Since the discovery of $X(3872)$, its structure has been in ceaseless dispute. The data of $X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi$ suggest that $X(3872)$ may be a high-spin charmoniumlike particle of $2^{-+}$. In terms of the light-front quark model we calculate the rates of the radiative decays $X(3872)\to J/\psi ({\psi }^{\prime })\gamma$ supposing $X(3872)$ to be a $2^{-+}$ charmonium. Within this framework, our theoretical prediction on $\mathcal{B}\mathcal{R}(X(3872)\to \psi (1S)\gamma )$ is at order of ${10}^{-3}$ which is slightly lower than the BABAR Collaboration’s data but close to the Belle Collaboration’s. Our prediction on $\mathcal{B}\mathcal{R}(X(3872)\to {\psi }^{\prime }\gamma )$ is at order of ${10}^{-5}$ if ${\psi }^{\prime }$ is a pure $2S$ state or ${10}^{-4}$ if ${\psi }^{\prime }$ is a $2S-1D$ mixture, which does not conflict with the upper bound set by Belle, but is much lower than BABAR’s data. Thus if the future measurement decides the branching ratio of $\mathcal{B}\mathcal{R}(X(3872)\to {\psi }^{\prime }\gamma )$ to be much larger than ${10}^{-4}$, the $2^{-+}$ assignment for $X(3872)$ should be ruled out.

We describe a method to measure and correct for the incoherent component of energy flow arising from multiple interactions from jet shape and substructure observables of massive jets. The correction is a function of the jet-shape variable of interest and not a universal property. Such a correction is expected to reduce biases in the corresponding distributions generated by the presence of multiple interactions and to improve measurement resolution. This data-driven technique is not subject to uncertainties coming from the use of theoretical calculations. Corrections are derived for jet mass, angularity, and planar flow, and are found to be in good agreement with data on massive jets observed by the CDF collaboration. Finally, we comment on the linkage with the concept of jet area and jet mass area.

We show that the Kobayashi-Maskawa (KM) parametrization of the $3\times 3$ lepton flavor mixing matrix is a useful language to describe the phenomenology of neutrino oscillations. In particular, it provides us with a convenient way to link the genuine flavor mixing parameters (${\theta }_1$, ${\theta }_2$, ${\theta }_3$ and ${\delta }_{\mathrm{KM}}$) to their effective counterparts in matter (${\tilde{\theta }}_1$, ${\tilde{\theta }}_2$, ${\tilde{\theta }}_3$ and ${\tilde{\delta }}_{\mathrm{KM}}$). We rediscover the Toshev-like relation $\sin {\tilde{\delta }}_{\mathrm{KM}}\sin 2{\tilde{\theta }}_2=\sin {\delta }_{\mathrm{KM}}\sin 2{\theta }_2$ in the KM parametrization. We make reasonable analytical approximations to the exact relations between the genuine and matter-corrected flavor mixing parameters in two different experimental scenarios: (a) the neutrino beam energy $E$ is above $\mathcal{O}(1)\mathrm{GeV}$ and (b) $E$ is below $\mathcal{O}(1)\mathrm{GeV}$. As an example, the probability of ${\nu }_{\mu }\to {\nu }_e$ oscillations and $CP$-violating effects are calculated for the upcoming $\mathrm{NO}\nu \mathrm{A}$ and Hyper-$K$ experiments.

There is a conjecture in the literature that indicates the tree-level $S$-matrix elements of graviton become symmetric under the $SL(2,Z)$ transformation after including the loops and the nonperturbative effects. Using the Ward identity corresponding to the global $S$-duality transformations, this conjecture can be extended to other $S$-matrix elements as well. While the $SL(2,Z)$ transformation on the background dilaton is nonlinear, the Ward identity dictates the $S$-duality transformations on external states should be the linearized $SL(2,R)$ transformations. We examine in detail various $S$-matrix elements involving massless closed string and/or open string vertex operators on the world volume of the ${\mathrm{D}}_3$-brane in favor of this conjecture.

We explore $1/4$-BPS objects in the Coulomb phase of the ADE-type 6-dim (2,0) superconformal theories. By using the previous work on the junctions of strings in 5-dim gauge theories and 6-dim superconformal theories, we count the number of $1/4$-BPS objects, which are made of waves on self-dual strings and junctions of self-dual strings, and show that for all cases the number matches exactly one-third of the anomaly constant $c_G=d_G{h}_G$ which is the product of dimension $d_G$ and dual Coxeter number $h_G$. This suggests the long sought after $N^3$ degrees of freedom are these $1/4$-BPS objects at least in the Coulomb phase.

In an influential paper of 2002, Babaev, Faddeev, and Niemi conjectured that two-component Ginzburg-Landau (TCGL) theory in three dimensions should support knot solitons, where the projective equivalence class of the pair of complex condensate fields $[{\psi }_1,{\psi }_2]\mathrm{\text{:}}{\mathbb{R}}^3\to \mathbb{C}{P}^1$ has nonzero Hopf degree. The conjecture was motivated by a certain truncation of the TCGL model which reduced it to the Faddeev-Skyrme model, long known to support knot solitons. Physically, the truncation amounts to ignoring the coupling between $[{\psi }_1,{\psi }_2]$ and the supercurrent of the condensates. The current paper presents a direct test of the validity of this truncation by numerically tracking the knot solitons as the supercurrent coupling is turned back on. It is found that the knot solitons shrink and disappear as the true TCGL model is reached. This undermines the reasoning underlying the conjecture and, when combined with other negative numerical studies, suggests the conjecture, in its original form, is very unlikely to be true.

In this work we study the hadron-quark phase transition matching relativistic hadrodynamical mean-field models (in the hadronic phase) with the more updated versions of the Polyakov-Nambu-Jona-Lasinio models (on the quark side). Systematic comparisons are performed showing that the predicted hadronic phases of the matching, named as RMF-PNJL, are larger than the confined phase obtained exclusively by the Polyakov quark models. This important result is due to the effect of the nuclear force that causes more resistance of hadronic matter to isothermal compressions. For sake of comparison, we also obtain the matchings of the hadronic models with the MIT bag model, named as RMF-MIT, showing that it presents always larger hadron regions, while shows smaller mixed phases than that obtained from the RMF-PNJL ones. Thus, studies of the confinement transition in nuclear matter, done only with quark models, still need nuclear degrees of freedom to be more reliable in the whole $T\times \mu$ phase diagram.

The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck’s curvature. These black holes only differ from their General Relativity counterparts very close to the center but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R-R^2/R_P$ the singularity is shifted to a finite radius, $r_{+}$, and the Kretschmann scalar diverges only as $1/(r-r_{+}{)}^2$.

Primordial inflation results in the production of a vast ensemble of highly infrared, massless, minimally coupled scalars. We use a recent fully renormalized computation of the one loop contribution to the graviton self-energy from these scalars to show that they have no effect on the propagation of dynamical gravitons. Our computation motivates a conjecture for the first correction to the vacuum state wave functional of gravitons. We comment as well on performing the same analysis for the more interesting contribution from inflationary gravitons, and on inferring one loop corrections to the force of gravity.

We examine the conformal equivalence between the $f(R)$ gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation that marks the strength of interaction between dark sectors. Instead of modeling $f(R)$ gravity in the Jordan frame, we construct the $f(R)$ gravity in terms of mass dilation function in the Einstein frame. We find that the condition to keep $f(R)$ gravity consistent with CMB observations ensures the energy flow from dark energy to dark matter in the corresponding interacting model, which meets the requirement to alleviate the coincidence problem in the Einstein framework.

If the conformal invariance of electromagnetism is broken during inflation, then primordial magnetic fields may be produced. If this symmetry breaking is generated by the coupling between electromagnetism and a scalar field—e.g. the inflaton, curvaton, or Ricci scalar—then these magnetic fields may be correlated with primordial density perturbations, opening a new window to the study of non-Gaussianity in cosmology. In order to illustrate, we couple electromagnetism to an auxiliary scalar field in a de Sitter background. We calculate the power spectra for scalar-field perturbations and magnetic fields, showing how a scale-free magnetic-field spectrum with rms amplitude of $\sim \mathrm{nG}$ at Mpc scales may be achieved. We explore the Fourier-space dependence of the cross correlation between the scalar field and magnetic fields, showing that the dimensionless amplitude, measured in units of the power spectra, can grow as large as $\sim 500H_I/M$, where $H_I$ is the inflationary Hubble constant and $M$ is the effective mass scale of the coupling.

In the symmetron mechanism, the fifth force mediated by a coupled scalar field (the symmetron) is suppressed in high-density regions due to the restoration of symmetry in the symmetron potential. In this paper we study the background cosmology and large-scale structure formation in the linear perturbation regime of the symmetron model. Analytic solutions to the symmetron in the cosmological background are found, which agree well with numerical results. We discuss the effect of the symmetron perturbation on the growth of matter perturbation, in particular, the implications of the brief period of tachyonic instability caused by the negative mass-squared of the symmetron during symmetry breaking. Our analysis and numerical results show that this instability has only very small effects on the growth of structures on subhorizon scales, and even at horizon scales its influence is not as drastic as naively expected. The symmetron fifth force in the nontachyonic regime does affect the formation of structure in a nontrivial way which could be cosmologically observable.

We investigate how the $CP$ quantum numbers of a neutral Higgs boson or spin-zero resonance $\Phi$, produced at the CERN Large Hadron Collider, can be determined in its $\tau$-pair decay mode $\Phi \to {\tau }^{-}{\tau }^{+}$. We use a method [S. Berge and W. Bernreuther, Phys. Lett. B 671, 470 (2009).] based on the distributions of two angles and apply it to the major 1-prong $\tau$ decays. We show for the resulting dilepton, lepton-pion, and two-pion final states that appropriate selection cuts significantly enhance the discriminating power of these observables. From our analysis we conclude that, provided a Higgs boson will be found at the LHC, it appears feasible to collect the event numbers needed to discriminate between a $CP$-even and -odd Higgs boson and/or between Higgs boson(s) with $CP$-conserving and $CP$-violating couplings after several years of high-luminosity runs.

We study the effect of squark generation mixing on gluino production and decays at LHC in the minimal supersymmetric standard model for the case that the gluino is lighter than all squarks and dominantly decays into three particles, $\tilde{g}\to q\overline{q}{\tilde{\chi }}_k^0$, $q{\overline{q}}^{\prime }{\tilde{\chi }}_l^{\pm }$. We assume mixing between the second and the third squark generations in the up-type and down-type squark sectors. We show that this mixing can lead to very large branching ratios of the quark-flavor violating gluino three-body decays despite the strong constraints on quark-flavor violation (QFV) from the experimental data on B mesons. We also show that the QFV gluino decay branching ratios are very sensitive not only to the generation mixing in the squark sector, but also to the parameters of the neutralino and chargino sectors. We show that the branching ratio of the QFV gluino decay $\tilde{g}\to c\overline{t}(\overline{c}t){\tilde{\chi }}_1^0$ can go up to $\sim 40\%$. Analogously, that of the QFV decay $\tilde{g}\to s\overline{b}(\overline{s}b){\tilde{\chi }}_1^0$ can reach $\sim 35\%$. We find that the rates of the resulting QFV signatures, such as $pp\to tt\overline{c}\overline{c}{E}_{\mathrm{T}}^{\mathrm{mis}}$, can be significant at LHC. This could have an important influence on the gluino searches at LHC.

Many extensions of the Standard Model lead to nonstandard neutrino interactions (NSI), which can affect the interpretation of current and future neutrino data. We explore an alternative approach to the study of these dimension-eight four-fermion interactions (of coefficient $4\epsilon G_F/\sqrt{2}$), by bringing into play collider data. In models where coefficients of potential dimension-six operators are suppressed by cancellations, LEP2 can provide interesting bounds on NSI operators ($\epsilon \lesssim {10}^{-2}–{10}^{-3}$). If NSI are contact interactions at LHC energies, they induce an effective interaction $\overline{q}q{W}^{+}{W}^{-}{e}_{\alpha }^{+}{e}_{\beta }^{-}$ (according to the Equivalence Theorem), to which the LHC at 14 TeV and with $100{\mathrm{fb}}^{-1}$ of data has excellent sensitivity ($\epsilon \lesssim 3\times {10}^{-3}$).

Using a data sample of $2.59\times {10}^7$ $\psi (2S)$ decays obtained with the CLEO-c detector, we perform amplitude analyses of the complementary decay chains $\psi (2S)\to \gamma {\chi }_{c1}$; ${\chi }_{c1}\to \eta {\pi }^{+}{\pi }^{-}$ and $\psi (2S)\to \gamma {\chi }_{c1}$; ${\chi }_{c1}\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$. We find evidence for an exotic $P$-wave ${\eta }^{\prime }\pi$ amplitude, which, if interpreted as a resonance, would have parameters consistent with the ${\pi }_1(1600)$ state reported in other production mechanisms. We also make the first observation of the decay $a_0(980)\to {\eta }^{\prime }\pi$ and measure the ratio of branching fractions $\mathcal{B}(a_0(980)\to {\eta }^{\prime }\pi )/\mathcal{B}(a_0(980)\to \eta \pi )=0.064\pm 0.014\pm 0.014$. The $\pi \pi$ spectrum produced with a recoiling $\eta$ is compared to that with ${\eta }^{\prime }$ recoil.

Pohlmeyer reduction of ${\mathrm{AdS}}_5\times S^5$ superstring, involving the solution of Virasoro conditions in terms of coset current variables, leads to a set of equations of motion following from an action containing a bosonic $Sp(2,2)\times Sp(4)/[SU(2){]}^4$ gauged Wess-Zumino-Witten (WZW) term, an integrable potential and a fermionic part coupling bosons from the two factors. The original superstring and the reduced model are in direct correspondence at the classical level but their relation at the quantum level remains an open question. As was found earlier, the one-loop partition functions of the two theories computed on the respective classical backgrounds match; here we explore the fate of this relation at the two-loop level. We consider the example of the reduced theory solution corresponding to the long folded spinning string in AdS. The logarithm of the ${\mathrm{AdS}}_5\times S^5$ superstring partition function computed on the spinning string background is known to be proportional to the universal scaling function which depends on the string tension $\frac{\sqrt{\lambda }}{2\pi }$. Its quantum part is $f(\lambda )=a_1+\frac{1}{\sqrt{\lambda }}{a}_2+\dots$, where the one-loop term is $a_1=-3\ln 2$ and the two-loop term is the negative of the Catalan’s constant, $a_2=-\mathrm{K}$. We find that the counterpart of $f(\lambda )$ in the reduced theory is $f(k)={\mathrm{a}}_1+\frac{2}{k}{\mathrm{a}}_2+\dots$, where $k$ is the coupling of the reduced theory. Here the one-loop coefficient is the same as in string theory, ${\mathrm{a}}_1=a_1$, while the two-loop one is ${\mathrm{a}}_2=a_2-\frac{1}{4}(a_1{)}^2$. Remarkably, the first Catalan’s constant term here matches the string-theory result if we identify the two couplings as $k=2\sqrt{\lambda }$. Nevertheless, the presence of the additional $(a_1{)}^2\sim (\ln 2{)}^2$ term suggests that the relation between the two quantum partition functions (if any) is not a simple equality. Similar results are found in the case of the ${\mathrm{AdS}}_3\times S^3$ string theory where $a_1=-2\ln 2$ and $a_2=0$, while in the corresponding reduced theory ${\mathrm{a}}_1=a_1$ and ${\mathrm{a}}_2=a_2-\frac{1}{4}(a_1{)}^2$.

This paper extends to the case of charged rotating black holes the conformally stationary, axisymmetric, conformally separable solutions presented for uncharged rotating black holes in a companion paper. In the present paper, the collisionless fluid accreted by the black hole may be charged. The charge of the black hole is determined self-consistently by the charge accretion rate. As in the uncharged case, hyper-relativistic counterstreaming between ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. If both ingoing and outgoing streams are charged, then conformal separability holds during early inflation, but fails as inflation develops. If conformal separability is imposed throughout inflation and collapse, then only one of the ingoing and outgoing streams can be charged: the other must be neutral. Conformal separability prescribes a hierarchy of boundary conditions on the ingoing and outgoing streams incident on the inner horizon. The dominant radial boundary conditions require that the incident ingoing and outgoing number densities be uniform with latitude, but the charge per particle must vary with latitude such that the incident charge densities vary in proportion to the radial electric field. The subdominant angular boundary conditions require specific forms of the incident number- and charge-weighted angular motions. If the streams fall freely from outside the horizon, then the prescribed angular conditions can be achieved by the charged stream, but not by the neutral stream. Thus, as in the case of an uncharged black hole, the neutral stream must be considered to be delivered ad hoc to just above the inner horizon.

A solution is obtained for the interior structure of an uncharged rotating black hole that accretes a collisionless fluid. The solution is conformally stationary, axisymmetric, and conformally separable, possessing a conformal Killing tensor. The solution holds approximately if the accretion rate is small but finite, becoming more accurate as the accretion rate tends to zero. Hyper-relativistic counter-streaming between collisionless ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. As ingoing and outgoing streams approach the inner horizon, they focus into twin narrow beams directed along the ingoing and outgoing principal null directions, regardless of the initial angular motions of the streams. The radial energy-momentum of the counter-streaming beams gravitationally accelerates the streams even faster along the principal directions, leading to exponential growth in the streaming density and pressure, and in the Weyl curvature and mass function. At exponentially large density and curvature, inflation stalls, and the spacetime collapses. As the spacetime collapses, the angular motions of the freely-falling streams grow. When the angular motion has become comparable to the radial motion, which happens when the conformal factor has shrunk to an exponentially tiny scale, conformal separability breaks down, and the solution fails. The condition of conformal separability prescribes the form of the ingoing and outgoing accretion flows incident on the inner horizon. The dominant radial part of the solution holds provided that the densities of ingoing and outgoing streams incident on the inner horizon are uniform, independent of latitude; that is, the accretion flow is “monopole.” The subdominant angular part of the solution requires a special nonradial pattern of angular motion of streams incident on the inner horizon. The prescribed angular pattern cannot be achieved if the collisionless streams fall freely from outside the horizon, so the streams must be considered as delivered ad hoc to just above the inner horizon.

This paper presents a concise derivation of a new set of solutions for the interior structure of accreting, rotating black holes. The solutions are conformally stationary, axisymmetric, and conformally separable. Hyper-relativistic counter-streaming between freely-falling collisionless ingoing and outgoing streams leads to mass inflation at the inner horizon, followed by collapse. The solutions fail at an exponentially tiny radius, where the rotational motion of the streams becomes comparable to their radial motion. The papers provide a fully nonlinear, dynamical solution for the interior structure of a rotating black hole from just above the inner horizon inward, down to a tiny scale.