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The asymmetry of antimatter in the proton

A Publisher Correction to this article was published on 08 April 2022

This article has been updated


The fundamental building blocks of the proton—quarks and gluons—have been known for decades. However, we still have an incomplete theoretical and experimental understanding of how these particles and their dynamics give rise to the quantum bound state of the proton and its physical properties, such as its spin1. The two up quarks and the single down quark that comprise the proton in the simplest picture account only for a few per cent of the proton mass, the bulk of which is in the form of quark kinetic and potential energy and gluon energy from the strong force2. An essential feature of this force, as described by quantum chromodynamics, is its ability to create matter–antimatter quark pairs inside the proton that exist only for a very short time. Their fleeting existence makes the antimatter quarks within protons difficult to study, but their existence is discernible in reactions in which a matter–antimatter quark pair annihilates. In this picture of quark–antiquark creation by the strong force, the probability distributions as a function of momentum for the presence of up and down antimatter quarks should be nearly identical, given that their masses are very similar and small compared to the mass of the proton3. Here we provide evidence from muon pair production measurements that these distributions are considerably different, with more abundant down antimatter quarks than up antimatter quarks over a wide range of momenta. These results are expected to revive interest in several proposed mechanisms for the origin of this antimatter asymmetry in the proton that had been disfavoured by previous results4, and point to future measurements that can distinguish between these mechanisms.

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Fig. 1: Ratios σD/(2σH).
Fig. 2: Ratios \(\mathop{{\boldsymbol{d}}}\limits^{{\boldsymbol{-}}}({\boldsymbol{x}})/\mathop{{\boldsymbol{u}}}\limits^{{\boldsymbol{-}}}({\boldsymbol{x}})\).

Data availability

Raw data were generated at the Fermi National Accelerator Laboratory. Derived data supporting the findings of this study are available from the corresponding author upon request.

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We thank G. T. Garvey for contributions to the early stages of this experiment. We also thank the Fermilab Accelerator Division and Particle Physics Division for their support of this experiment. This work was performed by the SeaQuest Collaboration, whose work was supported in part by the US Department of Energy under grants DE-AC02-06CH11357, DE-FG02-07ER41528, DE-SC0006963; the US National Science Foundation under grants PHY 0969239, PHY 1306126, PHY 1452636, PHY 1505458, PHY 1614456; the DP&A and ORED at Mississippi State University; the JSPS (Japan) KAKENHI through grant numbers 21244028, 25247037, 25800133; the Tokyo Tech Global COE Program, Japan; the Yamada Science Foundation of Japan; and the Ministry of Science and Technology (MOST), Taiwan. Fermilab is operated by Fermi Research Alliance, LLC, under contract number DE-AC02-07CH11359 with the US Department of Energy.

Author information

Authors and Affiliations



P.E.R. and D.F.G. are the co-spokespersons for the experiment. The entire SeaQuest Collaboration constructed the experiment and participated in the data collection and analysis. Substantial contributions to the cross-section ratio analysis were made by graduate students J.D., B.K., R.E.M., S.M., D.H.M., K. Nagai, S.P., F.S., M.B.C.S. and A.S.T. The development of the technique of extrapolation to zero intensity greatly benefited from the work of A.S.T. All authors reviewed the manuscript.

Corresponding author

Correspondence to P. E. Reimer.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Gerald Miller, Gunar Schnell and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Comparison of NuSea and SeaQuest data with NLO calculations.

a, b, Comparison of the data from the present work and the NuSea measurements with NLO calculations made at the integrated kinematics of SeaQuest (a) and average kinematics of NuSea (b) based on the CT18 and CTEQ6m parton distributions. Events in the SeaQuest data were produced by a 120-GeV proton beam, whereas in the NuSea data were from an 800-GeV beam. In addition, the spectrometers, although similar in concept, had different acceptances. As a consequence, the cross-section ratios, which convolve xt with xb, are expected to differ because of their distinct distributions in accepted xb. These kinematic effects can clearly be seen by the difference between the curves. Because an acceptance table analogous to Extended Data Table 3 was not available for NuSea, those calculations used xt, xb and M of the NuSea data. Both CTEQ6m and CT18 have included the NuSea data in their global analysis, so calculations based on those probability distribution functions are expected to agree better with the NuSea data. The red (violet) curve in a (b) is the same as that in Fig. 1a and is repeated here for comparison.

Extended Data Fig. 2 Extrapolation to zero intensity.

Extrapolation to zero intensity fits for representative xt bins (0.13 ≤ xt < 0.16 (a), 0.195 ≤ xt < 0.240 (b) and 0.290 ≤ xt < 0.350 (c)). The I (intensity) and I2 coefficients are common to all bins. χ2/d.o.f. = 38.7/40 for the simultaneous fit of all xt bins (d.o.f., degrees of freedom).

Extended Data Fig. 3 Reconstructed invariant mass spectra.

a, b, Reconstructed muon-pair invariant-mass spectra for the liquid hydrogen (a) and liquid deuterium (b) targets. In the lower mass region, the predominant signal is produced by J/ψ → μ+μ decay, followed by μ+μ decay of ψ′. The prominence of the J/ψ peak provides a calibration point for the absolute field of the solid iron magnet. At invariant masses above 4.5 GeV/c2, the Drell–Yan process becomes the dominant feature. The data are shown as red points. Additionally, Monte Carlo (MC) simulated distributions of Drell–Yan, J/ψ and ψ′, along with measured random-coincidence and empty-target backgrounds, are shown. The sum of these is shown in the blue solid curve labelled ‘MC sum’. The normalizations of the Monte Carlo and the random background were from a fit to the data.

Extended Data Table 1 Ratios σD/(2σH) as a function of PT
Extended Data Table 2 Ratios σD/(2σH) as a function of M
Extended Data Table 3 Spectrometer acceptance

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Dove, J., Kerns, B., McClellan, R.E. et al. The asymmetry of antimatter in the proton. Nature 590, 561–565 (2021).

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