Proton Radius Puzzle: Muons vs Electrons

[jk22]

Founding this : http://arxiv.org/abs/1502.05314 if I understood correctly the radius of the proton is smaller using muons instead of electrons.

Could this be due to the fact that the gravitation force becomes repulsive at small distances so that the particles are kind of compressed by it ?

I have done no calculation but surely the gravitational force is much too weak to induce such an effect.

 

[ohwilleke]

The observed radius of the proton is smaller using muons than electrons. The main explanations for this are:
(1) The margin of error in the less accurate and stale electron based measurements are bigger than claimed. The central value of the canonical measurement of the electric charge radius of protons in ordinary hydrogen is 54 sigma different from the muonic hydrogen radius, a clearly inconsistent result. But, the central value of the muonic hydrogen based estimate of the proton radius is only about 1.75 sigma from the central value of the measurement made in 1980 which were still the best available as of 2005 (see http://arxiv.org/pdf/physics/0410051.pdf). Thus, the possibility that the difference is simply due to experimental error in the inherently less accurate measurement of the proton radius in ordinary hydrogen is very plausible.
(2) There is a theoretical error that is pervasive in the leading analyses of the theoretical expectation for the measurement that is making a subtle mistake by treating observations that are made in different reference frames as if they were made in the same reference frame, when they shouldn't. See http://arxiv.org/abs/1311.0319 and http://arxiv.org/abs/1305.4552
(3) BSM physics to be determined.

Repulsive gravity at short distances is way, way, way down the list as plausible explanations. But, most BSM physics scenarios don't provide a good argument for why the lepton orbiting a nucleus should influence the proton nuclear radius.

 

[tzimie]

But after new experiments it is now 7 sigmas?

 

[newjerseyrunner]

I have a question: is there a mathematical reason that protons are expected to have a constant radius?

 

[gannordean]

Hi,
-to answer jk22: Yes, the magnitude of the gravitational force, associated with elementary particles is indeed way too weak, at least compared to others interactions gouverning their motion. Even if you consider bombarding your target with a heavy element nucleus-in theory!-yet the recoil caused by the electromagnetic interaction of mutual nuclear dipoles(not single nucleon) over exceed it by several orders(at Mev scales)! It's shown in nuclear textbooks.
Then how to explain the apparent shrinking of the proton's radius? if I understand well, muons are heavier than electrons so they get a little closer to the nucleus, thanks to their much more inertia, before being diffused. Try playing around with the formula of impact parameter for both types of particle and see yourself.

 

[Vanadium 50]

I have a question: is there a mathematical reason that protons are expected to have a constant radius?

If different protons had different radii they would not be identical, and that would have huge consequences for nuclear, atomic and thermal physics.

 

[newjerseyrunner]

If different protons had different radii they would not be identical, and that would have huge consequences for nuclear, atomic and thermal physics.

Ah, I forgot about that, but I'd like some clarification. Being identical doesn't mean acting identically in different circumstances. In terms of the quantum mechanics, are the circumstances the same?

 

[MathematicalPhysicist]

If different protons had different radii they would not be identical, and that would have huge consequences for nuclear, atomic and thermal physics.

How would you model such protons? I would think that it would be impossible to model such a situation, because of the vast multitude of protons.

If every proton had a different radius than the other protons you could not possibly account for all of them, am I wrong?

 

[Vanadium 50]

How would you model such protons?

I don't have to model a wrong theory in detail. I just need to know that it's predictions are different than we observe: in particular, you would get a different Pauli exclusion principle depending if you had two, three, seven, or an infinite number of distinguishable protons. But none of these match what we see, which does match what you expect for indistinguishable protons.

 

[bahamagreen]

So, pardon my ignorance, but it looks like the electron is employed as the test particle for determining the proton radius.
Theory leads one to assume that both the electron and heavier muon would serve identically as proton radius testers.

From ignorance, I would expect that the muon's angular "orbital" momentum would displace the proton's center of mass from the muon-proton couple center of mass... (more than the like displacement when testing with the electron).
If the proton COM is offset from the muon-proton couple's COM, will that not appear as a "lower orbit" when measured (because each measurement is an individual instant "snap shot" and not an average value?

I'm not suggesting this as a classical answer, but wondering if the QM version of the "same thing" exists or can be used to account for the discrepancy.

 

[MathematicalPhysicist]

I don't have to model a wrong theory in detail. I just need to know that it's predictions are different than we observe: in particular, you would get a different Pauli exclusion principle depending if you had two, three, seven, or an infinite number of distinguishable protons. But none of these match what we see, which does match what you expect for indistinguishable protons.

What Pauli exclusion principle has got to do with different protons, only their sizes are different but they still can be called fermions because of their spin, will different radius change their spin? even then it still can be half integer even if the radius is changed.

I don't understand your stance, can you elaborate on why will such hypothesis will contradict Pauli exculsion principle?

 

[Nugatory]

What Pauli exclusion principle has got to do with different protons?

The exclusion principle prevents two identical fermions from occupying the same state. Protons of different radius wouldn't be identical so they wouldn't be prevented from occupying the same state.

 

[Vanadium 50]

If there are two kinds of protons, Type A with radius x and Type B with radius y, they are distinguishable. That means that Pauli will let them both be in the same quantum state. Indistinguishable protons cannot be in the same quantum state.

 

[MathematicalPhysicist]

I thought that the exclusion principle applies to fermions with the same spin.

So if it were possible to change a radius of one proton, we could theoretically occupty a state with the two different protons.

Is it possible to change a proton's radius?

 

[Vanadium 50]

I thought that the exclusion principle applies to fermions with the same spin.

No, it applies only to identical fermions. (Which of course have the same spin) You can have an electron and a proton in a state with the same quantum numbers because they are not identical. You cannot have two protons in a state with the same quantum numbers because they are identical.

 

[MathematicalPhysicist]

You didn't answer my last question, is it possible to change a proton's radius?
How would you devise such an experiment if it were possible? (I know it's more of an engineering type kind of question, but first you need to answer it physically).

 

[BvU]

Not bad for a thread with a "B" tag .
Just to remind me and other dimwits: what on Earth IS the radius of a proton in this context ? Or are we discussing some kind of form factor ? Wasn't a proton a bag with three quarks inside ?

 

[MathematicalPhysicist]

@BvU that's the problem with QM we have the particle/wave duality so it's somesort of a wavefunction, i.e. somesort of a sphere of distribution in space.

Obviously we don't have here literally balls of snooker like in classical physics.

 

[Vanadium 50]

is it possible to change a proton's radius

You mean can you squeeze it? I guess - but the forces will be astronomical. You would need pressures around 10³⁰ atmospheres. Furthermore, I don't see how this aligns with the thread: it's not a puzzle if you squeeze something and it gets smaller.

 

[MathematicalPhysicist]

And increasing the radius?

 

[bahamagreen]

I ask again, more simply; is the radius measured from the COM of the proton or the COM of the proton-muon couple?

 

[Vanadium 50]

Neither. What is measured are energy levels, and these energy levels depend on the charge distribution, as does the derived quantity they call the "radius".

 

[bahamagreen]

Neither. What is measured are energy levels, and these energy levels depend on the charge distribution, as does the derived quantity they call the "radius".

Of course what is measured are energy levels... ultimately there is no other kind of measurement.
To avoid additional rounds, I'll be explicit, and you may indicate where it breaks down...

- the derived quantity they call the "radius"
- that radius is a distance?
- that distance may be represented as a line segment?
- that line segment has two endpoints?
- one endpoint is nearer to the proton?
- does that nearer endpoint coincide with the proton's COM or that of the proton muon couple?

If your answer is still "Neither", can you describe the geometry of this derived quantity with respect to the proton?

 

[no-ir]

What about leptoquarks (see this)? They could contribute an additional distance-dependent coupling between the quarks in the proton and the electron/muon. As the electron has a different Bohr radius than the muon this would provide a shift in the total energy that would be unaccounted for by the SM without leptoquarks. Would that work?

 

[Nugatory]

If your answer is still "Neither", can you describe the geometry of this derived quantity with respect to the proton?

The paper that this thread was about (link in the first post of this thread) is good starting point.

 

[bahamagreen]

I looked at it again and found little relating to geometry... from the many calculations (and 20 corrections) it is clear they are using different "spaces" than a geometric space.
One thing I find curious is that the authors did not reference this 13 year old paper:
Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen

 

[cube137]

http://www.scientificamerican.com/article/the-proton-radius-puzzle/

for those still perflexed. check out the sci am article about it that is even in the cover page..

 

[cube137]

I reread the article and remembered all the details. It quoted "Perhaps the universe contains a heretofore undetected particle that somehow makes muons behave differently from electrons. Scientists have been exploring this option but have found it difficult to model a new particle that does not also produce observable consequences that violate the results of other experiments."

What is the ramification if the muon anomaly was real.. what other theories involved..

What is the purpose of muons in the Standard Model again? If there were no muons or taus and only first generation particles exist.. would we have a universe just like ours too with trees or oceans or planets?