Q-weak: First Direct Measurement of the Weak Charge of the Proton

The Q-weak experiment at Hall C of Thomas Jefferson National Accelerator Facility has made the first direct measurement of the weak charge of the proton, Qweak(p), through a precision measurement of the parity-violating asymmetry in elastic e-p scattering at low momentum transfer Q^2= 0.025 (GeV/c)^2 with incident electron beam energy of 1.155 GeV. The Q-weak experiment, along with earlier results of parity violating elastic scattering experiments, is expected to determine the most precise value of Qweak(p) which is suppressed in the Standard Model. If this result is further combined with the 133Cs atomic parity violation (APV) measurement, significant constraints on the weak charge of the up quark, down quark, and neutron can be extracted. This data will also be used to determine the weak-mixing angle, sin^2 theta_?W, with a relative uncertainty of<0.5% that will provide a competitive measurement of the running of sin^2 theta_?W to low Q^2. An overview of the experiment and its results using the commissioning dataset, constituting approximately 4% of the data collected in the experiment, are reported here.


Introduction
The Standard Model (SM) is the most successful elementary particle theory developed so far. However, it is considered to be a low energy effective theory due to the missing phenomena like gravity and dark matter. The weak charge of the proton, Q p W , is the neutral current analog to the proton's electric charge. The SM precisely predicts the weak charge of the proton (Table 1), which is suppressed in the SM. It is therefore a good candidate for an indirect search [1][2][3][4][5] for new parity-violating (PV) physics between electrons and light quarks.
The Q weak experiment [6] at Hall C of Thomas Jefferson National Accelerator Facility (TJNAF) has made the first direct measurement of the weak charge of the proton through the precision measurement of the PV asymmetry in elastic e-p scattering at low momentum transfer Q 2 = 0.025 (GeV/c) 2 with incident electron beam energy of 1.155 GeV. The experiment was performed during the period of November 2010 to May 2012. Herein, we report the results obtained from only about 4% of the total data collected in the experiment.
The measured asymmetry in the experiment is the difference over the sum of the elastic e-p scattering yield for electrons with positive and negative helicity and is expressed as, where kinematic quantities can be written as G F is the Fermi constant, sin 2 θ W reflects the weak mixing angle, Q 2 is the negative four momentum transfer squared, α is the fine structure constant, τ = Q 2 /4M 2 , M is the proton mass, and θ is the electron scattering angle in the laboratory frame. If we express the factor −G F Q 2 4πα √ 2 = A 0 , then the reduced asymmetry in the forward angle limit (θ → 0) and at low Q 2 can be written conveniently [9] as Then Q p W is the intercept of A ep /A 0 vs. Q 2 fit in eq. 4. The term Q 2 B(θ, Q 2 ) is determined experimentally from existing parity violating electron scattering (PVES) data at higher Q 2 and is suppressed at low Q 2 . It contains only the nucleon structure defined in terms of EM, strange quark, and weak form factors. The Q 2 of the measurement reported here is 4 times smaller than of any previously reported e-p PV experiment, which ensures a reliable extrapolation to Q 2 → 0 using eq. 4.

Apparatus
As the Q weak PV asymmetry and its required absolute uncertainty are an order of magnitude smaller than in previous experiments, a dedicated design, significant improvement to hardware and software, and additional control of systematic uncertainties were needed to reach the proposed precision goals.
A longitudinally polarized electron beam was reversed at a rate of 960 Hz in a sequence of "pseudorandom helicity quartets" (± ∓ ∓±), which helps minimize noise due to slow linear drifts, and limits noise due to fluctuations in the target density and in beam properties. The beam current was measured using radio frequency resonant cavities. Five beam position monitors (BPMs) upstream of the target were used to extract the beam position and angle at the target whereas energy changes were measured using a BPM at the point of highest dispersion in the beam line. The electron beam of 180 µA scattered from a 34.4 cm long liquid hydrogen target [10] contained in an aluminum alloy container. A series of collimators were used to define the scattered electrons. A toroidal magnet focused elastically scattered electrons onto eight radiation-hard synthetic fused quartzČerenkov detectors which were symmetrically oriented about the beam axis at a radius of 3.4 m, 12.2 m downstream from the target ( Figure 1). This azimuthal symmetry of the detectors helped reduce uncertainties from helicitycorrelated beam motion and transverse beam polarization. Two photo multiplier tubes (PMTs) were optically coupled on the end of the detector bars. The PMT anode current fed custom low noise current to voltage preamplifiers whose output signals were digitized with 18 bit analog to digital converters (ADCs) sampling at 500 kHz. Basic parameters and typical operating conditions during the experiment are described in Table 2.

Analysis
The measured asymmetry (A msr ) can be derived (eq. 5) from the raw asymmetry A raw , which was calculated over each helicity quartet from the PMT integrated charge and normalized to beam charge Y ± . A T is the remnant transverse asymmetry and is separately measured using transversely polarized beam. Here, A L accounts for potential nonlinearity in the PMT response. The ∆χ i are the helicity correlated differences in beam trajectory parameters (X, X , Y, Y ) or energy (E) over the helicity quartet. The slopes ∂A ∂χ i were determined from linear regression using the natural and driven beam motion [11] of the beam. The regression corrections A reg were obtained using differences and slopes and applied at the helicity quartet level.  Table 2: Basic parameters and typical operating conditions of the Q weak experiment [6]. The nominal beam current during production data taking was 180 µA, but for this commissioning dataset the current was 145 µA.
The PV asymmetry can be extracted from the measured asymmetry after correcting for the beam polarization, false asymmetries and backgrounds as shown in eq. 7. The beam polarization was ∼89% and was measured using a M∅ller polarimeter [12]. Here the multiplicative correction R total = R RC R Det R Bin R Q 2 . R RC = 1.010 ± 0.005 is a radiative correction deduced from simulations with and without bremsstrahlung as described in Refs. [13,14]. R Det = 0.987 ± 0.007 accounts for the measured light variation and non-uniform Q 2 distribution across the detector bars. R Bin = 0.980 ± 0.010 is an effective kinematics correction [13] that corrects the asymmetry from <A(Q 2 )> to A(<Q 2 >), and R Q 2 = 1.000 ± 0.030 represents the precision in calibrating the central Q 2 . The background corrections were coming from target windows (b1), beamline scattering (b2), other neutral background (b3), and inelastics (b4). The contribution of each background to the measured asymmetry is shown in Table 3. The most significant correction for this dataset was from the aluminum target windows.  [14][15][16][17][18][19][20][21][22][23][24][25] were used to extract Q p W . A zoomed asymmetry vs Q 2 is shown here for better visualization. The measured absolute asymmetry and absolute uncertainty from this measurement are ∼3 times smaller than the previous PVES measurements.

Result
The measured parity violating asymmetry, A ep , using the commissioning data (eq. 7) at <Q 2 > = 0.0250 ± 0.0006 (GeV/c) 2 is -279 ± 35 (statistics) ± 31 (systematics) parts per billion (ppb). This is the most precise absolute parity violating electron-proton scattering measurement to date (Figure 2). This reported asymmetry was then combined with other PVES results [14][15][16][17][18][19][20][21][22][23][24][25] on hydrogen, deuterium, and helium in a global fit following the prescription in [4] to extract the weak charge of the proton using eq. 4 and is shown in Figure 3. The angle dependence of the strange and axial form-factor contributions was removed by subtracting [A calc (θ, Q 2 ) -A calc (0, Q 2 )] from A ep (θ, Q 2 ) to demonstrate the two-dimensional global fit (θ, Q 2 ) in a single dimension (Q 2 ). The calculated asymmetries A calc are determined from eq. 3 using the results of the fit. The extracted weak charge of the proton using the measured asymmetry from this experiment and PVES data is Q p W = 0.064 ± 0.012 [29]. At the effective kinematics the predicted weak charge by the SM [26] Q p W (SM) is 0.0710 ± 0.0007 as shown by an arrow in Figure 3.
uncertainty with full statistics and improved analysis of systematic uncertainties. These data will also be used to determine the weak-mixing angle, sin 2 θ W , with a relative uncertainty of <0.5% that will provide a competitive measurement of the running of sin 2 θ W to low Q 2 . This work was supported by DOE contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, operates Thomas Jefferson National Accelerator Facility. I would like to thank the Q weak collaboration for the opportunity to present on its behalf.