{"id":1021,"date":"2014-09-02T01:20:10","date_gmt":"2014-09-02T01:20:10","guid":{"rendered":"http:\/\/www.particlebites.com\/?p=1021"},"modified":"2017-02-19T01:33:24","modified_gmt":"2017-02-19T01:33:24","slug":"the-proton-radius-problem","status":"publish","type":"post","link":"https:\/\/www.particlebites.com\/?p=1021","title":{"rendered":"The Proton Radius Problem"},"content":{"rendered":"

The hydrogen atom is one of\u00a0the primary examples studied\u00a0in\u00a0a typical introductory quantum mechanics course. Recent measurements indicate that this simple system may still have surprises for us. Could this be a hint of new physics? This post is based on the following papers:<\/p>\n

\n“Muonic hydrogen and MeV forces” by D. Tucker-Smith and I. Yavin [1011.4922<\/a>], Phys. Rev.\u00a0D83<\/strong> (2011) 101702<\/br>
\n“Proton size anomaly” by V. Barger, C. Chiang, W. Keung, D. Marfatia [1011.3519<\/a>], Phys. Rev. Lett.\u00a0106<\/strong> (2011) 153001<\/br>
\n“The Size of the Proton” by Pohl et al. in\u00a0Nature 466 (2010) 213<\/a>\n<\/div>\n

Quantum mechanically, the proton\u00a0is an object whose\u00a0electric charge is smeared out over a\u00a0small region.\u00a0Experiments that scatter electrons off protons can probe this spatial extent and recent measurements indicate an effective proton charge radius of 0.877(7) femtometers.<\/p>\n

\"Electron<\/a>
Electron scattering experiments measure a particular proton radius. (Image by\u00a0the author.)<\/figcaption><\/figure>\n

Muons are\u00a0heavy copies of electrons and can similarly form muonic hydrogen: an atom formed from a proton and a muon. Because the muons are heavier, they exist closer to the nucleus and are more sensitive to the\u00a0extent of the proton charge: the effective Coulomb force\u00a0is reduced as one dips into the charge distribution in the same way that the gravitational force decreases as one digs towards\u00a0the center of the Earth.<\/p>\n

By ‘tickling’ the muon into a higher energy level\u00a0with\u00a0a laser and then measuring the resulting X-ray emission, one can deduce the proton radius. Since lasers can be tuned to very\u00a0precise frequencies,\u00a0one can\u00a0make a very precise measurement of the Lamb shift\u00a0in the muonic hydrogen energy levels. This, in turn,\u00a0can be\u00a0converted into a measurement of the\u00a0proton radius because the energy levels are sensitive to the overlap of the muon and proton\u00a0probability distributions. Intuitively,\u00a0when the muon is inside the proton charge radius, it\u00a0experiences a weaker Coulomb potential due to screening.<\/p>\n

The big surprise is that\u00a0the muonic hydrogen measurement gives a radius of 0.842(7) femtometers, this\u00a0is over five standard deviations smaller\u00a0than the expected result based on regular hydrogen!<\/p>\n

\"Measurements<\/a>
Measurements of the proton charge radius from the Lamb shift of muonic hydrogen are smaller than that from electron scattering by five standard deviations. (Image by the author)<\/figcaption><\/figure>\n

This discrepancy remains an open question despite several proposed\u00a0solutions based on more precise theoretical\u00a0calculations to relate the Lamb shift to the proton radius. One optimistic approach is to entertain\u00a0the possibility that this is an indicator of new\u00a0fundamental physics, such as a heretofore undiscovered force that tugs on the muon and electron differently. It turns out that these types of models are difficult to construct. One of the main constraints\u00a0is actually\u00a0nearly 40 years old<\/a>\u00a0and comes from the effect of such a\u00a0new force on neutron–lead scattering.<\/p>\n

Meanwhile,\u00a0a new set of experiments to probe\u00a0the proton radius anomaly are already underway. One of these\u00a0is the\u00a0Muon-Proton Scattering Experiment (MUSE); this would directly probe if\u00a0the origin of the discrepancy came\u00a0from the two different proton radius measurements\u00a0described above: scattering for electrons versus\u00a0spectroscopy for muons.<\/p>\n

Further reading:<\/p>\n