These quarks just don't add up.

[Seffywuff]

I noticed a peculilarity today. I found a big chart on Wikipedia with a bunch of little particles on it. You can find it here:
http://upload.wikimedia.org/wikipedia/en/4/4c/Particle_chart.jpg

So anyways. According to the chart, a proton is composed of two up quarks and one down quark. Also acording to this chart, a down quark has a mass of 0.006 GeV, and and ups have a mass of 0.003 GeV. Adding these up, it does not come anywhere near the 0.938 GeV of a proton! What am I doing wrong here? Am I just that out of practice with math? Are the figures depicted on the chart incorrect? Or do I need to know some advanced form of adding things up?

 

[Physics Monkey]

No form of special adding is required, you just have to make sure you add everything! The thing you must remember is that those three quarks aren't the whole story. They interact very strongly with one another via the strong force, and this interaction energy contributes to the mass of the proton. You are probably aware of a similar effect in nuclei, where the nucleus is less massive than the sum of its parts due to the binding energy. It's the same basic idea here, except that in this case almost all the mass comes from the interaction energy and the proton is actually more massive than its naive constituents.

I find it amazing that we can now actually calculate such masses fairly accurately using lattice QCD:
http://Newton.ex.ac.uk/aip/physnews.731.html

 

[marlon]

I noticed a peculilarity today. I found a big chart on Wikipedia with a bunch of little particles on it. You can find it here:
http://upload.wikimedia.org/wikipedia/en/4/4c/Particle_chart.jpg
So anyways. According to the chart, a proton is composed of two up quarks and one down quark. Also acording to this chart, a down quark has a mass of 0.006 GeV, and and ups have a mass of 0.003 GeV. Adding these up, it does not come anywhere near the 0.938 GeV of a proton! What am I doing wrong here? Am I just that out of practice with math? Are the figures depicted on the chart incorrect? Or do I need to know some advanced form of adding things up?

Hey,

I have already answered to this question (or a variant of it) in this thread

The short answer is : extra mass in a three-quark configuration (like the neutron, proton) comes from the virtual quark anti-quark pairs that pop up and disappear in the "region" around the three constituent quarks.

Keep in mind that most of the actual proton mass does not come from the three masses of the quarks but from interactions and kinetic energy of these virtual pairs...

regards
marlon

ps in the thread i made reference , you will find some great links to the CERN courier that explain very well what is going on here.

 

[marlon]

Or do I need to know some advanced form of adding things up?

YES, you sure do. Let me ask you this question :

Quarks have spin 1/2 and a proton has spin 1/2. There are three quarks in one proton, so you'd think that a proton spin must be 3/2. Ofcourse this is NOT the case.

Ever wondered why that is ?


ENJOY

regards
marlon

ps : the answer can be found on page 3 of the "elementary particles presented" thread

 

[humanino]

YES, you sure do. Let me ask you this question :
Quarks have spin 1/2 and a proton has spin 1/2. There are three quarks in one proton, so you'd think that a proton spin must be 3/2. Ofcourse this is NOT the case.
Ever wondered why that is ?
ENJOY
regards
marlon
ps : the answer can be found on page 3 of the "elementary particles presented" thread

My dear Marlon, I devoted my life to accounting for this 0.5 :)
And group theory forces it to be exactly 0.5000000... no matter how hard you look (cf renormalization, and evolution of the different contributions the hadron spin with respect to the energy scale) !
Anyway, I always found it annoying that people at CERN claim they will explain the origin of mass by detecting the Higgs boson. Most of the mass around us on Earth comes from strong interaction. And most of the mass of the universe remains a mystery for which nobody has the slightest clue (well... maybe some they have a clue. In any case, dark matter and dark energy might open Pandora's box)
I recently became aware of Gribov's scenario for quark confinement. I find it very neat
QCD at large and short distances (annotated version)
Disclaimer : this scenario is not (yet?) thought by the entire community to be valid.

 

[arivero]

exactly 0.5000000...

0.500000... times h. I mean, after all it is not an abstract number, it is an angular momentum.

 

[marlon]

I recently became aware of Gribov's scenario for quark confinement. I find it very neat
QCD at large and short distances (annotated version)
Disclaimer : this scenario is not (yet?) thought by the entire community to be valid.

Seems great...

Mon cher Humanino, tu est retourne depuis quand ? Il y a quelques semaines, j'ai visite Paris...ahh, que de belles filles la-bas...quel paradis...
(je m'excuse pour l'absence des accents graves, etc...

regards
marlon

 

[humanino]

Mon cher Humanino, tu est retourne depuis quand ? Il y a quelques semaine s, j'ai visite Paris...ahh, que de belles filles la-bas...quel paradis...
(je m'excuse pour l'absence des accents graves, etc...
regards
marlon

My dear Marlon, you are going to trigger censorship if you keep speaking french. I wish I could answer in your language

I just came back today. I miss physics forum so badly.
But I must admit that all the time I do not spend here, I can spend it learn new stuff about confinement

 

[marlon]

My dear Marlon, you are going to trigger censorship if you keep speaking french. I wish I could answer in your language
I just came back today. I miss physics forum so badly.
But I must admit that all the time I do not spend here, I can spend it learn new stuff about confinement

how's the phd going ?

did you change topic ?

marlon

 

[humanino]

0.500000... times h. I mean, after all it is not an abstract number, it is an angular momentum.

well... in my world $$\hbar = 1$$, $$c=1$$... "god given units" as they say...

So, 1/2 comes from SU(2) representation. But what about experiment ? Do we not always measure it with an additional g (Landé) factor ?

Besides, I am always amazed, that the quarks' spin + quarks' orbital momentum + gluons' spin + gluons' orbital momentum = 0.5000... wherease none of them is constant with scale !

 

[marlon]

I am always amazed, that the quarks' spin + quarks' orbital momentum + gluons' spin + gluons' orbital momentum = 0.5000... wherease none of them is constant with scale !

Well, i think this would be the mathematical physicist'ts answer : "Rotational" Symmetry does NOT depend on energy/distance scale. Obviously,...

A tennis ball being hit off from Pete Sampras' racket still has the same symmetry compared to being hit off from Marlon's racket. Let's not bring in the mechanical deformation during and just after the hit, ok ?

marlon

 

[humanino]

how's the phd going ?

PhD is an ambitious thing to do... I have only one year remaining. Well, not even really. But I'll have to finish in time anyway.

did you change topic ?
marlon

no, same old loves as before

"Rotational" Symmetry does NOT depend on energy/distance scale.

You're right. SU(2) representations are the same in Paris and in Leuven

 

[Evo]

Welcome back humanino!

Your PM box is full.

 

[Seffywuff]

Neat. I seem to have stumbled upon a great community.