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Register a new userThe Proton Radius Puzzle
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Carl E. Carlson
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The proton size, specifically its charge radius, was thought known to about 1% accuracy. Now a new method probing the proton with muons instead of electrons finds a radius about 4% smaller, and to boot gives an uncertainty limit of about 0.1%. We review the different measurements, some of the calculations that underlie them, some of the suggestions that have been made to resolve the conflict, and give a brief overview new related experimental initiatives. At present, however, the resolution to the problem remains unknown.
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In 2010 the proton charge radius was extracted for the first time from muonic hydrogen, a bound state of a muon and a proton. The value obtained was five standard deviations away from the regular hydrogen extraction. Taken at face value, this might be an indication of a new force in nature coupling to muons, but not to electrons. It also forces us to reexamine our understanding of the structure of the proton. Here I describe an ongoing theoretical research effort that seeks to address this proton radius puzzle. In particular, I will present the development of new effective field theoretical tools that seek to directly connect muonic hydrogen and muon-proton scattering.
High-precision measurements of the proton radius from laser spectroscopy of muonic hydrogen demonstrated up to six standard deviations smaller values than obtained from electron-proton scattering and hydrogen spectroscopy. The status of this discrepancy, which is known as the proton radius puzzle will be discussed in this paper, complemented with the new insights obtained from spectroscopy of muonic deuterium.
The FAMU (Fisica degli Atomi Muonici) experiment has the goal to measure precisely the proton Zemach radius, thus contributing to the solution of the so-called proton radius puzzle. To this aim, it makes use of a high-intensity pulsed muon beam at RIKEN-RAL impinging on a cryogenic hydrogen target with an high-Z gas admixture and a tunable mid-IR high power laser, to measure the hyperfine (HFS) splitting of the 1S state of the muonic hydrogen. From the value of the exciting laser frequency, the energy of the HFS transition may be derived with high precision and thus, via QED calculations, the Zemach radius of the proton. The experimental apparatus includes a precise fiber-SiPMT beam hodoscope and a crown of eight LaBr3 crystals and a few HPGe detectors for detection of the emitted characteristic X-rays. Preliminary runs to optimize the gas target filling and its operating conditions have been taken in 2014 and 2015-2016. The final run, with the pump laser to drive the HFS transition, is expected in 2018.
We review the status of the proton charge radius puzzle. Emphasis is given to the various experiments initiated to resolve the conflict between the muonic hydrogen results and the results from scattering and regular hydrogen spectroscopy.
We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $mathcal{O}(a)$-improved Wilson fermions and an $mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $mu=4.71(11)_{mathrm{stat}}(13)_{mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $langle r_mathrm{M}^2rangle~=~0.661(30)_{mathrm{stat}}(11)_{mathrm{sys}},~mathrm{fm}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $langle r_mathrm{E}^2rangle = 0.800(25)_{mathrm{stat}}(22)_{mathrm{sys}},~mathrm{fm}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.
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