variables --
the four-vector machinery in :mod:`physicskit.particle.kinematics` and
:mod:`physicskit.particle.scattering`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In the last of his 1905 papers, Einstein showed that a body&#x27;s rest mass and rest energy are the same quantity, E_0=mc^2 -- the rest-frame special case of the fully relativistic relation E^2=(pc)^2+(mc^2)^2. FourVector builds exactly this object, with its .mass property returning the invariant \sqrt{E^2-|\vec p|^2}. This example checks that the invariant mass a moving observer computes agrees exactly with the rest energy measured in the particle&#x27;s own rest frame -- true at every boost velocity, however fast -- and that summing four-vectors before taking the mass, rather than after, is what makes invariant mass differ from simply adding up individual particle masses.">

.. only:: html

  .. image:: /api/gallery/particle/kinematics/images/thumb/sphx_glr_plot_01_mass_energy_equivalence_thumb.png
    :alt:

  :doc:`/api/gallery/particle/kinematics/plot_01_mass_energy_equivalence`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Einstein's mass-energy equivalence</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="X-rays scattered off light elements came back with a wavelength shift depending only on the scattering angle -- a result the classical wave picture of light could not explain. Compton (1923) treated the X-ray as a genuine relativistic particle, a photon of energy E=h\nu and momentum p=h\nu/c, colliding elastically with a free electron and imposing ordinary four-momentum conservation on the two-body collision \gamma+e^-\to\gamma&#x27;+e^{-\prime}. This example does not assume the textbook formula at all: it solves the conservation equations directly with FourVector arithmetic and a numerical root-find for the outgoing photon energy, then checks the result against the closed-form Compton formula.">

.. only:: html

  .. image:: /api/gallery/particle/kinematics/images/thumb/sphx_glr_plot_02_compton_scattering_thumb.png
    :alt:

  :doc:`/api/gallery/particle/kinematics/plot_02_compton_scattering`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Compton scattering: the photon as a relativistic particle</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mandelstam (1958) introduced three Lorentz-invariant combinations of a 2-to-2 collision&#x27;s four-momenta, s=(p_1+p_2)^2, t=(p_1-p_3)^2, u=(p_1-p_4)^2, satisfying s+t+u=\sum_i m_i^2 for on-shell particles -- frame-independent coordinates for any scattering amplitude or cross section. This example computes all three with mandelstam_s, mandelstam_t, and mandelstam_u for an elastic 2\to2 scatter, checks the sum rule, and checks that s itself -- unlike the lab-frame energy of either particle -- comes out identical whether evaluated in the lab frame or after boosting the whole event into a new frame with boost_to_com.">

.. only:: html

  .. image:: /api/gallery/particle/kinematics/images/thumb/sphx_glr_plot_03_mandelstam_variables_thumb.png
    :alt:

  :doc:`/api/gallery/particle/kinematics/plot_03_mandelstam_variables`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mandelstam variables and relativistic collision kinematics</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Nuclear physics
------------------

Rutherford scattering, the neutron and the semi-empirical mass formula,
and the fusion/fission energy release at opposite ends of the
binding-energy curve, from :mod:`physicskit.particle.scattering` and
:mod:`physicskit.particle.nuclear`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Geiger and Marsden&#x27;s 1909 observation that some alpha particles fired at gold foil bounced back at large angles was inexplicable under Thomson&#x27;s diffuse &quot;plum pudding&quot; atom. Rutherford (1911) showed that treating the alpha particle and nucleus as point charges interacting via the Coulomb force predicts exactly this large-angle scattering, via the differential cross section">

.. only:: html

  .. image:: /api/gallery/particle/nuclear/images/thumb/sphx_glr_plot_01_rutherford_scattering_thumb.png
    :alt:

  :doc:`/api/gallery/particle/nuclear/plot_01_rutherford_scattering`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Rutherford scattering and the discovery of the nucleus</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Chadwick (1932) replaced the proton-electron nucleus with the modern picture: a nucleus of mass number A and atomic number Z is exactly Z protons and N=A-Z neutrons. Three years later, Weizsacker combined this proton-neutron picture with a liquid-drop model into a single closed-form estimate of nuclear binding energy,">

.. only:: html

  .. image:: /api/gallery/particle/nuclear/images/thumb/sphx_glr_plot_02_neutron_and_semf_thumb.png
    :alt:

  :doc:`/api/gallery/particle/nuclear/plot_02_neutron_and_semf`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Chadwick's neutron and the Weizsacker semi-empirical mass formula</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Cockcroft and Walton (1932) fired accelerated protons at lithium-7 and found it split into two alpha particles, {}^1{\rm H}+{}^7{\rm Li}\to2\,{}^4{\rm He} -- the first nuclear reaction ever induced entirely by artificial acceleration, and the first direct laboratory confirmation of Q=\Delta mc^2. Six years later, Hahn, Strassmann, Meitner, and Frisch found that uranium bombarded by neutrons could split into two much lighter nuclei, releasing roughly 200 MeV -- because the liquid drop&#x27;s Coulomb repulsion overwhelms its surface tension once Z is large enough. This example computes both reactions&#x27; energy release with q_value, and shows they sit at opposite ends of the same binding-energy curve: Cockcroft-Walton fuses light nuclei toward the curve&#x27;s peak, fission splits a heavy nucleus back down toward it.">

.. only:: html

  .. image:: /api/gallery/particle/nuclear/images/thumb/sphx_glr_plot_03_fusion_and_fission_thumb.png
    :alt:

  :doc:`/api/gallery/particle/nuclear/plot_03_fusion_and_fission`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cockcroft-Walton's disintegration and the discovery of fission</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Quantum chromodynamics
-------------------------

Confinement and string breaking, from
:mod:`physicskit.particle.confinement`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gross, Wilczek, and Politzer (1973) showed that the strong coupling decreases at short distances (asymptotic freedom), the opposite of QED -- and, at long distances, lattice QCD (systematized by Wilson, 1974) confirms the coupling grows enough to confine quarks permanently inside color-neutral hadrons, via a linear potential V(r)=\kappa r at large separation. This example evolves a receding quark-antiquark pair with string_break_chain: the confining string&#x27;s stored energy, string_tension_energy, grows without bound as the quarks separate -- unlike a Coulomb-like potential that would let them escape to infinity -- until it exceeds the threshold to pair-produce a new light quark-antiquark pair from the vacuum and the string breaks, repeatedly, rather than ever freeing a single isolated quark.">

.. only:: html

  .. image:: /api/gallery/particle/qcd/images/thumb/sphx_glr_plot_01_confinement_thumb.png
    :alt:

  :doc:`/api/gallery/particle/qcd/plot_01_confinement`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Asymptotic freedom and confinement: a receding quark pair's string</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Radioactivity
---------------

The exponential decay law and Bateman's closed-form solution for
multi-species radioactive decay chains, from
:mod:`physicskit.particle.decays`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Becquerel&#x27;s 1896 chance discovery -- a uranium salt spontaneously exposing a photographic plate with no external excitation -- opened radioactivity as a field; Rutherford and Soddy (1902-1903) showed the underlying law is a simple exponential,">

.. only:: html

  .. image:: /api/gallery/particle/radioactivity/images/thumb/sphx_glr_plot_01_decay_law_thumb.png
    :alt:

  :doc:`/api/gallery/particle/radioactivity/plot_01_decay_law`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The radioactive decay law: Becquerel, Rutherford, and Soddy</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Real radioactive samples rarely decay in one step: uranium and thorium each head long chains of successive daughters. Bateman (1910) solved the resulting linear system in closed form, giving the population of the k-th species in a chain N_1\to N_2\to\cdots\to N_n as an explicit sum of exponentials in the decay constants \lambda_1,\ldots,\lambda_n. This example builds a three-species chain with bateman_decay_chain, watches the parent deplete while an intermediate daughter first rises and then falls (it has to be produced before it can decay away), and checks total population conservation at every instant.">

.. only:: html

  .. image:: /api/gallery/particle/radioactivity/images/thumb/sphx_glr_plot_02_decay_chains_thumb.png
    :alt:

  :doc:`/api/gallery/particle/radioactivity/plot_02_decay_chains`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bateman's equations for radioactive decay chains</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

Resonance discovery
----------------------

The invariant-mass "bump hunt" -- the generic technique behind the
discovery of the J/psi, the W/Z bosons, the top quark, and the Higgs
boson -- built on :func:`physicskit.particle.kinematics.invariant_mass`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Four of this chronology&#x27;s landmark discoveries -- the J/psi (1974), the W and Z bosons (1983), the top quark (1995), and the Higgs boson (2012) -- were all found the same way: reconstruct the invariant mass of a candidate particle&#x27;s decay products event by event, histogram it over many collisions, and look for a resonance peak standing above a smooth combinatorial background. This example builds exactly that &quot;bump hunt&quot; with invariant_mass: a population of true resonance decays (fixed parent mass, isotropic decay angles) is buried inside a much larger population of random, uncorrelated background pairs, and the resonance peak is recovered directly from the histogram alone -- the generic technique behind every one of these four discoveries, applied here to a single representative example resonance.">

.. only:: html

  .. image:: /api/gallery/particle/resonance_discovery/images/thumb/sphx_glr_plot_01_invariant_mass_bump_hunt_thumb.png
    :alt:

  :doc:`/api/gallery/particle/resonance_discovery/plot_01_invariant_mass_bump_hunt`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The invariant-mass bump hunt: J/psi, the W/Z, the top quark, and Higgs</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

The weak interaction
-----------------------

Two-body vs. three-body decay kinematics, inverse beta decay, parity
violation, and neutrino oscillations, from
:mod:`physicskit.particle.decays` and :mod:`physicskit.particle.neutrinos`.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Beta decay&#x27;s continuous electron spectrum was, on the assumption that it was a two-body process, a genuine puzzle: two-body decay kinematics forces the daughter to a single, sharply fixed momentum in the parent&#x27;s rest frame. Pauli (1930) proposed a third, undetected particle -- the neutrino -- making beta decay three-body instead, with the continuous spectrum simply reflecting three-body phase space. Fermi (1933-1934) built this into a full quantitative theory; Lattes, Occhialini, and Powell&#x27;s 1947 discovery of the charged pion supplied a clean, genuinely two-body confirmation of the other side of the same contrast: \pi^\pm\to\mu^\pm+\nu_\mu gives the muon one single, sharply fixed momentum, exactly as two-body kinematics demands. This example puts both cases side by side with two_body_decay_momentum and muon_decay_event.">

.. only:: html

  .. image:: /api/gallery/particle/weak_interaction/images/thumb/sphx_glr_plot_01_two_and_three_body_decay_thumb.png
    :alt:

  :doc:`/api/gallery/particle/weak_interaction/plot_01_two_and_three_body_decay`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pauli, Fermi, and the pion: two-body vs. three-body decay kinematics</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="More than two decades after Pauli&#x27;s postulate, Cowan and Reines caught the &quot;undetectable&quot; particle directly, searching for inverse beta decay,">

.. only:: html

  .. image:: /api/gallery/particle/weak_interaction/images/thumb/sphx_glr_plot_02_inverse_beta_decay_thumb.png
    :alt:

  :doc:`/api/gallery/particle/weak_interaction/plot_02_inverse_beta_decay`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cowan and Reines: direct detection of the neutrino</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Wu&#x27;s 1957 experiment cooled spin-polarized cobalt-60 nuclei and counted emitted electrons above and below the sample: if parity held, electrons should emerge equally often parallel and antiparallel to the nuclear spin. She found instead a pronounced asymmetry, dN/d\cos\theta\propto1+A\cos\theta with A\neq0 -- parity is violated in the weak interaction. This example reproduces exactly that signature using two_body_decay&#x27;s cos_theta parameter: sampling decay angles uniformly (the parity-conserving null hypothesis) gives a flat count-vs-\cos\theta histogram, while weighting the sample by 1+A\cos\theta for A\neq0 reproduces Wu&#x27;s asymmetric distribution directly.">

.. only:: html

  .. image:: /api/gallery/particle/weak_interaction/images/thumb/sphx_glr_plot_03_parity_violation_thumb.png
    :alt:

  :doc:`/api/gallery/particle/weak_interaction/plot_03_parity_violation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Lee, Yang, and Wu: the discovery of parity violation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="If neutrinos carry a small mass, nothing forbids oscillation between flavors over macroscopic distances. In the simplest two-flavor treatment, a neutrino produced in flavor e oscillates into flavor \mu with probability">

.. only:: html

  .. image:: /api/gallery/particle/weak_interaction/images/thumb/sphx_glr_plot_04_neutrino_oscillations_thumb.png
    :alt:

  :doc:`/api/gallery/particle/weak_interaction/plot_04_neutrino_oscillations`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pontecorvo, Maki, Nakagawa, and Sakata: neutrino oscillations</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /api/gallery/particle/collider_pipeline/index.rst
   /api/gallery/particle/detector_signatures/index.rst
   /api/gallery/particle/electroweak/index.rst
   /api/gallery/particle/flavor_physics/index.rst
   /api/gallery/particle/kaon_system/index.rst
   /api/gallery/particle/kinematics/index.rst
   /api/gallery/particle/nuclear/index.rst
   /api/gallery/particle/qcd/index.rst
   /api/gallery/particle/radioactivity/index.rst
   /api/gallery/particle/resonance_discovery/index.rst
   /api/gallery/particle/weak_interaction/index.rst



.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_