Abstract
Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean-square charge radius of the nucleon $⟨{r}_{\mathrm{isov}}^{2}⟩$ and the quark-connected contributions to $⟨{r}_{p}^{2}⟩$ and $⟨{r}_{n}^{2}⟩$ for the proton and neutron, respectively. Computations are performed using a single gauge ensemble with ${N}_{f}=2+1+1$ maximally twisted mass clover-improved fermions at physical quark mass and a lattice spacing of $a=0.08\text{ }\text{ }\mathrm{fm}$.
Highlights
The radius of the proton is a fundamental quantity for atomic, nuclear, and particle physics
On the right-hand side, uðpi; siÞ, uðpf; sfÞ denote Dirac spinors, mN the nucleon mass, and we have introduced the Dirac and Pauli form factors F1ðQ2Þ and F2ðQ2Þ, which depend on the Euclidean four-momentum transfer Q2 1⁄4 −q2 with q⃗ 1⁄4 p⃗ f − p⃗ i
The lattice data for the electric Sachs form factor that are used as input in our calculation of the nucleon radii are shown in Fig. 3 as a function of Q2
Summary
The radius of the proton is a fundamental quantity for atomic, nuclear, and particle physics. In atomic physics, it enters in the determination of the Rydberg constant, the most precisely known constant in nature, as well as in precision tests of quantum electrodynamics. It enters in the determination of the Rydberg constant, the most precisely known constant in nature, as well as in precision tests of quantum electrodynamics In nuclear physics, it characterizes the size of the most abundant hadron in nature and in particle physics it is an input for beyond the standard model physics, testing lepton universality and the possible existence of new particles.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
