1 Precision Measurement of the Weak Charge of the Proton The �weak Collaboration: D. Androić 1, D.S. Armstrong2, A. Asaturyan3, T. Averett2, J. Balewski4, K. Bartlett2, J. Beaufait5, R.S. Beminiwattha6, J. Benesch5, F. Benmokhtar7, J. Birchall8, R.D. Carlini5,2*, J.C. Cornejo2, S. Covrig Dusa5, M.M. Dalton9, C.A. Davis10, W. Deconinck2, J. Diefenbach11, J.F. Dowd2, J.A. Dunne12, D. Dutta12, W.S. Duvall13, M. Elaasar14, W.R. Falk8,†, J.M. Finn2,†, T. Forest15,16, C. Gal9, D. Gaskell5, M.T.W. Gericke8, J. Grames17, V.M. Gray2, K. Grimm16,2, F. Guo4, J.R. Hoskins2, D. Jones9, M. Jones5, R. Jones18, M. Kargiantoulakis9, P.M. King6, E. Korkmaz19, S. Kowalski4, J. Leacock13, J. Leckey2, A.R. Lee13, J.H. Lee6,2, L. Lee10,8, S. MacEwan8, D. Mack5 , J.A. Magee2, R. Mahurin8, J. Mammei13, J.W. Martin20, M.J. McHugh21, D. Meekins5, J. Mei5, K.E. Mesick21, R. Michaels5, A. Micherdzinska21, A. Mkrtchyan3,H. Mkrtchyan3, N. Morgan13, A. Narayan12, L.Z. Ndukum12, V. Nelyubin9, H. Nuhait16, Nuruzzaman11,12, W.T.H. van Oers10,8, A.K. Opper21, S.A. Page8, J. Pan8, K.D. Paschke9, S.K. Phillips22, M.L. Pitt13, M. Poelker17, J.F. Rajotte4, W.D. Ramsay10,8, J. Roche6, B. Sawatzky5, T. Seva1, M.H. Shabestari12, R. Silwal9, N. Simicevic16, G.R. Smith5*, P. Solvignon5,†, D.T. Spayde23, A. Subedi12, R. Subedi21, R. Suleiman17, V. Tadevosyan3, W.A. Tobias9, V. Tvaskis20,8, B. Waidyawansa6, P. Wang8, S.P. Wells16, S.A. Wood5, S. Yang2, R.D. Young24, P. Zang25, and S. Zhamkochyan3. *Corresponding author, †Deceased Collaborating Institutions: 1Department of Physics, University of Zagreb, Zagreb HR-10002, Croatia. 2Department of Physics, William & Mary, Williamsburg, Virginia 23185, USA. 3Division of Experimental Physics, A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan 0036, Armenia. 4Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. 5Physics Division, Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA. 6Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA. 7Department of Physics, Christopher Newport University, Newport News, Virginia 23606, USA. 8Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada. 9Department of Physics, University of Virginia, Charlottesville, Virginia 22903, USA. 10Science Division, TRIUMF, Vancouver, British Columbia V6T 2A3, Canada. 11Department of Physics, Hampton University, Hampton, Virginia 23668, USA. 12Department of Physics and Astronomy, Mississippi State University, Mississippi State, Mississippi 39762, USA. 13Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA. 14Department of Natural Sciences, Southern University at New Orleans, New Orleans, Louisiana 70126, USA. 15Department of Physics, Idaho State University, Pocatello, Idaho 83209, USA. 16Department of Physics, Louisiana Tech University, Ruston, Louisiana 71272, USA. 17Accelerator Division, Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA. 18Department of Physics, University of Connecticut, Storrs-Mansfield, Connecticut 06269, USA. 19Department of Physics, University of Northern British Columbia, Prince George, British Columbia V2N 4Z9, Canada. 20Department of Physics, University of Winnipeg, Winnipeg, Manitoba R3B 2E9, Canada. 21Department of Physics, George Washington University, Washington, D.C. 20052, USA. 22Department of Physics, University of New Hampshire, Durham, New Hampshire 03824, USA. 23Physics Department, Hendrix College, Conway, Arkansas 72032, USA. 24Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, South Australia 5005, Australia. 25Department of Physics, Syracuse University, Syracuse, New York 13244, USA. 2 Abstract: The fields of nuclear and particle physics have undertaken extensive programs to search for evidence of physics beyond that explained by current theories. The observation of the Higgs boson at the Large Hadron Collider completed the set of particles predicted by the Standard Model (SM), currently the best description of fundamental particles and forces. However, the theory’s limitations include a failure to predict fundamental parameters and the inability to account for dark matter/energy, gravity, and the matter-antimatter asymmetry in the universe, among other phenomena. Given the lack of additional particles found so far through direct searches in the post- Higgs era, indirect searches utilizing precise measurements of well-predicted SM observables allow highly-targeted alternative tests for physics beyond the SM. Indirect searches have the potential to reach mass/energy scales beyond those directly accessible by today’s high-energy accelerators. The � value of the weak charge of the proton �� is an example of such an indirect search, as it sets the strength of the proton’s interaction with other particles via the well-predicted neutral electroweak force. Parity symmetry (invariance under spatial inversion (x,y,z) → (-x,-y,-z)) is violated only in the weak interaction, thus providing a unique tool to isolate the weak interaction in order to measure the 1 � proton’s weak charge . Here we report �� = 0.0719 ± 0.0045, as extracted from our measured parity- violating (PV) polarized electron-proton scattering asymmetry, ��� = –226.5 ± 9.3 ppb. Our value of � 2 �� is in excellent agreement with the SM , and sets multi-TeV-scale constraints on any semi-leptonic PV physics not described within the SM. In the electroweak SM, elastic scattering is 8 :8 mediated by the exchange of neutral currents 9 ; (2) 0 �7* = (virtual photons and Z bosons) between 89<8; fundamental particles. A particle’s weak charge Here � represents the helicity-dependent elastic ± �( is analogous to but distinct from its electric scattering �⃗� cross section integrated over the charge �: the former quantifies the vector 0 scattered-electron detector acceptance. Helicity coupling of the Z boson to the particle, while the (±1) indicates the spin direction of the electrons latter quantifies the vector coupling of the photon * in the beam as either parallel (+1) or anti-parallel to the particle. The proton’s weak charge �( is (−1) to their momenta. 1 defined as the sum of the weak vector couplings 0 �,- of the Z boson to its constituent u and d Measuring �7* at small four-momentum transfer quarks: (�B) suppresses contributions from the proton's * extended structure relative to the proton’s weak �( = −2(2�,2 + �,4). (1) * charge � . However, �7* is smaller at smaller ( �B, making its measurement more challenging. In The Z0 exchange contribution to electron-proton this low �B limit, the PV asymmetry can be scattering can be isolated via the weak expressed1 as interaction’s unique PV signature (see Fig. 1). Interference between electromagnetic (EM) and ⁄ * B B weak scattering amplitudes leads to a PV �7* �C = �( + � �(� , �) (3) asymmetry �7* that can be measured with a :H JK longitudinally-polarized electron beam incident where � = I , −�B is the four-momentum C LMN√B on an unpolarized-proton target: transfer squared, �(�B, �) represents the proton’s 3 extended structure defined in terms of EM, for each one-ms-long helicity state of the beam. strange and axial form factors, � is the (polar) For calibration purposes, and to demonstrate scattering angle of the electron in the lab frame understanding of the acceptance and with respect to the beam axis, �Q is the Fermi backgrounds, drift chambers were periodically constant, and � is the fine structure constant. inserted to track individual particles during dedicated periods of low-current running. In order to achieve <10 ppb precision, this experiment pushed existing boundaries on many fronts: higher polarized-beam intensity (180 µA), faster beam-helicity reversal (960/s), better GeV- scale beam polarimetry5 precision (±0.6%), higher liquid-hydrogen target6 luminosity (1.7 x 1039/(cm2-s)) and cooling power (3 kW), and higher total detector rates (7 GHz). Following a brief commissioning period, the experiment was divided into two roughly six-month run periods, between which improvements were made Figure 1 | Parity-violating electron scattering from the proton. The incoming electron with helicity +1 primarily to polarimetry and helicity-correlated scatters away from the plane of the “Parity-Violating beam-monitoring and control instrumentation. (PV) mirror” in this schematic. The image in the PV Further details, including the backgrounds and mirror shows the incoming electron with the opposite corrections associated with each of the two halves helicity −1, and instead of scattering into the plane of of the experiment, are provided in Methods. the PV mirror (as it would in a real mirror), it scatters out of the plane of the PV mirror. The dominant electromagnetic interaction, mediated by the photon The asymmetry-measurement results are �7* = – (γ, blue wave), conserves parity. The weak interaction, 223.5 ± 15.0 (stat) ± 10.1 (syst) ppb in the first mediated by the neutral Z0 boson (dashed red line), half, and –227.2 ± 8.3 (stat) ± 5.6 (syst) ppb in the violates parity. The weak interaction is studied experimentally by exploiting PV through reversals of second half of the experiment. They are in the incident-beam helicity, which mimic the PV mirror excellent agreement with each other, and “reflection”. consistent with our previously-published commissioning result3. Accounting for 3,4 The �weak experiment (see Extended Data Fig. correlations