Letter | Published:

# Precision measurement of the weak charge of the proton

## Abstract

Large experimental programmes in the fields of nuclear and particle physics search for evidence of physics beyond that explained by current theories. The observation of the Higgs boson completed the set of particles predicted by the standard model, which currently provides the best description of fundamental particles and forces. However, this theory’s limitations include a failure to predict fundamental parameters, such as the mass of the Higgs boson, and the inability to account for dark matter and energy, gravity, and the matter–antimatter asymmetry in the Universe, among other phenomena. These limitations have inspired searches for physics beyond the standard model in the post-Higgs era through the direct production of additional particles at high-energy accelerators, which have so far been unsuccessful. Examples include searches for supersymmetric particles, which connect bosons (integer-spin particles) with fermions (half-integer-spin particles), and for leptoquarks, which mix the fundamental quarks with leptons. Alternatively, indirect searches using precise measurements of well predicted standard-model observables allow highly targeted alternative tests for physics beyond the standard model because they can reach mass and energy scales beyond those directly accessible by today’s high-energy accelerators. Such an indirect search aims to determine the weak charge of the proton, which defines the strength of the proton’s interaction with other particles via the well known neutral electroweak force. Because parity symmetry (invariance under the spatial inversion (x, y, z) → (−x, −y, −z)) is violated only in the weak interaction, it provides a tool with which to isolate the weak interaction and thus to measure the proton’s weak charge1. Here we report the value 0.0719 ± 0.0045, where the uncertainty is one standard deviation, derived from our measured parity-violating asymmetry in the scattering of polarized electrons on protons, which is −226.5 ± 9.3 parts per billion (the uncertainty is one standard deviation). Our value for the proton’s weak charge is in excellent agreement with the standard model2 and sets multi-teraelectronvolt-scale constraints on any semi-leptonic parity-violating physics not described within the standard model. Our results show that precision parity-violating measurements enable searches for physics beyond the standard model that can compete with direct searches at high-energy accelerators and, together with astronomical observations, can provide fertile approaches to probing higher mass scales.

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## Change history

• ### 22 May 2018

In the originally published article, equation (6) was corrupted. This has now been corrected.

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## Acknowledgements

This work was supported by the US Department of Energy (DOE) Contract number DEAC05-06OR23177, under which Jefferson Science Associates, LLC, operates the Thomas Jefferson National Accelerator Facility. Construction and operating funding for the experiment was provided through the US DOE, the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Foundation for Innovation (CFI), and the National Science Foundation (NSF) with university matching contributions from the College of William and Mary, Virginia Tech, George Washington University and Louisiana Tech University. We thank the staff of Jefferson Laboratory, in particular the accelerator operations staff, the target and cryogenic groups, the radiation control staff, as well as the Hall C technical staff for their help and support. We are grateful for the contributions of our undergraduate students. We thank TRIUMF for its contributions to the development of the spectrometer and integrated electronics, and BATES for its contributions to the spectrometer and Compton polarimeter. We are indebted to P. G. Blunden, J. D. Bowman, J. Erler, N. L. Hall, W. Melnitchouk, M. J. Ramsey-Musolf and A. W. Thomas for discussions. We also thank P. A. Souder for contributions to the analysis. Figure 2 was adapted with permission from ref. 3 (copyrighted by the American Physical Society).

## Author information

### Author notes

1. A list of participants and their affiliations appears at the end of this Letter.

2. Deceased: W. R. Falk, J. M. Finn, P. Solvignon.

### Affiliations

• D. Androić
•  & T. Seva
2. #### Department of Physics, College of William and Mary, Williamsburg, VA, USA

• D. S. Armstrong
• , T. Averett
• , K. Bartlett
• , R. D. Carlini
• , J. C. Cornejo
• , W. Deconinck
• , J. F. Dowd
• , J. M. Finn
• , V. M. Gray
• , K. Grimm
• , J. R. Hoskins
• , J. Leckey
• , J. H. Lee
• , J. A. Magee
•  & S. Yang
3. #### Division of Experimental Physics, A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan, Armenia

• A. Asaturyan
• , A. Mkrtchyan
• , H. Mkrtchyan
• , V. Tadevosyan
•  & S. Zhamkochyan
4. #### Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

• J. Balewski
• , F. Guo
• , S. Kowalski
•  & J. F. Rajotte
5. #### Physics Division, Thomas Jefferson National Accelerator Facility, Newport News, VA, USA

• J. Beaufait
• , J. Benesch
• , R. D. Carlini
• , S. Covrig Dusa
• , D. Gaskell
• , M. Jones
• , D. Mack
• , D. Meekins
• , J. Mei
• , R. Michaels
• , B. Sawatzky
• , G. R. Smith
• , P. Solvignon
•  & S. A. Wood
6. #### Department of Physics and Astronomy, Ohio University, Athens, OH, USA

• R. S. Beminiwattha
• , P. M. King
• , J. H. Lee
• , J. Roche
•  & B. Waidyawansa
7. #### Department of Physics, Christopher Newport University, Newport News, VA, USA

• F. Benmokhtar
8. #### Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada

• J. Birchall
• , W. R. Falk
• , M. T. W. Gericke
• , L. Lee
• , S. MacEwan
• , R. Mahurin
• , W. T. H. van Oers
• , S. A. Page
• , J. Pan
• , W. D. Ramsay
• , V. Tvaskis
•  & P. Wang
9. #### Department of Physics, University of Virginia, Charlottesville, VA, USA

• M. M. Dalton
• , C. Gal
• , D. Jones
• , M. Kargiantoulakis
• , V. Nelyubin
• , K. D. Paschke
• , R. Silwal
•  & W. A. Tobias
10. #### Science Division, TRIUMF, Vancouver, British Columbia, Canada

• C. A. Davis
• , L. Lee
• , W. T. H. van Oers
•  & W. D. Ramsay
11. #### Department of Physics, Hampton University, Hampton, VA, USA

• J. Diefenbach
•  &  Nuruzzaman
12. #### Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS, USA

• J. A. Dunne
• , D. Dutta
• , A. Narayan
• , L. Z. Ndukum
• ,  Nuruzzaman
• , M. H. Shabestari
•  & A. Subedi
13. #### Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

• W. S. Duvall
• , J. Leacock
• , A. R. Lee
• , J. Mammei
• , N. Morgan
•  & M. L. Pitt

• M. Elaasar

• T. Forest
16. #### Department of Physics, Louisiana Tech University, Ruston, LA, USA

• T. Forest
• , K. Grimm
• , H. Nuhait
• , N. Simicevic
•  & S. P. Wells
17. #### Accelerator Division, Thomas Jefferson National Accelerator Facility, Newport News, VA, USA

• J. Grames
• , M. Poelker
•  & R. Suleiman

• R. Jones

• E. Korkmaz
20. #### Department of Physics, University of Winnipeg, Winnipeg, Manitoba, Canada

• J. W. Martin
•  & V. Tvaskis
21. #### Department of Physics, George Washington University, Washington, DC, USA

• M. J. McHugh
• , K. E. Mesick
• , A. Micherdzinska
• , A. K. Opper
•  & R. Subedi
22. #### Department of Physics, University of New Hampshire, Durham, NH, USA

• S. K. Phillips
23. #### Physics Department, Hendrix College, Conway, AR, USA

• D. T. Spayde
24. #### Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, South Australia, Australia

• R. D. Young

• W. R. Falk
•  & P. Zang

### Contributions

Authors contributed to one or more of the following areas: proposing, leading and running the experiment; design, construction, optimization and testing of the experimental apparatus and data acquisition system; data analysis; simulation; extraction of the physics results from measured asymmetries; and the writing of this Letter.

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to R. D. Carlini or G. R. Smith.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Apparatus.

a, Schematic of critical accelerator components and the Qweak apparatus4. The electron beam is generated at the photocathode, accelerated by the Continuous Electron Beam Accelerator Facility (CEBAF) and sent to experimental Hall C, where it is monitored by beam position monitors and beam current monitors. The insertable half-wave plate (IHWP) provides slow reversal of the electron beam helicity. The data acquisition system records the data. b, Computer-aided design drawing of the experimental apparatus. c, The Qweak apparatus, before the final shielding configuration was installed. d, Interior of the hut shielding the detectors, showing two of the Cherenkov detectors (right) and a pair of tracking chambers (left).

2. ### Extended Data Fig. 2 Beamline background.

Determination of Abb, the false asymmetry arising from beamline background events. Uncertainties are 1 s.d. a, Correlation of the main detector asymmetry to that of the upstream luminosity monitors, measured when the signal from elastically scattered electrons in the main detectors was blocked at the first collimator. b, Correlation of asymmetries from the upstream luminosity monitors with one of the other background detectors (a bare PMT located in the detector shield house). c, Correlation of the unblocked main detector asymmetry to that of the upstream luminosity monitor for Run 2. Our Abb determination was based on this slope.

3. ### Extended Data Fig. 3 Rescattering bias.

a, Schematic illustrating the precession of longitudinally polarized electrons through the spectrometer magnet, generating sizeable transverse spin components upon arrival at the detector array (spin directions indicated by red and blue arrows for the two electron helicity states). An end-view of the detector array, indicating the right (R) and left (L) PMT positions, is shown on the left. b, Difference between the asymmetry measured by the two (R and L) PMT tubes versus the detector number (Run 2 data). c, Calculated rescattering bias Abias versus detector number, with the eight-detector-averaged value shown by the red lines. Uncertainties (1 s.d.) are systematic.

4. ### Extended Data Fig. 4 Electron beam polarization.

Measurements from the Compton (closed blue circles) and Møller (open red squares) polarimeters during Run 2. Inner error bars denote statistical uncertainties and outer error bars show the statistical and point-to-point systematic uncertainties added in quadrature. Normalization, or scale-type, uncertainties are shown by the solid blue (Compton) and red (Møller) bands. All uncertainties are 1 s.d. The yellow band shows the derived polarization values used in the evaluation of the parity-violating asymmetry Aep. The time dependence of the reported polarization is driven primarily by the continuous Compton measurements, with a small-scale correction (0.21%, not included in this figure) determined from an uncertainty-weighted global comparison of the Compton and Møller polarimeters.

5. ### Extended Data Fig. 5 Asymmetry from aluminium.

Parity-violating asymmetry from the aluminium alloy target versus the dataset number. All uncertainties are 1 s.d. The labels ‘IN’ and ‘OUT’ refer to the state of the insertable half-wave plate at the electron source, which generated a 180° flip of the electron spin when IN. The subscripts denote the setting of the Wien filter, with L and R corresponding to the presence and absence, respectively, of an additional 180° rotation of the spin direction of the electron beam. A period in which a further 180° flip was generated through (ge − 2) precession (ge, electron gyromagnetic ratio) via a modified accelerator configuration during Wien 6 is indicated. The combinations OUT–R and IN–L with no (ge − 2) spin flip reveal the physical sign of the asymmetry. Solid lines represent the time-averaged values, and the horizontal dashed line indicates zero asymmetry. The vertical dashed lines delineate particular data subsets with a given Wien filter setting. Source Data

6. ### Extended Data Fig. 6 Asymmetry from the proton.

Observed parity-violating asymmetry Aep after all corrections, versus the dataset number (acquired in the double-Wien-filter configuration). The Wien filter reversed the beam helicity at approximately monthly intervals. The subscripts denote the setting of the Wien filter as L or R, corresponding to the presence or absence, respectively, of a 180° rotation of the spin direction of the electron beam. IN and OUT refer to the state of the insertable half-wave plate at the electron source, generating an additional 180° flip of the spin when IN. A period in which a further 180° flip was generated through (ge − 2) precession via a modified accelerator configuration is indicated. The combinations OUT–R and IN–L with no (ge − 2) flip reveal the physical sign of the asymmetry. Solid lines represent the time-averaged values and the dashed line indicates zero asymmetry. The uncertainties (1 s.d.) shown are those of the corresponding Amsr values (see text) only—that is, they do not include time-independent uncertainties—so as to illustrate the time stability of the results. The weighted mean and P-value of the upper OUT–L and IN–R data are 226.9 ± 10.2, P = 0.59 (upper solid line), respectively. For the opposite combination, OUT–R and IN–L, we find a weighted mean of −226.1 ± 10.5 and P = 0.36 (lower solid line). Source Data