Scalar and tensor interactions were once competitors to the now well-established V − A structure of the Standard Model weak interactions. We revisit these interactions and survey constraints from low-energy probes (neutron, nuclear, and pion decays) as well as collider searches. Currently, the most stringent limit on scalar and tensor interactions arise from 0 + → 0 + nuclear decays and the radiative pion decay π → eνγ, respectively. For the future, we find that upcoming neutron beta decay and LHC measurements will compete in setting the most stringent bounds. For neutron beta decay, we demonstrate the importance of lattice computations of the neutronto-proton matrix elements to setting limits on these interactions, and provide the first lattice estimate of the scalar charge and a new average of existing results for the tensor charge. Data taken at the LHC is currently probing these interactions at the 10 −2 level (relative to the standard weak interactions), with the potential to reach the < ∼ 10 −3 level. We show that, with some theoretical assumptions, the discovery of a charged spin-0 resonance decaying to an electron and missing energy implies a lower limit on the strength of scalar interactions probed at low energy.
The binding energies of a range of nuclei and hypernuclei with atomic number A ≤ 4 and strangeness |s| ≤ 2, including the deuteron, di-neutron, H-dibaryon, 3 He, ΛΛ He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange-quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n f = 3 dynamical light quarks using an isotropic clover discretization of the quark action in three lattice volumes of spatial extent L ∼ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ∼ 0.145 fm.2
We have simulated QCD using 2 þ 1 flavors of domain wall quarks and the Iwasaki gauge action on a ð2:74 fmÞ 3 volume with an inverse lattice scale of a À1 ¼ 1:729ð28Þ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617, and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter B K , and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulas from both approaches fit our data for light quarks, we find the higher-order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the baryon, and the and K mesons to set the lattice scale and determine the quark masses. We then find f ¼ 124:1ð3:6Þ stat  ð6:9Þ syst MeV, f K ¼ 149:6ð3:6Þ stat ð6:3Þ syst MeV, and f K =f ¼ 1:205ð0:018Þ stat ð0:062Þ syst . Using nonperturbative renormalization to relate lattice regularized quark masses to regularization independent momentum scheme masses, and perturbation theory to relate these to MS, we find m MS ud ð2 GeVÞ ¼ 3:72ð0:16Þ stat ð0:33Þ ren ð0:18Þ syst MeV, m MS s ð2 GeVÞ ¼ 107:3ð4:4Þ stat ð9:7Þ ren ð4:9Þ syst MeV, and mud : ms ¼ 1:28:8ð0:4Þ stat ð1:6Þ syst . For the kaon bag parameter, we find B MS K ð2 GeVÞ ¼ 0:524ð0:010Þ stat ð0:013Þ ren  ð0:025Þ syst . Finally, for the ratios of the couplings of the vector mesons to the vector and tensor currents (f V and f T V , respectively) in the MS scheme at 2 GeV we obtain f T =f ¼ 0:687ð27Þ; f T K à =f K à ¼ 0:712ð12Þ, and f T =f ¼ 0:750ð8Þ.
We present results for the isovector axial, scalar and tensor charges g The lattice-QCD calculations were done using nine ensembles of gauge configurations generated by the MILC Collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings a ≈ 0.06, 0.09 and 0.12 fm and light-quark masses corresponding to the pion masses Mπ ≈ 135, 225 and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses for the connected contributions. Our final estimates, in the MS scheme at 2 GeV, of the isovector charges are g (51)(20). The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for g 194(14). Combining our new estimates with precision low-energy experiments, we present updated constraints on novel scalar and tensor interactions, S,T , at the TeV scale.
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