We discuss several phenomenological implications of very special relativity (VSR). It is assumed that there is a small violation of Lorentz invariance, and the true symmetry group of nature is a subgroup called SIM(2). This symmetry group postulates the existence of a fundamental or preferred direction in space-time. We study its implications by using an effective action which violates Lorentz invariance but respects VSR. We find that the problem of finding the masses of fundamental fermions is, in general, intractable in the presence of a VSR term. The problem can be solved only in special cases, which we pursue. We next determine the signal of VSR in a torsion pendulum experiment as well as a clock comparison experiment. We find that VSR predicts a signal which is different from other Lorentz violating theories, and hence a dedicated data analysis is needed in order to impose reliable limits. Assuming that a signal is absent in the data, we determine the limits that can be imposed on the VSR parameters. We also study the implications of VSR in particle decay experiments taking the charged pion and kaon decay as an example. The effective interaction between the charged pion and the final state leptons is related to the fundamental VSR mass terms through a loop calculation. We also predict a shift in the angular dependence of the decay products due to VSR. Specifically, we find that these no longer display azimuthal symmetry with respect to the momentum of the pion. Furthermore, the azimuthal and polar angle distributions show time dependence with a period of a sidereal day. This time dependence provides us with a novel method to test VSR in future experiments.

We define a focus point (FP) asymmetry, $A_{\mathrm{FP}}$, obtained by integrating the normalized transverse momentum distribution of either lepton produced in the Drell-Yan (DY) process below and above a point where a variety of popular $Z^{\prime }$ models all have the same magnitude. For a given $Z^{\prime }$ mass the position of this FP is predictable, depending only on the collider energy and on the low transverse momentum cut chosen in the normalization procedure. The resulting $A_{\mathrm{FP}}$ is very sensitive to the $Z^{\prime }$ width and can be used to constrain this parameter in experimental fits.

We find that the quark propagator constructed from the domain-wall fermion operator has $L_s-1$ extra poles as well as the pole that realizes the physical quark in the continuum limit. We show the energy-momentum dispersion relation for the physical and unphysical poles of Möbius domain-wall fermions in free field theory at finite $L_s$. The dependence of extra pole energies on the Möbius parameter $b-c$ and on the domain-wall height $M_5$ is investigated. Our result suggests that small values of $b-c$ set a large lower bound on the unphysical pole masses and the contribution of these poles could be suppressed well by calculating with small $b-c$.

Effective Polyakov line actions are a powerful tool to study the finite temperature behavior of lattice gauge theories. They are much simpler to simulate than the original lattice model and are affected by a milder sign problem, but it is not clear to which extent they really capture the rich spectrum of the original theories. We propose here a simple way to address this issue based on the so-called second moment correlation length ${\xi }_{2nd}$. The ratio $\xi /{\xi }_{2nd}$ between the exponential correlation length and the second moment one is equal to 1 if only a single mass is present in the spectrum, and it becomes larger and larger as the complexity of the spectrum increases. Since both $\xi$ and ${\xi }_{2nd}$ are easy to measure on the lattice, this is a cheap and efficient way to keep track of the spectrum of the theory. As an example of the information one can obtain with this tool, we study the behavior of $\xi /{\xi }_{2nd}$ in the confining phase of the ($D=3+1$) SU(2) gauge theory and show that it is compatible with 1 near the deconfinement transition, but it increases dramatically as the temperature decreases. We also show that this increase can be well understood in the framework of an effective string description of the Polyakov loop correlator. This nontrivial behavior should be reproduced by the Polyakov loop effective action; thus, it represents a stringent and challenging test of existing proposals, and it may be used to fine-tune the couplings and to identify the range of validity of the approximations involved in their construction.

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{\mu }^{\mathrm{hvp}}$, is proposed. This approach combines data on $e^{+}{e}^{-}$ annihilation into hadrons, perturbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, ${\mathrm{\Pi }}_{\mathrm{EM}}^{\prime }(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{\mu }^{\mathrm{hvp}}$ to $e^{+}{e}^{-}$ annihilation data, behaves like $1/s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_{\mu }$ in terms of ${\mathrm{\Pi }}_{\mathrm{EM}}^{\prime }(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{\mu }^{\mathrm{hvp}}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.

We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self-coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function, and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be complete asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.

We evaluate the production cross sections of $X(3872)$ at the LHC and Tevatron at NLO in ${\alpha }_s$ in NRQCD by assuming that the short-distance production proceeds dominantly through its ${\chi }_{c1}^{\prime }$ component in our ${\chi }_{c1}^{\prime }-D^0{\overline{D}}^{*0}$ mixing model for $X(3872)$. The outcomes of the fits to the CMS $p_T$ distribution can well account for the recent ATLAS data in a much larger range of transverse momenta ($10\mathrm{GeV}<p_T<70\mathrm{GeV}$) and the CDF total cross section data, and are also consistent with the value of $k=Z_{c\overline{c}}·\mathrm{Br}(X\to J/\psi {\pi }^{+}{\pi }^{-})$ constrained by the $B$-meson decay data. For LHCb, the predicted $X(3872)$ total cross section is larger than the data by a factor of 2, which is due to the problem of the fixed-order NRQCD calculation that may not be applicable for the region with small $p_T$ ($p_T\sim 5\mathrm{GeV}$) and large forward rapidity ($2.5<y<4.5$). In comparison, the prediction of the molecule production mechanism for $X(3872)$ is inconsistent with both $p_T$ distributions and total cross sections of CMS and ATLAS, and the total cross section of CDF.

We calculate several differential distributions for the production of charm and dijets. Both single-parton scattering (SPS) and double-parton scattering (DPS) contributions are calculated in the $k_T$-factorization approach. The Kimber-Martin-Ryskin unintegrated parton distributions are used in our calculations. Relatively low cuts on jet transverse momenta are imposed to enhance the double-parton scattering mechanism contribution. We find dominance of the DPS contribution over the SPS one. We have found regions of the phase space where the SPS contribution is negligible compared to the DPS contribution. The distribution in transverse momentum of charm quark/antiquark or charmed mesons can be used to observe transition from the dominance of DPS at low transvsverse momenta to the dominance of SPS at large transverse momenta. Very distinct azimuthal correlation patterns (for $c\overline{c}$, $c\text{−}\text{jet}$, jet-jet, $D^0\text{−}\text{jet}$, $D^0\overline{D^0}$) are predicted as a result of the competition of the SPS and DPS mechanisms.

We study the heat capacity of a static system of self-gravitating radiations analytically in the context of general relativity. To avoid the complexity due to a conical singularity at the center, we excise the central part and replace it with a regular spherically symmetric distribution of matters of which specifications we are not interested in. We assume that the mass inside the inner boundary and the locations of the inner and the outer boundaries are given. Then, we derive a formula relating the variations of physical parameters at the outer boundary with those at the inner boundary. Because there is only one free variation at the inner boundary, the variations at the outer boundary are related, which determines the heat capacity. To get an analytic form for the heat capacity, we use the thermodynamic identity $\delta S_{\mathrm{rad}}=\beta \delta M_{\mathrm{rad}}$ additionally, which is derived from the variational relation of the entropy formula with the restriction that the mass inside the inner boundary does not change. Even if the radius of the inner boundary of the shell goes to zero, in the presence of a central conical singularity, the heat capacity does not go to the form of the regular sphere. An interesting discovery is that another legitimate temperature can be defined at the inner boundary which is different from the asymptotic one ${\beta }^{-1}$.

Impulsive, nondiverging, Petrov-Segre type-N gravitational wave solutions to a general massive three-dimensional gravity in the de Sitter, anti–de Sitter, and flat Minkowski backgrounds are constructed in a unified manner by using the exterior algebra of differential forms.

A detailed perturbative construction of globally regular, asymptotically anti–de Sitter (AdS) time-periodic solutions of Einstein’s equations with a negative cosmological constant (AdS geons) is presented. Starting with the most general superposition of the $l=2$ even parity (scalar) eigenmodes of AdS at linear order, it is shown that at the fifth order in perturbation theory one obtains five one-parameter geon families, two of which have a helical Killing vector, one with axial symmetry, and two others without continuous symmetries. The details and some subtle aspects of the perturbative expansions are also presented.

The attenuation effect is the effect of weakening contributions to the oscillation signal from remote structures of the matter density profile. The effect is a consequence of integration over the neutrino energy within the energy resolution interval. Structures of a density profile situated at distances larger than the attenuation length, ${\lambda }_{\mathrm{att}}$, are not “seen” at the level $\epsilon \equiv 2EV/\mathrm{\Delta }{m}^2$, where $V$ is the matter potential. We show that the origins of attenuation are (i) the averaging of oscillations in certain layer(s) of matter, (ii) the smallness of the matter effect: $\epsilon \ll 1$, and (iii) the specific initial and final states on neutrinos. We elaborate on the graphic description of the attenuation that allows us to compute explicitly the effects in the ${\epsilon }^2$ order for various density profiles and oscillation channels. The attenuation in the case of partial averaging is described. The effect is crucial for the interpretation of oscillation data and for the oscillation tomography of the Earth with low energy (solar, supernova, atmospheric, etc.) neutrinos.

The statistical significance of a candidate gravitational-wave (GW) event is crucial to the prospects for a confirmed detection, or for its selection as a candidate for follow-up electromagnetic observation. To determine the significance of a GW candidate, a ranking statistic is evaluated and compared to an empirically-estimated background distribution, yielding a false alarm probability or $p$-value. The reliability of this background estimate is limited by the number of background samples and by the fact that GW detectors cannot be shielded from signals, making it impossible to identify a pure background data set. Different strategies have been proposed: in one method, all samples, including potential signals, are included in the background estimation, whereas in another method, coincidence removal is performed in order to exclude possible signals from the estimated background. Here we report on a mock data challenge, performed prior to the first detections of GW signals by Advanced LIGO, to compare these two methods. The all-samples method is found to be self-consistent in terms of the rate of false positive detection claims, but its $p$-value estimates are systematically conservative and subject to higher variance. Conversely, the coincidence-removal method yields a mean-unbiased estimate of the $p$-value but sacrifices self-consistency. We provide a simple formula for the uncertainty in estimate significance and compare it to mock data results. Finally, we discuss the use of different methods in claiming the detection of GW signals.

We present a simple model of defects embedded in flat spacetime, where the model is designed to maintain Lorentz invariance over large length scales. Even without remnant Lorentz violation, there are still effects from these spacetime defects on the propagation of physical fields, notably mass generation for scalars and Dirac fermions.

The first hint of the neutrino mass hierarchy is believed to come from the long-baseline experiment $\mathrm{NO}\nu \mathrm{A}$. Recent results from $\mathrm{NO}\nu \mathrm{A}$ shows a mild preference towards the $CP$ phase ${\delta }_{13}=-90°$ and normal hierarchy. Fortunately this is the favorable area of the parameter space which does not suffer from the hierarchy-${\delta }_{13}$ degeneracy and thus $\mathrm{NO}\nu \mathrm{A}$ can have good hierarchy sensitivity for this true combination of hierarchy and ${\delta }_{13}$. Apart from the hierarchy-${\delta }_{13}$ degeneracy there is also the octant-${\delta }_{13}$ degeneracy. But this does not affect the favorable parameter space of $\mathrm{NO}\nu \mathrm{A}$ as this degeneracy can be resolved with a balanced neutrino and antineutrino run. However, if we consider the existence of a light sterile neutrino then there may be additional degeneracies which can spoil the hierarchy sensitivity of $\mathrm{NO}\nu \mathrm{A}$ even in the favorable parameter space. In the present work we find that apart from the degeneracies mentioned above, there are additional hierarchy and octant degeneracies that appear with the new phase ${\delta }_{14}$ in the presence of a light sterile neutrino in the eV scale. In contrast to the hierarchy and octant degeneracies appearing with ${\delta }_{13}$, the parameter space for hierarchy-${\delta }_{14}$ degeneracy is different in neutrinos and antineutrinos though the octant-${\delta }_{14}$ degeneracy behaves similarly in neutrinos and antineutrinos. We study the effect of these degeneracies on the hierarchy sensitivity of $\mathrm{NO}\nu \mathrm{A}$ for the true normal hierarchy.

We consider the noncommutative Standard Model that contains Lorentz symmetry violation as a subset of the Standard Model extension. We introduce a constant electromagnetic field as a background to derive mutual relations between the free parameters of both theories. As the Lorentz violation parameters of the Standard Model extension are extensively explored in different experiments and many stringent bounds on these parameters are available, we can find new bounds on the scale of noncommutativity of the order of a few to tens of teraelectron volts.

Distinguishing the Dirac and Majorana nature of neutrinos remains one of the most important tasks in neutrino physics. By assuming that the ${\tau }^{-}\to {\pi }^{-}{\mu }^{-}{e}^{+}\nu (\text{or}\overline{\nu })$ decay is resonantly enhanced by the exchange of an intermediate mass sterile neutrino $N$, we show that the energy spectrum of emitted pions and muons can be used to easily distinguish between the Dirac and Majorana nature of $N$. This method takes advantage of the fact that the flavor of light neutrinos is not identified in the tau decay under consideration. We find that it is particularly advantageous, because of no competing background events, to search for $N$ in the mass range $m_e+m_{\mu }\le m_N\le m_{\mu }+m_{\pi }$, where $m_X$ denotes the mass of particle $X\in \{e,\mu ,\pi ,N\}$.

We investigate the possibility of testing supergravity unified models with scalar masses in the range 50–100 TeV and much lighter gaugino masses at the Large Hadron Collider. The analysis is carried out under the constraints that models produce the Higgs boson mass consistent with experiment and also produce dark matter consistent with WMAP and PLANCK experiments. A set of benchmarks in the supergravity parameter space are investigated using a combination of signal regions which are optimized for the model set. It is found that some of the models with scalar masses in the 50–100 TeV mass range are discoverable with as little as $100{\mathrm{fb}}^{-1}$ of integrated luminosity and should be accessible at the LHC RUN II. The remaining benchmark models are found to be discoverable with less than $1000{\mathrm{fb}}^{-1}$ of integrated luminosity and thus testable in the high luminosity era of the LHC, i.e., at HL-LHC. It is shown that scalar masses in the 50–100 TeV range but gaugino masses much lower in mass produce unification of gauge coupling constants, consistent with experimental data at low scale, with as good an accuracy (and sometimes even better) as models with low [$\mathcal{O}(1)\mathrm{TeV}$] weak scale supersymmetry. Decay of the gravitinos for the supergravity model benchmarks are investigated and it is shown that they decay before the big bang nucleosynthesis (BBN). Further, we investigate the nonthermal production of neutralinos from gravitino decay and it is found that the nonthermal contribution to the dark matter relic density is negligible relative to that from the thermal production of neutralinos for reheat temperature after inflation up to $10^9\mathrm{GeV}$. An analysis of the direct detection of dark matter for supergravity grand unified models (SUGRA) with high scalar masses is also discussed. SUGRA models with scalar masses in the range 50–100 TeV have several other attractive features such as they help alleviate the supersymmetric $CP$ problem and help suppress proton decay from baryon and lepton number violating dimension five operators.

Pseudorapidity and azimuthal three-particle correlations are studied based on a correlated-cluster model of multiparticle production. The model provides a common framework for correlations in proton-proton and heavy-ion collisions allowing easy comparison with the measurements. It is shown that azimuthal cluster correlations are definitely required in order to understand three-particle correlations in the near-side ridge effect. This is similar to the explanation of the ridge phenomenon found in our previous analysis of two-particle correlations and generalizes the model to higher-order correlations.

In this paper we study the dependence of Bose-Einstein correlations on the multiplicity of an event. We find that events with large multiplicity stem from the production of several-parton showers, while the additional production of small multiplicity in the central rapidity region (central diffraction) gives a negligible contribution due to emission of soft gluons, which leads to the Sudakov suppression of the exclusive production of two-gluon jets. Hence, the Bose-Einstein correlation is the main source of the azimuthal angle correlations which generate $v_n$ with odd and even $n$. We find that without this suppression, the measurement of an event with given multiplicity yields $v_{n,n}<0$ for odd $n$. It appears that in hadron-nucleus and nucleus-nucleus collisions, the Bose-Einstein correlations do not depend on multiplicity, while for hadron-hadron scattering such dependence can be considerable. We propose a simple Kharzeev-Levin-Nardi type model to describe the dependence of azimuthal angle correlations on the centrality of the event in ion-ion collisions.