This sim lays out the 17 particles of the Standard Model as one table and ties them to the Lagrangian, the equation that governs them. You can recolour the table, switch matter to antimatter, open a mass scale and read each particle's card.

What's on screen

• Quarks (purple): the top two rows of columns I–III.
• Leptons (green): the bottom two rows, the charged leptons e, μ, τ and the three neutrinos.
• Gauge bosons (red): the force carriers g, γ, Z and W.
• The Higgs (gold), alone in the last column. It is selected when the sim opens.
• Card (right): the selected tile's mass, charge, spin, colour, weak isospin, hypercharge and year found.
• Mass ladder (bottom, when Mass log scale is on): masses on a log axis from 0.1 MeV to 1 TeV, with a separate box for the massless particles and the neutrinos (< 1 eV).

Press ⌖ on a row to see where that control sits in the sim. Opening values are those of Free exploration.

Fixed: the masses on the cards are the sim's catalogue values, and the Higgs field's value is v = 246 GeV. The three neutrino masses show as < 1 eV, an upper limit.

Each tile is a field, and the table groups them by role. Twelve are matter: six quarks and six leptons. Four carry forces: the gluon (strong), the photon (electromagnetic) and the W and Z (weak). The last is the Higgs. The g tile stands for eight gluons and the W tile for W⁺ and W⁻.

• Quarks feel the strong, electromagnetic and weak forces.
• The charged leptons e, μ and τ feel the electromagnetic and weak forces.
• Neutrinos feel only the weak force.

The Lagrangian ℒ writes all of this as one equation. Its five terms are the five chips of the sim's Lagrangian view; click a chip and the panel names the term and says what it does.

Columns I, II and III are the three generations. Along each row of matter tiles the charge is the same: u, c, t carry +⅔; d, s, b carry −⅓; e, μ, τ carry −1; the neutrinos carry 0. Spin is ½ ħ in every matter tile. What changes from column to column is the mass.

• From the electron (0.511 MeV) to the top (172.6 GeV) is about five and a half decades of mass.
• The top is the heaviest particle in the table. It outweighs the Higgs (125.2 GeV), the Z (91.19 GeV) and the W (80.37 GeV).
• The Standard Model contains the three copies but does not explain why there are three, or why their masses differ so much.

In the Lagrangian, the derivative D_μ is where matter meets the forces. Each force field multiplies one kind of charge: G reads colour (strength g_s), W reads weak isospin (g) and B reads hypercharge (g′).

Electric charge is a mix of two of them, and it is what the card's rows add up to:

• Each quark and charged lepton has a left-chiral (L) and a right-chiral (R) part. The weak force acts only on the L part, which has T = ½. The R part has T = 0.
• The L | R chip shows both. The electron has T₃ = −½, Y = −1 (L) and T₃ = 0, Y = −2 (R). Q = −1 either way.
• Antimatter flips the signs of Q, T₃ and Y. The mass does not change.

A fermion gets its mass from a Yukawa term, a coupling y between the fermion (L̄ and f_R) and the Higgs field φ. Once φ takes its value v = 246 GeV, the coupling is the mass:

• y is proportional to the mass. The top has y = 0.99 and the electron y = 2.9 × 10⁻⁶, so the spread of masses is a spread of couplings.
• The Standard Model predicts none of the y values. Each is measured and put into the equation.
• The neutrinos have no Yukawa term here, because the model has no right-chiral neutrino. Their masses are tiny but not zero, and need an extension.

The potential has a negative μ² term, so φ = 0 is a hilltop. The field settles on the brim of the hat, at v = 246 GeV.

With φ nonzero, the term |D_μφ|² gives the W and Z their masses:

• m_W = 80.37 GeV gives g = 0.653. m_Z = 91.19 GeV gives √(g² + g′²) = 0.741, so cos θ_W = m_W/m_Z = 0.881.
• The photon is the mix of W³ and B that the field's value leaves alone, so it stays massless. The gluon stays massless because colour is never broken.

• The Higgs discovery. In 2012 ATLAS and CMS at the LHC found the Higgs boson, at 125.2 GeV. Measuring how strongly it couples to each particle tests the Yukawa picture of section 06.
• A short-range weak force. The W and Z masses limit the weak force's range to about ħ/(m_Wc) ≈ 2.5 × 10⁻¹⁸ m, far smaller than a proton.
• The Sun. Its first fusion step, p + p → d + e⁺ + ν, is a weak process, so it runs slowly and the Sun burns for billions of years.

Key points

• The 17 tiles are 12 matter fields, 4 force carriers and the Higgs.
• Along a row, charge and spin repeat and mass grows. The top (172.6 GeV) is the heaviest tile.
• Q = T₃ + ½Y. The L and R parts of a fermion have different T₃ and Y.
• With v = 246 GeV, m = y v/√2 for fermions, m_W = ½ g v and m_Z = ½ √(g² + g′²) v. The photon and gluon stay massless.

Common mix-ups

• "The last particle found is the heaviest." The Higgs, found in 2012, is 125.2 GeV. The top, found in 1995, is 172.6 GeV.
• "The Higgs field gives matter all its mass." It gives the fermions, W and Z their masses. Most of a proton's mass is strong-force energy: its quark masses add up to about 1 %.
• "An antiparticle has the opposite mass." The mass is the same. Q, T₃ and Y flip.

Things to try on your own

• Colour by Charge, then switch Fermions to Antimatter. List which tiles change colour and which do not.
• Select the electron, then the top, and compare their y values in section 06 with their masses.
• Select the up quark and flip L to R. Check Q = T₃ + ½Y for both.