The order of the thermal phase transition in the chiral limit of quantum chromodynamics (QCD) with two dynamical flavors of quarks is a long-standing issue and still not known in the continuum limit. Whether the transition is first or second order has important implications for the QCD phase diagram and the existence of a critical end point at finite densities. We follow a recently proposed approach to explicitly determine the region of first order chiral transitions at imaginary chemical potential, where it is large enough to be simulated, and extrapolate it to zero chemical potential with known critical exponents. Using unimproved Wilson fermions on coarse $N_t=4$ lattices, the first order region turns out to be so large that no extrapolation is necessary. The critical pion mass $m_{\pi }^c\approx 560\mathrm{MeV}$ is by nearly a factor 10 larger than the corresponding one using staggered fermions. Our results are in line with investigations of three-flavor QCD using improved Wilson fermions and indicate that the systematic error on the two-flavor chiral transition is still of order 100%.

We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a “sudden death” and the steering from anti-Bob to Bob experiences a “sudden birth” with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed $\ln 2$, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) $s=\mathrm{arccosh}\frac{{\cosh }^{2}r}{1-{\sinh }^{2}r}$ is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.

We compute the Rényi entropy and the supersymmetric Rényi entropy for the six-dimensional free (2, 0) tensor multiplet. We make various checks on our results, and they are consistent with the previous results about the (2, 0) tensor multiplet. As a by-product, we have established a canonical way to compute the Rényi entropy for $p$-form fields in $d$-dimensions.

Based on a simple geometrical approach, we analyze the evolution of the Kozai-Lidov mechanism for stars around shrinking massive black hole binaries on circular orbits. We find that, due to a peculiar bifurcation pattern induced by the Newtonian potential of stellar clusters, the orbit of stars could become highly eccentric. This transition occurs abruptly for stars with small initial eccentricities. The approach presented in this paper may be useful for studying the Kozai-Lidov mechanism in various astrophysical contexts.

We discuss a class of models for gravity based on a scalar field. The models include and generalize the old approach by Nordström which predated and, in some ways, inspired general relativity. The class include also a model that we have recently introduced and discussed in terms of its cosmological aspects (GSG). We present here a complete characterization of the Schwarschild geometry as a vacuum solution of GSG and sketch a discussion of the first post-Newtonian approximation.

We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the Arnowitt-Deser-Misner formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration in confrontation with Planck2015 observational data and find some constraints on the model’s parameters. Our treatment shows that this model in some ranges of the parameters is consistent with the observational data. Also, in some ranges of model’s parameters, the model predicts blue-tilted power spectrum. Finally, we show that nonminimal derivative model in the presence of the Gauss-Bonnet term has capability to have large non-Gaussianity.

The phase transition of a four-dimensional charged AdS black hole solution in the $R+f(R)$ gravity with constant curvature is investigated in the grand canonical ensemble, where we find novel characteristics quite different from that in the canonical ensemble. There exists no critical point for $T-S$ curve while in former research critical point was found for both the $T-S$ curve and $T-r_{+}$ curve when the electric charge of $f(R)$ black holes is kept fixed. Moreover, we derive the explicit expression for the specific heat, the analog of volume expansion coefficient and isothermal compressibility coefficient when the electric potential of $f(R)$ AdS black hole is fixed. The specific heat $C_{\mathrm{\Phi }}$ encounters a divergence when $0<\mathrm{\Phi }<b$ while there is no divergence for the case $\mathrm{\Phi }>b$. This finding also differs from the result in the canonical ensemble, where there may be two, one or no divergence points for the specific heat $C_Q$. To examine the phase structure newly found in the grand canonical ensemble, we appeal to the well-known thermodynamic geometry tools and derive the analytic expressions for both the Weinhold scalar curvature and Ruppeiner scalar curvature. It is shown that they diverge exactly where the specific heat $C_{\mathrm{\Phi }}$ diverges.

We analyze the vacuum static spherically symmetric spacetime for a specific class of nonconservative theories of gravity based on Rastall’s theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild–de Sitter solution in the general relativity theory obtained with a cosmological constant playing the role of source. We further discuss the structure (in particular, the coupling to matter fields) and some cosmological aspects of the underline nonconservative theory.

We investigate an inflationary model involving a gauge singlet scalar and fermionic dark matter. The mixing between the singlet scalar and the Higgs boson provides a portal to dark matter. The inflaton could either be the Higgs boson or the singlet scalar, and slow roll inflation is realized via its nonminimal coupling to gravity. In this setup, the effective scalar potential is stabilized by the mixing between two scalars and coupling with dark matter. We study constraints from collider searches, relic density and direct detection, and find that dark matter mass should be around half the mass of either the Higgs boson or singlet scalar. Using the renormalization group equation improved scalar potential and putting all the constraints together, we show that the inflationary observables $n_s-r$ are consistent with current Planck data.

We propose a new method to model cluster scaling relations in modified gravity. Using a suite of nonradiative hydrodynamical simulations, we show that the scaling relations of accumulated gas quantities, such as the Sunyaev-Zel’dovich effect (Compton-y parameter) and the x-ray Compton-y parameter, can be accurately predicted using the known results in the $\mathrm{\Lambda }\mathrm{CDM}$ model with a precision of $\sim 3\%$. This method provides a reliable way to analyze the gas physics in modified gravity using the less demanding and much more efficient pure cold dark matter simulations. Our results therefore have important theoretical and practical implications in constraining gravity using cluster surveys.

Observations of the microwave background fluctuations suggest a scale-dependent amplitude asymmetry of roughly $2.5\sigma$ significance. Inflationary explanations for this “anomaly” require non-Gaussian fluctuations which couple observable modes to those on much larger scales. In this paper, we describe an analysis of such scenarios which significantly extends previous treatments. We identify the non-Gaussian “response function” which characterizes the asymmetry and show that it is nontrivial to construct a model which yields a sufficient amplitude; many independent fine-tunings are required, often making such models appear less likely than the anomaly they seek to explain. We present an explicit model satisfying observational constraints and determine for the first time how large its bispectrum would appear to a Planck-like experiment. Although this model is merely illustrative, we expect it is a good proxy for the bispectrum in a sizeable class of models which generate a scale-dependent response using a large $\eta$ parameter.

We briefly review the supernatural supersymmetry (SUSY), which provides a most promising solution to the SUSY electroweak fine-tuning problem. In particular, we address its subtle issues as well. Unlike the minimal supersymmetric standard model (MSSM), the next to MSSM (NMSSM) can be scale invariant and has no mass parameter in its Lagrangian before SUSY and gauge symmetry breakings. Therefore, the NMSSM is a perfect framework for supernatural SUSY. To give the SUSY breaking soft mass to the singlet, we consider the moduli and dilaton dominant SUSY breaking scenarios in M-theory on $S^1/Z_2$. In these scenarios, SUSY is broken by one and only one $F$ term of moduli or dilaton, and the SUSY breaking soft terms can be determined via the Kähler potential and superpotential from Calabi-Yau compactification of M-theory on $S^1/Z_2$. Thus, as predicted by supernatural SUSY, the SUSY electroweak fine-tuning measure is of unity order. In the moduli dominant SUSY breaking scenario, the right-handed sleptons are relatively light around 1 TeV, stau can even be as light as 580 GeV and degenerate with the lightest neutralino, chargino masses are larger than 1 TeV, the light stop masses are around 2 TeV or larger, the first two-generation squark masses are about 3 TeV or larger, and gluinos are heavier tha.n squarks. In the dilaton dominant SUSY breaking scenario, the qualitative picture remains the same but we have heavier spectra as compared to the moduli dominant SUSY breaking scenario. In addition to it, we have Higgs $H_2/A_1$-resonance solutions for dark matter (DM). In both scenarios, the minimal value of DM relic density is about 0.2. To obtain the observed DM relic density, we can consider the dilution effect from supercritical string cosmology or introduce the axino as the lightest supersymmetric particle.

A 750 GeV resonance has been observed at the run 2 LHC in the diphoton channel. In this paper, we explain this resonance as a $CP$-even scalar $\mathbb{S}$ that triggers the spontaneous breaking of local $U(1{)}_B$ or $U(1{)}_{B+L}$ gauge symmetries. $\mathbb{S}$ couples to gluon and photon pairs at the one-loop level, where particles running in the loop are introduced to cancel anomalies, and the gluon fusion is the dominate production channel of $\mathbb{S}$ at the LHC. The model contains a scalar dark matter candidate stabilized by the new gauge symmetry. Our study shows that both the observed production cross section at the LHC and the best fit decay width of $\mathbb{S}$ can be explained in this model without conflicting with any other experimental data. Constraints on couplings associated with $\mathbb{S}$ are studied, which show that $\mathbb{S}$ has a negligible mixing with the standard model Higgs boson but sizable coupling with the dark matter.

A hint of a new resonance at a mass of 750 GeV has been shown in the diphoton channel of the Run-2 LHC data. The observed signal rate is usually too large to interpret it as a new scalar boson in the context of weakly coupled renormalizable models. One way is to reduce its total decay rate, which is possible if the $CP$-even heavy Higgs boson $H^0$ in the aligned two Higgs doublet model becomes top-phobic. To ensure sufficient gluon fusion production, we introduce vector-like quarks (VLQ). The Higgs precision data as well as the exclusion limits from no excesses in other resonance searches through $Z\gamma$, $b\overline{b}$, ${\tau }^{+}{\tau }^{-}$, and $jj$ channels at the Run-1 LHC are comprehensively studied. In Type I, the top-phobic $H^0$ cannot simultaneously explain the 750 GeV diphoton excess and the Higgs precision data since the same Yukawa couplings of the up-type and down-type VLQs to $H^0$ always make more contribution to the diphoton signal rate of the standard model Higgs boson than that of $H^0$. In Type II, small Yukawa coupling of the up-type VLQ but sizable Yukawa coupling of the down-type VLQ is shown to explain the signal while satisfying other LHC exclusion limits.

Recently, the ATLAS and CMS collaborations report excesses around 750 GeV in the diphoton channels. This might be the evidence which reveals new physics beyond the Standard Model. In this paper, we consider models with a 750 GeV scalar and vectorlike particles, which couple each other through Yukawa couplings. The decay of the scalar to diphoton is given by the loop diagrams involving the extra colored particles. We investigate not only the setup required by the excesses, but also the LHC constraints, especially concerned with the vectorlike particles. In our scenario, the extra colored particles decay to quarks and a dark matter (DM) via Yukawa couplings. Then, the signals from the vectorlike particles are dijet, $b\overline{b}$ and/or $t\overline{t}$ with large missing energy. We discuss two possibilities for the setups: One is a model with vectorlike fermions and a scalar DM, and the other is a model with vectorlike scalars and a fermionic DM. We suggest the parameter region favored by the excess in each case, and study the constraints based on the latest LHC results at $\sqrt{s}=8\mathrm{TeV}$ and 13 TeV. We conclude that the favored region is almost excluded by the LHC bounds, especially when the 750 GeV scalar dominantly decays to DMs. The mass differences between the vectorlike particles and the DM should be less than $\mathcal{O}(100)\mathrm{GeV}$ [$\mathcal{O}(10)\mathrm{GeV}$] to realize the large diphoton signal and the large decay width, if the extra colored particle only decays to a top (bottom) quark and a dark matter. Otherwise, these scenarios are already excluded by the latest LHC results.

We consider the possibility of an enlarged QCD color group, $\mathrm{SU}(3+N^{\prime })$ spontaneously broken to $\mathrm{SU}(3{)}_c\times \mathrm{SU}(N^{\prime })$ with extra vectorlike quarks transforming in the fundamental representation. When the heavy quarks are integrated out below the PQ-breaking scale, they generate an axion coupling which simultaneously solves the strong $CP$ problem for both gauge groups. However, the axion mass now receives a new nonperturbative contribution from the $\mathrm{SU}(N^{\prime })$ confinement scale, which can be substantially larger than the QCD scale. This can increase the axion mass to be at or above the electroweak scale. This visible axion can then decay into gluons and photons giving rise to observable signals at run II of the LHC. In particular, if the mass is identified with the 750 GeV diphoton resonance, then the new confinement scale is $\sim \mathrm{TeV}$ and the PQ-breaking scale is $\sim 10\mathrm{TeV}$. This predicts vectorlike quarks and a PQ scalar resonance in the multi-TeV range, with the possibility that dark matter is an $\mathrm{SU}(N^{\prime })$ baryon.

We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a $2+1$-flavor ensemble with lattices of size ${32}^3\times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081\mathrm{fm}$ and with $M_{\pi }=312\mathrm{MeV}$. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation $t_{\mathrm{sep}}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of $t_{\mathrm{sep}}$ needed to demonstrate convergence of the isovector charges of the nucleon to the $t_{\mathrm{sep}}\to \infty$ estimates is presented.

Two-body charmed meson decays $D\to VP$ are studied within the framework of the diagrammatic approach. Under flavor SU(3) symmetry, all the flavor amplitude sizes and their associated strong phases are extracted by performing a ${\chi }^2$ fit. Thanks to the recent measurement of $D_s^{+}\to {\pi }^{+}{\rho }^0$, the magnitudes and the strong phases of the $W$-annihilation amplitudes $A_{P,V}$ have been extracted for the first time. As a consequence, the branching fractions of all the $D\to VP$ decays are predicted, especially those modes that could not be predicted previously due to the unknown $A_{P,V}$. Our working assumption, the flavor SU(3) symmetry, is tested by comparing our predictions with experiment for the singly and doubly Cabibbo-suppressed decay modes based on the flavor amplitudes extracted from the Cabibbo-favored decays using the current data. The predictions for the doubly Cabibbo-suppressed channels are in good agreement with the data, while those for the singly Cabibbo-suppressed decay modes are seen to have flavor SU(3) symmetry breaking effects. We find that the inclusion of SU(3) symmetry breaking in color-allowed and color-suppressed tree amplitudes is needed in general in order to have a better agreement with experiment. Nevertheless, the exact flavor SU(3)-symmetric approach alone is adequate to provide an overall explanation for the current data.

We study the effects of curvature in the expansion of the logarithm of the differential elastic scattering cross section near $t=0$ as $d\sigma (s,t)/dt=d\sigma (s,0)/dt\times \exp (Bt+C{t}^2+D{t}^3\cdots )$ in an eikonal model for $pp$ and $\overline{p}p$ scattering, and use the results to discuss the extrapolation of measured differential cross sections and the slope parameters $B$ to $t=-q^2=0$. We find that the curvature effects represented by the parameters $C$ and $D$, while small, lead to significant changes in the forward slope parameter relative to that determined in a purely exponential fit, and to smaller but still significant changes in the forward elastic scattering and total cross sections. Curvature effects should therefore be considered in future analyses or reanalyses of the elastic scattering data.

We first study the charmless two-body ${\mathrm{\Lambda }}_b$ decays with scalar mesons as the final states and predict that $\mathcal{B}({\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{f}_0(980,1500))=(2.9\pm 0.7,12.4\pm 3.8)\times {10}^{-6}$ and $\mathcal{B}({\mathrm{\Lambda }}_b\to p{K}_0^{*-}(800,1430))=(1.9\pm 0.5,14.1\pm 4.5)\times {10}^{-6}$. With the resonant $f_0(980,1500)\to ({\pi }^{+}{\pi }^{-},K^{+}{K}^{-})$ and $K_0^{*-}\to {\overline{K}}^0{\pi }^{-}$ decays, we then obtain $\mathcal{B}({\mathrm{\Lambda }}_b\to \mathrm{\Lambda }({\pi }^{+}{\pi }^{-},K^{+}{K}^{-}))=(4.2\pm 1.0,3.5\pm 0.7)\times {10}^{-6}$ and $\mathcal{B}({\mathrm{\Lambda }}_b\to p{\overline{K}}^0{\pi }^{-})=(10.4\pm 2.9)\times {10}^{-6}$, in comparison with the data of $(4.6\pm 1.9,15.9\pm 2.6)\times {10}^{-6}$ and $(12.6\pm 4.0)\times {10}^{-6}$, respectively, from LHCb. Our results for ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\pi }^{+}{\pi }^{-}$ and ${\mathrm{\Lambda }}_b\to p{\overline{K}}^0{\pi }^{-}$ would be regarded as the first evidence of scalar meson production in the antitriplet $b$ baryon decays. The smaller predicted value of $\mathcal{B}({\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{K}^{+}{K}^{-})$ indicates the existence of other resonant contributions to the decay, such as ${\mathrm{\Lambda }}_b\to K^{-}(N^{*+}\to )\mathrm{\Lambda }{K}^{+}$.