We study the Higgs pair production in the standard model of strong and electroweak interactions at future $e^{+}{e}^{-}$ collider energies, with the reaction $e^{+}{e}^{-}\to t\overline{t}\mathrm{HH}.\mathrm{}$ We evaluate the total cross section of $t\overline{t}\mathrm{HH}$ and calculate the total number of events considering the complete set of Feynman diagrams at the tree level. The numerical computation is done for an energy which is expected to be available at a possible Next Linear $e^{+}{e}^{-}$ Collider with a center-of-mass energy 800, 1600 GeV and a luminosity of $1000{\mathrm{fb}}^{-1}.$

The higher twist corrections $h^N{\mathrm{}\left(x\right)/Q}^2$ to the spin dependent proton and neutron $g_1$ structure functions are extracted in a model independent way from experimental data on $g_1^N{(x,Q}^2)$ and found to be non-negligible. It is shown that the NLO QCD polarized parton densities determined from the data on $g_1,$ including higher twist effects are in good agreement with those found earlier from our analysis of the data on $g_1{/F}_1$ and $A_1$ where higher twist effects are negligible. On the contrary, the LO QCD polarized parton densities obtained from the data on $g_1,$ including higher twist, differ significantly from our previous results.

We study the neutral current flavor changing rare decay mode $\overrightarrow{B}K\gamma \gamma$ within the framework of the standard model, including the long distance contributions. It is found that these long distance contributions can be of the same order as the short distance contribution.

Differential distributions for heavy quark production depend on the heavy quark mass and other momentum scales, which can yield additional large logarithms and inhibit accurate predictions. Logarithms involving the heavy quark mass can be summed in heavy quark parton distribution functions in the Aivazis-Collins-Olness-Tung (ACOT) factorization scheme. A second class of logarithms involving the heavy-quark transverse momentum can be summed using an extension of the Collins-Soper-Sterman (CSS) formalism. We perform a systematic summation of logarithms of both types, thereby obtaining an accurate description of heavy-quark differential distributions at all energies. Our method essentially combines the ACOT and CSS approaches. As an example, we present angular distributions for bottom quarks produced in parity-conserving events at large momentum transfers Q at the DESY ep collider HERA.

We improve the calculations of the $\overrightarrow{\eta }{\pi }^0\gamma \gamma$ decay within the context of meson chiral Lagrangians. We use a chiral unitary approach for the meson-meson interaction, thus generating the $a_0\mathrm{}\left(980\right)\mathrm{}$ resonance and fixing the long standing sign ambiguity on its contribution. This also allows us to calculate the loops with one vector meson exchange, thus removing a former source of uncertainty. In addition we ensure the consistency of the approach with other processes, first, by using vector meson dominance couplings normalized to agree with radiative vector meson decays and, second, by checking the consistency of the calculations with the related $\gamma \overrightarrow{\gamma }{\pi }^0\eta$ reaction. We find an $\overrightarrow{\eta }{\pi }^0\gamma \gamma$ decay width of $0.47\pm 0.10\mathrm{eV},$ in clear disagreement with published data but in remarkable agreement with the most recent measurement.

Recent results from the NuTeV experiment at Fermilab and the deviation of the Z invisible width, measured at CERN LEP and the SLAC Linear Collider, from its standard model (SM) prediction suggest the suppression of neutrino-Z couplings. Such suppressions occur naturally in models which mix the neutrinos with heavy gauge singlet states. We postulate a universal suppression of the $Z\nu \nu$ couplings by a factor of $\left(1\mathrm{}-\varepsilon \right)$ and perform a fit to the Z-pole and NuTeV observables with $\varepsilon$ and the oblique correction parameters S and T. Compared to a fit with S and T only, the inclusion of $\varepsilon$ leads to a dramatic improvement in the quality of the fit. The values of S and T preferred by the fit can be obtained within the SM by a simple increase in the Higgs boson mass. However, if the W mass is also included in the fit, a non-zero U parameter becomes necessary which cannot be supplied within the SM. The preferred value of $\varepsilon$ suggests that the seesaw mechanism may not be the reason why neutrinos are so light.

We use geometrical conformal field theory methods to investigate tachyon fluctuations about the butterfly projector state in vacuum string field theory. We find that the on-shell condition for the tachyon field is equivalent to the requirement that the quadratic term in the string-field action vanish on shell. This further motivates the interpretation of the butterfly state as a D-brane. We begin a calculation of the tension of the butterfly, and conjecture that this will match the case of the sliver and further strengthen this interpretation.

We study the $O\left(N\right)\mathrm{}$ linear sigma model with spontaneous symmetry breaking, using a Hartree-like Ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We compute numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the Hartree approximation. We also discuss some implications of the fact that, in this order, the decay of the sigma into two pions affects the thermal diagrams.

We analyze the possibility of constructing a supersymmetric invariant that contains the $R^4$ term among its components as a superpotential term in type IIB on-shell superspace. We consider a scalar superpotential, i.e. an arbitrary holomorphic function of a chiral scalar superfield. In general, type IIB superspace does not allow for the existence of chiral superfields, but the obstruction vanishes for a specific superfield, the dilaton superfield. This superfield contains all fields of type IIB supergravity among its components, and its existence is implied by the solution of the Bianchi identities. The construction requires the existence of an appropriate chiral measure, and we find an obstruction to the existence of such a measure. The obstruction is closely related to the obstruction for the existence of chiral superfields and is non-linear in the fields. These results imply that the type IIB superinvariant related to the $R^4$ term is not associated with a scalar chiral superpotential.

We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua (even in the absence of an explicit cosmological constant), and asymptotically constant curvature solutions with nontrivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal (Weyl) gravity. We also study the string-inspired Einstein-Gauss-Bonnet model and show that both its flat and anti–de Sitter vacua are stable.

In this work we present a model of the universe in which dark energy is modeled explicitly with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a future collapsing universe (for a given region of the parameter space), which is necessary for a consistent formulation of both string and quantum field theories. The predictions of this model for distance modulus of supernovae are similar to those of the standard $\Lambda \mathrm{CDM}$ model.

Black-hole quasinormal modes (QNM) have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We compare numerical results for the QNM spectrum of the (rotating) Kerr black hole with an exact formula $\mathrm{Re}\overrightarrow{\omega }{T}_{\mathrm{BH}}\ln 3+\Omega m,$ which is based on Bohr’s correspondence principle. We find a close agreement between the two. The possible implications of this result to the area spectrum of quantum black holes are discussed.

We show how a radiation dominated universe subject to space-time quantization may give rise to inflation as the radiation temperature exceeds the Planck temperature. We consider dispersion relations with a maximal momentum (i.e., a minimum Compton wavelength, or quantum of space), noting that some of these lead to a trans-Planckian branch where energy increases with decreasing momenta. This feature translates into negative radiation pressure and, in well-defined circumstances, into an inflationary equation of state. We thus realize the inflationary scenario without the aid of an inflaton field. As the radiation cools down below the Planck temperature, inflation gracefully exits into a standard big bang universe, dispensing with a period of reheating. Thermal fluctuations in the radiation bath will in this case generate curvature fluctuations on cosmological scales whose amplitude and spectrum can be tuned to agree with observations.

In models involving new TeV-scale $Z^{\prime }$ gauge bosons, the new ${U\left(1\right)\mathrm{}}^{\prime }$ symmetry often prevents the generation of Majorana masses needed for a conventional neutrino seesaw mechanism, leading to three superweakly interacting “right-handed” neutrinos ${\nu }_R,$ the Dirac partners of the ordinary neutrinos. These can be produced prior to big bang nucleosynthesis by the $Z^{\prime }$ interactions, leading to a faster expansion rate and too much ${}^4\mathrm{He}.$ We quantify the constraints on the $Z^{\prime }$ properties from nucleosynthesis for $Z^{\prime }$ couplings motivated by a class of $E_6$ models parametrized by an angle ${\theta }_{E6\mathrm{}}.$ The rate for the annihilation of three approximately massless right-handed neutrinos into other particle pairs through the $Z^{\prime }$ channel is calculated. The decoupling temperature, which is higher than that of ordinary left-handed neutrinos due to the large $Z^{\prime }$ mass, is evaluated, and the equivalent number of new doublet neutrinos $\Delta N_{\nu }$ is obtained numerically as a function of the $Z^{\prime }$ mass and couplings for a variety of assumptions concerning the $Z-Z^{\prime }$ mixing angle and the quark-hadron transition temperature $T_c.$ Except near the values of ${\theta }_{E6\mathrm{}}$ for which the $Z^{\prime }$ decouples from the right-handed neutrinos, the $Z^{\prime }$ mass and mixing constraints from nucleosynthesis are much more stringent than the existing laboratory limits from searches for direct production or from precision electroweak data, and are comparable to the ranges that may ultimately be probed at proposed colliders. For the case $T_c=150\mathrm{}\mathrm{MeV}$ with the theoretically favored range of $Z-Z^{\prime }$ mixings, $\Delta N_{\nu }\lesssim 0.3$ for $M_{Z^{\prime }}\gtrsim 4.3\mathrm{TeV}$ for any value of ${\theta }_{E6\mathrm{}}.$ Larger mixing or larger $T_c$ often lead to unacceptably large $\Delta N_{\nu }$ except near the ${\nu }_R$ decoupling limit.

The proton, neutron and deuteron structure functions $F_2{(x,Q}^2)$ and $g_1{(x,Q}^2),$ measured at intermediate $Q^2,$ are analyzed within a Regge approach. This analysis serves to fix the parameters of this scheme which are then used to calculate, in a unified Regge approach, the properties of ${\rho }^0$ meson electroproduction on the proton and the deuteron. In this way, the double-spin asymmetry observed at HERMES in ${\rho }^0$ electroproduction on the proton can be related to the anomalous behavior of the flavor-singlet part of the spin-dependent structure function $g_1{(x,Q}^2)$ at small x.

By resorting to recent results on the relativistic currents for mixed (flavor) fields, we calculate a space-time dependent neutrino oscillation formula in quantum field theory. Our formulation provides an alternative to existing approaches for the derivation of space dependent oscillation formulas and it also accounts for the corrections due to the nontrivial nature of the flavor vacuum. By exploring different limits of our formula, we recover already known results. We study in detail the case of one-dimensional propagation with Gaussian wave packets both in the relativistic and in the nonrelativistic regions: in the last case, numerical evaluations of our result show significant deviations from the standard formula.

If neutrino masses have a radiative origin, their smallness can be naturally understood even when lepton number violation occurs near the weak scale. We analyze a specific model of this type wherein the neutrino masses arise as two-loop radiative corrections. We show that the model admits the near bimaximal mixing pattern suggested by the current neutrino oscillation data. Unlike the conventional seesaw models, these two-loop models can be directly tested in lepton flavor violating decays $\overrightarrow{\tau }3\mu$ and $\overrightarrow{\mu }e+\gamma$ as well as at colliders by the direct observation of charged scalars needed for the mass generation. It is shown that consistency with the neutrino oscillation data requires that the leptonic rare decays should be within reach of forthcoming experiments and that the charged scalars are likely to be within reach of the CERN LHC.

We compute the $\mathcal{O}\left({\alpha }_s^3\right)$ inclusive cross section for the process $p\overrightarrow{p}t\overline{t}h$ in the standard model, at $\sqrt{s_H}=14\mathrm{}\mathrm{TeV}.$ The next-to-leading order corrections drastically reduce the renormalization and factorization scale dependence of the Born cross section and increase the total cross section for renormalization and factorization scales larger than $m_t.$ These corrections have important implications for models of new physics involving the top quark.

We prove a factorization theorem for heavy-to-light form factors. Our result differs in several important ways from previous proposals. A proper separation of scales gives hard kernels that are free of end point singularities. A general procedure is described for including soft effects usually associated with the tail of wave functions in hard exclusive processes. We give an operator formulation of these soft effects using the soft-collinear effective theory, and show that they appear at the same order in the power counting as the hard spectator contribution.

We study the string modes in $\mathrm{pp}$-wave light-cone string field theory. First, we clarify the discrepancy between the Neumann coefficients for the supergravity vertex and the zero mode of the full string one. We also repeat our previous manipulation of the prefactor for the string modes and find that the prefactor reduces to the energy difference of the cos modes minus that of the sin modes. Finally, we discuss impurity number nonpreserving three-string processes.