An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lemaître-Robertson-Walker (FLRW) models consisting of an arbitrary number of noninteracting species, each with a constant ratio of pressure to density. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit a unique candidate for a gravitational epoch function—a function which gives a global time-orientation without reference to observers. The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda \mathrm{CDM}$ model, it is shown that the epoch function exists for all models with $\Lambda >0$, but for almost no models with $\Lambda <0$.

The generation of the baryon asymmetry of the Universe from the hypermagnetic helicity, the physical interpretation of which is given in terms of hypermagnetic knots, is studied in inflationary cosmology, taking into account the breaking of the conformal invariance of hypercharge electromagnetic fields through both a coupling with the dilaton and with a pseudoscalar field. It is shown that, if the electroweak phase transition is strongly first order and the present amplitude of the generated magnetic fields on the horizon scale is sufficiently large, a baryon asymmetry with a sufficient magnitude to account for the observed baryon-to-entropy ratio can be generated.

We consider fluid perturbations close to the “phantom divide” characterized by $p=-\rho$ and discuss the conditions under which divergencies in the perturbations can be avoided. We find that the behavior of the perturbations depends crucially on the prescription for the pressure perturbation $\delta p$. The pressure perturbation is usually defined using the dark energy rest-frame, but we show that this frame becomes unphysical at the divide. If the pressure perturbation is kept finite in any other frame, then the phantom divide can be crossed. Our findings are important for generalized fluid dark energy used in data analysis (since current cosmological data sets indicate that the dark energy is characterized by $p\approx -\rho$ so that $p<-\rho$ cannot be excluded) as well as for any models crossing the phantom divide, like some modified gravity, coupled dark energy, and braneworld models. We also illustrate the results by an explicit calculation for the “Quintom” case with two scalar fields.

Landshoff and Donnachie [A. Donnachie and P. V. Landshoff, Phys. Lett. B 296, 227 (1992).; P. V. Landshoff, hep-ph/0509240] parametrize the energy behavior of $pp$ and $p\overline{p}$ scattering cross sections with five parameters, using: ${\sigma }^{+}=56.08s^{-0.4525}+21.70s^{0.0808}$ for $pp$, ${\sigma }^{-}=98.39s^{-0.4525}+21.70s^{0.0808}$ for $p\overline{p}$. Using the four analyticity constraints of Block and Halzen [M. M. Block and F. Halzen, Phys. Rev. D 72, 036006 (2005).], we simultaneously fit the Landshoff-Donnachie form to the same sieved set of $pp$ and $p\overline{p}$ cross section and $\rho$ data that Block and Halzen used for a very good fit to a ${ln}^{2}s$ parametrization. We show that the satisfaction of the analyticity constraints will require modification of the Landshoff-Donnachie parametrization for lower energies, thus altering its inherent appeal of simplicity and universality.

The coupling constants of $K$ and $\pi$ mesons with the octet baryons are studied in light cone QCD sum rules taking into account $\mathrm{SU}(3{)}_f$ flavor symmetry breaking effects, but keeping the $\mathrm{SU}(2)$ isospin symmetry intact. It is shown that, in the $\mathrm{SU}(3{)}_f$ flavor symmetry breaking case, all of the couplings can be written in terms of four universal functions instead of $F$ and $D$ couplings which exist in the $\mathrm{SU}(3{)}_f$ symmetry case. A comparison of our results of kaon and pion-baryon couplings with existing theoretical and experimental results in the literature is performed.

We study the branching fractions and the lepton polarization asymmetries of rare $B\to X_s{\tau }^{+}{\tau }^{-}$ and $B\to K^{(*)}{\tau }^{+}{\tau }^{-}$ modes within the standard model and in the Appelquist-Cheng-Dobrescu model, which is a New Physics scenario with a single universal extra dimension. In particular, we investigate the sensitivity of the observables to the radius $R$ of the compactified extra dimension, which is the only new parameter in this New Physics model. For the exclusive transitions we study the uncertainties due to the hadronic matrix elements using two set of form factors, finding that in many cases such uncertainties are small. In particular, we show that the ${\tau }^{-}$ polarization asymmetries become free of hadronic uncertainties if Large Energy relations for the form factors, valid for low momentum transfer to the lepton pair, are used. We also consider $K^{*}$ helicity fractions and their sensitivity to the compactification parameter.

We present a supersymmetric grand unification model based on SO(10) group with $S4$ flavor symmetry. In this model, the fermion masses are from Yukawa couplings involving $\mathbf{10}$ and $\overline{\mathbf{126}}$ Higgs multiplets and the flavor structures of mass matrices of both quarks and leptons are determined by spontaneously broken $S4$. This model fits all of the masses and mixing angles of the quarks and leptons. For the most general $CP$-violation scenario, this model gives $\sin {\theta }_{13}$ a wide range of values from zero to the current bound with the most probable values 0.02–0.09. With certain assumptions where leptonic phases have same $CP$-violation source as CKM phase, one gets a narrower range 0.03–0.06 for $\sin {\theta }_{13}$ with the most probable values 0.04–0.08. This model gives leptonic Dirac $CP$ phase the most probable values 2–4 radians in the general $CP$-violation case.

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment ($dt$) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator’s spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ($\chi \mathrm{QCD}$). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.

We compute the masses of the flavor singlet $0^{++}$ mesons using ($n_f=2$) unquenched lattice QCD with the Iwasaki and Wilson gauge actions. Both fermionic and glueball interpolating operators are used to create the states. The mass of the lightest $0^{++}$ meson is suppressed relative to the mass of the $0^{++}$ glueball in quenched QCD at an equivalent lattice spacing. The low value for mass of the lightest flavor singlet $0^{++}$ meson obtained in our calculation could be due to either: that the mass of the meson is much lower than that of the $0^{++}$ glueball in quenched QCD, or due to the effect of lattice artifacts. We present arguments for the first option, but we are unable to rule out the explanation due to lattice artifacts.

We calculate the ${\pi }^{+}{K}^{+}$ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of $b=0.125\mathrm{fm}$, lattice spatial size of $L=2.5\mathrm{fm}$ and at pion masses of $m_{\pi }\sim 290$, 350, 490 and 600 MeV. The lattice data, analyzed at next-to-leading order in chiral perturbation theory, allows an extraction of the full $\pi K$ scattering amplitude at threshold. Extrapolating to the physical point gives $m_{\pi }{a}_{3/2}=-0.0574\pm {0.0016}_{-0.0058}^{+0.0024}$ and $m_{\pi }{a}_{1/2}=0.1725\pm {0.0017}_{-0.0156}^{+0.0023}$ for the $I=3/2$ and $I=1/2$ scattering lengths, respectively, where the first error is statistical and the second error is an estimate of the systematic due to truncation of the chiral expansion.

An unresolved problem in $J/\psi$ phenomenology is a systematic understanding of the differential photoproduction cross section, $d\sigma /dz[\gamma +p\to J/\psi +X$], where $z=E_{\psi }/E_{\gamma }$ in the proton rest frame. In the nonrelativistic QCD (NRQCD) factorization formalism, fixed-order perturbative calculations of color-octet mechanisms suffer from large perturbative and nonperturbative corrections that grow rapidly in the endpoint region, $z\to 1$. In this paper, NRQCD and soft collinear effective theory are combined to resum these large corrections to the color-octet photoproduction cross section. We derive a factorization theorem for the endpoint differential cross section involving the parton distribution function and the color-octet $J/\psi$ shape functions. A one-loop matching calculation explicitly confirms our factorization theorem at next-to-leading order. Large perturbative corrections are resummed using the renormalization group. The calculation of the color-octet contribution to $d\sigma /dz$ is in qualitative agreement with data. Quantitative tests of the universality of color-octet matrix elements require improved knowledge of shape functions entering these calculations as well as resummation of the color-singlet contribution which accounts for much of the total cross section and also peaks near the endpoint.

We construct a family of supersymmetric solutions in time-dependent backgrounds in supergravity theories. One class of the solutions are intersecting brane solutions and another class are brane solutions in pp-wave backgrounds, and their intersection rules are also given. The relation to existing literature is also discussed. An example of D1–D5 with linear null dilaton together with its possible dual theory is briefly discussed.

We study the dimensional reduction of M5-branes wrapping special Lagrangian 3-cycles of a Calabi-Yau manifold and show explicitly that they result in 2-branes coupled to the hypermultiplets of ungauged $\mathcal{N}=2$ $D=5$ supergravity theory. In addition to confirming previously known results, the calculation proves the relationship between them and provides further insight on how the topological properties of the compact space affect the lower dimensional fields.

Recent experiments suggest that polarized photons may couple significantly to pseudoscalar particles such as axions. We study the possible observational signatures of axion-photon coupling for radiation from magnetic stars, with particular focus on neutron stars. We present general methods for calculating the axion-photon conversion probability during propagation through a varying magnetized vacuum as well as across an inhomogeneous atmosphere. Partial axion-photon conversion may take place in the vacuum region outside the neutron star. Strong axion-photon mixing occurs due to a resonance in the atmosphere and, depending on the axion coupling strength and other parameters, significant axion-photon conversion can take place at the resonance. Such conversions may produce observable effects on the radiation spectra and polarization signals from the star. We also apply our results to axion-photon propagation in the Sun and in magnetic white dwarfs. We find that there is no appreciable conversion of solar axions to photons during the propagation.

Gravitational lensing distorts the cosmic microwave background (CMB) temperature and polarization fields and encodes valuable information on distances and growth rates at intermediate redshifts into the lensed power spectra. The non-Gaussian band-power covariance induced by the lenses is negligible to $l=2000$ for all but the $B$ polarization field where it increases the net variance by up to a factor of 10 and favors an observing strategy with 3 times more area than if it were Gaussian. To quantify the cosmological information, we introduce two lensing observables, characterizing nearly all of the information, which simplify the study of non-Gaussian impact, parameter degeneracies, dark energy models, and complementarity with other cosmological probes. Information on the intermediate-redshift parameters rapidly becomes limited by constraints on the cold dark matter density and initial amplitude of fluctuations as observations improve. Extraction of this information requires deep polarization measurements on only 5%–10% of the sky, and can improve Planck lensing constraints by a factor of $\sim 2–3$ on any one of the parameters $\{w_0,w_a,{\Omega }_K,\sum _{}^{}{m}_{\nu }\}$ with the others fixed. Sensitivity to the curvature and neutrino mass is the highest due to the high-redshift weight of CMB lensing but degeneracies between the parameters must be broken externally.

Little Higgs models may provide a solution to the gauge hierarchy problem in the mass of the Higgs boson. In this framework the Higgs boson arises as the pseudo-Nambu-Goldstone (PNG) boson. We show that the lepton triplet introduced in a little Higgs model explains a small mass parameter in the double see-saw mechanism for neutrino masses, and it can also gives an explanation for the axionlike particle recently reported by PVLAS collaboration.

We calculate the spectra of ultrahigh-energy cosmic rays (UHECRs) in an explicit top-down model based on the decays of metastable neutral “crypton” states in a flipped SU(5) string model. For each of the eight specific 10th-order superpotential operators that might dominate crypton decays, we calculate the spectra of both protons and photons, using a code incorporating supersymmetric evolution of the injected spectra. For all the decay operators, the total UHECR spectra are compatible with the available data. Also, the fractions of photons are compatible with all the published upper limits, but may be detectable in future experiments.

We calculate the vector form factor in $K\to \pi l\nu$ semileptonic decays at zero momentum transfer $f_{+}(0)$ from numerical simulations of two-flavor QCD on the lattice. Our simulations are carried out on ${16}^3\times 32$ at a lattice spacing of $a\simeq 0.12\mathrm{fm}$ using a combination of the DBW2 gauge and the domain-wall quark actions, which possesses excellent chiral symmetry even at finite lattice spacings. The size of fifth dimension is set to $L_s=12$, which leads to a residual quark mass of a few MeV. Through a set of double ratios of correlation functions, the form factor calculated on the lattice is accurately interpolated to zero momentum transfer, and then is extrapolated to the physical quark mass. We obtain $f_{+}(0)=0.968(9)(6)$, where the first error is statistical and the second is the systematic error due to the chiral extrapolation. Previous estimates based on a phenomenological model and chiral perturbation theory are consistent with our result. Combining with an average of the decay rate from recent experiments, our estimate of $f_{+}(0)$ leads to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{us}|=0.2245(27)$, which is consistent with CKM unitarity. These estimates of $f_{+}(0)$ and $|V_{us}|$ are subject to systematic uncertainties due to the finite lattice spacing and quenching of strange quarks, though nice consistency in $f_{+}(0)$ with previous lattice calculations suggests that these errors are not large.

I show that Sudakov resummation takes a transparent form if one deals with the second logarithmic derivative of the short distance coefficient functions for deep inelastic scattering and the Drell-Yan process. A uniquely defined Sudakov exponent emerges, and the constant terms not included in the exponent are conjectured to be given by the second logarithmic derivative of the massless quark form factor. The precise framework for the implementation of the dispersive approach to power corrections is set-up, yielding results in agreement with infrared renormalon expectations, but which are not tied to the single (dressed) gluon exchange approximation. Indications for a Banks-Zaks type of perturbative fixed point in the Sudakov effective coupling at low $N_f$ are pointed out. Existence of a fixed point in the Sudakov coupling is argued to imply its universality.