When the SU(2) symmetry is broken
by the Higgs mechanism,
the W bosons acquire mass
and become the well-known W^+ and W^-
bosons discovered at CERN in the 1980s.

So before the breaking, the Ws had no mass.
Did they have any charge?

If yes: No particle is known
without mass but with charge. Are the W
before symmetry breaking the first?

If no: how can charge appear through
symmetry breaking?

No textbook on the Higgs mechanism
seems to address the issue. Maybe
the question is ill-posed?

François

Hello Fran=E7ois,

I'll try my best to answer this accurately -- though I think one could
make a case for both answers depending on how one interprets your
question. :-)

The bottom line is that the Higgs mechanism breaks electroweak
SU(2)xU(1) symmetry to a U(1) subgroup. Before breaking, there are the
W1, W2, W3 bosons of SU(2) and the B boson of U(1). Electroweak
breaking gives masses to these particles in such a way that the
combinations W+ = (W1+iW2) and W- = (W1-iW2) are mass eigenstates with
electric charge +/- and the combinations Z = (g2*W3 - g1*B) and A =
(g2*W3 + g1*B) are mass eigenstates with electric charge 0. (This is
standard textbook material so I'm just setting conventions.)

So your question is: do the Ws have a charge before electroweak
breaking?

1. They have two charges, in fact. They are charged under the SU(2)
symmetry and the U(1) symmetry of the unbroken electroweak theory.

2. You probably meant ELECTRIC charge, so let's focus on that.

The electric charge quantum number of a particle is given by a
relation between its SU(2)xU(1) quantum numbers. Depending on your
normalization, it is something like: Q = Y + T3, where Y is the U(1)
`eigenvalue' and T3 is the eigenvalue of the diagonal SU(2) generator
(the one proportional to the third Pauli matrix).

So in a sense yes, you could say that the W3 and B are electrically
neutral while the W1 and W2 are in some sense charged.

Said slightly differently, the U(1) electric symmetry is still a
subgroup of the SU(2)xU(1) electroweak symmetry, so indeed one can
still define a conserved quantum number for this symmetry.

BUT this isn't really a meaningful thing to look at because the
physical (i.e. energy eigenstate) gauge bosons before electroweak
symmetry breaking are different from the gauge bosons after
electroweak breaking. The things that actually mediate forces obey a
more restrictive symmetry.

Does that help? I hope I haven't made the situation more confusing.

Let me see if I can help by addressing some of your follow up
questions.

"Are the W bosons the first known massive charged bosons?"

I suppose you could say that. What's important, however, is that the
Ws and Z get their mass from `eating' the degree of freedom provided
by the Higgs Goldstone boson. The charge of the W+/-, in some sense,
comes from the off diagonal nature of the generators they correspond
to (the first and second pauli matrices).

"How can charge appear through symmetry breaking?"

So what's happening in symmetry breaking is that a very restrictive
symmetry SU(2)_LxU(1)_Y is breaking into a less restrictive symmetry
U(1)_EM, where I've put the subscripts to make it clear that the
electromagnetic U(1) is different from the hypercharge U(1).

So before electroweak symmetry breaking, there were actually MORE
conserved quantum numbers, i.e. more charges. After EWSB, only the
particular combination of charges that we now call electric charge
(Q=T3 + Y) is a good quantum number.

I hope that helps,
Flip

On Aug 19, 10:39=A0am, wrote:
When the SU(2) symmetry is broken
by the Higgs mechanism,
the W bosons acquire mass
and become the well-known W^+ and W^-
bosons discovered at CERN in the 1980s.

So before the breaking, the Ws had no mass.
Did they have any charge?

If yes: No particle is known
without mass but with charge. Are the W
before symmetry breaking the first?

If no: how can charge appear through
symmetry breaking?

No textbook on the Higgs mechanism
seems to address the issue. Maybe
the question is ill-posed?

Fran=E7ois