Hi Axel,

From my limited studies in particle physics, I asked this question because of the conflicting information I was receiving on the following wikipedia page http://en.wikipedia.org/wiki/Meson. Although I don't rely on Wikipedia for all my learning of new knowledge, it was a bit confusing when I have been reading that mesons have a baryon charge 0 resulting from a bounded quark and its corresponding anti-quark such as an up quark (charge +2/3) and a up anti-quark (charge -2/3). Then on reading this in wikipedia, had I understood correctly that a meson could carry a charge of 1 or -1 if the positive pion is made up of one up quark (charge +2/3) and one down anti-quark((charge +1/3) ?

"Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa. For example, a positive pion (π+) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark." (http://en.wikipedia.org/wiki/Meson)

As I explained in the topic about free quarks, the electric charge and the colour charge are different.

The positive and negative pions have positive and negative electric charge. The baryon number is not related to the electric charge, but to the colour charge. A meson has a colour and and the corresponding anticolour on the quarks (in the simplified quark model, see Axel's post), while a baryon has a red, a green and a blue colour charge, corresponding to a baryon number of +1. Go through the list of quarks and their charges I gave you in the other topic (or find them anywhere else), and notice that the baryon number is related to the colour (1/3 of the sum of the colour charges), not the electric charges. I'm sure you will figure it out.

One more issue: there are mesons like π_0, which are identical to their anti-particle pieces. So anti-π_0 is the same thing as π_0. It is all about quarks, concerning the charge of mesons. (e.g. K0 and anti-K0 are different mesons, again, because of quarks contained).

Short comment: Baryon number of quarks is the assumed quantity. There are other models of baryon number, which attribute it to the "gluonic junction" inside baryons.

It is this non-trivial gluonic field configuration which can be responsible for the conservation of the baryon number...

so you could have a meson consisting of an up-quark of +2/3 electrical charge, +1 red colour charge; and a down anti-quark of -2/3 electrical charge , -1 anti-red colour charge?

What part does electrical charge play in quark interactions as it seems that it all has to do with colour charge?

And as an unrelated question to the above on colour and electrical charge, do both quarks in a meson have the same spin state, and if this is so, does this constitute as what is referred to in particle physics as symmetrical spin?

Electric charge doesn't matter much in quark interaction. The colour (strong) force is so much stronger that the electromagnetic forces can be neglected in most cases. The electric charge of the quark sets the electric charge of the meson though.

In your example, an anti-down quark has an electric charge of +1/3 (as the down charge is -1/3), so the total electric charge of the meson would be +1. A meson formed by an up and an anti-down is the pi plus meson. The colour structure is then a superposition of red + antired quark, blue + antiblue and green + antigreen, but the total electric charge is conserved and remains +1. (There are a lot of other things going on as well, with virtual gluons and quark-antiquark pairs popping up and going away, but let's not focus on that for now.)

Hi Christopher and other contributors, my example above should read, an up-quark of +2/3 electrical charge, +1 red colour charge; and an up anti-quark of -2/3 electrical charge , -1 anti-red colour charge?

In this case electrical charge of +1 is not conserved. As such, I was trying to find out if there are rules for which flavour of quark-antiquarkl pairs can form mesons? It seems that the total meson charge must be +/-1.

So do you think electrical charge is only important for the when it comes to the more macro scale physics involving nucleons and atoms; whereas on the more micro quark scale electrical charge seems too unstable with all the quark interaction (binding and unbinding)?

Hi marc!

Ok, at that point it is a pi zero. Electric charge is 0 and is always conserved, as is total colour charge, not sure why I even mentioned that in my previous post. Sorry for the confusion.

You can pair up any two flavours, as long as the colours match. Some combinations (for example anything containing heavy quarks) will decay into lighter particles though.

It is not a matter of electric charge being unstable, but electromagnetism is just a much weaker force at this low energy scale. It is similar to how we can ignore the gravitational force between the electrons and nucleus of an atom (although the difference in strength is much larger when it comes to gravity).

Can someone explain conservation of (electric) charge? Does it mean that if you have a baryon for example each of the three quarks in that baryon structure that is involved in a meson interaction with another quark must have the same combined electric charge as one of the other quarks in that baryon structure that may be also bound in a meson?

Also, can a single quark co-exist in several baryons and mesons simulatenously?; and if so, would this imply that such a quark would emit and absorb several gluons to form these multiple bound states?

Hi, in order to revel some response from the community, I should expand on the first paragraph in my previous question to show you more clearly (hopefully) of where my issue lies and the need to have a better understanding of how electric charge conservation works.

If I have a proton made up of three quarks (two up and one down); then if an up and down quark form a meson with an anti-down and anti-up quark respectively in an anti-proton, I have this understanding that there will be an electric charge of 1 and -1. Then there is an up quark and up anti-quark that remains unbound; if these two particles were to bind then the electric charge between them is zero.

How can electric charge in the proton be conserved if the single one-to-one bound quark, anti-quark pairs form mesons with different electric charge? This jaded and probably misinformed idea of electric charge conservation that I have for baryons generally, and in this example specifically protons binding to anti-protons, does however work for single one-to-one bound quark-anti-quark pairs where the total meson charge is zero (e.g. up quark paired with up anti-quark x 2, down quark paired with down ant-quark x1) despite the failure to do so with a meson charge of 1 or -1 . The example above using protons also applies to the same meson structure created between neutrons and anti-neutrons; that is, only zero electric charge can be conserved.

This overall 'misunderstanding' I have of electric charge conservation I think stems with my preoccupation in assuming that for a baryon and anti-baryon to become bound there needs to be this single one-to-one bound quark-anti-quark pairing to form mesons connecting the matter and anti-matter subatomic particles.

Hi Axel, In my query I am only using examples of mesons as quark+anti-quark pairs.

I have probably been confusing when I have said 'up quark paired with up anti-quark x 2', by this I mean 'two mesons of up quark+up anti-quark'. Given this clarification can you help me out; or am I making the matter of charge conservation too confusing?

Hi Axel,

Firstly, I should point out that before I was corrected by Christoff in my other post on free quarks about 'how mesons bind matter and anti-matter' , I was under the assumption that for a baryon to bind with an anti-baryon each quark from the baryon had to bind to one of the anti-quarks in the anti-baryon thus forming three mesons. Given this, I couldn't understand how the electric charge for each meson could have the same value; it was this feature of the same electric charge for each meson that I somehow took to mean that electric charge is conserved. But now I think 'conservation' just means 'stability' and has nothing to do with finding symmetries in the magnitude of the charge for this incorrect view of how I thought mesons were formed between baryons and anti-baryons.

Anyway, here is an example of how I thought electric charge conservation might work before I was enlightened :

Meson 1: UQ (+2/3) + DAQ (+1/3) = 1

Meson 2: UQ (+2/3) + UAQ (-2/3) = 0

Meson 3: DQ(-1/3) + UAQ(-2/3)= -1

The charge for all three mesons is different; I interpreted this as electric charge conservation is not conserved.

However, for the following structure

Meson 1: UQ (+2/3) + UAQ (-2/3) = 0

Meson 2: UQ (+2/3) + UAQ (-2/3) = 0

Meson 3: DQ(-1/3)+DAQ(+1//3)= 0

The charge for all three mesons is the same; I interpreted this as electric charge conservation as being conserved.

Charge conservation means that the charge doesn't change over time. So if you have a meson, quark, or anything, the charge (electric or strong) will stay the same. Only way to change the charge is to emit something taking your charge away, and then the total charge is still conserved.

An example from atomic physics is a neutral atom (ie charge 0) emitting an electron (charge -1) and the remaining ion is now charged +1, so that the total charge of the entire system is still 0. The charge is conserved.

Another application of this is two colliding protons. The total electric charge is +2, so whatever particles comes out from the collision, the sum of the electric charge of all the outgoing particles is +2.

The same goes for colour charge. The total red, green and blue charges are all conserved.

So charge conservation on itself does not tell us anything about which quarks will pair up or how, it only says that whatever comes out, the total charge (electric and colour) will be the same as when we started.

Regarding charge conservation and symmetries, they are related in a way, but it is a bit mathematical. There is a theorem (Noethers theorem: http://en.wikipedia.org/wiki/Noether%27s_theorem) saying that a symmetry of the model is associated to a conservation of something. Common examples are translation symmetry associated with conservation of momentum, and rotational symmetry associated to conservation of angular momentum. Similarly the symmetry of the phase (aka gauge symmetry) of the wave function is associated to charge conservation. Not sure how much lagrange emchanics/quantum mechanics/QFT you have studied, so this may be out of your scoop.

Meson particles is a class of particles of an intermediate mass in between leptons (light particles) and baryons (heavy particles). Once the muon with mass about 200 times the mass of the electron was considered a meson, although it is now classified as a lepton together with the electron and the tau. Since the introduction of quarks mesons are now considered color less states of quark anti quark combinations, irrespective of their charge. Because the quark charge can have values +2/3 or -1/3 any quark anti quark combination will have charge +1, 0 or -1.

By the way, another conservation law derived from Noether's theorem regarding invariance against translations in time is that of the energy.

Yes, Prof. Juan lacruz

It is very much familiar that "Meson particles is a class of particles of an intermediate mass in between leptons (light particles) and baryons (heavy particles)".

A meson is a composite quantum field. At energy scale smaller than the electroweak unification scale, internal symmetries of the theory (excluding gravity) are SU(3)c x U(1)em; which are to be distinguished from global space time symmetries. Quantum fields can thus be labelled by color charge and electric charge. Therefore quarks can be labelled by their color charge and electric charge. Due to color confinement, free quarks cannot exist. They have to form bound states. There are two differnt types of bound states 1) q-qbar 2) qqq. The qqq state is a baryon, while q-qbar state is called a meson as it has a total baryon number zero, and so it cannot be called a baryon.

Electric charge for a q-qbar state is also zero. So the question really is how can they have a electric charge + one and - one ? Notice quarks can have electric charge 2/3 and -1/3. If a 2/3 quark combines with a -1/3 charge anti quark then the total charge of the bound state becomes 2/3+1/3=1. This bound state thus have a total charge plus one. Similarly, if a -1/3 charge quark combines with a 2/3 charge antiquark, then the total charge now becomes -1/3-2/3=-1. This bound state thus have a total charge minus one.

Notice that mesons are not elementary particles. They are bound states of quarks which are color neutral, but transforms nontrivially under U(1)em.