There exists a paradox in quantum field theory: substituting a field configuration, which solves a subset of the field equations into the action, and varying it is not necessarily equivalent to substituting that configuration into the remaining field equations. We take the $S^4$ and Freund-Rubin–like instantons as two examples to clarify the paradox. One must match the specialized configuration field variables with the corresponding boundary conditions by adding appropriate Legendre terms to the action. Some comments are made regarding exceptional degenerate cases.

We study the decay $B^{-}\to D{K}^{*-}$ using a sample of $379\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II $B$ factory. We perform a Gronau-London-Wyler analysis where the $D$ meson decays into either a $CP$-even ($CP+$) eigenstate ($K^{+}{K}^{-}$, ${\pi }^{+}{\pi }^{-}$), $CP$-odd ($CP-$) eigenstate ($K_S^0{\pi }^0$, $K_S^0\varphi$, $K_S^0\omega$) or a non-$CP$ state ($K^{-}{\pi }^{+}$). We also analyze $D$ meson decays into $K^{+}{\pi }^{-}$ from a Cabibbo-favored ${\overline{D}}^0$ decay or doubly suppressed $D^0$ decay [Atwood-Dunietz-Soni (ADS) analysis]. We measure observables that are sensitive to the Cabibbo-Kobayashi-Maskawa angle $\gamma$: the partial-rate charge asymmetries ${\mathcal{A}}_{CP\pm }$, the ratios ${\mathcal{R}}_{CP\pm }$ of the $B$-decay branching fractions in $CP\pm$ and non-$CP$ decay, the ratio ${\mathcal{R}}_{\mathrm{ADS}}$ of the charge-averaged branching fractions, and the charge asymmetry ${\mathcal{A}}_{\mathrm{ADS}}$ of the ADS decays: ${\mathcal{A}}_{CP+}=0.09\pm 0.13\pm 0.06$, ${\mathcal{A}}_{CP-}=-0.23\pm 0.21\pm 0.07$, ${\mathcal{R}}_{CP+}=2.17\pm 0.35\pm 0.09$, ${\mathcal{R}}_{CP-}=1.03\pm 0.27\pm 0.13$, ${\mathcal{R}}_{\mathrm{ADS}}=0.066\pm 0.031\pm 0.010$, and ${\mathcal{A}}_{\mathrm{ADS}}=-0.34\pm 0.43\pm 0.16$, where the first uncertainty is statistical and the second is systematic. Combining all the measurements and using a frequentist approach yields the magnitude of the ratio between the Cabibbo-suppressed and favored amplitudes, $r_B=0.31$ with a one (two) sigma confidence level interval of [0.24, 0.38] ([0.17, 0.43]). The value $r_B=0$ is excluded at the 3.3 sigma level. A similar analysis excludes values of $\gamma$ in the intervals [0, 7]°, [55, 111]°, and [175, 180]° ([85, 99]°) at the one (two) sigma confidence level.

It has been suggested that relic long-lived strongly interacting massive particles (SIMPs, or $X$ particles) existed in the early universe. We study effects of such long-lived unstable SIMPs on big bang nucleosynthesis (BBN) assuming that such particles existed during the BBN epoch, but then decayed long before they could be detected. The interaction strength between an $X$ particle and a nucleon is assumed to be similar to that between nucleons. We then calculate BBN in the presence of the unstable neutral charged $X^0$ particles taking into account the capture of $X^0$ particles by nuclei to form $X$ nuclei. We also study the nuclear reactions and beta decays of $X$ nuclei. We find that SIMPs form bound states with normal nuclei during a relatively early epoch of BBN. This leads to the production of heavy elements which remain attached to them. Constraints on the abundance of $X^0$ particles during BBN are derived from observationally inferred limits on the primordial light element abundances. Particle models which predict long-lived colored particles with lifetimes longer than $\sim 200\mathrm{s}$ are rejected based upon these constraints.

Gravitational waves (GWs) from cosmological double neutron star binaries ($\mathrm{NS}+\mathrm{NS}$) can be significantly demagnified by the strong gravitational lensing effect, and the proposed future missions such as the Big Bang Observer or Deci-hertz Interferometer Gravitational Wave Observatory might miss some of the demagnified GW signals below a detection threshold. The undetectable binaries would form a GW foreground, which might hamper detection of a very weak primordial GW signal. We discuss the outlook of this potential problem, using a simple model based on the singular isothermal sphere lens profile. Fortunately, it is expected that, for a presumable merger rate of $\mathrm{NS}+\mathrm{NSs}$, the residual foreground would be below the detection limit ${\Omega }_{\mathrm{GW},\lim }\sim {10}^{-16}$ realized with the Big Bang Observer/Deci-hertz Interferometer Gravitational Wave Observatory by correlation analysis.

We calculate the relic density of the lightest neutralino in a supersymmetric seesaw type-II (“triplet seesaw”) model with minimal supergravity boundary conditions at the grand unified theory (GUT) scale. The presence of a triplet below the GUT scale, required to explain measured neutrino data in this setup, leads to a characteristic deformation of the sparticle spectrum with respect to the pure minimal supergravity (mSUGRA) expectations, affecting the calculated relic dark matter (DM) density. We discuss how the DM allowed regions in the $(m_0,M_{1/2})$ plane change as a function of the (type-II) seesaw scale. We also compare the constraints imposed on the models parameter space form upper limits on lepton flavor violating decays to those imposed by DM. Finally, we briefly comment on uncertainties in the calculation of the relic neutralino density due to uncertainties in the measured top and bottom masses.

A secluded U(1) sector with weak admixture to photons, $O({10}^{-2}-{10}^{-3})$, and the scale of the breaking below 1 GeV represents a natural yet poorly constrained extension of the standard model. We analyze $g-2$ of muons and electrons together with other precision QED data, as well as radiative decays of strange particles to constrain the mass-mixing angle ($m_V-\kappa$) parameter space. We point out that $m_V\simeq 214\mathrm{MeV}$ and ${\kappa }^2>3\times {10}^{-5}$ can be consistent with the hypothesis of the HyperCP Collaboration, which seeks to explain the anomalous energy distribution of muon pairs in the ${\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-}$ process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to an $O(\mathrm{\text{few}}\times {10}^{-9})$ upward correction to the anomalous magnetic moment of the muon, possibly relaxing some tension between the experimental value and theoretical determinations of $g-2$. The ultrafine energy resolution scan of the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ cross section and dedicated analysis of lepton spectra from $K^{+}\to {\pi }^{+}{e}^{+}{e}^{-}$ decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the $Z{b}_L{\overline{b}}_L$ coupling from large corrections. This “doublet-extended standard model” adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an $O(4)\times U(1{)}_X\sim SU(2{)}_L\times SU(2{)}_R\times P_{LR}\times U(1{)}_X$ symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged $SU(2{)}_L\times U(1{)}_Y$ electroweak symmetry by a Dirac mass $M$ for the new doublet; adjusting the value of $M$ allows us to explore the range of possibilities between the $O(4)$-symmetric ($M\to 0$) and standard-model-like ($M\to \infty$) limits. In this simple model, we find that the experimental limits on the $Z{b}_L{\overline{b}}_L$ coupling favor smaller $M$ while the presence of a potentially sizable negative contribution to $\alpha T$ strongly favors large $M$. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to $\alpha T$, $\alpha S$, and the $Z{b}_L{\overline{b}}_L$ coupling in this model arise from an effective operator coupling right-handed top quarks to the $Z$ boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to $\alpha T$ and the $Z{b}_L{\overline{b}}_L$ coupling, while leaving the standard model contributions essentially unchanged.

A careful reanalysis of both Argonne National Laboratory and Brookhaven National Laboratory data for weak single pion production is done. We consider deuteron nuclear effects and normalization (flux) uncertainties in both experiments. We demonstrate that these two sets of data are in good agreement. For the dipole parametrization of $C_5^A(Q^2)$, we obtain $C_5^A(0)=1.19\pm 0.08$, $M_A=0.94\pm 0.03\mathrm{GeV}$. As an application we present the discussion of the uncertainty of the neutral current $1{\pi }^0$ production cross section, important for the T2K neutrino oscillation experiment.

In this paper we study the effect of spacetime noncommutativity in the five-dimensional Randall-Sundrum braneworlds on the Casimir force acting on a pair of parallel plates. We show that the presence of a noncommutative scale length affects the nature of the Casimir force for small plate separation. Using accurate experimental bounds for the Casimir force in parallel plate geometry, we find an upper bound for the noncommutative cutoff of the order of ${10}^3\mathrm{TeV}$; we also find that the size of the interbrane distance in the first Randall-Sundrum model is approximately given by $kR\lesssim 20.5$ and $kR\lesssim 18.4$ for $k={10}^{19}\mathrm{GeV}$ and $k={10}^{16}\mathrm{GeV}$, respectively.

The predictive power of the Nambu–Jona-Lasinio model is considered in the light of a novel strategy to handle the divergences typical of perturbative calculations. The referred calculational strategy eliminates unphysical dependencies on the arbitrary choices for the routing of internal momenta and symmetry violating terms. In the present work we extend a previous one on the same issue by including vector interactions and performing the discussion in a more general context: the role of scale arbitrariness for the consistency of the calculations is considered. We show that the imposition of arbitrary scale independence for the consistent regularized amplitudes lead to additional properties for the irreducible divergent objects. These properties allow us to parametrize the remaining freedom in terms of a unique constant where resides all the arbitrariness involved. By searching for the best value for the arbitrary parameter we find a critical condition for the existence of an acceptable physical value for the dynamically generated quark mass. Such critical condition fixes the remaining arbitrariness turning the Nambu–Jona-Lasinio into a predictive model in the sense that its phenomenological consequences do not depend on possible choices made in intermediary steps. Numerical results are obtained for physical quantities like the vector and axial-vector masses and their coupling constants as genuine predictions.

We investigate the possibility that the dark matter consists of clusters of the heavy family quarks and leptons with zero Yukawa couplings to the lower families. Such a family is predicted by the approach unifying spin and charges as the fifth family. We make a rough estimation of properties of baryons of these new family members, of their behavior during the evolution of the Universe and when scattering on the ordinary matter, and study possible limitations on the family properties due to the cosmological and direct experimental evidences.

Cosmological observations are normally fit under the assumption that the dark sector can be decomposed into dark matter and dark energy components. However, as long as the probes remain purely gravitational, there is no unique decomposition and observations can only constrain a single dark fluid; this is known as the dark degeneracy. We use observations to directly constrain this dark fluid in a model-independent way, demonstrating, in particular, that the data cannot be fit by a dark fluid with a single constant equation of state. Parametrizing the dark fluid equation of state by a variety of polynomials in the scale factor $a$, we use current kinematical data to constrain the parameters. While the simplest interpretation of the dark fluid remains that it is comprised of separate dark matter and cosmological constant contributions, our results cover other model types including unified dark energy/matter scenarios.

Building on earlier work, we develop an equation-of-motion method for calculating magnetic seed fields generated from currents arising from charged $W^{\pm }$ fields in bubble collisions during a first-order primordial electroweak phase transition allowed in some proposed extensions of the standard model. The novel feature of our work is that it takes into account, for the first time, the dynamics of the bubble walls in such collisions. We conclude that for bubbles with sufficiently thin surfaces the magnetic seed fields may be comparable to, or larger than, those found in earlier work. Thus, our results strengthen the conclusions of previous studies that cosmic magnetic fields observed today may originate from seeds created during the electroweak phase transition, and consequently that these fields may offer a clue relevant to extensions of the standard model.

Hořava-Lifshitz theory has been recently put forth as a proposal for a renormalizable theory of quantum gravity [1]. It explicitly breaks Lorentz invariance, introducing an apparent extra scalar degree of freedom. I show that the low energy limit of (non-projectible) Hořava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, minimally coupled to Einstein gravity. This implies that the extra scalar is nondynamical to all orders in perturbation theory. Cosmological constraints on the quadratic cuscuton model constrain the low energy Lorentz breaking parameter of Hořava-Lifshitz theory to $|\lambda -1|<0.014$. We also point out that the spatial hypersurfaces are constant mean curvature or uniform expansion surfaces and introduce geometrical symmetries that can protect the nondynamical nature of these theories.

Affleck-Dine baryogenesis, accompanied by the formation and subsequent decay of $Q$-balls, can generate both the baryon asymmetry of the Universe and dark matter in the form of gravitinos. The gravitinos from $Q$-ball decay dominate over the thermally produced population if the reheat temperature $T_R\lesssim {10}^7\mathrm{GeV}$. We show that a gravitino with mass $\sim 1\mathrm{GeV}$ is consistent with all observational bounds and can explain the baryon-to-dark-matter ratio in the gauge-mediated models of supersymmetry breaking for a wide range of cosmological and $Q$-ball parameters. Moreover, decaying $Q$-balls can be the dominant production mechanism for $m_{3/2}<1\mathrm{GeV}$ gravitinos if the $Q$-balls are formed from a $(B-L)=0$ condensate, which produces no net baryon asymmetry. Gravitinos with masses in the range $50\mathrm{eV}\lesssim m_{3/2}\lesssim 100\mathrm{keV}$ produced in this way can act as warm dark matter and can have observable imprint on the small-scale structure.

One-loop corrections to the $Z^{\prime }$ decay width are derived and analyzed in the framework of the general form of the 3-3-1 models. We identify two important sources of corrections: oblique corrections associated to the $Z^{\prime }$ propagator through vacuum polarizations induced by virtual particle-antiparticle pairs of new heavy quarks $J$, and vertex corrections to the $Z^{\prime }q\overline{q}$ vertex through virtual exchange of new $K^{Q_{1,2}}$ gauge bosons. Fixing a specific renormalization scheme, we obtain dominant oblique corrections that exhibit a quadratic dependence on the $J$ quark mass, which are absorbed into two oblique parameters: a global parameter ${\rho }_f^{\prime }$ which modify the $Z^{\prime }$ decay width, and a parameter ${\kappa }_f^{\prime }$ that define effective $Z^{\prime }$ couplings. Numerical results in an specific 3-3-1 model gives a strong contribution of the oblique corrections from about 1.3% in the $d(s)$ quark channel to 10.5% in the neutrino channel, for $m_J=2\mathrm{TeV}$. The vertex corrections contribute to the oblique corrections up to 1.4% for the same channel and $m_J$ value. For $pp$ collisions at the CERN LHC collider, we find that the corrections significantly modify the shape of the cross section distributions for $e^{+}{e}^{-}$ and $t\overline{t}$ final states, where the distributions including the radiative corrections increases up to 1.23 times the tree-level distribution for the dielectron events and to 1.07 for the top events when $m_J=3\mathrm{TeV}$.

Inspired by the newly observed $D_{sJ}(3040{)}^{+}$ state, in this work we systemically study the two-body strong decays of P-wave charmed-strange mesons with the first radial excitation. Under the assignment of $1^{+}(j^P={\frac{1}{2}}^{+})$, i.e. the first radial excitation of $D_{s1}(2460{)}^{+}$, we find that the width of $D_{sJ}(3040{)}^{+}$ is close to the lower limit of the BABAR measurement. This indicates that it is reasonable to interpret $D_{sJ}(3040{)}^{+}$ as the first radial excitation of $D_{s1}(2460{)}^{+}$. Our calculation further predicts that $0^{-}+1^{-}$ channels, e.g., $D^{+}{K}^{*0}$, $D^0{K}^{*+}$, and $D_s^{+}\varphi$, are important for the search for $D_{sJ}(3040{)}^{+}$. To help future experiments find the remaining three P-wave charmed-strange mesons with the first radial excitation, we present the predictions for the strong decays of these three P-wave charmed-strange mesons.

We show that, within the seesaw mechanism, an almost decoupled right-handed (RH) neutrino species $N_{\mathrm{DM}}$ with mass $M_{\mathrm{DM}}\gtrsim 100\mathrm{GeV}$ can play the role of dark matter (DM). The $N_{\mathrm{DM}}$’s can be produced from nonadiabatic conversions of thermalized (source) RH neutrinos with mass $M_S$ lower than $M_{\mathrm{DM}}$. This is possible if a nonrenormalizable operator is added to the minimal type I seesaw Lagrangian. The observed DM abundance can be reproduced for $M_{\mathrm{DM}}{\delta }^{1/4}\sim {10}^{-13}{\Lambda }_{\mathrm{eff}}\xi$, where ${\Lambda }_{\mathrm{eff}}$ is a very high energy new physics scale, $\delta \equiv (M_{\mathrm{DM}}-M_S)/M_{\mathrm{DM}}$, and $\xi \lesssim 1$ is a parameter determined by the RH neutrino couplings.

We suggest a simple highly predictive ansatz for charged lepton and light neutrino mass matrices, based on the assumption of universality of Yukawa couplings. Using as input the charged lepton masses and light neutrino masses, the six parameters characterizing the leptonic mixing matrix $V_{\mathrm{PMNS}}$ are predicted in terms of a single phase $\varphi$, which takes a value around $\varphi =\frac{\pi }{2}$. Correlations among various physical quantities are obtained; in particular $V_{13}^{\mathrm{PMNS}}$ is predicted as a function of $\Delta m_{21}^2$, $\Delta m_{31}^2$, and ${sin}^2({\theta }_{\mathrm{sol}})$, and restricted to the range $0.167<|V_{13}^{\mathrm{PMNS}}|<0.179$.