Information on weak charge sought

frank_k_sheldon@yahoo.co.uk

All books have tables with the electrical charge of all elementary
particles, including electron, neutrino, quarks, Z, W, etc.

Why are there no tables with the *weak charge* of these particles?
If one searches for the topic in google, one gets no clear information.

One finds statements that W,Z, quarks and leptons all have
weak charge, but no values are given.

Is the weak charge a number? What are the values for all
fermions and bosons? Is it conserved? (If so, how can a W
decay into an electron and an antineutrino?)

Frank

Meir Achuz

frank_k_sheldon@yahoo.co.uk Wrote:
> All books have tables with the electrical charge of all elementary
> particles, including electron, neutrino, quarks, Z, W, etc.
>
> Why are there no tables with the *weak charge* of these particles?
> If one searches for the topic in google, one gets no clear
> information.
>
> One finds statements that W,Z, quarks and leptons all have
> weak charge, but no values are given.
>
> Is the weak charge a number? What are the values for all
> fermions and bosons? Is it conserved? (If so, how can a W
> decay into an electron and an antineutrino?)
>
> Frank


All leptons and quarks have weak charge, that is the stength for the
interaction e-->W^- nu,
or nu-->Z^0 nu, for example. The magnitude of the weak charge is the
same as the electric charge unit e, but the mass of the W or the Z in
the propagator makes the effect at low energies much weaker. The
actual interaction strength for different particles is complicated by
mixing angles, so the strength is different for different particle
combinations. For quarks, the angles are in a 3X3 matrix (the "KM
matrix"). For leptons, the mixing angle is called \theta_W, where the
W stands for either Weinberg or weak, depending on how well you know
Steve.
The various mixing angles are given in the PDG tables.




--
Meir Achuz

frank_k_sheldon@yahoo.co.uk

Meir Achuz wrote:
> All leptons and quarks have weak charge, that is the stength for the
> interaction e-->W^- nu,
> or nu-->Z^0 nu, for example.

I read that the W also has weak charge.
So if a virtual W decays into an electron and an antineutrino
the weak charge of the W is transferred to the electron, whereas
the neutrino gets none? Is that correct?

In fact, I see an apparent contradiction between the statement
"all leptons have weak charge" (thus including the neutrino)
and the statement
"the weak charge is proportional to the electric charge"
(which makes the neutrino have a zero weak charge).
Can you (or someone else) clarify this
(and the way weak charge behaves in the W decay)?

Thank you!

Frank

Meir Achuz

frank_k_sheldon@yahoo.co.uk Wrote:
> Meir Achuz wrote:-
> All leptons and quarks have weak charge, that is the stength for the
> interaction e--W^- nu,
> or nu--Z^0 nu, for example.-
>
> I read that the W also has weak charge.
> So if a virtual W decays into an electron and an antineutrino
> the weak charge of the W is transferred to the electron, whereas
> the neutrino gets none? Is that correct?
>
> In fact, I see an apparent contradiction between the statement
> "all leptons have weak charge" (thus including the neutrino)
> and the statement
> "the weak charge is proportional to the electric charge"
> (which makes the neutrino have a zero weak charge).
> Can you (or someone else) clarify this
> (and the way weak charge behaves in the W decay)?
>
> Thank you!
>
> Frank
1. The W and the Z are like the photons of weak interactions.
They are considered to have no weak charge, but interact with leptons
or quarks with a strength proportional to the weak charge of the
fermion.

2. The weak charge is different than the electric charge, but they
have the same magnitude.
The neutrino has a weak charge, but no electric charge.

3. The interaction W^- --> e + neutrino is the weak equivalent of
photon --> electron + positron.

--
Meir Achuz

frank_k_sheldon@yahoo.co.uk

Meir Achuz wrote:
> 1. The W and the Z are like the photons of weak interactions.
> They are considered to have no weak charge, but interact with leptons
> or quarks with a strength proportional to the weak charge of the
> fermion.
>
> 2. The weak charge is different than the electric charge, but they
> have the same magnitude.
> The neutrino has a weak charge, but no electric charge.
>
> 3. The interaction W^- --> e + neutrino is the weak equivalent of
> photon --> electron + positron.

But there are some people (professors..) on the net who say that
the reaction W-> W + Z
implies that W has weak charge (as the reaction for gluons
g -> g+g implies that gluons have color).

So does the W have weak charge or not? And if it has,
how is weak charge conserved in W -> e+n?

Frank

Dallas Kennedy

The W and Z do have weak charges, based on the full electroweak symmetry
group SU(2)L x U(1)Y.

Weak isospin is the vector of generators for left-chirality (I1, I2, I3).
The hypercharge Y is defined such that electric charge Q is: Q = I3 + Y/2.

The fermions fall into doublets of SU(2)L: that is, (nuE, e), (nuMu, mu),
etc. The primitive gauge bosons form a triplet of SU(2)L: (W1, W2, W3) and
a singlet of U(1)Y: B. The charged W+- bosons are W1 +- iW2. The neutral
photon and Z0 are linear combinations of B and W3.

The charged W+- are not eigenstates of weak charge, but associated instead
with the raising/lower operators of SU(2). These are off-diagonal in the
charge/I3/hypercharge basis.

<frank_k_sheldon@yahoo.co.uk> wrote in message
news:1165166984.589999.58790@80g2000cwy.googlegroups.com...
> Meir Achuz wrote:
>> 1. The W and the Z are like the photons of weak interactions.
>> They are considered to have no weak charge, but interact with leptons
>> or quarks with a strength proportional to the weak charge of the
>> fermion.
>>
>> 2. The weak charge is different than the electric charge, but they
>> have the same magnitude.
>> The neutrino has a weak charge, but no electric charge.
>>
>> 3. The interaction W^- --> e + neutrino is the weak equivalent of
>> photon --> electron + positron.
>
> But there are some people (professors..) on the net who say that
> the reaction W-> W + Z
> implies that W has weak charge (as the reaction for gluons
> g -> g+g implies that gluons have color).
>
> So does the W have weak charge or not? And if it has,
> how is weak charge conserved in W -> e+n?
>
> Frank