Calculating the Theoretical Mass of Quarks and Hadrons: Is it Possible?

[Hluf]

Hi people, I've read some articles about the calculation of mass spectrum. But I'm not clear with this concept. Can we calculate theoretically the mass of quarks. If yes, how? because we never see an isolate quark. Off curse experimentally we can. And my second question is about the mass of mesons ,if we know the values of single quark mass we can calculate the mass of hadrons, if we don't know how can we calculate the theoretical values of hadron mass. THANK YOU !

 

[gabriel.dac]

We already know the mass of most elementary particles: http://www.thingsmadethinkable.com/item/elementary_particles.php

They measure the mass of these particles in places like CERN, where they collide,say, protons at high speed and study the subatomic elements

 

[mfb]

Hi people, I've read some articles about the calculation of mass spectrum. But I'm not clear with this concept. Can we calculate theoretically the mass of quarks.

Not based on theory alone. The quark masses are free parameters in the Standard Model (not exactly, but the point is: you cannot predict them).

If you assume some quark masses, you can estimate the mass of hadrons (messy QCD calculations, I have no idea about details) and some other observables. This can be compared to observed values and then the quark masses are tuned to give correct results.

because we never see an isolate quark.

The top quark decays before it hadronizes, it is isolated.

 

[Hluf]

top quark is extremely massive than up and down quarks. So can we see an isolate of these light quarks?

 

[mfb]

top quark is extremely massive than up and down quarks. So can we see an isolate of these light quarks?

Not according to current physics.
You can "see" unbound individual quarks in quark-gluon-plasmas, but they are not isolated.

 

[michael879]

top quark is extremely massive than up and down quarks. So can we see an isolate of these light quarks?

The thing that makes the top quark special is its mass. It's so massive that it's half life for a weak decay is much shorter than the time it takes isolated quarks to hadronize. All other quarks hadronize before they can decay

 

[amitbashyal]

On the question that if we can see the mass of isolated quarks, we cannot get isolated quarks. Quarks are always coupled together. For example, if you have a system with udd quarks and if you try to isolate a down quark, at one point you will provide enough energy on the vacuum that it will produce a down and an anti down quark. The down quark will go and group together with ud and again form udd whereas the anti down quark will go and annihilate down quark. The end result is that you will end up having a udd system back before isolating one of the quarks. Quarks were isolated in the earilest time of universe ( some nano seconds or less i am not sure) but then as the universe cooled down they sticked together.

 

[michael879]

^ except for top quarks, which are
special and never hadronize. Also, it's quark-gluon plasma where quarks are "free" and don't form bound states. In the early universe this plasma state was possible, whereas nowadays you only see it in places like the LHC

 

[RGevo]

Though technically, with top decay you have to reconstruct the b quark which does hadronize.

You can never see a quark in isolation because it is coloured and must hadronize before we detect the decay products.

 

[michael879]

Though technically, with top decay you have to reconstruct the b quark which does hadronize.

You can never see a quark in isolation because it is coloured and must hadronize before we detect the decay products.

You can "see" a top quark the same as any other non-stable particle (e.g. W/Z/Higgs bosons). It may not be stable but it is surely isolated

 

[RGevo]

What you measure is a colour singlet.

The top quark is not a colour singlet. Therefore you never see a top quark in isolation. Unlike w, z etc.

 

[michael879]

That's a good point, but the only reason you see a color singlet is because the top decay products hadronize. So while you're right that color charge can not be seen in isolation, I would still argue that the top quark is (even if it's charge is not). Either way it's just semantics and not really relevant to the OP

 

[RGevo]

Semantics I guess :) but if we want to know whether our universe is stable, stable enough it depends on the top mass. At the moment it is unclear what is actually measured by these direct mass measurement of top quarks.

For hadrons, some of these are done using heavy quark effective theory ( for b hadrons) while *i think* lighter hadrons octets etc. are done using lattice simulations. I believe this is also true for quark masses, which can be varied in simulation and matched to data.

 

[K^2]

This is a very ambiguous question. When you start talking about particle theory, there is an entire collection of properties that you could call the mass of the particle. For quark, there is the constituent mass, current mass, and the running mass. Each one can be estimated given some assumptions.

Constituent mass is the most straight forward one. It's the fraction of hadron's mass for which a given valence quark is responsible. Unfortunately, because this includes all of the sea contributions, this is going to be entirely dependent on the properties of the particle and not on the quark itself.

Then there is the current mass. That's the thing that goes into Lagrangian of the theory. That's the mass that would be zero if it weren't for the Higgs Mechanism, and I suspect you could make some estimates based on that, but I'm not really an expert on Higgs, so I don't know what the state of the art there.

Finally, there is current mass. If quark did not interact with anything, it'd have the propagator $\frac{i}{\gamma_{\mu}p^{\mu}}$ same as any other elementary fermion. Here m is the same current mass as above. But it does interact, so instead of constant mass, you get running mass m(p²). This can be computed from Gap Equation for certain values of p² under a whole list of assumptions and with a bit of phenomenology mixed in.

And it's worth noting that for most particles, there is one more important case, which is what you'd most commonly call mass of a particle. It's the solution of m²(p²) = p². In other words, requirement that momentum is on the mass shell of the particle. Such a solution exist for any free-propagating particle, but since quarks are confined, there is no p² at which this is true.