Precision determination of electroweak coupling from atomic parity violation and implications for particle physics

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic ^{133}Cs. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Implications of W-Boson Mass Anomaly for Atomic Parity Violation

We consider the implications of the recent measurement of the W-boson mass MW=80,433.5±9.4MeV/c2 for atomic parity violation experiments. We show that the change in MW shifts the Standard Model prediction for the 133Cs nuclear weak charge to QW(133Cs)=−73.11(1), i.e., by 8.5σ from its current value, and the proton weak charge by 2.7%. The shift in QW(133Cs) ameliorates the tension between existing determinations of its value and motivates more accurate atomic theory calculations, while the shift in QW(p) inspires next-generation atomic parity violation experiments with hydrogen. Using our revised value for QW(133Cs), we also readjust constraints on parameters of physics beyond the Standard Model. Finally, we reexamine the running of the electroweak coupling for the new W boson mass.

Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of ^{229}Th

Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2)  eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.

Scalable Codes for Precision Calculations of Properties of Complex Atomic Systems

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that enables computations that were not previously possible due to system complexity. This code package also allows much quicker computations to be run with higher accuracy for simple systems. We explored different methods of load-balancing matrix element calculations for many-electron systems, which are very difficult due to the intrinsic nature of the computational methods used to calculate them. Furthermore, dynamic memory allocation and MPI parallelization have been implemented to optimize and accelerate the computations. We have achieved near-perfect linear scalability and efficiency with the number of processors used for calculation, paving the way towards the future where most open-shell systems will finally be able to be treated with good accuracy. We present several examples illustrating new capabilities of the newly developed codes, specifically correlating up to all 60 electrons in the highly charged Ir17+ ion and predicting certain properties of Fe16+.

Multi-reference ab initio calculations of Hg spectral data and analysis of magic and zero-magic wavelengths

We have identified magic wavelengths for ¹S₀ ↔ ³P_1,2 (m_J = 0) transitions and zero-magic wavelengths for the ³P_1,2 (m_J = 0) states of ²⁰⁰Hg atoms, analysed the robustness of the magic conditions with respect to wavelength and polarization imperfections. We show that the most experimentally feasible magic wavelength for the ¹S₀ ↔ ³P₂ transition is 351.8 nm of π polarized light. Relevant transition wavelengths and transition strengths are calculated using the state-of-the-art Complete Active Space Self-Consistent-Field (CASSCF) method with a perturbative inclusion of spin-orbit coupling. The transition wavelengths are a posteriori corrected for the dynamical energy using the second-order perturbation theory.

Determination of the Scalar and Vector Polarizabilities of the Cesium 6s^{2}S_{1/2}→7s^{2}S_{1/2} Transition and Implications for Atomic Parity Nonconservation

Using recent high-precision measurements of electric dipole matrix elements of atomic cesium, we make an improved determination of the scalar (α) and vector (β) polarizabilities of the cesium 6s^{2}S_{1/2}→7s^{2}S_{1/2} transition calculated through a sum-over-states method. We report values of α=-268.82(30)a_{0}^{3} and β=27.139(42)a_{0}^{3} with the highest precision to date. We find a discrepancy between our value of β and the past preferred value, resulting in a significant shift in the value of the weak charge Q_{w} of the cesium nucleus. Future work to resolve the differences in the polarizability will be critical for interpretation of parity nonconservation measurements in cesium, which have implications for physics beyond the standard model.

Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules

In the presence of P-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, Ba^{+}, Yb, Tl, Fr, and Ra^{+} using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ^{133}Cs, we constrain the P-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

High steady-state column density of I((2)P3/2) atoms from I2 photodissociation at 532 nm: Towards parity non-conservation measurements

Steady-state column densities of 10¹⁷ cm⁻² of I(²P_3/2) atoms are produced from photodissociation of I₂ vapour at 290.5 K using 5 W of 532 nm laser light. Recombination of the I(²P_3/2) atoms at the cell walls is minimized by coating the cell surface with a hydrophobic silane (dimethyldichlorosilane/DMDCS). Operation at room temperature, and at an I₂ vapour pressure of ~0.2 mbar, without using a buffer gas, allows relatively low Lorentz and Doppler widths of ~2π × 1.5 (FWHM) and ~2π × 150 (HW at 1/e²) Mrad/s, respectively, at the M1 transition of atomic iodine at 1315 nm. These high column densities and low linewidths are favorable for parity nonconservation optical rotation measurements near this M1 transition. Furthermore, as the cell is completely sealed, this method of production of high-density ¹²⁷I(²P_3/2) atoms is also compatible with using iodine radioisotopes, such as for the production of high-density ¹²⁹I(²P_3/2).

Limiting P-odd interactions of cosmic fields with electrons, protons, and neutrons

We propose methods for extracting limits on the strength of P-odd interactions of pseudoscalar and pseudovector cosmic fields with electrons, protons, and neutrons, by exploiting the static and dynamic parity-nonconserving amplitudes and electric dipole moments they induce in atoms. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by Lorentz-violating standard model extensions. Atomic calculations are performed for H, Li, Na, K, Rb, Cs, Ba(+), Tl, Dy, Fr, and Ra(+). From these calculations and existing measurements in Dy, Cs, and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be 7 × 10(-15) GeV with an electron, and 3 × 10(-8) GeV with a proton.

Measurement of weak optical transition moments through two-pathway coherent control

We present a full description of the (ω, 2ω) two-pathway coherent control interference technique for measurement of weak, highly forbidden optical transitions. We have recently applied this technique to the measurement of the magnetic dipole transition moment M1 of the 6s 2S1/2 → 7s 2S1/2 transition in atomic cesium. We also demonstrate detailed methods by which this technique may be used for measurement of the electroweak-induced parity nonconserving amplitude in atomic cesium. The principal benefits of this technique include reduced systematic errors related to field reversals often encountered in related measurements, reduced interference from adjacent, noninterfering transitions, and the absence of electric quadrupole transitions. We present a critical evaluation of the effects induced by stray fields and other systematic effects.

γZ box corrections to weak charges of heavy nuclei in atomic parity violation

We present a new dispersive formulation of the γZ box radiative corrections to weak charges of bound protons and neutrons in atomic parity violation measurements on heavy nuclei such as 133Cs and 213Ra. We evaluate for the first time a small but important additional correction arising from Pauli blocking of nucleons in a heavy nucleus. Overall, we find a significant shift in the γZ correction to the weak charge of 133Cs, approximately 4 times larger than the current uncertainty on the value of sin2 θ(W), but with a reduced error compared to earlier estimates.

Precision measurement of transition matrix elements via light shift cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Revisiting parity nonconservation in cesium

We apply the sum-over-states approach to calculate partial contributions to parity nonconservation (PNC) in cesium [Porsev, Beloy, and Drevianko, Phys. Rev. Lett. 102, 181601 (2009)]. We find significant corrections to two nondominating terms coming from the contribution of the core and highly excited states (n>9, the so called tail). When these differences are taken into account the result of Porsev et al., E(PNC)=0.8906(24)×10(-11)i(-Q(W)/N) changes to 0.8977 (40), coming into good agreement with our previous calculations, 0.8980 (45). The interpretation of the PNC measurements in cesium still indicates reasonable agreement with the standard model (1.5σ); however, it gives new constraints on physics beyond it.

Muon anomaly and dark parity violation

The muon anomalous magnetic moment exhibits a 3.6σ discrepancy between experiment and theory. One explanation requires the existence of a light vector boson, Z(d) (the dark Z), with mass 10-500 MeV that couples weakly to the electromagnetic current through kinetic mixing. Support for such a solution also comes from astrophysics conjectures regarding the utility of a U(1)(d) gauge symmetry in the dark matter sector. In that scenario, we show that mass mixing between the Z(d) and ordinary Z boson introduces a new source of "dark" parity violation, which is potentially observable in atomic and polarized electron scattering experiments. Restrictive bounds on the mixing (m(Z(d))/m(Z))δ are found from existing atomic parity violation results, δ2<2×10(-5). Combined with future planned and proposed polarized electron scattering experiments, a sensitivity of δ2∼10(-6) is expected to be reached, thereby complementing direct searches for the Z(d) boson.

New formulation of γZ box corrections to the weak charge of the proton

We present a new formulation of one of the major radiative corrections to the weak charge of the proton-that arising from the axial-vector hadron part of the γZ box diagram, ℜe□(γZ)(A). This formulation, based on dispersion relations, relates the γZ contributions to moments of the F(3)(γZ) interference structure function. It has a clear connection to the pioneering work of Marciano and Sirlin, and enables a systematic approach to improved numerical precision. Using currently available data, the total correction from all intermediate states is ℜe□(γZ)(A)=0.004 4(4) at zero energy, which shifts the theoretical estimate of the proton weak charge from 0.071 3(8) to 0.070 5(8). The energy dependence of this result, which is vital for interpreting the Q(weak) experiment, is also determined.

Analysis of parity violation in chiral molecules

In order to guide the experimental search for parity violation in molecular systems, in part motivated by the possible link to biomolecular homochirality, we present a detailed analysis in a relativistic framework of the mechanism behind the tiny energy difference between enantiomers induced by the weak force. A decomposition of the molecular expectation value into atomic contributions reveals that the effect can be thought of as arising from a specific mixing of valence s(1/2) and p(1/2) orbitals on a single center induced by a chiral molecular field. The intra-atomic nature of the effect is further illustrated by visualization of the electron chirality density and suggests that a simple model for parity violation in molecules may be constructed by combining pre-calculated atomic quantities with simple bonding models. A 2-component relativistic computational procedure is proposed which bridges the relativistic and non-relativistic approaches to the calculation of parity violation in chiral molecules and allows us to explore the single-center theorem in a variational setting.

Precision constraints on extra fermion generations

There has been recent renewed interest in the possibility of additional fermion generations. At the same time there have been significant changes in the relevant electroweak precision constraints, in particular, in the interpretation of several of the low energy experiments. We summarize the various motivations for extra families and analyze them in view of the latest electroweak precision data.

Observation of a large atomic parity violation effect in ytterbium

Atomic parity violation has been observed in the 6s(2 1)S(0)-->5d6s(3)D(1) 408-nm forbidden transition of ytterbium. The parity-violating amplitude is found to be 2 orders of magnitude larger than in cesium, where the most precise experiments to date have been performed. This is in accordance with theoretical predictions and constitutes the largest atomic parity-violating amplitude yet observed. This also opens the way to future measurements of neutron distributions and anapole moments by comparing parity-violating amplitudes for various isotopes and hyperfine components of the transition.