What is hadron composition given strangeness and mass

[catkin]

Homework Statement

This is from Advanced Physics by Adams and Alday, section 9.11, question 2 c.

What is the quark content of [snip] Λ baryon, strangeness = -1, mass 1.12 GeV/c²?

Homework Equations

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

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 uds (all anti-quarks) as the answer 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 do not understand how the book's answers to part a and b of the question can be correct either but chose this as a sample to ask about.

 

[anathema]

Hello,

Thank you for your post. I am a scientist and I would be happy to help you with this question.

First, let's review the basic properties of a Λ baryon. As you mentioned, a baryon is composed of three quarks or three anti-quarks. The Λ baryon specifically has a strangeness of -1, meaning it contains at least one s quark. The other two quarks can be any combination of u, d, or s quarks.

In this case, the mass of the Λ baryon is given as 1.12 GeV/c2. We know that the s quark has a mass of 104 MeV, leaving us with 1.016 GeV for the other two quarks. It is important to note that this is the combined mass of the two quarks, not the individual masses.

Now, let's look at the options provided in the book. The answer given is uds, which is all anti-quarks. As you correctly pointed out, this would result in a total strangeness of +1, which does not match the strangeness of the Λ baryon. Additionally, the combined mass of uds is only 111 MeV, which is significantly lower than the given mass of the Λ baryon.

Therefore, the book's answer is incorrect. The correct answer would be either usd or dss, which both have a strangeness of -1 and a combined mass of approximately 1.016 GeV.

I hope this helps clarify the confusion. Please let me know if you have any further questions.

 

[thomate1]

Dear student,

Thank you for bringing this question to my attention. After reviewing the provided information, I believe there may be a mistake in the book's answer for part c. While the quark content of a Λ baryon with strangeness -1 would indeed require an s quark, the remaining two quarks cannot be anti-quarks as that would result in a positive strangeness value for the baryon.

Based on the provided information, I also cannot find a combination of quarks that would add up to a mass of 1.12 GeV/c2. It is possible that there may be a typo or error in the given mass value. I suggest double-checking the source or consulting with your instructor for clarification.

In general, the quark content of a hadron can be determined by considering its quantum numbers, including strangeness and mass, and using the known properties of the quarks. However, in this case, the given information does not seem to be consistent and further investigation is needed.

I hope this helps. Best of luck with your studies.

Sincerely,