We analyze the two-loop renormalization group (RG) flow of the gauge and Yukawa couplings within the $E_6$ inspired supersymmetric models with extra $U(1{)}_N$ gauge symmetry under which right-handed neutrinos have zero charge. In these models, single discrete ${\tilde{Z}}_2^H$ symmetry forbids the tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. We consider two different scenarios A and B that involve extra matter beyond the minimal supersymmetric Standard Model contained in three and four $5+\overline{5}$ representations of $SU(5)$, respectively, plus three $SU(5)$ singlets which carry $U(1{)}_N$ charges. In scenario A, the measured values of the $SU(2{)}_W$ and $U(1{)}_Y$ gauge couplings lie near the fixed points of the RG equations. In scenario B, the contribution of two-loop corrections spoils the unification of gauge couplings, resulting in the appearance of the Landau pole below the grand unification scale $M_X$. The solutions for the Yukawa couplings also approach the quasifixed points with increasing their values at the scale $M_X$. We calculate the two-loop upper bounds on the lightest Higgs boson mass in the vicinity of these quasifixed points and compare the results of our analysis with the corresponding ones in the next-to-minimal supersymmetric Standard Model. In all these cases, the theoretical restrictions on the Standard-Model-like Higgs boson mass are rather close to 125 GeV.

We determine the free energy of strongly interacting matter as a function of an applied constant and uniform magnetic field. We consider $N_f=2+1$ QCD with physical quark masses, discretized on a lattice by stout improved staggered fermions and a tree-level improved Symanzik pure gauge action, and we explore three different lattice spacings. For magnetic fields of the order of those produced in noncentral heavy ion collisions ($eB\sim 0.1{\mathrm{GeV}}^2$), strongly interacting matter behaves like a medium with a linear response, and is paramagnetic both above and below the deconfinement transition, with a susceptibility which steeply rises in the deconfined phase. We compute the equation of state, showing that the relative increase in the pressure due to the magnetic field gets larger around the transition and is of the order of 10% for $eB\sim 0.1{\mathrm{GeV}}^2$.

Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong-coupling constant $\alpha$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The onset of the dominance of the dimension-four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\overline{\mathrm{MS}}$ scheme. We also comment on the impact of the renormalon on nonperturbative determinations of the gluon condensate.

We study the Landau gauge gluon propagator $D(p)$ in the three-dimensional $\mathit{SU}(2)$ lattice gauge theory. We show that in the infinite-volume limit the expectation values over the Gribov region $\mathrm{\Omega }$ are different (in the infrared) from that calculated in the fundamental modular region $\mathrm{\Gamma }$. Also we show that this conclusion does not change when spacing $a$ tends to zero.

In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension 10 in a consistent way in the operator product expansion, study the masses and pole residues of the $J^{PC}=1^{+\pm }$ hidden charmed tetraquark states with the QCD sum rules, and explore the energy-scale dependence in detail for the first time. The predictions $M_X=3.87_{-0.09}^{+0.09}\text{GeV}$ and $M_Z=3.91_{-0.09}^{+0.11}\text{GeV}$ support assigning the $X(3872)$ and $Z_c(3900)$ [or $Z_c(3885)$] as the $1^{++}$ and $1^{+-}$ diquark-antidiquark type tetraquark states, respectively.

It is shown that the large $N_c$ limit of QCD with quarks in the two-index antisymmetric color representation [QCD(AS)] has narrow tetraquark states with exotic flavor quantum numbers. They decay into mesons with a width that is parametrically $O(1/N_c^2)$. Tetraquarks with nonexotic quantum numbers mix at leading order with mesons of the same overall quantum numbers. QCD(AS) at $N_c=3$ corresponds to ordinary QCD; its large $N_c$ limit represents an alternative starting point for a $1/N_c$ expansion to the standard one with quarks in the fundamental color representation.

The low-energy structure of hadrons can be described systematically using effective field theory, and the parameters of the effective theory can be determined from lattice QCD computations. Recent work, however, points to inconsistencies between the background field method in lattice QCD and effective field theory matching conditions. We show that the background field problem necessitates inclusion of operators related by equations of motion. In the presence of time-dependent electromagnetic fields, for example, such operators modify Green’s functions, thereby complicating the isolation of hadronic parameters which enter on-shell scattering amplitudes. The particularly simple case of a scalar hadron coupled to uniform electromagnetic fields is investigated in detail. At the level of the relativistic effective theory, operators related by equations of motion are demonstrated to be innocuous. The same result does not hold in the nonrelativistic effective theory, and inconsistencies in matching are resolved by carefully treating operators related by equations of motion. As uniform external fields potentially allow for surface terms, the problem is additionally analyzed on a torus where such terms are absent. Temporal image corrections are derived for charged scalar correlation functions in uniform electric fields as a useful byproduct.

We consider the gluon propagator in the Landau gauge at low spacelike momenta and with the dressing function $Z(Q^2)$ at the two-loop order. We incorporate the nonperturbative effects by making the (noninteger) powers of the QCD coupling in the dressing function $Z(Q^2)$ analytic (holomorphic) via the fractional analytic perturbation theory (FAPT) model, and simultaneously introducing the gluon dynamical mass in the propagator as motivated by the previous analyses of the Dyson-Schwinger equations. The obtained propagator has behavior compatible with the unquenched lattice data ($N_f=2+1$) at low spacelike momenta $0.4\mathrm{GeV}<Q\lesssim 10\mathrm{GeV}$. We conclude that the removal of the unphysical Landau singularities of the powers of the coupling via the (F)APT prescription, in conjunction with the introduction of the dynamical mass $M\approx 0.62\mathrm{GeV}$ of the gluon, leads to an acceptable behavior of the propagator in the infrared regime.

In this paper, by employing the $k_T$ factorization theorem, we calculate first the next-to-leading-order (NLO) twist-3 contributions to the pion electromagnetic form factors in the $\pi {\gamma }^{*}\to \pi$ process. From the analytical and numerical calculations we find the following points: (a) for the leading-order (LO) twist-2, twist-3, and the NLO twist-2 contributions, our results agree very well with those obtained in previous works, (b) we extract out two factors $F_{\text{T3}}^{(1)}(x_i,t,Q^2)$ and ${\overline{F}}_{\text{T3}}^{(1)}(x_i,t,Q^2)$, which describe directly the NLO twist-3 contributions to the pion electromagnetic form factors $F^{+}(Q^2)$, (c) the NLO twist-3 contribution is negative in sign and cancels partially with the NLO twist-2 part, so the total NLO contribution can therefore provide a roughly $\pm 20\%$ corrections to the total LO contribution in the considered ranges of $Q^2$, and (d) the theoretical predictions for $Q^2{F}^{+}(Q^2)$ in the low-$Q^2$ region agree well with currently available data, which can be improved by the inclusion of the NLO contributions.

We propose a new mechanism where both Dirac masses for the charged leptons and Majorana masses for neutrinos are generated via quantum levels. The charged-lepton masses are given by the vacuum expectation values (VEVs) of the Higgs doublet field and that of a triplet field. On the other hand, neutrino masses are generated by two VEVs of triplet Higgs fields. As a result, the hierarchy between the masses for charged leptons and neutrinos can be explained by the triplet VEVs which have to be much smaller than the doublet VEV due to the constraint from the electroweak rho parameter. We construct a concrete model to realize this mechanism with discrete ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$ symmetries, in which masses for neutrinos and those for the muon and electron are generated at the one-loop level. As a bonus in our model, the deviation in the measured muon $g-2$ from the standard model prediction can be explained by contributions of extra particle loops. Besides, the lightest ${\mathbb{Z}}_2$-odd neutral particle can be a dark matter candidate. The collider phenomenology is also discussed, especially focusing on doubly charged scalar bosons which are necessary to introduce to occur our mechanism.

We report results of a study of doubly charmed baryons and charmed strange baryons. The analysis is performed using a $980{\mathrm{fb}}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We search for doubly charmed baryons ${\mathrm{\Xi }}_{cc}^{+(+)}$ with the ${\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+}({\pi }^{+})$ and ${\mathrm{\Xi }}_c^0{\pi }^{+}({\pi }^{+})$ final states. No significant signal is observed. We also search for two excited charmed strange baryons, ${\mathrm{\Xi }}_c(3055{)}^{+}$ and ${\mathrm{\Xi }}_c(3123{)}^{+}$ with the ${\mathrm{\Sigma }}_c^{++}(2455)K^{-}$ and ${\mathrm{\Sigma }}_c^{++}(2520)K^{-}$ final states. The ${\mathrm{\Xi }}_c(3055{)}^{+}$ signal is observed with a significance of 6.6 standard deviations including systematic uncertainty, while no signature of the ${\mathrm{\Xi }}_c(3123{)}^{+}$ is seen. We also study properties of the ${\mathrm{\Xi }}_c(2645{)}^{+}$ and measure a width of $2.6\pm 0.2(\text{stat})\pm 0.4(\text{syst})\mathrm{MeV}/c^2$, which is the first significant determination.

We employ the holographic method to study fluctuations and dissipation of an $n$-dimensional moving mirror coupled to quantum critical theories in $d$ spacetime dimensions. The bulk counterpart of the mirror with perfect reflection is a $n+1$-dimensional membrane in the Lifshitz geometry of $d+1$ dimensions. The motion of the mirror can be realized from the dynamics of the brane at the boundary of the bulk. The excited modes of the brane in the bulk render the mirror undergoing Brownian motion. For small displacement of the mirror, we derive the analytical results of the correlation functions and response functions. The dynamics of the mirror due to small fluctuations around the brane vacuum state in the bulk is found supraohmic so that after initial growth, the velocity fluctuations approach a saturated value at late time with a power-law behavior. On the contrary, in the Lifshitz black hole background, the mirror in thermal fluctuations shows that its relaxation dynamics becomes ohmic, and the saturation of velocity fluctuations is reached exponentially in time. Finally a comparison is made with the result of a moving mirror driven by free fields.

The space of local operators in three-dimensional quantum electrodynamics contains monopole operators that create $n$ units of gauge flux emanating from the insertion point. This paper uses the state-operator correspondence to calculate the anomalous dimensions of these monopole operators perturbatively to next-to-leading order in the $1/N_f$ expansion, thus improving on the existing leading-order results in the literature. Here, $N_f$ is the number of two-component complex fermion flavors. The scaling dimension of the $n=1$ monopole operator is $0.265N_f-0.0383+O(1/N_f)$ at the infrared conformal fixed point.

We raise on theoretical grounds the question of the physical relevance of Israel matching conditions and their generalizations to higher codimensions, the standard cornerstone of the braneworld and other membrane scenarios. Our reasoning is based on the incapability of the conventional matching conditions to accept the Nambu-Goto probe limit, the inconsistency of codimension-2 and -3 classical defects for $D=4$ and the probable inconsistency of high enough codimensional defects for any $D$ since there is no high enough Lovelock density to support them. We propose alternative matching conditions which seem to overcome the previous puzzles. Instead of varying the brane-bulk action with respect to the bulk metric at the brane position, we vary with respect to the brane embedding fields so that the gravitational backreaction is included (“gravitating Nambu-Goto matching conditions”). Here, we consider in detail the case of a codimension-2 brane in 6-dim Einstein-Gauss-Bonnet gravity, prove its consistency for an axially symmetric cosmological configuration and show that the theory possesses richer structure compared to the standard theory. The cosmologies found have the Friedmann behavior and extra correction terms. For a radiation brane one solution avoids a cosmological singularity and undergoes accelerated expansion near the minimum scale factor. In the presence of an induced gravity term, there naturally appears in the theory the effective cosmological constant scale $\lambda /(M_6^4{r}_c^2)$, which for a brane tension $\lambda \sim M_6^4$ (e.g. ${\mathrm{TeV}}^4$) and $r_c\sim H_0^{-1}$ gives the observed value of the cosmological constant.

Polymer quantum mechanics, the mechanical analogue of the loop quantization of gravity, has been applied recently to scalar field modes yielding interesting behavior for its corresponding propagator at high, possibly Planck’s, energy. Clearly other matter components are worth investigating along these lines, and thus we focus here on the Dirac field. To proceed to the polymer analysis of the Dirac field, a previous canonical analysis of its modes is advantageous. We show that this yields an energy spectrum suggesting a natural Fermi oscillator decomposition and, moreover, that both Fourier modes and Fermi oscillators lead to the corresponding free propagator in flat space-time. Finally, we advance a model entailing the polymer quantization of the Fermi oscillators that make up the Dirac field. It consists of a discrete set that replaces one of the two real anticommutative lines forming the reduced phase space of a Fermi oscillator. This is in analogy to the bosonic harmonic oscillator in which the corresponding polymer quantization involves replacing the real line by a regular lattice. The resulting polymer propagator contains as its body the standard Dirac field propagator plus soul terms involving up to second-order powers in two anticommutative parameters. Some possible physical implications are mentioned in the discussion.

We give the general form of supersymmetric backgrounds with two real supercharges of M theory and type IIA supergravity (with nonzero Romans mass in general) of the form ${\mathbb{R}}^{1,d}\times {\mathcal{M}}_8$, $d=1,2$, on eight-dimensional manifolds with $SU(4)$ structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua, and we show that unbroken supersymmetry does not in general require the 4-form flux to be (2,2) or primitive. Our results could be used to construct novel higher dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua, our results are in agreement with partial supersymmetry breaking in three-dimensional $\mathcal{N}=2$ supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real “superpotential” in accordance with three-dimensional $\mathcal{N}=1$ supergravity. We present explicit examples of M-theory flux vacua on $\mathrm{K}3\times \mathrm{K}3$, which however do not appear to possess $F$-theory duals with four-dimensional Poincaré invariance.

We obtain the Lifshitz UV completion in a specific model for $z=2$ Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosen bulk fields. We show that the geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry with a specific torsion tensor. We explicitly compute all the vacuum expectation values (VEVs) including the boundary stress-energy tensor and their Ward identities. After using local symmetries or Ward identities the system exhibits 6+6 sources and VEVs. The Fefferman-Graham expansion exhibits, however, an additional free function which is related to an irrelevant operator whose source has been turned off. We show that this is related to a second UV completion.

An analysis of the Dirac neutrino magnetic moment with standard model interactions gives ${\mu }_{\nu }\sim 3\times 10^{-19}{\mu }_B(m_{\nu }/1\text{eV})$. The observation of a significantly larger magnetic moment will provide a clear signal of new physics beyond the standard model. The current experimental limits on the neutrino magnetic moments are orders of magnitude larger than the prediction with the standard model interactions and thus its test appears out of reach. Here we give an analysis of the Dirac neutrino magnetic moments within the framework of a minimal supersymmetric standard model extension with a vectorlike lepton generation. Specifically we compute the moments arising from the exchange of $W$ and the charged leptons in the loop, as well as from the exchange of charginos, charged sleptons and charged mirror sleptons. It is shown that the neutrino moment in this case can be several orders of magnitude larger than the one with standard model-like interactions, lying close to and below the current experimental upper limits and should be accessible in an improved future experiment. A correlated prediction of the heaviest neutrino lifetimes from radiative decays to the lighter neutrinos via exchange of charginos and sleptons in the loops is also made. The predicted lifetimes are several orders of magnitude smaller than the one with the standard model interactions and also lie close to the current experimental limits from analyses using the cosmic background neutrino data.