.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "api/gallery/particle/electroweak/plot_03_unification.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_api_gallery_particle_electroweak_plot_03_unification.py: Glashow, Weinberg, and Salam: electroweak unification ============================================================ Glashow (1961), Weinberg (1967), and Salam (1968) showed that the electromagnetic and weak interactions are two faces of a single :math:`SU(2)\times U(1)` gauge theory, spontaneously broken by the Higgs mechanism into the massless photon (electromagnetism) and the massive :math:`W^\pm,Z^0` bosons (the weak force) -- unifying two of nature's four fundamental interactions. Gargamelle's 1973 discovery of weak neutral currents, mediated by the previously unobserved :math:`Z^0`, was the theory's first direct experimental confirmation. This example puts the theory's two already-modeled pieces side by side: :func:`~physicskit.particle.electroweak.qed_dsigma_domega_mumu`, the electromagnetic sector reproduced at low energy, and :func:`~physicskit.particle.electroweak.higgs_vev`, the symmetry-breaking scale that gives the :math:`W`/:math:`Z` their mass while leaving the photon massless -- exactly the two ingredients the unification joins. .. GENERATED FROM PYTHON SOURCE LINES 22-27 .. code-block:: Python import matplotlib.pyplot as plt import numpy as np from physicskit.particle.electroweak import higgs_potential, higgs_vev, qed_total_cross_section_mumu .. GENERATED FROM PYTHON SOURCE LINES 28-34 Piece 1: the electromagnetic sector, reproduced at low energy -------------------------------------------------------------------- Below the Z pole (sqrt(s) << M_Z ~ 91 GeV), the electroweak theory's prediction for e+e- -> mu+mu- reduces to pure photon exchange -- the same QED cross section already checked on its own terms in the renormalized-QED example. .. GENERATED FROM PYTHON SOURCE LINES 34-47 .. code-block:: Python sqrt_s_values = np.linspace(3.0, 80.0, 200) sigma_qed = np.array([qed_total_cross_section_mumu(s) for s in sqrt_s_values]) M_Z = 91.19 # GeV, for reference -- not itself predicted by the pieces modeled here fig1, ax1 = plt.subplots(figsize=(6.5, 4.5)) ax1.loglog(sqrt_s_values, sigma_qed, color="steelblue") ax1.axvline(M_Z, color="firebrick", ls="--", label=f"$M_Z$={M_Z} GeV (where the full electroweak theory departs from pure QED)") ax1.set_xlabel(r"$\sqrt{s}$ (GeV)") ax1.set_ylabel(r"$\sigma$ (photon-exchange piece)") ax1.set_title("The electromagnetic sector this theory reproduces at low energy") ax1.legend(fontsize=8) fig1.tight_layout() .. image-sg:: /api/gallery/particle/electroweak/images/sphx_glr_plot_03_unification_001.png :alt: The electromagnetic sector this theory reproduces at low energy :srcset: /api/gallery/particle/electroweak/images/sphx_glr_plot_03_unification_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 48-55 Piece 2: the symmetry-breaking scale setting the W/Z masses ------------------------------------------------------------------- The same spontaneous-symmetry-breaking mechanism modeled in the Higgs example gives the W and Z bosons their mass (schematically, M_W, M_Z ~ g*v for the theory's gauge couplings g) while leaving the photon exactly massless -- a direct structural consequence of *which* combination of the SU(2)xU(1) generators remains unbroken. .. GENERATED FROM PYTHON SOURCE LINES 55-70 .. code-block:: Python a, b = 1.0, 1.0 v = higgs_vev(a, b) print(f"symmetry-breaking scale v = {v:.6f} (schematic units)") print("the W and Z acquire mass proportional to this scale (times the theory's gauge couplings);") print("the photon corresponds to the one gauge direction left exactly unbroken -- massless by construction.") phi_range = np.linspace(-1.3 * v, 1.3 * v, 400) fig2, ax2 = plt.subplots(figsize=(6, 4.5)) ax2.plot(phi_range, higgs_potential(phi_range, a, b), color="gray") ax2.plot([v, -v], [higgs_potential(v, a, b), higgs_potential(-v, a, b)], "o", color="firebrick", ms=8) ax2.set_xlabel(r"$\phi$") ax2.set_ylabel(r"$V(\phi)$") ax2.set_title("The symmetry-breaking scale that sets M_W, M_Z (schematic)") fig2.tight_layout() .. image-sg:: /api/gallery/particle/electroweak/images/sphx_glr_plot_03_unification_002.png :alt: The symmetry-breaking scale that sets M_W, M_Z (schematic) :srcset: /api/gallery/particle/electroweak/images/sphx_glr_plot_03_unification_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none symmetry-breaking scale v = 0.707107 (schematic units) the W and Z acquire mass proportional to this scale (times the theory's gauge couplings); the photon corresponds to the one gauge direction left exactly unbroken -- massless by construction. .. GENERATED FROM PYTHON SOURCE LINES 71-83 Gargamelle (1973): the first evidence for the Z boson this theory predicts --------------------------------------------------------------------------------- Gargamelle's bubble-chamber neutrino events showing a struck electron with no accompanying charged lepton -- a neutral current, mediated by exactly the Z0 boson this unification requires -- were the theory's first direct experimental confirmation, a decade before the W and Z were produced and detected directly (see the 1983 entry in this chronology). Nothing in the toy pieces modeled here computes a neutral-current cross section directly; the qualitative point is that both the QED piece and the symmetry-breaking piece above are ingredients of the single theory Gargamelle's neutral currents confirmed. .. GENERATED FROM PYTHON SOURCE LINES 83-87 .. code-block:: Python print("\nGargamelle (1973): observed neutrino-electron neutral-current scattering, mediated by the Z0") print("this unification predicts -- confirming the theory a decade before the W/Z were produced directly.") plt.show() .. rst-class:: sphx-glr-script-out .. code-block:: none Gargamelle (1973): observed neutrino-electron neutral-current scattering, mediated by the Z0 this unification predicts -- confirming the theory a decade before the W/Z were produced directly. .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.100 seconds) .. _sphx_glr_download_api_gallery_particle_electroweak_plot_03_unification.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_03_unification.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_03_unification.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_03_unification.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_