A question regarding Y=B+S by a nuclear physics toddler

[rpndixit5]

If Q=e[I+0.5Y] and Y=B+S. What is the Q/e and S value for ρ and k mesons, Ω and Δ baryons?
I means third component of isospin and Y,B,S,Q,e have usual meanings?

This is the question. I don't even know what these symbol means. Can someone please explain the symbols and solve this problem.

 

[Simon Bridge]

Welcome to PF;
Where did you see the equation written down?

By default:
http://en.wikipedia.org/wiki/Baryon_number
... see sidebar on the right.

 

[rpndixit5]

It was in my question paper that I had to solve.

 

[Simon Bridge]

Your question paper? <puzzled>
Is this a "question paper" that forms part of an education program of some kind which you are a student of?
... and you don't know what any of the symbols mean?

Please note: a bunch of letters and symbols written down are meaningless without the context.
The wikipedia link I gave you is my best guess based on the little information you have provided.
i.e. something to do with nuclear physics and isospin.
Have you had a look?

 

[dauto]

If you're taking a nuclear physics class, how can you not know the meaning of these symbols?

 

[rpndixit5]

Well the problem is the teacher supposed to take this nuclear physics class is dead and we don't have a replacement. So...
Yes I had a look at your link Mr. Dauto. I also stumbled upon stuff like Baryon Octet and Baryon Decouplet and it helped me solve the problem

 

[dauto]

So you're taking a Nuclear physics class without a lecturer? How does that work? Who decides the grades?

 

[Simon Bridge]

If there is no teacher - who set the question? What are you using for course materials?
Who was the teacher supposed to be and which institution is this?
(The whole class will be in trouble and so will the school so I'd best spend my time assisting them.)

 

[rpndixit5]

It is expected that the grades will be decided by Research Scholars.
Mr.Bridge I appreciate your offer but the problem is the exam of this Nuclear Physics Paper is on 20 May. Plus the syllabus is divided in two parts the teacher supposed to teach this Particle Physics section is unavailable. Other parts like Nuclear Models,Detectors,Alpha Beta and GammaDecays etc have been taught.

 

[gfd43tg]

I like how nonchalantly you mention that your teacher is just dead. This is kind of comical, I think this is a troll post.

 

[vanhees71]

No matter, whether this is a troll post or not. I don't understand, what you have against this (admittedly not very well posed) problem. It's all correct.

Usually, in introductory HEP class, and nuclear physics without HEP is not on top of research nowadays, one starts with stating the conservation laws for charge-like quantum numbers. The deeper real understanding comes of course only when you treat it within relativistic QFT and the Standard Model of elementary particles, but that's not the point here. Here it's simply asked about the quantum numbers of some hadrons.

The formulae given are correct. When restricting yourself to the three lightest quarks (up, down, and strange), the relation the hypercharge is indeed given by
$$Y=B+S,$$
where B is the baryon number and S the strangeness number. The hypercharge is conserved under strong interactions (but not under weak interactions). In terms of constituent-quark numbers of the naive parton model the baryon number is related to the "quark content" by B=(Number of quarks - Number of antiquarks)/3. E.g., a proton is made of 2 up and 1 down quark and no antiquarks, leading to B=1 for the proton.

I must be isospin (the usual naming is T_3, i.e., it's the three-component of isospin but that are conventions). The electric charge is then indeed given by Q/e=Y/2+I. E.g. the proton has isospin 1/2 and hypercharge 1, leading to a charge number of 1 as it must be (a neutron belonging to the same isospin dublett has isospin -1/2 and hypercharge 1 and thus Q=0 as it must be).

I don't know, how you are supposed to solve this exercise, i.e., what you are allowed to use. I'd suggest to look up the quark content of the particles and obtain the quantum numbers from it. You just need to know

u and d quarks build an isospin (isospin meant in relation to the strong interactions in the SU(3) constituent quark model aka the "eightold way") doublet with I=1/2 and I=-1/2, respectively. Both have strangeness S=0 and hypercharges Y=1/3. This leads to Q/e=(I+Y/2)=2/3 and -1/3, respectively, as it must be. Both have baryon number 1/3.

The s quark has isospin I=0 and strangeness S=-1 and hypercharge Y=-2/3. The charge is thus Q/e=-1/3 and baryon number B=1/3.

Why the quarks have these quantum numbers can only be understood from SU(3) group and representation theory. A good starting point is the Wikipedia article

http://en.wikipedia.org/wiki/Quark_model

 

[rpndixit5]

I assure you Ms. Maylis this is not a troll post. I am an Indian student enrolled in Banaras Hindu University,Varanasi. The reason I stated he is dead because he chose to attend some conferences instead of teaching his share. Thats it!

 

[Simon Bridge]

Oh, metaphorical "dead" as in "dead to us" ... no worries.
BHU is supposed to be good, so not replacing a lecturer seems uncharacteristic: you have my sympathy.

Anyway - I hope your question has been answered.