QED confronts the radius of the proton

Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Two reasons justify a further look at this subject: 1) One of the approximations used in [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by $\sim 3$ of the standard deviations of [1], in the "right" direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius "runs", much as the QCD coupling "constant" does. 2) The result of [1] requires a choice of the "third Zemach moment". Its published independent determination is based on an analysis with a $p$-value --the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis-- of $3.92\times 10^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently {\it at most} $\sim 4\sigma$. There is no tension between the results of [1] and the proton radius determined with help of the analyticity of its form factors.Comment: Extended for publication in Physics Letter

QED is not endangered by the proton's size

Pohl et al. have reported a very precise measurement of the Lamb-shift in muonic Hydrogen, from which they infer the radius characterizing the proton's charge distribution. The result is 5 standard deviations away from the one of the CODATA compilation of physical constants. This has been interpreted as possibly requiring a 4.9 standard-deviation modification of the Rydberg constant, to a new value that would be precise to 3.3 parts in $10^{13}$, as well as putative evidence for physics beyond the standard model. I demonstrate that these options are unsubstantiated.Comment: Modified following comments in arXiv:1008.4345v1. 4 pages, 2 figure

Comment on "The third Zemach moment of the proton", by Cloet and Miller

Cloet and Miller, in arXiv:1008.4345, state that "existing data rule out a value of the third Zemach moment large enough to explain the current puzzle with the proton charge radius determined from the Lamb shift in muonic Hydrogen. This is in contrast with the recent claim of De R\'ujula [arXiv:1008.3861]". To be more precise: it is not. It is, however, contrary to what they claim that I claim. Cloet and Miller have simply misinterpreted my claims.Comment: 2 pages, no figure

Two old ways to measure the electron-neutrino mass

Three decades ago, the measurement of the electron neutrino mass in atomic electron capture (EC) experiments was scrutinized in its two variants: single EC and neutrino-less double EC. For certain isotopes an atomic resonance enormously enhances the expected decay rates. The favoured technique, based on calorimeters as opposed to spectrometers, has the advantage of greatly simplifying the theoretical analysis of the data. After an initial surge of measurements, the EC approach did not seem to be competitive. But very recently, there has been great progress on micro-calorimeters and the measurement of atomic mass differences. Meanwhile, the beta-decay neutrino-mass limits have improved by a factor of 15, and the difficulty of the experiments by the cube of that figure. Can the "calorimetric" EC theory cope with this increased challenge? I answer this question affirmatively. In so doing I briefly review the subject and extensively address some persistent misunderstandings of the underlying quantum physics.Comment: 11 pages. 17 figure

Measuring the W-Boson mass at a hadron collider: a study of phase-space singularity methods

The traditional method to measure the W-Boson mass at a hadron collider (more precisely, its ratio to the Z-mass) utilizes the distributions of three variables in events where the W decays into an electron or a muon: the charged-lepton transverse momentum, the missing transverse energy and the transverse mass of the lepton pair. We study the putative advantages of the additional measurement of a fourth variable: an improved phase-space singularity mass. This variable is statistically optimal, and simultaneously exploits the longitudinal- and transverse-momentum distributions of the charged lepton. Though the process we discuss is one of the simplest realistic ones involving just one unobservable particle, it is fairly non-trivial and constitutes a good "training" example for the scrutiny of phenomena involving invisible objects. Our graphical analysis of the phase space is akin to that of a Dalitz plot, extended to such processes.Comment: 11 pages. 9 figures. Version to be published in JHE

The calorimetric spectrum of the electron-capture decay of 163^{163}Ho. A preliminary analysis of the preliminary data

It is in principle possible to measure directly the electron neutrino mass (or masses and mixing angles) in weak electron-capture decays. The optimal nuclide in this respect is $^{163}$Ho. The favoured experimental technique, currently pursued in various experiments (ECHo, HOLMES and NuMECS) is "calorimetric". The calorimetric energy spectrum is a sum over the unstable vacant orbitals, or "holes", left by the electrons weakly captured by the nucleus. We discuss the current progress in this field and analize the preliminary data. Our conclusion is that, as pointed out by Robertson, the contribution of two-hole states is not negligible. But --in strong contradistinction with the tacit conclusion of previous comparisons of theory and observations-- we find a quite satisfactory agreement. A crucial point is that, in the creation of secondary holes, electron shakeoff and not only electron shakeup must be taken into account.Comment: 6 pages, 5 figures. Section IV and Fig.3 added. Minor text modification

Will relativistic heavy-ion colliders destroy our planet?

Experiments at the Brookhaven National Laboratory will study collisions between gold nuclei at unprecedented energies. The concern has been voiced that ``strangelets''-hypothetical products of these collisions - may trigger the destruction of our planet. We show how naturally occurring heavy-ion collisions can be used to derive a safe and stringent upper bound on the risk incurred in running these experiments.Comment: LaTeX, no figure

The calorimetric spectrum of the electron-capture decay of 163^{163}Ho. The spectral endpoint region

The electron-neutrino mass (or masses and mixing angles) may be directly measurable in weak electron-capture decays. The favoured experimental technique is "calorimetric". The optimal nuclide is $^{163}$Ho, and several experiments (ECHo, HOLMES and NuMECS) are currently studying its decay. The most relevant range of the calorimetric-energy spectrum extends for the last few hundred eV below its endpoint. It has not yet been well measured. We explore the theory, mainly in the cited range, of electron capture in $^{163}$Ho decay. A so far neglected process turns out to be most relevant: electron-capture accompanied by the shake-off of a second electron. Our two main conclusions are very encouraging: the counting rate close to the endpoint may be more than an order of magnitude larger than previously expected; the "pile-up" problem may be significantly reduced.Comment: Clarifying changes suggested by a referee. Results unchanged. 14 pages, 15 figure

Is the diffuse gamma background radiation generated by galactic cosmic rays?

We explore the possibility that the diffuse gamma-ray background radiation (GBR) at high galactic latitudes could be dominated by inverse Compton scattering of cosmic ray (CR) electrons on the cosmic microwave background radiation and on starlight from our own galaxy. Assuming that the mechanisms accelerating galactic CR hadrons and electrons are the same, we derive simple and successful relations between the spectral indices of the GBR above a few MeV, and of the CR electrons and CR nuclei above a few GeV. We reproduce the observed intensity and angular dependence of the GBR, in directions away from the galactic disk and centre, without recourse to hypothetical extragalactic sources.Comment: Submitted for publicatio

Neutrino Helioseismology

The observed deficit of $\rm ^8B$ solar neutrinos may call for an improved standard model of the sun or an expanded standard model of particle physics ({\it e.g.,} with neutrino masses and mixing). In the former case, contemporary fluid motions and thermal fluctuations in the sun's core may modify nuclear reaction rates and restore agreement. To test this notion, we propose a search for short--term variations of the solar neutrino flux.Comment: 4 pages, HUTP-92/A03