Received 19 March 2022; 

online 24 March 2022

Using new data, this study delivers the first model-independent prediction for the proton valence-quark ratio: d_V/u_V(x_B→1)=0.230(57), thereby establishing a benchmark against which all pictures of the proton can be measured in future.

Figure 1. lim_x→1F₂ⁿ(x)/F₂^p(x). MARATHON-based SPM prediction compared with results inferred from: nuclear DIS; Dyson–Schwinger equation analyses (DSE); quark counting (helicity conservation); and a phenomenological fit (CJ15).  The vertical red line marks the physical lower limit on this ratio.

The proton is a bound state of three valence quarks, 1 down (d) and 2 up (u).  At large values of the Bjorken scaling variable, which equates to a quark’s fraction of the proton’s total momentum, the in-proton d-quark/u-quark ratio of number-densities defines what is meant by a valence quark, i.e., what most people really think of when they hear the word “quark”.  Despite the simple 1:2 ratio of valence-quark numbers, owing to the character of quantum field theory, the d/u ratio needs not be ½.  Thus, determining the ratio’s value has been the subject of intense experimental and theoretical effort for almost 50 years. 

An international team, joining physicists in China, Germany, and Italy, introduced a new mathematical technique – the Schlessinger point method (SPM) – into the analysis of data collected in deep inelastic scattering experiments on light mirror nuclei.  Specifically designed to ensure extraction of all objective information contained in the data, the approach is also mathematically guaranteed to deliver a robust extrapolation onto any unmeasured domain with a sound estimate of uncertainty at each point.  The result, shown in Fig. 1, is the first model-independent prediction for the neutron-to-proton structure function ratio that extends onto the crucial valence-quark domain: lim_xB→1⁡F₂ⁿ(x_B)/F₂^P(x_B)=0.454(47).

This study opens the door to new insights into the character of the proton, Nature’s most fundamental bound state, which lies at the core of atoms and defines nuclear physics.  It emphasizes the role of two types of complex quark+quark correlations within the proton and establishes with a 99.999986% level of confidence that the proton wave function contains both such correlations.  This is a very tight constraint on proton structure theory, which can be used to eliminate many existing models.  Further, in establishing the importance of such correlations, it shows that hadron structure studies have many similarities with bound state problems in other areas of physics.