We study QCD evolution equations of the first transverse-momentum moment of the naive-time-reversal-odd fragmentation functions—the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece the same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.

Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large-$p_T$ jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading unpolarized or (pseudo)scalar hadrons, namely pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum–dependent (TMD) parton distribution and fragmentation functions, with special attention to the Sivers, Boer-Mulders, and transversity quark distributions, and to the Collins fragmentation function for quarks (and to the analogous functions for gluons). For each of these effects we evaluate, at central and forward rapidities and for kinematical configurations accessible at BNL-RHIC, the corresponding potentially maximized asymmetry (for ${\pi }^{+}$ production), obtained by saturating natural positivity bounds (and the Soffer bound for transversity) for the distribution and fragmentation functions involved and summing additively all partonic contributions. We then estimate, for both neutral and charged pions, the asymmetries involving TMD functions for which parametrizations are available. We also study the role of the different mechanisms, and the corresponding transverse single-spin asymmetries, for large-$p_T$ inclusive-jet production.

The evolution of the Cabibbo-Kobayashi-Maskawa matrix and the quark Yukawa couplings is performed for the one-loop renormalization group equations in the universal extra dimension model. It is found that the evolution of mixing angles and the $CP$ violation measure $J$ may rapidly vary in the presence of the Kaluza-Klein modes, and this variation becomes dramatic as the energy approaches the unification scale.

In dynamic critical phenomena, singular behaviors appear not only in the order parameter but also in the other transport coefficients (due to the mode-mode coupling). However, this effect has not been observed in the AdS/CFT duality. We point out that this mode-mode coupling is suppressed by $1/N^2$ in the large-$N$ gauge theories which correspond to model H in the classification of Hohenberg and Halperin. Thus, the effect cannot be seen in the classical supergravity approximation. We illustrate this point using the example of the $\mathcal{N}=4$ super–Yang-Mills theory at a finite chemical potential. We also discuss the implications of this result to heavy-ion collisions.

We consider four supergravities with $16+16$, $32+32$, $64+64$, $128+128$ degrees of freedom displaying some curious properties: (1) They exhibit minimal supersymmetry ($\mathcal{N}=1$, 2, 2, 1) but maximal rank ($r=7$, 6, 4, 0) of the scalar coset in $D=4$, 5, 7, 11. (2) They couple naturally to supermembranes and admit these membranes as solutions. (3) Although the $D=4$, 5, 7 supergravities follow from truncating the maximally supersymmetric ones, there nevertheless exist $M$-theory compactifications with $G_2$, $SU(3)$, $SU(2)$ holonomy having these supergravities as their massless sectors. (4) They reduce to $\mathcal{N}=1$, 2, 4, 8 theories all with maximum rank 7 in $D=4$ which (5) correspond to 0, 1, 3, 7 lines of the Fano plane and hence admit a division algebra $(\mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O})$ interpretation consistent with the black-hole/qubit correspondence, (6) are generalized self-mirror, and hence (7) have a vanishing on-shell trace anomaly.

We present a steepest descent calculation of the Källén-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators. As the presence of complex masses and the use of Euclidean space brings the theory outside of the strict validity of the Cutkosky cut rules, we discuss an alternative method based on the Widder inversion operator of the Stieltjes transformation. It turns out that the results coincide with those obtained by naively applying the cut rules. We also point out the potential usefulness of the Stieltjes (inversion) formalism when nonstandard propagators are used, in which case cut rules are not available at all.

We construct a class of coherent spin-network states that capture properties of curved space-times of the Friedmann-Lamaître-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial ($t=\mathrm{const}$) section with a dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex $SL(2,\mathbb{C})$ variables, one for each link of the graph, and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in spin foams.

We study the thermodynamics of Gödel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed timelike curves and the absence of a globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, we extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and the effective action give the same Hawking fluxes as those from the Planck distribution for blackbody radiation in the background of the charged rotating Gödel black holes. Our results further support that Hawking radiation is a quantum phenomenon arising at the event horizon.

We explore stability of gravitating $Q$-balls with potential $V_4(\varphi )=\frac{m^2}{2}{\varphi }^2-\lambda {\varphi }^4+\frac{{\varphi }^6}{M^2}$ via catastrophe theory, as an extension of our previous work on $Q$-balls with potential $V_3(\varphi )=\frac{m^2}{2}{\varphi }^2-\mu {\varphi }^3+\lambda {\varphi }^4$. In flat spacetime $Q$-balls with $V_4$ in the thick-wall limit are unstable and there is a minimum charge $Q_{\min }$, where $Q$-balls with $Q<Q_{\min }$ are nonexistent. If we take self-gravity into account, on the other hand, there exist stable $Q$-balls with arbitrarily small charge, no matter how weak gravity is. That is, gravity saves $Q$-balls with small charge. We also show how stability of $Q$-balls changes as gravity becomes strong.

We study the potential impact of detecting the inflationary gravitational wave background by the future space-based gravitational wave detectors, such as DECIGO and BBO. The signal-to-noise ratio of each experiment is calculated for chaotic/natural/hybrid inflation models by using the precise predictions of the gravitational wave spectrum based on numerical calculations. We investigate the dependence of each inflation model on the reheating temperature which influences the amplitude and shape of the spectrum, and find that the gravitational waves could be detected for chaotic/natural inflation models with high reheating temperature. From the detection of the gravitational waves, a lower bound on the reheating temperature could be obtained. The implications of this lower bound on the reheating temperature for particle physics are also discussed.

We revisit the dynamics of a false vacuum bubble in a background de Sitter spacetime. We find that there exists a large parameter space that allows the bubble to collapse into a black hole or to form a wormhole. This may have interesting implications for the creation of a baby universe in the laboratory, the string landscape where the bubble nucleation takes place among a plenitude of metastable vacua, and the inflationary physics.

We study the reconstruction of the lensing potential power spectrum from CMB temperature data, with an eye to the Planck experiment. We work with the optimal quadratic estimator of Okamoto and Hu, which we characterize thoroughly in an application to the reconstruction of the lensing power spectrum. We find that at multipoles $L<250$, our current understanding of this estimator is biased at the 15% level by beyond-gradient terms in the Taylor expansion of lensing effects. We present the full lensed trispectrum to fourth order in the lensing potential to explain this effect. We show that the low-$L$ bias, as well as a previously known bias at high $L$, is relevant to the determination of cosmology and must be corrected for in order to avoid significant parameter errors. We also investigate the covariance of the reconstructed power, finding broad correlations of $\approx 0.1\%$. Finally, we discuss several small improvements which may be made to the optimal estimator to mitigate these problems.

We present a study of single top and single antitop quark production in the $t$-channel mode at the LHC $pp$ collider at 7 TeV, 10 TeV and 14 TeV, including next-to-leading order QCD corrections to the production and decay of the top quark. We discuss the effects of different $O({\alpha }_s)$ contributions on the inclusive cross section and important kinematic distributions, after imposing the relevant cuts to select $t$-channel single top quark events.

It has become clearer recently that the regular pattern of three flavor nonets describing the low spin meson multiplets seems to require some modification for the case of the spin 0 scalar mesons. One picture, which has had some success, treats the scalars in a chiral Lagrangian framework and considers them to populate two nonets. These are, in turn, taken to result from the mixing of two “bare” nonets, one of which is of quark-antiquark type and the other of two-quark–two-antiquark type. Here we show that such a mixing is, before chiral symmetry breaking terms are included, only possible for three flavors. In other cases, the two types of structure cannot have the same chiral symmetry transformation property. Specifically, our criterion would lead one to believe that scalar and pseudoscalar states containing charm would not have “four quark” admixtures. This work is of potential interest for constructing chiral Lagrangians based on exact chiral symmetry which is then broken by well-known specific terms. It may also be of interest in studying some kinds of technicolor theories.

The collection of a large number of $B$-hadron decays to hadronic final states at the CDF II Detector is possible due to the presence of a trigger that selects events based on track impact parameters. However, the nature of the selection requirements of the trigger introduces a large bias in the observed proper-decay-time distribution. A lifetime measurement must correct for this bias, and the conventional approach has been to use a Monte Carlo simulation. The leading sources of systematic uncertainty in the conventional approach are due to differences between the data and the Monte Carlo simulation. In this paper, we present an analytic method for bias correction without using simulation, thereby removing any uncertainty due to the differences between data and simulation. This method is presented in the form of a measurement of the lifetime of the $B^{-}$ using the mode $B^{-}\to D^0{\pi }^{-}$. The $B^{-}$ lifetime is measured as ${\tau }_{B^{-}}=1.663\pm 0.023\pm 0.015\mathrm{ps}$, where the first uncertainty is statistical and the second systematic. This new method results in a smaller systematic uncertainty in comparison to methods that use simulation to correct for the trigger bias.

We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains ${\varphi }^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the termination of inflation. For a negative nonminimal coupling, inflation takes place in the vacuum-dominated region, in the large field region, or near the local minimum/maximum. Inflation in the vacuum-dominated region becomes either the type (I) or (II), resulting in a blue or red spectrum of the curvature perturbations, respectively. Inflation around the local maximum can be either the type (I) or the type (II), which results in the red spectrum of the curvature perturbations, while around the local minimum it must be the type (I), which results in the blue spectrum. In the large field region, to terminate inflation, potential in the Einstein frame must be positively tilted, always resulting in the red spectrum. We then numerically solve the equations of motion to investigate the whole dynamics of inflaton and confirm that the spectrum of curvature perturbations changes from red to blue ones as scales become smaller.

The question of what happens when the heterotic $SO(32)$ instanton becomes small was answered sometime back by Witten. The heterotic theory develops an enhanced $Sp(2k)$ gauge symmetry for $k$ small instantons, besides the allowed $SO(32)$ gauge symmetry. An interesting question now is to ask what happens when we take the large $k$ limit. In this paper we argue that in some special cases, where Gauss’ law allows the large $k$ limit, the dynamics of the large $k$ small instantons can be captured by a dual gravitational description. For the cases that we elaborate in this paper, the gravity duals are non-Kähler manifolds although in general they could be nongeometric. These small instantons are heterotic five-branes and the duality allows us to study the strongly coupled field theories on these five-branes. We review and elaborate on some of the recent observations pointing towards this duality and argue that in certain cases the gauge-gravity duality may be understood as small instanton transitions under which the instantons smoothen out and consequently lose the $Sp(2k)$ gauge symmetry. This may explain how branes disappear on the dual side and are replaced by fluxes. We analyze the torsion classes before and after the transitions and discuss briefly how the Atiyah-Drinfeld-Hitchin-Manin sigma model and related vector bundles could be studied for these scenarios.

We investigate the infrared (strong-coupling) regime of SU($N$)-Yang-Mills theory on a self-dual background. We present an evaluation of the full effective potential for the field-strength invariant $F_{\mu \nu }{F}^{\mu \nu }$ from nonperturbative gauge correlation functions and find a nontrivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the $\beta$ function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators. Consistency between both gauges in the infrared imposes a new upper bound on the infrared exponents of the propagators. For the scaling solution, this bound reads ${\kappa }_c<23/38$ which, together with Zwanziger’s horizon condition ${\kappa }_c>1/2$, defines a rather narrow window for this critical exponent. Current estimates from functional methods indeed satisfy these bounds.

The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories, in particular. We give an explicit construction reducing integrals with massless propagators to a finite basis for planar integrals at two loops, both to all orders in the dimensional regulator $ϵ$, and also when all integrals are truncated to $\mathcal{O}(ϵ)$. We show how to reorganize integration-by-parts equations to obtain elements of the first basis efficiently, and how to use Gram determinants to obtain additional linear relations reducing this all-orders basis to the second one. The techniques we present should apply to nonplanar integrals, to integrals with massive propagators, and beyond two loops as well.