The energy levels of the $n=1$ and $n=2$ bound states of the $μ^+μ^-$ atom (true muonium) are calculated starting from a previously derived potential that correctly describes positronium to order $α^5$. All electron vacuum polarization corrections on the true muonium levels are computed to the same $α^5$ order and a few of order $α^6$ are examined to get a sense of size of these contributions. Additional order $α^6$ contributions from the two photon and three photon annihilation processes are included in the evaluation of the ground state ($1^3S_1-1^1S_0$) hyperfine splitting.

The n = 2 and n = 3 levels for muonic helium are calculated using a potential that includes all one-loop and recoil effects. Electronic vacuum polarization corrections are calculated using an extension of the Kinoshita and Nio method. For n = 2, the results are 2p(1/2) - 2s(1/2) = 1374.24 +/- 1.4 meV and 2p(3/2) - 2s(1/2) = 1520.83 +/- 1.4 meV, essentially in agreement with the latest summary of the current calculations. The n = 3 results are summarized in tabular form and give 3p(1/2) - 3s(1/2) = 394.48 +/- 0.43 meV and 3d(3/2) - 3p(3/2) = 111.40 meV.

The method proposed by Kinoshita and Nio to compute higher order vacuum polarization contributions to the Coulomb potential in muonic hydrogen is generalized to obtain relativistic corrections to their results.

We reexamine the structure of the n = 2 levels of muonic hydrogen using a two-body potential that includes all relativistic, recoil and one-loop corrections. The potential was originally derived from QED to describe the muonium atom and accounts for all contributions to order alpha(5). Since one-loop corrections are included, the anomalous magnetic moment contributions of the muon can be identified and replaced by the proton anomalous magnetic moment to describe muonic hydrogen with a pointlike proton. This serves as a convenient starting point to include the dominant electron vacuum polarization corrections to the spectrum and extract the proton's mean squared radius r(p) = root < r(2)>. Our results are consistent with other theoretical calculations that find that the muonic hydrogen value for r(p) is smaller than the result obtained from electron scattering.

Higgs boson radiative decays of the form H → f ¯ f γ are calculated in the Standard Model using the complete one-loop expressions for the decay amplitudes. Contributions to the radiative width from leptons and light quarks are given. We also present e¯ e invariant mass distributions for H → e¯ eγ, which illustrate the importance of the photon pole contribution and the effects of the box diagrams.

We extend our treatment of the spectroscopy and decays of the charm-strange quarkonium system to include the effect of using the full three-loop QCD correction to the static short distance potential. As before, our potential model consists of the relativistic kinetic energy term, a scalar linear confining term including its relativistic corrections and the perturbative QCD spin-dependent terms. A set of unperturbed wave functions for the various states is obtained using a variational technique that is further constrained by requiring that the wave functions also satisfy the relativistic virial theorem. These are then used in a perturbative treatment of the potential to fit the mass spectrum of the cs¯ system and calculate the radiative decay widths. Our results accurately describe the Ds spectrum and are compatible with the little data that is available for the radiative decays of the Ds states.

To gain some sense about the likelihood of measuring the Higgs boson quartic coupling, we calculate the contribution to the triple Higgs production cross section from the subprocesses q (q) over bar -> ZHHH and q (q) over bar' -> WHHH. Our results illustrate that determining this coupling, or even providing experimental evidence that it exists, will be very difficult.

To gain some sense about the likelihood of measuring the Higgs boson quartic coupling, we calculate the contribution to the triple Higgs production cross section from the subprocesses $q\overline{q}\ensuremath{\rightarrow}ZHHH$ and $q{\overline{q}}^{\ensuremath{'}}\ensuremath{\rightarrow}WHHH$. Our results illustrate that determining this coupling, or even providing experimental evidence that it exists, will be very difficult.

We show that the dominant channel proposed for the determination of the Higgs boson trilinear coupling, pp -> HH + X via gluon fusion, exhibits an interference structure that is independent of the collider energy for collider energies in the range 8 TeV <= root s <= = 100 TeV and is almost maximally destructive. This insensitivity to the collider energy remains approximately true for a variety of other two Higgs production mechanisms although the magnitude of the interference varies widely.

The Dalitz decay H. f(f) over bar gamma is calculated for very small f (f) over bar invariant masses where the f (f) over bar pair could be mistaken for a photon in the analysis of H -> gamma gamma decays. Using the ATLAS cuts and the full Dalitz decay amplitude, we estimate this fraction to be 7.06%.

The Dalitz decay $H\to\,f\bar{f}\gamma$ is calculated for very small $f\bar{f}$ invariant masses where the $f\bar{f}$ pair could be mistaken for a photon in analysis of $H\to\gamma\gamma$ decays. Using the ATLAS cuts and the full Dalitz decay amplitude, we estimate this fraction to be 7.06%.

The results previously obtained from the model-independent application of a generalized hidden horizontal Z2 symmetry to the neutrino mass matrix are updated using the latest global fits for the neutrino oscillation parameters. The resulting prediction for the Dirac CP phase δD is in agreement with recent results from T2K. The distribution for the Jarlskog invariant Jν has become sharper and appears to be approaching a particular region. The approximate effects of matter on long-baseline neutrino experiments are explored, and it is shown how the weak interactions between the neutrinos and the particles that make up the Earth can help to determine the mass hierarchy. A similar strategy is employed to show how NOνA and T2K could determine the octant of θa(≡θ23). Finally, the exact effects of matter are obtained numerically in order to make comparisons with the form of the approximate solutions. From this analysis there emerge some interesting features of the effective mass eigenvalues.

The Dalitz decay $H\to\,f\bar{f}\gamma$ is calculated for very small $f\bar{f}$ invariant masses where the $f\bar{f}$ pair could be mistaken for a photon in analysis of $H\to\gamma\gamma$ decays. Using the ATLAS cuts and the full Dalitz decay amplitude, we estimate this fraction to be 7.06%.

We investigate the effects of including the full three-loop QCD correction to the static short distance 1/r potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full three-loop corrected potential to determine a set of unperturbed trial wave functions and treat the relativistic and one-loop corrections as perturbations. The perturbed results are compared to the subset of the charmonium and upsilon spectra using a χ2 test. This approach results in more accurate descriptions of the hyperfine splittings in both the bb¯ and cc¯ systems.

A precise comparison is made between the Dalitz decay H -> l (l) over bar gamma and the two-body decay H ->gamma Z,Z -> l (l) over bar for electrons and for muons including experimental cuts appropriate for the ATLAS detector. The widths for these two processes differ by 8% for electrons and 3% for muons. Given that there remain uncertainties of this order that are not included, this suggests that the isolation of the Dalitz decay will be challenging.

The phenomenological consequences of the residual Z2s and Z¯2s symmetries are explored in detail. With a precisely measured value of the reactor angle, these two residual symmetries predict distinct distributions for the Dirac CP phase and the atmospheric angle, which lead to the possibility of identifying them at future neutrino experiments. For both symmetries, it is possible to resolve the neutrino mass hierarchy in most of the parameter space, and they can be distinguished from one another if the true residual symmetry is Z2s and the atmospheric angle is non-maximal. These results are obtained using an equally split schedule: a 1.5-year run of neutrinos and a 1.5-year run of antineutrinos at NOνA together with a 2.5-year run of neutrinos and a 2.5-year run of antineutrinos at T2K. This schedule can significantly increase and stabilize the sensitivities to the mass hierarchy and the octant of the atmospheric angle with only a moderate compromise to the sensitivity of distinguishing Z2s and Z¯2s.

The Dalitz decay $H\to\,f\bar{f}\gamma$ is calculated for very small $f\bar{f}$ invariant masses where the $f\bar{f}$ pair could be mistaken for a photon in analysis of $H\to\gamma\gamma$ decays. Using the ATLAS cuts and the full Dalitz decay amplitude, we estimate this fraction to be 7.06%.

We provide an analytic solution to the general wavelength integro-differential equation describing the damping of tensor modes of gravitational waves due to free streaming neutrinos in the early universe. Our result is expressed as a series of spherical Bessel functions whose coefficients are functions of the reduced wave number $Q$.