The Standard Model

[Yevgeny Kats]

Can anyone summarize for me the Standard Model? :beer:

[Xerxes314]

Short version: SU(3)xSU(2)xU(1) gauge theory

Middling version: SU(3)xSU(2)xU(1) gauge theory with vector bosons (8 SU(3) color-coupled gluons, 3 doublet-coupled SU(2) W\'s, 1 hypercharge-coupled U(1) B).

Three generations of spinor fermions divided into:
1) colored doublet left-quarks (ups and downs)
2) doublet left-leptons (electrons and neutrinos)
3) colored right-ups
4) colored right-downs
5) right-electrons
with various hypercharges.

The SU(2)xU(1) sector is spontaneously broken by a doublet scalar higgs, making 3 bosons heavy and leaving a massless U(1) photon. The higgs also couples to the fermions, giving them mass. The flavor and mass eigenstates of the quarks are not the same, leading to the CKM mixing matrix.

Long version: Would have to include the various couplings and charges and CKM elements. Might go on about confinement in the SU(3) sector. Probably talk about other symmetries: lepton or baryon number, chirality, C,P and T. The axial anomaly. Have to add that neutrinos appear to mix also, implying the existence of right-neutrinos and another mixing matrix called MNS. Anyway, there\'s at least a couple semesters\' worth of material to it.

Xerxes

[Yevgeny Kats]

Thank you! It is great!

1. Where can I read about it (preferably, a nice book to read in the bus)?

2. What is the meaning of SU(3)? SU(2)? U(1)?

3. In your list of spinor fermions:
I understand that (1) are the quarks (up, down, strange, charm, top, botton), and (2) are the leptons (electron, muon, tau, and their neutrinos). What are (3), (4) and (5)?
And what are the hypercharges?

[Xerxes314]

Well, I can\'t think of any books off the top of my head about gauge theory that are accessible enough for bus reading. If you like Griffiths, he has a book on particle physics that I think is pretty good.

SU is a class of lie groups, the Special Unitary groups. The group SU(N) is made up of complex N by N matrices with the properties

1) Unitary. The transpose-complex-conjugate of the matrix times itself is the identity.

2) Special. The determinant of the matrix is 1.

The fields in the standard model all have this special property of gauge invariance. If you transform each set of fields at any point by any matrix in the gauge group, the physics of the whole system is unchanged. By doing a lot of interesting (but sorta difficult) math, you can show that just this gauge invariance implies the existence of additional fields: the gauge bosons (gluons, W\'s, B). People first noticed this in QED which is a U(1) gauge theory whose gauge boson is the photon. It turns out the U(1) of QED isn\'t the same as the U(1) in the standard model because of the whole higgs thing.

The extra 3, 4 and 5 are necessary because the left-handed components of spinors are fundamentally different from the right-handed components. This is because the weak SU(2) interaction does not respect parity. It treats a particle left-electron and it\'s mirror right-electron completely differently. So in the standard model, you can\'t just talk about electrons, you have to talk about left-electrons and right-electrons. In real life, the two of them get mixed up by their coupling to the higgs boson, and the weak interaction is pretty weak, so you don\'t tend to notice unless you\'re looking for it in the lab.

Hypercharge determines the strength of the coupling of particles to the B boson. In real life, the higgs mixes up the third W and the B into the heavy neutral Z and the photon. So you can express hypercharge as a sum of regular charge and what\'s called the third component of weak isospin.

Xerxes

[Yevgeny Kats]

Xerxes,

Thank you for giving such a beautiful exposition to this subject!

Yevgeny.