Recently, Feng Xu's research group at the School of Physics of Peking University and Jin Luchang, assistant professor at the University of Connecticut, cooperated to study the Lamb displacement of the Miu hydrogen atom for the first time using lattice quantum chromodynamics (lattice QCD), and successfully obtained the correction of the lamb displacement by two-photon exchange. The results were published online in the Physical Review Letters.
Image courtesy of Physical Review Letters
Protons are one of the elementary particles that make up the material world, and it has a complex internal structure consisting of charged quarks and uncharged gluons. The radius of charge distribution inside a proton is also commonly used to measure proton size.
In 2010, physicists determined the charge distribution radius by accurately measuring the Lamb shift of the mire hydrogen atom (that is, the electrons in the hydrogen atom are replaced by muses) to capture the small effects of the charge distribution inside the proton on the energy level of the miu hydrogen atom. The Lamb shift is the difference in energy levels between 2S (1/2) and 2P (1/2) of hydrogen atoms measured by physicists Lamb and Retherford in 1947 using microwave technology.
The fine structure of the hydrogen atom, the ultra-fine structure, and the Lamb displacement, image from HyperPhysics
Although the accuracy of the Miu hydrogen spectroscopy experiment is much higher than other experiments, the radius of charge distribution obtained from it is 5 standard deviations from the previous global average, the so-called proton size mystery. In 2019, the latest electron-proton scattering and hydrogen atom spectroscopy experiments are in line with the results of the Miu hydrogen experiment, indicating that the mystery of proton size is gradually being solved, and the experimental divergence is gradually narrowing.
So far, the Miu hydrogen spectroscopy experiment is still the most accurate experimental means to obtain the radius of proton charge. High-precision measurements in spectroscopy make QCD's contribution even more important in theoretical and experimental comparisons. In fact, the main theoretical error in extracting the charge distribution radius from the Miu Hydrogen Lamb displacement comes from the non-perturbed QCD-dominated two-photon exchange Feyns diagram.
Hydrogen atom and Miu hydrogen atom (left), two-photon exchange Feynman diagram (right), picture from Peking University
This time, the research group of Researcher Feng Xu of the Institute of Theoretical Physics of the School of Physics of Peking University cooperated with Assistant Professor Jin Luchang of connecticute University to solve the infrared divergence problem of two-photon diagram, develop a new long-range subtraction scheme to reduce statistical errors, and rely on the "Tianhe-3" supercomputer of China Supercomputer Tianjin Center to realize the grid point calculation of two-photon diagram for the first time. On this basis, the team plans to further carry out more systematic and accurate calculations in order to finally solve the basic scientific problem of "how big are protons".
The aforementioned study shows that the lattice point method can also be used to study other important spectroscopic physical quantities such as ultra-fine spectroscopy. One of the future priorities of the Peking University Grid Point team is to expand the study of grid point QCD to atomic spectroscopy, building an interdisciplinary bridge between high-energy physics research at the quark and gluon scale and extremely high-precision atomic spectroscopy research.
Two-photon exchange contributed to the lattice QCD calculation results, picture from Peking University
The first author of the paper is Fu Yang, a doctoral student at the School of Physics of Peking University, and Lu Chenfei, an undergraduate student, who participated in some calculations and data analysis. The above research work has been supported by the National Natural Science Foundation of China, the National Key Research and Development Program, the Collaborative Innovation Center for Quantum Matter Science, the Center for High Energy Physics of Peking University, and the National Supercomputing Tianjin Center.