**The Muonic Hydrogen Problem**

Two recent physics papers address the fact that protons in muonic hydrogen apparently has a different radius than ordinary hydrogen when not quantum electrodynamics effects should make that possible.

One of the papers argues that this flows from failing to consider general and special relativity correctly in the calculations:

M.M. Giannini, E. Santopinto, "On the proton radius problem" (1 Nov 2013)This result is identical to that of a paper earlier this year by D. Robson, but does so in a manner that the authors of the new paper believes is more rigorous and theoretically correct. As the earlier paper explains:

The recent values of the proton charge radius obtained by means of muonic-hydrogen laser spectroscopy are about 4% different from the electron scattering data. It has been suggested that the proton radius is actually measured in different frames and that, starting from a non relativistic quark model calculation, the Lorentz transformation of the form factors accounts properly for the discepancy. We shall show that the relation between the charge radii measured in different frames can be determined on very general grounds by taking into account the Lorentz transformation of the charge density. In this way, the discrepancy between muonic-hydrogen laser spectroscopy and electron scattering data can be removed.

Associating the muonic-hydrogen data analysis for the proton charge radius of 0.84087 fm with the rest frame and associating the electron scattering with the Breit frame yields a prediction 0f 0.87944 fm for the proton radius in the relativistic frame. The most recent value deduced via electron scattering from the proton is 0.877(6)fm so that the frame dependence used here yields a plausible solution to the proton radius puzzle.Another paper, using very general realizations from lattice QCD argues that high energy hadrons are more compact than low energy hadrons (contrary to widespread intuition expressed in some QCD effective theories), and that the high energy of hadrons in the muonic hydrogen system may provide a QCD as opposed to a QED explanation:

Tamar Friedmann, "No Radial Excitations in Low Energy QCD. II. The Shrinking Radius of Hadrons" (Submitted on 12 Oct 2009 (v1), last revised 4 Nov 2013 (this version, v4))

We discuss the implications of our prior results obtained in our companion paper [arXiv:0910.2229]. Inescapably, they lead to three laws governing the size of hadrons, including in particular protons and neutrons that make up the bulk of ordinary matter: a) there are no radial excitations in low-energy QCD; b) the size of a hadron is largest in its ground state; c) the hadron's size shrinks when its orbital excitation increases. The second and third laws follow from the first law. It follows that the path from confinement to asymptotic freedom is a Regge trajectory. It also follows that the top quark is a free, albeit short-lived, quark. [For Note Added regarding experimental support, including the experiments studying muonic hydrogen, and other experiments, see last page.]

**Gravitational Impacts on Weak Sector Interactions**

Along the same lines as Giannini and Santopinto's paper, a recent paper looks at the role of gravity in Higgs boson and weak boson scattering. The paper predicts scattering effects that can be discerned at the TeV scale and hence that should be possible to observe at the LHC.

**Warm Dark Matter**

A recent paper compares three varieties of sterile neutrino production: non-resonant, oscillation based; non-resonant, non-oscillation based; and resonant. The paper argues that the first method of sterile neutrino production is inconsistent with Milky Way data, while not ruling out the other two. It also compares the conventional way of stating sterile neutrino mass of 2.5 keV is equivalent of a 0.7 keV thermal mass. The paper also engages in some critical analysis of the assumptions that go into sterile neutrino warm dark matter mass boundaries from other kinds of observations.

**Snowmass Paper On New Particles**

The latest Snowmass white paper on new particles is a disappointingly unimaginative and unpersuasive argument for building new very expensive colliders to detect new supersymmetric or other new particles or extra dimensions.

The discussion of WIMP dark matter in the white paper, for example, fails to meaningfully acknowledge the serious problems presented by astronomy models and observations with very heavy dark matter particles, despite abundant research on the subject that essentially rules out such heavy WIMPs based on observed dark matter phenomenology at galactic and smaller scales. Similarly, the discussion of compositeness fails to really grapple with the very high energy scales at which compositeness by the measures suggested have already been ruled out.

In areas where the paper really needed to be specific, like low energy blind spots at the LHC, or the waning solidity of the motivation for new TeV scale physics in light of the developments of the last couple years, it was decidely vague.

**A Low Energy Effective Weak Force Theory**

While mostly interesting as a historical novelty, an effective weak force theory for energies well below the W boson small scale, that does not require W bosons, Z bosons, Higgs bosons, or top quarks, that was explored by some of the leading physicists before these high energy particles were discovered (e.g. Fermi, Feynman, Gell-Mann, Marshak, and Sudarshan), is explored and refined in a recent paper.

The theory works at these low energies, and hence could be applied as a way to simplify calculations where the elaborations necessary to handle high energy situations is not required. It also is useful as a way of elaborating in a historically authentic way how a low energy effective theory can be transformed into a more exact higher energy effective theory and to clarify why the paradigm shift to the Standard Model approach was necessary.

**Within The Standard Model Neutrino Mixing Parameter Predictions**

A recent paper looks at an approach to add additional group symmetries (C

_{2}*D

_{3}) to the Standard Model lepton interactions in a manner that makes it possible to predict the three theta mixing angles of the PMNS matrix from a single parameter (which can be derived from a function of the three charged lepton masses). It also illustrates the interaction of the lepton masses and the neutrino oscillation mixing parameters.

## 9 comments:

"a recent paper looks at the role of gravity in Higgs boson and weak boson scattering. The paper predicts scattering effects that can be discerned at the TeV scale and hence that should be possible to observe at the LHC."

These aren't effects that anyone would expect to actually see. The paper concerns the xi parameter of Higgs inflation, which says how strong the coupling between Higgs and curvature is. For Higgs inflation, usually xi is around 10^4. For an LHC-detectable effect, xi needs to be about 10^15, an order of magnitude already noticed by Atkins and Calmet (ref 8 in this paper). I would be surprised if that magnitude of xi wasn't already ruled out by something in cosmology.

So I think the value of the paper is more the calculations that were carried out, than the predictions that were made. New calculations can be a prototype for further calculations in different regimes or with different assumptions.

The abstract states: "we derive unitarity bound on the Higgs gravitational coupling ξ in Einstein frame, which is stronger than that inferred from the current LHC Higgs measurements. We further study ξ-dependent weak boson scattering cross sections at TeV scale, and propose a new LHC probe of the Higgs-gravity coupling ξ via weak boson scattering experiments."

If I am awry, I have done so in reliance on a misleading abstract.

Andrew,

Thanks for the summary of recent papers. I'm glad to see that there is a science journalist who covers this material without assuming that supersymmetry & WIMP-cold-dark-matter have already been proven, such as is the case for most journalists at Scientific American and New Scientist.

My question is related to the discussion of warm-dark-matter in your post. I've been loosely following this research, and I see that you have been covering in detail for a while. My question is: there was a recent paper (covered by New Scientist) that states that the RMS speed of dark matter must be less than 54 m/s.

http://www.newscientist.com/article/dn24361-speed-limit-found-for-sluggish-dark-matter.html#.UnpS3_nku88

In the paper, the authors rule out dark matter with a rest mass of less than 1 keV. However, it seems to me that if there is a limit of 54 m/s, then this likely rules out dark matter with rest masses less than scales ~GeV.

Are you familiar with the paper with the 54 m/s RMS speed limit? And if so, does this rule of the possibility of ~2 keV warm dark matter? (which de Vega et al. has shown to fit some astrophysical data really well)

Thanks for any additional thoughts on this subject of warm-dark-matter.

Thanks for the tip. I'll look into it. I haven't looked at the paper. I have seen multiple papers rule out dark matter with a rest mass of less than 1 keV on various grounds.

This paper is tricky to interpret.

Page 20: the temperature T0 is not the actual present-day DM temperature, it is (apparently) what the temperature would be if the DM hadn't clumped together because of gravity.

Page 21: the bound on "DM temperature" is not so far from a corresponding (counterfactual?) temperature for baryonic matter. So perhaps these bounds are less constraining than it seems?

It also seems that the bounds become weaker as the DM mass gets smaller, because the bound is for T0/M.

Page 26: an absolute lower-bound of 1 keV for DM particles which interact according to equation 49. I wonder if there is a DM model in which the mass is *caused* to be on the edge of the bound, much as the Higgs boson mass is caused to be at the edge of criticality in some models?

But all these comments should be treated as suspect until we really understand the paper.

Andrew and Mitchell,

Thanks for looking into this.

I was confused on what value to use for T in their "sqrt(T/m)" equation.

I'm especially confused now that I read the paper you link to in this post, which states that there's a difference between the rest mass and what they are calling "thermal mass." So, now I'm not even sure what to use for m (rest mass or this thermal mass?).

The Horiuchi paper seems to be setting a limit of ~9 keV (assuming that there is only one type of dark matter particle.) But what's great about the Horiuchi paper is that one can also infer a maximum rest energy of ~14 keV. Though, I didn't see them put a constraint on maximum rest mass. Their data clearly rules out Cold Dark Matter, but they didn't focus on that in their conclusions.

Eddie - there's no way that paper rules out CDM, but I can't even figure out what your argument is. Where do you get this maximum of 14 keV from?

Horiuchi et al's concept of thermal mass is supposedly explained somewhere in reference 32, perhaps near its equation 5, but so far I cannot parse what is being said there. In particle physics, a "thermal mass" is often some sort of effective mass, e.g. a particle being slowed down in a thermal medium as if it were heavier, but this seems to be something else.

Mitchell,

In Table II, the observed number of subhalo counts is 18, and in Figure 2, one sees that, if the mass is greater than 14 keV, then the model predicts more subhalo counts than observed.

CDM models consistently overpredict the amount of dark matter at the center of galaxies.

All I was point out is that the paper by Vega et al as well as this paper pretty much rule out CDM.

The only reason that I'm hesitant to say that this is 100% true is due to the fact that researchers haven't found a 2-14 keV dark matter particle and due to the 54 m/s RMS speed minimum that Horiuchi found.

I'm still working all this out, but I can now say two things:

Sterile neutrinos produced by the Dodelson-Widrow mechanism have a distribution of velocities that deviates slightly from a perfect thermal (equilibrium) distribution. However, their cosmological effects could be imitated by a truly thermal distribution of dark matter particles, if the DM particle had a slightly different mass than the Dodelson-Widrow neutrino. This "other mass that would have looked the same" is the "thermal mass".

54 m/s is a bound on the RMS variance of CDM particle speeds. It just means that they would all be almost at rest with respect to each other - if gravity hadn't caused them to clump; remember that it's a counterfactual quantity, the velocity dispersion of CDM today *if there had been no small-scale structure formation*, and not a statement about how fast they should be moving in the real world of today.

So bizarrely, neither quantity refers directly to present-day reality.

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