# Homework Help: What is quark content given strangeness and mass

1. Nov 28, 2008

### catkin

1. The problem statement, all variables and given/known data
This is from Advanced Physics by Adams and Allday, section 9.11, question 2 c.

What is the quark content of each of the following particles?

[snip]

c) Λ baryon, strangeness = -1, mass 1.12 GeV/c2?

2. Relevant equations
No equations. Table of masses at http://en.wikipedia.org/wiki/List_of_particles" [Broken]. Strangeness of s quark is -1 and anti-s quark is +1

3. The attempt at a solution
A baryon, so composed of three qwarks or three anti-quarks.

The strangeness of -1 requires an s quark so the other two quarks cannot be anti-quarks.

The s quark has mass 104 MeV leaving 1.016 GeV for the other two quarks. I cannot find any combination of quarks that adds up to ~1 GeV.

The book lists the answer as uds (all anti-quarks) but an anti-s would have strangeness +1 and the mass of mass of uds is 2.4 MeV + 4.8 MeV + 104 MeV = 111 MeV which is ~ a tenth of the given mass.

I must be misunderstanding something fundamental here because I cannot deduce the same answers as the book for any of parts a through d so have picked c as a sample to ask about.

Last edited by a moderator: May 3, 2017
2. Nov 28, 2008

### malawi_glenn

Think like this, you know the quark content of the nucleons, and their mass is 940MeV/c^2

A strange quark has strangeness -1, and has mass approx 130MeV/c^2 larger the mass of up and down quarks.

The only combination which can give you strangeness -1 and mass 1120 is thus 2"ordinary"quarks and one strange quark. Ordinary quark is u , d....

940 + approx 130 = 1070, so it is ok.

The other combination wich gives you -1 straneness is 2s quakrs and one anti-s, so the mass of that particle should be approx:
940 + approx 390 = approx 1300

So that combination is ruled out.

Never think that the mass of the baryon is equal to the mass of its constituent quarks..

The bare mass of the u,d quarks are rougly 1-5MeV, but the mass of the proton is 940MeV/c^2...

3. Nov 29, 2008

### catkin

Ah! Many thanks Glenn :)

4. Nov 29, 2008

### malawi_glenn

No problem, sorry if I helped you too much! :-)

5. Nov 29, 2008

### catkin

No problem -- but it was that one key misunderstanding that was the problem.

With the benefit of that new understanding am I right in thinking I need to assume an integer charge to be able to answer "What is the quark content of a K+ meson, strangeness = +l, mass = 493 MeV/c2"?

6. Nov 29, 2008

### malawi_glenn

You need to know the basic quark structure of Mesons.

Also you need to know that the Kaons are the second lighest mesons. The lighest ones are the Pions. *hint*

7. Nov 29, 2008

### catkin

A meson, so one quark and one anti-quark.
Strangeness of 1 requires an anti-s quark.
Integer charge requires making up the anti-s quark's +1/3 to 1, so needs a quark with +2/3 charge.
Of the +2/3 charge quarks (u, c and t) only the u will fit within the mass constraint.
Conclusion: the K+ meson comprises an anti-s and a u.

8. Nov 29, 2008

Excellent

9. Dec 1, 2008

### catkin

Thanks Glenn

But I think I can do better ...

Firstly, how could I have used your hint, "the Kaons are the second lightest mesons. The lightest ones are the Pions"?

Secondly, rather than the general principle of mesons having an integer charge does the single + superscript in the question's "K+ meson" indicate a charge of plus one?

This is critical for some of the other parts of the question where assuming an integer charge is not enough to produce a unique solution. I assumed that the charge is always indicated by the superscript (and zero superscript optional); it seemed to work out.

Finally, I got two answers for one part of the question. The book listed the one using quarks. Was the answer using anti-quarks wrong? Here it is, using underlining to indicate anti-quarks.

Question: Δ+ baryon, strangeness = 0, mass = 1.23 GeV/c2
A baryon, so three quarks or three anti-quarks.
Strangeness of 0 means no s or s quarks.
The mass constraint does not allow c, t or b, which individually have more mass that the Δ+.
This leaves only (u and d) or (u and d).
The + superscript indicates a charge of +1.
Using the permissible quarks, both uud and ddd give a charge of +1.
Conclusion: the Δ+ baryon is either uud or ddd.

Best, Charles

10. Dec 1, 2008

### malawi_glenn

Regarding kaons, I said that so you did not thought of combinations with charm quarks etc.

Yes, the "+" means that the kaon has electric charge +1e

Now the delta+ particle: consider ddd, you would have the Delta-minus particle. And if you would assign the d-bar d-bar d-bar to Delta+, so then the antiparticle to Delta-minus would be Delta+? Would seem strange, don't you think?

Better to call all particles which you can combine with d and u quarks Delta-Particles, and the particles with anti-up/down for delta-bar particles.

With baryons you have a different logic than for mesons, the antiparticle to K+ is K-, not K-bar+. That is due to the fact that mesons naturally have one quark and one anti-quark, and can also be their own antiparticle (the neutral pion for instance)

11. Dec 2, 2008

### catkin

Hello Glenn

Thank you for keeping with me this far.

I thought about it several times and, sorry, could not get it to seem strange. I guess I'm too new to this stuff. I have been taught "Every particle has an anti-matter partner with the same mass, but some of its properties are opposite (electric charge for example)". If that's OK then it doesn't seem strange for the Delta-plus to be the Delta-minus' anti-particle.

OK, I'm trying to understand. So ... the d-bar d-bar d-bar particle would have the same charge and strangeness as the Delta-plus but would actually be an anti-Delta-minus?

Best

Charles

12. Dec 2, 2008

### malawi_glenn

Well, you have to be careful when consindering composite systems such as baryons.

The antiparticle of the neutron for instance, the antineutron, is: d-bar, d-bar, u-bar, and is electrical neutral. Consider antiproton: u.bar,ubar d-bar, is electrical negative.

As a matter of fact, the "Anti-deltaminus" particle (resonance) has as far as I know not even been found experimentally. Ask in the Nuclear And Particle physics subforum for experimentally found antibaryons if you want.

So the main point here is to look at the hadrons (mesons and baryons) as composite particles of quarks. The antihadron is found by taking the antiquarks of what make up the hadron under consideration.

Try and verify for yourself for the pions, kaons and proton and neutron :-)

13. Dec 2, 2008

### catkin

Ah, yes! Each baryon has a corresponding antiparticle (anti-baryon) where quarks are replaced by their corresponding antiquarks and antiquarks replaced by their corresponding quarks. That's clear enough but didn't sink in on previous readings.

As per Wikipedia; a key concept to base understanding on. Thanks for it.

Will do, as we go along.

Thanks again for bringing me from the gloomy doom of doubt and confusion to the cheery light of understanding. Especially appreciated because I don't have personal access to an expert and there's little introductory material, even on the Internet.

Best

Charles

14. Dec 2, 2008

### malawi_glenn

I can recomend several introductory resources on particle physics if you want. Internet based of course!

15. Dec 2, 2008

### catkin

That would be very welcome. We are studying Particle Physics as an optional extra part of the British A-level. It is intended to take students planning on studying Particle Physics at first degree level that little bit further. I've spent a long time looking on the Internet and found almost nothing at the right level; most of it is at first degree level.

16. Dec 2, 2008

### malawi_glenn

ok then wikipedia and hyperphysics might be good sites for you, though you were post-bachelor

17. Dec 11, 2008

### catkin

Thanks, they are very good but better for reference than for introductory learning. For the record, Electricity and Thermal Physics by Ellse + Honeywill has turned out to be good for introductory learning. It covers the Excel A-level optional topics as well as the material of its title.

I am effectively post-bachelor, thrown by circumstance into teaching pre-degree Physics, last studied in 1972 when we touched on quanta but didn't hear of quarks or leptons.

18. Dec 11, 2008

### malawi_glenn

Maybe a quick course in quantum mechanics then you are ready to digest more advanced texts on elementary particles? :-)

19. Dec 12, 2008

### turin

Is that an SU(3) singlet?