The dependence of functional renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if this newly introduced parameter is sent to infinity in the end of calculation. One-loop renormalization flow equations of QCD are derived. The novelty is that both the coupling running equation and the mass running equation are mass-dependent. Different flow patterns are explored. A mechanism for nonoccurrence of dynamical chiral symmetry breaking is arrived at. The existence of a conformal window is also discussed in the language of renormalization flow.

According to Noether’s theorem, each symmetry of the dynamics comes with an associated conservation law. Despite the importance of relativity symmetries—i.e., invariances under Galileo or Lorentz boosts—their associated conservation laws are never emphasized. Here we clarify the physical interpretation of such conservation laws: there exists a collective coordinate—the center-of-mass position—that undergoes uniform motion. This does not happen for theories that do not obey a relativity principle. As an application, we derive the Noether currents and charges associated with an internal Galilean invariance $\pi (x)\to \pi (x)+b_{\mu }{x}^{\mu }$—a symmetry recently postulated in the context of so-called Galileon theories.

The most studied doubly special-relativity scenarios, theories with both the speed-of-light scale and a length/inverse-momentum scale as nontrivial relativistic invariants, have concerned the possibility of relativistically enforcing some nonlinear laws on momentum space. For the recently proposed “relative-locality framework” a central role is played by nonlinear laws on momentum space, with the guiding principle that they should provide a characterization of the geometry of momentum space. Building on previous doubly special-relativity results, here I identify a requirement necessary for “DSR compatibility”; i.e. when the requirement is not satisfied a preferred-frame formulation of theories on that momentum space inevitably emerges. I find that, within a natural parametrization of momentum-space geometry, the requirement takes the form of an elementary algorithm. By working out a few examples I provide evidence that my requirement might be not only necessary but also sufficient: when the requirement is satisfied one does manage to produce a relativistic formulation. The examples I use to illustrate the applicability of my criterion also have some intrinsic interest, including two particularly noteworthy cases of $\kappa$-Poincaré-inspired momentum spaces.

In the standard hot big bang theory, when the Universe was about $1–10\mu \mathrm{s}$ old, the cosmological matter is conjectured to undergo quantum chromodynamics (QCD) phase transition(s) from quark matter to hadrons. In the present work, we study the cosmological quark-hadron phase transition in two different physical scenarios. First, by assuming that the phase transition would be described by an effective nucleation theory (prompt first-order phase transition), we analyze the evolution of the relevant cosmological parameters of the early universe (energy density $\rho$, temperature $T$, Hubble parameter $H$, and the scale factor $a$) before, during, and after the phase transition. To study the cosmological dynamics and the time evolution, we use both analytical and numerical methods. The case where the Universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles is also considered in detail. The numerical estimation of the cosmological parameters, $a$ and $H$ for instance, shows that the time evolution of the Universe varies from phase to phase. As the QCD era turns to be fairly accessible in the high-energy experiments and the lattice QCD simulations, the QCD equation of state is very well defined. In light of these QCD results, we develop a systematic study of the crossover quark-hadron phase transition, and an estimation for the time evolution of the Hubble parameter during the crossover.

In a companion paper [J. L. Jaramillo, R. P. Macedo, P. Moesta, and L. Rezzolla, preceding Article, Phys. Rev. D 85, 084030 (2012).], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test screens. More specifically, dynamical horizons provide appropriate inner screens in a $3+1$ setting and, in this context, we have shown that an effective-curvature vector measured at the common horizon produced in a head-on collision merger can be correlated with the flux of linear Bondi momentum at null infinity. In this paper we provide a more sound geometric basis to this picture. First, we show that a rigidity property of dynamical horizons, namely, foliation uniqueness, leads to a preferred class of null tetrads and Weyl scalars on these hypersurfaces. Second, we identify a heuristic horizon newslike function, depending only on the geometry of spatial sections of the horizon. Fluxes constructed from this function offer refined geometric quantities to be correlated with Bondi fluxes at infinity, as well as a contact with the discussion of quasilocal 4-momentum on dynamical horizons. Third, we highlight the importance of tracking the internal horizon dual to the apparent horizon in spatial 3-slices when integrating fluxes along the horizon. Finally, we discuss the link between the dissipation of the nonstationary part of the horizon’s geometry with the viscous-fluid analogy for black holes, introducing a geometric prescription for a “slowness parameter” in black-hole recoil dynamics.

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging problem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black-hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [L. Rezzolla, R. P. Macedo, and J. L. Jaramillo, Phys. Rev. Lett. 104, 221101 (2010).] with Robinson-Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a $3+1$ approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualitative aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a “slowness parameter” and how this can be computed from the local properties of the horizon. In a companion paper [J. L. Jaramillo, R. P. Macedo, P. Moesta, and L. Rezzolla, following article, Phys. Rev. D 85, 084031 (2012).] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.

In this paper we find new scaling laws for the evolution of $p$-brane networks in $N+1$-dimensional Friedmann-Robertson-Walker universes in the weakly interacting limit, giving particular emphasis to the case of cosmic superstrings ($p=1$) living in a universe with three spatial dimensions ($N=3$). In particular, we show that, during the radiation era, the root-mean-square velocity is $\overline{v}=1/\sqrt{2}$ and the characteristic length of non-interacting cosmic string networks scales as $L\propto a^{3/2}$ ($a$ is the scale factor), thus leading to string domination even when gravitational backreaction is taken into account. We demonstrate, however, that a small non-vanishing constant loop chopping efficiency parameter $\tilde{c}$ leads to a linear scaling solution with constant $LH\ll 1$ ($H$ is the Hubble parameter) and $\overline{v}\sim 1/\sqrt{2}$ in the radiation era, which may allow for a cosmologically relevant cosmic string role even in the case of light strings. We also determine the impact that the radiation-matter transition has on the dynamics of weakly interacting cosmic superstring networks.

In a recent paper [K. R. Dienes and B. Thomas, Phys. Rev. D 85, 083523 (2012).], we introduced “dynamical dark matter,” a new framework for dark-matter physics, and outlined its underlying theoretical principles and phenomenological possibilities. Unlike most traditional approaches to the dark-matter problem which hypothesize the existence of one or more stable dark-matter particles, our dynamical dark-matter framework is characterized by the fact that the requirement of stability is replaced by a delicate balancing between cosmological abundances and lifetimes across a vast ensemble of individual dark-matter components. This setup therefore collectively produces a time-varying cosmological dark-matter abundance, and the different dark-matter components can interact and decay throughout the current epoch. While the goal of our previous paper was to introduce the broad theoretical aspects of this framework, the purpose of the current paper is to provide an explicit model of dynamical dark matter and demonstrate that this model satisfies all collider, astrophysical, and cosmological constraints. The results of this paper therefore constitute an “existence proof” of the phenomenological viability of our overall dynamical dark-matter framework, and demonstrate that dynamical dark matter is indeed a viable alternative to the traditional paradigm of dark-matter physics. Dynamical dark matter must therefore be considered alongside other approaches to the dark-matter problem, particularly in scenarios involving large extra dimensions or string theory in which there exist large numbers of particles which are neutral under standard-model symmetries.

In this paper, we propose a new framework for dark-matter physics. Rather than focus on one or more stable dark-matter particles, we instead consider a multicomponent framework in which the dark matter of the universe comprises a vast ensemble of interacting fields with a variety of different masses, mixings, and abundances. Moreover, rather than impose stability for each field individually, we ensure the phenomenological viability of such a scenario by requiring that those states with larger masses and standard-model decay widths have correspondingly smaller relic abundances, and vice versa. In other words, dark-matter stability is not an absolute requirement in such a framework, but is balanced against abundance. This leads to a highly dynamical scenario in which cosmological quantities such as ${\Omega }_{\mathrm{CDM}}$ experience nontrivial time-dependences beyond those associated with the expansion of the universe. Although it may seem difficult to arrange an ensemble of states which have the required decay widths and relic abundances, we present one particular example in which this balancing act occurs naturally: an infinite tower of Kaluza-Klein (KK) states living in the bulk of large extra spacetime dimensions. Remarkably, this remains true even if the stability of the KK tower itself is entirely unprotected. Thus theories with large extra dimensions—and by extension, certain limits of string theory—naturally give rise to dynamical dark matter. Such scenarios also generically give rise to a rich set of collider and astrophysical phenomena which transcend those usually associated with dark matter.

The idea of unifying quarks and leptons in a gauge symmetry is very appealing. However, such a unification gives rise to leptoquark-type gauge bosons for which current collider experiments put strong limits on their masses, well beyond the TeV scale. We present a model in the framework of extra dimensions which breaks such quark-lepton unification symmetry via compactification at the TeV scale. These color triplet leptoquark gauge bosons, as well as the new quarks present in the model, can be produced at the LHC with distinctive final-state signatures. These final-state signals include high $p_T$ multijets and multileptons with missing energy, monojets with missing energy, as well as the heavy charged particles passing through the detectors, which we also discuss briefly. The model also has a neutral standard model singlet heavy lepton which is stable, and can be a possible candidate for dark matter.

We consider vectorial, asymptotically free $\mathcal{N}=1$ supersymmetric $\mathrm{SU}(N_c)$ gauge theories with $N_f$ copies of massless chiral superfields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare with exact results. We make use of two-loop and three-loop calculations of the beta function and anomalous dimension of the quadratic chiral superfield operator product for this purpose. The specific chiral superfield contents that we consider are $N_f$ copies of (i) $F+\overline{F}$, (ii) $Adj$, (iii) $S_2+{\overline{S}}_2$, and (iv) $A_2+{\overline{A}}_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,\mathrm{cr}}$ relative to the respective exact results for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories.

We derive the general structure of dimension-six derivative interactions in the $N$ Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone modes of a strongly interacting sector. We show that there are several relations among the dimension-six operators, and therefore the number of independent operators decreases compared with models on which only $SU(2{)}_L\times U(1{)}_Y$ invariance is imposed. As an explicit example, we derive scattering amplitudes and cross sections of longitudinal gauge bosons and Higgs bosons at high energy on models involving two Higgs doublets, and compare them with those of one Higgs doublet.

We extend the standard model to include a weak-triplet and color-octet scalar. This “octo-triplet” field consists of three particles, two charged and one neutral, whose masses and renormalizable interactions depend only on two new parameters. The charged octo-triplet decay into a $W$ boson and a gluon is suppressed by a loop factor and an accidental cancellation. Thus, the main decays of the charged octo-triplet may occur through higher-dimensional operators, mediated by a heavy vectorlike fermion, into quark pairs. For an octo-triplet mass below the $t\overline{b}$ threshold, the decay into $Wb\overline{b}$ or $Wb\overline{s}$ through an off shell top quark has a width comparable to that into $c\overline{s}$ or $c\overline{b}$. Pair production with one octo-triplet decaying into two jets and the other decaying into a $W$ and two soft $b$ jets may explain the dijet-plus-$W$ excess reported by the CDF Collaboration. Using a few kinematic distributions, we compare two mechanisms of octo-triplet pair production: through an $s$-channel coloron and through the coupling to gluons. The higher-dimensional operators that allow dijet decays also lead to $CP$ violation in $B_s-{\overline{B}}_s$ mixing.

Models of new physics induce $K-\overline{K}$ mixing operators having Dirac structures other than the “left-left” form of the standard model. We calculate the functional form of the corresponding $B$ parameters at next-to-leading order in both SU(3) and SU(2) staggered chiral perturbation theory (SChPT). Numerical results for these matrix elements are being generated using improved staggered fermions; our results can be used to extrapolate these matrix elements to the physical light and strange quark masses. The SU(3) SChPT results turn out to be much simpler than that for the standard model $B_K$ operator, due to the absence of chiral suppression in the new operators. The SU(2) SChPT result is of similar simplicity to that for $B_K$. In fact, in the latter case, the chiral logarithms for two of the new $B$ parameters are identical to those for $B_K$, while those for the other two new $B$ parameters are of opposite sign. In addition to providing results for the $2+1$ flavor theory in SU(3) SChPT and the $1+1+1$ flavor theory in SU(2) SChPT, we present the corresponding continuum partially quenched results, as these are not available in the literature.

In this work, we investigate the associated production of prompt heavy quarkonium and a massive (anti)bottom quark to leading order in the nonrelativistic QCD factorization formalism at the LHC. We present numerical results for the processes involving $J/\psi$, ${\chi }_{cJ}$, ${\rm Y}$ and ${\chi }_{bJ}$. From our work, we find that the production rates of these processes are quite large, and these processes have the potential to be detected at the LHC. When $p_T$ is smaller than about 10 GeV, the $c\overline{c}[{}^{1}S_0^{(8)}]$ states give the main contribution to the $p_T$ distribution of prompt $J/\psi$ with a massive (anti)bottom quark production. For the process $pp\to {\rm Y}+b(\overline{b})$, the contribution of the color-singlet mechanism is larger than that in the color-octet mechanism at low $p_T$ region. We also investigate the processes $pp\to {\chi }_{cJ}+b(\overline{b})$ and $pp\to {\chi }_{bJ}+b(\overline{b})$; the $p_T$ distributions are dominated by the color-octet Fock-state contribution at large $p_T$. These processes provide an interesting signature that could be studied at the LHC, and the measurement of these processes is useful to test the color-singlet mechanism and color-octet mechanism.

We develop a gauge-invariant linear response theory for relativistic Bardeen-Cooper-Schrieffer (BCS) superfluids based on a consistent fluctuation of the order-parameter (CFOP) approach. The response functions from the CFOP approach satisfy important generalized Ward identities. The gauge invariance of the CFOP theory is a consequence of treating the gauge transformation and the fluctuations of the order parameter on equal footing so collective-mode effects are properly included. We demonstrate that the pole of the response functions is associated with the massless Goldstone boson. Important physical quantities such as the compressibility and superfluid density of relativistic BCS superfluids can also be inferred from our approach. We argue that the contribution from the massless Goldstone boson is crucial in obtaining a consistent expression for the compressibility.

We consider the problem of neutrino masses and mixing within the general framework of standard (type-I) seesaw models leading to three light neutrinos. Under the assumption of a hierarchical neutrino mass spectrum ${\lambda }^4:\lambda :1$, consistent with present data, we examine possible lopsided patterns for the neutrino Yukawa couplings that can account for the observed mixing angles, including a small but nonvanishing $|U_{e3}|$. An embedding of the above within a general class of $SO(10)$ models is also considered.

We report a new sensitive search for $CPT$ violation, which includes improved measurements of the $CPT$-violating parameter $z$ and the total decay-width difference normalized to the averaged width $\Delta {\Gamma }_d/{\Gamma }_d$ of the two $B_d$ mass eigenstates. The results are based on a data sample of $535\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain $\mathcal{R}e(z)=[+1.9\pm 3.7(\mathrm{stat})\pm 3.3(\mathrm{syst})]\times {10}^{-2}$, $\mathcal{I}m(z)=[-5.7\pm 3.3(\mathrm{stat})\pm 3.3(\mathrm{syst})]\times {10}^{-3}$, and $\Delta {\Gamma }_d/{\Gamma }_d=[-1.7\pm 1.8(\mathrm{stat})\pm 1.1(\mathrm{syst})]\times {10}^{-2}$, all of which are consistent with zero. This is the most precise single measurement of these parameters in the neutral $B$-meson system to date.

We compute the spectrum of photons emitted by the finite-temperature large-$N$ $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills plasma coupled to electromagnetism, at strong yet finite ’t Hooft coupling. We work in the holographic dual description, extended by the inclusion of the full set of $\mathcal{O}({\alpha }^{\prime 3})$ type IIB string theory operators that correct the minimal supergravity action. We find that, as the t’ Hooft coupling decreases, the peak of the spectrum increases, and the momentum of maximal emission shifts toward the infrared, as expected from weak-coupling computations. The total number of emitted photons also increases as the ’t Hooft coupling weakens.

In this paper we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto anomaly matching equation. It is shown that the Son-Yamamoto relation in the IR implies a nontrivial interplay between the kinetic and Wess-Zumino-Witten terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.