s have several degrees of freedom
, one of which is the symmetry
of weak isospin
. This is a technical term meaning, roughly, that every quark is one of two types, up-type and down-type: the symmetry operation
s include a symmetry that mixes or replaces one with the other. The two types can be interconverted through the exchange
of a W boson
, which mediate
s the weak nuclear force
. If you have one variety and it spits out a W, it changes into the other.
To say this mathematically, when we write down the quark field to show this degree of freedom explicitly we usually do so in terms of a column vector:
/ u \
q = ( ) .
\ d /
The names "up" and "down" don't refer to any definite physical direction, they're just an accident of history -- probably related to the notation. Of course you could write down exactly the same theory with the "up" quarks at the bottom of the column if you wanted to.
The W's that convert up to down and vice versa correspond to particular elements of the symmetry (strictly, to generators of SU(2) -- more technical terms of Lie algebra, sorry). The W- corresponds to the matrix
/ 0 0 \
τ- = ( )
\ 1 0 /
Crudely, the action of the W-
can be seen when you left multiply
the q field by τ-
: it converts a u quark into a d quark. (Strictly, the multiplet really involves a d', which is a mixture of the down quark, strange quark and bottom quark.)
The notation shows that the two components of q have different values of a quantity known as the third component of weak isospin, denoted as I3 or T3. This is just a fancy way of saying they are in different places in the column vector. The rule is that the values of I3 decrease by one unit from one entry of a column vector to the one below, and the average of I3 over a whole vector has to be 0. Thus the u quark has I3 = +1/2 and the d has I3 = -1/2. The d is referred to as a "quark with I3 of -1/2".
Since the first and most common such quark to be classified was the down quark, the usual physicist-speak for these is "down-type quark". Physicists also refer to the two types of quark by their electric charge Q: this takes the value +2/3 for up-type quarks with I3 = +1/2 and -1/3 for down-type quarks with I3 = -1/2. Hence we also talk of the "charge +2/3 quarks" and "charge -1/3 quarks". The other down-type quarks are the strange and bottom.
One interesting aspect of the distinction between up-type and down-type quarks is the fact that their mass spectra are different -- despite the presence of the weak isospin (or SU(2)) symmetry. The masses are as follows (in GeV/c^2):
| d | s | b |
| ~ 0.007 | ~ 0.12 | ~ 4.1 |
| ~ 0.004 | ~ 1.5 | ~ 175 |
| u | c | t |
Usually if two particles are related by a symmetry they have to have the same mass. But, the symmetry of the weak interaction
s is a spontaneously broken symmetry
: the vacuum
we live in is not invariant
under the τ-
generator (or the τ+
one which I've not shown). In the vacuum there is a nonzero value of the Higgs boson
, which just like the quarks has two components, and the value is asymmetric
between the two components. This allows the two types of quarks to get different properties through their interactions with the Higgs. But this is a story for another node
To convert this into a writeup about up-type quark
s, simply replace 'down' with 'up', 'strange' with 'charm', and 'bottom' with 'top', reverse the polarity
of the I3
values and interchange Q = -1/3 with Q = +2/3. I won't be making a separate writeup about the other ones. You have to break the symmetry somehow!