We study the $\Delta I=1/2$ rule for kaon decays and the $B_K$ parameter for $K^0-{\overline{K}}^0$ mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current correlators, which depend upon self-interactions among the 5D bulk fields. Spontaneous chiral symmetry breaking ($\chi \mathrm{SB}$) is realized through boundary conditions on the bulk fields. Numerical results are analyzed in comparison with QCD, chiral perturbation theory ($\chi \mathrm{PT}$) and data, finding reasonable agreement with the experimental values of the $g_8$ and $g_{27}$ parameters describing the $\Delta I=1/2$, $3/2$ decay channels.

We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-’t Hooft operators, since in the purely electric case they reduce to the well-known Wilson loops, while in general they may carry ’t Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on ${\mathrm{AdS}}_E^2\times S^2$. We show that Wilson-’t Hooft operators are classified by a pair of weights (electric and magnetic) for the gauge group and its magnetic dual, modulo the action of the Weyl group. If the magnetic weight does not belong to the coroot lattice of the gauge group, the corresponding operator is topologically nontrivial (carries nonvanishing ’t Hooft magnetic flux). We explain how the spectrum of Wilson-’t Hooft operators transforms under the shift of the $\theta$-angle by $2\pi$. We show that, depending on the gauge group, either $SL(2,\mathbb{Z})$ or one of its congruence subgroups acts in a natural way on the set of Wilson-’t Hooft operators. This can be regarded as evidence for the $S$-duality of $N=4$ super-Yang-Mills theory. We also compute the one-point function of the stress-energy tensor in the presence of a Wilson-’t Hooft operator at weak coupling.

We examine the linear stability of various configurations in Bose-Einstein condensates with steplike sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon, and a combination of both. We discuss the role of different boundary conditions in this stability analysis, paying special attention to their meaning in gravitational terms. We highlight that the stability of a given configuration, not only depends on its specific geometry, but especially on these boundary conditions. Under boundary conditions directly extrapolated from those in standard general relativity, black hole configurations, white hole configurations, and the combination of both into a black hole-white hole configuration are shown to be stable. However, we show that under other (less stringent) boundary conditions, configurations with a single black hole horizon remain stable, whereas white hole and black hole-white hole configurations develop instabilities associated to the presence of the sonic horizons.

We consider nonstandard cosmological models in which the late decay of a scalar field $\varphi$ reheats the Universe to a low reheating temperature, between 5 MeV and the standard freeze-out temperature of neutralinos of mass $m_{\chi }$. We point out that in these models all neutralinos with standard density ${\Omega }_{\mathrm{std}}\gtrsim {10}^{-5}(100\mathrm{GeV}/m_{\chi })$ can have the density of cold dark matter, provided the right combination of the following two parameters can be achieved in the high-energy theory: the reheating temperature, and the ratio of the number of neutralinos produced per $\varphi$ decay over the $\varphi$ field mass. We present the ranges of these parameters where a combination of thermal and nonthermal neutralino production leads to the desired density, as functions of ${\Omega }_{\mathrm{std}}$ and $m_{\chi }$.

We consider a baryogenesis scenario, where the difference of baryon ($B$) and lepton ($L$) number is conserved in such a way that the $B-L$ asymmetry in the standard model sector is compensated by an asymmetry of opposite sign stored in the dark energy sector. Therefore, we introduce a toy model in which a complex quintessence field carries a $B-L$ asymmetry at late times. We determine the produced baryon asymmetry in the visible sector for a large range of initial conditions and find it easy to achieve a value of the observed order of magnitude. While the size of the produced baryon asymmetry depends on details of the underlying inflationary model, it turns out to be independent of the reheating temperature in many cases. We also discuss possible sources of instability like the formation of Q-Balls.

We investigate the relic abundance of dark matter in the minimal universal extra dimension model including resonance processes by second Kaluza-Klein particles in all coannihilation processes. After including second Kaluza-Klein resonance processes, the relic abundance of dark matter is reduced by about 30%. Thus, the compactification scale $1/R$ of the extra dimension consistent with the WMAP observation is increased by a few hundred GeV. As a result, the cosmologically allowed compactification scale is $600\mathrm{GeV}\lesssim 1/R\lesssim 1400\mathrm{GeV}$ for $\Lambda R=20$.

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly noninformative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a nonzero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the $\Lambda \mathrm{CDM}$ concordance cosmology.

Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields the semiclassical model used recently to derive the “Optical Hall Effect” for polarized light (alias the “Optical Magnus Effect”).

Recently, Mekhfi [Phys. Rev. D 72, 114014 (2005)] remarked that when studying spin-orbital separation of the nucleon magnetic moment with the Gordon decomposition, one should keep a time-derivative term because the quark fields depend on time. We clarify that this term vanishes identically in a rigorous formulation of the nucleon magnetic moment, which then can be elegantly separated into a spin part related to quark tensor charge, and an orbital part related to quark convection angular momentum. In a quark model description of the nucleon, however, such a time-derivative term might contribute because it is hard to construct a true Hamiltonian eigenstate of relativistic interacting quarks.

The littlest Higgs model is the most economical little Higgs model. The observation of the new gauge bosons predicted by the littlest Higgs model could serve as a robust signature of the model. The International Linear Collider (ILC), with the high energy and luminosity, can open an ideal window to probe these new gauge bosons, specially, the lightest $B_H$. In the framework of the littlest Higgs model, we study a gauge boson $B_H$ production process $\gamma \gamma \to W^{+}{W}^{-}{B}_H$. The study shows that the cross section of the process can vary in a wide range (${10}^{-1}–{10}^1\mathrm{fb}$) in most parameter spaces preferred by the electroweak precision data. The high center of mass energy (for example, $\sqrt{s}=1500\mathrm{GeV}$) can obviously enhance the cross section to the level of tens of fb. For the favorable parameter spaces, the sufficient typical events could be assumed at the ILC. Therefore, our study about the process $\gamma \gamma \to W^{+}{W}^{-}{B}_H$ could provide a useful theoretical instruction for probing $B_H$ experimentally at ILC. Furthermore, such process would offer a good chance to study the triple and quartic gauge couplings involving $B_H$ and the SM gauge bosons which shed important light on the symmetry breaking features of the littlest Higgs model.

We construct extended technicolor (ETC) models that can produce the large splitting between the masses of the $t$ and $b$ quarks without necessarily excessive contributions to the $\rho$ parameter or to neutral flavor-changing processes. These models make use of two different ETC gauge groups, such that left- and right-handed components of charge $Q=2/3$ quarks transform under the same ETC group, while left- and right-handed components of charge $-1/3$ quarks and charged leptons transform under different ETC groups. The models thereby suppress the masses $m_b$ and $m_{\tau }$ relative to $m_t$, and $m_s$ and $m_{\mu }$ relative to $m_c$ because the masses of the $Q=-1/3$ quarks and charged leptons require mixing between the two ETC groups, while the masses of the $Q=2/3$ quarks do not. A related source of the differences between these mass splittings is the effect of the two hierarchies of breaking scales of the two ETC groups. We analyze a particular model of this type in some detail. Although we find that this model tends to suppress the masses of the first two generations of down-type quarks and charged leptons too much, it gives useful insights into the properties of theories with more than one ETC group.

In this work we study an SO(10) GUT model with minimum Higgs representations belonging only to the $\mathbf{210}$ and $\mathbf{16}$ dimensional representations of SO(10). We add a singlet fermion $S$ in addition to the usual $\mathbf{16}$ dimensional representation containing quarks and leptons. There are no Higgs bi-doublets and so charged fermion masses come from one-loop corrections. Consequently all the fermion masses, Dirac and Majorana, are of the seesaw type. We minimize the Higgs potential and show how the left-right symmetry is broken in our model where it is assumed that a $D$-parity odd Higgs field gets a vacuum expectation value at the grand unification scale. From the renormalization group equations we infer that in our model unification happens at ${10}^{15}\mathrm{GeV}$ and left-right symmetry can be extended up to some values just above ${10}^{11}\mathrm{GeV}$. The Yukawa sector of our model is completely different from most of the standard grand unified theories and we explicitly show how the Yukawa sector will look in the different phases and briefly comment on the running of the top-quark mass. We end with a brief analysis of lepton number asymmetry generated from the interactions in our model.

The simulation of QCD on dynamical ($N_f=2$) anisotropic lattices is described. A method for nonperturbative renormalisation of the parameters in the anisotropic gauge and quark actions is presented. The precision with which this tuning can be carried out is determined in dynamical simulations on $8^3\times 48$ and $8^3\times 80$ lattices.

We present results for masses of excited baryons from a quenched calculation with chirally improved quarks at pion masses down to 350 MeV. Our analysis of the correlators is based on the variational method. In order to provide a large basis set for spanning the physical states, we use interpolators with different Dirac structures and Jacobi smeared quark sources of different width. Our spectroscopy results for a wide range of ground state and excited baryons are discussed.

If the fundamental Planck scale is near a TeV, then TeV scale black holes should be produced in proton-proton collisions at the LHC where $\sqrt{s}=14\mathrm{TeV}$. As the temperature of the black holes can be $\sim 1\mathrm{TeV}$ we also expect production of Higgs bosons from them via Hawking radiation. This is a different production mode for the Higgs boson, which would normally be produced via direct pQCD parton fusion processes. In this paper we compare total cross sections and transverse momentum distributions $d\sigma /d{p}_T$ for Higgs production from black holes at the LHC with those from direct parton fusion processes at next-to-next-to-leading order and next-to-leading order, respectively. We find that the Higgs production from black holes can be larger or smaller than the direct pQCD production depending upon the Planck mass and black hole mass. We also find that $d\sigma /d{p}_T$ of Higgs production from black holes increases as a function of $p_T$ which is in sharp contrast with the pQCD predictions where $d\sigma /d{p}_T$ decreases so we suggest that the measurement of an increase in $d\sigma /d{p}_T$ as $p_T$ increases for Higgs (or any other heavy particle) production can be a useful signature for black holes at the LHC.

We study the effects of a set of dimension six flavor changing effective operators on several processes of production of top quarks at the Large Hadron Collider. Namely, $t\overline{t}$ production and associated production of a top and a gauge or Higgs boson. Analytical expressions for the cross sections of these processes are derived and presented.

We derive the triply differential spectrum for the inclusive rare decay $B\to X_s{\ell }^{+}{\ell }^{-}$ in the shape-function region, in which $X_s$ is jetlike with $m_X^2\lesssim m_b{\Lambda }_{\mathrm{QCD}}$. Experimental cuts make this a relevant region. The perturbative and nonperturbative parts of the matrix elements can be defined with the soft-collinear effective theory, which is used to incorporate ${\alpha }_s$ corrections consistently. We prove that, with a suitable power counting for the dilepton invariant mass, the same universal jet and shape functions appear as in $B\to X_s\gamma$ and $B\to X_u\ell \overline{\nu }$ decays. Parts of the usual ${\alpha }_s(m_b)$ corrections go into the jet function at a lower scale, and parts go into the nonperturbative shape function. For $B\to X_s{\ell }^{+}{\ell }^{-}$, the perturbative series in ${\alpha }_s$ are of a different character above and below $\mu =m_b$. We introduce a “split matching” method that allows the series in these regions to be treated independently.

Expressions for decay amplitudes of ${\overline{B}}^0$, $B^{-}$, and ${\overline{B}}_s^0$ mesons to two light pseudoscalar or vector mesons, including isosinglet mesons $\eta$, ${\eta }^{\prime }$, $\omega$, $\varphi$, are obtained using soft collinear effective theory (SCET) at LO in $1/m_b$. These are then used to predict unmeasured branching ratios, direct, and indirect $CP$ asymmetries in ${\overline{B}}^0$, $B^{-}$, and ${\overline{B}}_s^0$ decays into two light pseudoscalars, following a determination of nonperturbative SCET parameters from existing data using a ${\chi }^2$-fit. A separate discussion of indirect $CP$ asymmetries in penguin dominated ${\overline{B}}^0\to {\eta }^{{(}^{\prime })}{K}_{S,L}$, ${\pi }^0{K}_{S,L}$ decays is given.

We construct a family of solutions in IIB supergravity theory. These are time-dependent or depend on a light-like coordinate and can be thought of as deformations of ${\mathrm{AdS}}_5\times S^5$. Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the $\mathcal{N}=4$ gauge theory in a $3+1$ dimensional space-time with a metric and a gauge coupling that is varying with time or the light-like direction, respectively. This identification allows us to map the question of singularity resolution to the dual gauge theory.

Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both $1/N$ and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self-energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an $O(N)$ model to next-to-next-to-leading order in the 2PI-$1/N$ expansion. Because of the appearance of internal vertices the resulting equations appear intractable for a full-fledged $3+1$ dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in $0+1$ dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schrödinger equation.