A study of chiral-odd generalized parton distributions (GPDs) of the nucleon is presented in the bag model demonstrating that in this model all four chiral-odd GPDs are nonzero contrary to other claims in literature. The bag model results for the GPDs $H_T^q(x,\xi ,t)$, $E_T^q(x,\xi ,t)$, ${\tilde{H}}_T^q(x,\xi ,t)$ agree with other models within a typical quark model accuracy. We present one of the few quark model calculations where polynomiality is satisfied and the sum rule $\int dx{\tilde{E}}_T^q(x,\xi ,t)=0$ holds. We confront our results with predictions from the large-$N_c$ limit, and with lattice QCD calculations. We conclude that the bag model successfully catches the main features of chiral-odd GPDs.

We calculate several differential distributions for diffractive dijets production in $ep\to e^{\prime }\mathrm{jet}$ $\mathrm{jet}p$ in the perturbative QCD dipole approach using off diagonal unintegrated gluon distributions (generalized transverse momentum dependent distributions, GTMDs). Different models from the literature are used. We concentrate on the contribution from exclusive $q\overline{q}$ dijets. Results of our calculations are compared to H1 and ZEUS data, including specific experimental cuts in our calculations. In general, except for one GTMD, our results are below the HERA data. The considered mechanism is expected to gives a sizeable contribution to the ZEUS data, while it is negligible in the kinematics of the H1 measurement. This is in contrast to recent results from the literature where the normalization was adjusted to some selected distributions of the H1 collaboration and no agreement with other observables was checked. The ZEUS data provide stricter limitations on the GTMDs than the H1 data. We conclude, based on comparison to different observables, that the calculated cross sections are only a small fraction of the measured ones which contain probably also processes with pomeron remnant. Alternatively one could try to explain the experimental data by inclusion of $q\overline{q}g$ component of the photon wave function. We present also azimuthal correlations between the sum and the difference of dijet transverse momenta. The cuts on transverse momenta of jets generate corresponding azimuthal correlations that can be misidentified as due to elliptic gluon distributions.

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-$N_c$ limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions.

We analyze the photoproduction of ${\eta }_{c,b}$ off a proton in the threshold region, in terms of C-odd gluonic correlations in the off-forward proton matrix element. Near threshold, the skewness is large, leading to a production amplitude that is dominated by four C-odd twist-3 gluon GPDs. We use the QCD instanton vacuum to estimate these C-odd contributions in the proton. The results are used to estimate the differential cross sections for coherent photoproduction of ${\eta }_{c,b}$ in the threshold region, at current electron facilities.

The process $e^{+}{e}^{-}\to p\overline{p}{\pi }^0$ is studied at 20 center-of-mass energies ranging from 2.1000 to 3.0800 GeV using $636.8{\mathrm{pb}}^{-1}$ of data collected with the BESIII detector operating at the BEPCII collider. The Born cross sections for $e^{+}{e}^{-}\to p\overline{p}{\pi }^0$ are measured with high precision. Since the lowest center-of-mass energy, 2.1000 GeV, is less than 90 MeV above the $p\overline{p}{\pi }^0$ energy threshold, we can probe the threshold behavior for this reaction. However, no anomalous threshold enhancement is found in the cross sections for $e^{+}{e}^{-}\to p\overline{p}{\pi }^0$.

We detail the Higgs branches of 6D (1, 0) superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6D (2, 0) SCFTs and LSTs of type DE. Generically, such theories are geometrically engineered in F-theory via a configuration of ($-2$)-curves, arranged in an (affine) DE-type Dynkin diagram, and supporting special unitary gauge algebras; this describes the effective field theory on the tensor branch of the SCFT. For the Higgsable to D-type (2, 0) SCFTs/LSTs, there generically also exists a type IIA brane description, involving a Neveu-Schwarz orientifold plane, which allows for the derivation of a magnetic quiver for the Higgs branch. These are 3D $\mathcal{N}=4$ unitary-orthosymplectic quivers whose Coulomb branch is isomorphic to the Higgs branch of the 6D theories. From this magnetic quiver, together with an extended quiver subtraction algorithm that we explain, the foliation structure of the Higgs branch as a symplectic singularity is unveiled. For this class of 6D SCFTs, we observe a simple rule, which we refer to as “slice subtraction,” to read off the transverse slice in the foliation from the tensor branch. Based on this slice subtraction observation, we conjecture the transverse slices in the Higgsable to E-type (2, 0) Hasse diagram, where the SCFTs lack any known magnetic quiver for their Higgs branches.

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation.

We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer enhances a symmetry. We elaborate these scenarios for template fermionic and Yukawa theories in three dimensions where mass can be generated either by fluctuations, strong dynamics, or the vacuum expectation value of a scalar field. We find that fluctuation-induced contributions to fermion mass are parametrically suppressed in the number of fermion flavors $N$. The generation of fermion mass then takes the form of a rapid crossover which turns into a second order quantum phase transition for large $N$, much like in settings with fundamental chiral symmetry. We further discuss theories where fermion mass can be generated spontaneously without breaking any symmetry other than scale symmetry. Implications of our findings are discussed.

The detection method of gravitational waves (GW) using electromagnetic (EM) cavities has garnered significant attention in recent years. This paper thoroughly examines the analysis for the perturbation of the EM field and raises some issues in the existing literature. Our work demonstrates that the rigidity condition imposed on the material, as provided in the literature, is inappropriate due to its reliance on a gauge-dependent quantity that cannot be controlled experimentally. Instead, we incorporate elasticity into the material and revise the governing equations for the electric field induced by GWs, expressing them solely in terms of gauge-invariant quantities. Applying these equations to cylindrical cavities, we present the GW antenna patterns for the detector.

We present an efficient technique for calculating the angular two-point correlation functions (or “overlap reduction functions”) induced by gravitational waves in both the pulse arrival times of pulsars and in the angular deflections of distant sources. In the most general case, there are six autocorrelations and cross-correlations for the pulse arrival times and the two components of the angular deflection. We provide results for spin-2 (i.e., general-relativistic) gravitational waves as well as the spin-1 modes that may arise in alternative-gravity theories. These calculations can be easily implemented for future analysis or study, and we provide code to do so.

In Papers I–III [T. Matsubara, Phys. Rev. D 110, 063543 (2024); 110, 063544 (2024); 110, 063545 (2024)], we use the flat-sky and distant-observer approximations to develop a formalism with which the correlation statistics of cosmological tensor fields are calculated by the nonlinear perturbation theory, generalizing the integrated perturbation theory for scalar fields. In this work, the formalism is extended to include the full-sky and wide-angle effects in evaluating the power spectra and correlation functions of cosmological tensor fields of any rank. With the newly developed formalism, one can evaluate the nonlinear power spectra and correlation functions to arbitrary higher orders in principle. After describing the general formalism, we explicitly derive and give analytic results of the lowest-order linear theory for an illustrative purpose in this paper. The derived linear formulas with full-sky and wide-angle effects are numerically compared with the previous formulas with flat-sky and distant-observer limits in a simple model of tensor bias.

The integrated perturbation theory (iPT) is a set of methods in nonlinear perturbation theory for the structure formation in the Universe. In Papers I and II [T. Matsubara, Phys. Rev. D 110, 063543 (2024); 110, 063544 (2024).], the basic formalism and technical methods of the iPT for cosmological tensor fields are developed, generalizing the corresponding theory for scalar fields. In previous papers, methods to predict statistical quantities, such as power spectra, correlation functions, etc., of three-dimensional tensor fields are developed based on the iPT. However, observations of tensors, such as angular momenta and shapes of galaxies, etc., are only possible after the three-dimensional tensors are projected onto the two-dimensional sky. In this paper, power spectra and correlation functions of projected two-dimensional tensors are related to those of original three-dimensional tensors, so that one can make predictions for the observable statistics of projected tensor fields from the iPT. The relations are consistently represented on the basis of irreducible decomposition of both two- and three-dimensional tensors.

In the previous paper [T. Matsubara, Phys. Rev. D 110, 063543 (2024).], the nonlinear perturbation theory of the cosmological density field is generalized to include the tensor-valued bias of astronomical objects, such as spins and shapes of galaxies and any other tensors of arbitrary ranks which are associated with objects that we can observe. We apply this newly developed method to explicitly calculate nonlinear power spectra and correlation functions both in real space and in redshift space. Multidimensional integrals that appear in loop corrections are reduced to combinations of one-dimensional Hankel transforms, thanks to the spherical basis of the formalism, and the final expressions are numerically evaluated in a very short time using an algorithm of the fast Fourier transforms such as fftlog. As an illustrative example, numerical evaluations of loop corrections of the power spectrum and correlation function of the rank-2 tensor field are demonstrated with a simple model of tensor bias.

In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signal that can be observed. Beyond the spatial distributions of astronomical objects, the spatial correlations of tensor fields, such as galaxy spins and shapes, are ones of promising sources that can be accessed in the era of large surveys in the near future. The perturbation theory is a powerful tool to analytically describe the behaviors and evolutions of correlation statistics on large scales for a given cosmology. In this paper, we formulate a nonlinear perturbation theory of tensor fields in general, based on the formulation of integrated perturbation theory for the scalar-valued bias, generalizing it to include the tensor-valued bias. To take advantage of rotational symmetry, the formalism is constructed on the basis of the irreducible decomposition of tensors, identifying physical variables which are invariant under the rotation of the coordinates system.

We propose that the merger rate of primordial black hole (PBH) binaries can be a probe of Hubble parameter by constraining PBH mass function in the redshifted mass distribution of PBH binaries. In next-generation gravitational wave (GW) detectors, the GWs from PBH binaries would be detected at high redshifts, which gives their redshifted mass and luminosity distances. From a number of detected events, the redshifted mass distribution of PBH binaries can be statistically obtained, and it depends on PBH mass function and redshift distribution of detected PBH binaries. The PBH mass function can be inversely solved by applying the gradient descent method in the relation between redshifted mass distribution and redshift distribution. However, the construction of redshift distribution requires an assumed Hubble parameter in a background cosmology to extract redshift from luminosity distances, which causes solved PBH mass function also depends on assumed Hubble parameter. To determine the Hubble parameter, the merger rate of PBH binaries constrains on this Hubble parameter-dependent PBH mass function by comparing calculated merger rate distribution with observed one, and the best-fit result produces an approximate mass distribution of the physical PBH mass function and pins down the Hubble parameter.

We systematically derive the quantum generalized nonlinear Langevin equation using Morozov’s projection operator method. This approach extends the linear Mori-Zwanzig projection operator technique, allowing for the inclusion of nonlinear interactions among macroscopic modes. Additionally, we obtain the quantum generalized Fokker-Planck equation within the Heisenberg picture, which is consistent with Morozov’s original formulation. These equations are fundamentally significant in nonequilibrium statistical physics, particularly in scenarios characterized by enhanced fluctuations, such as anomalous transport phenomena near critical points. The quantum nature of the derived generalized Langevin and Fokker-Planck equations is anticipated to provide a more detailed description than their classical equivalents. Specifically, the noise kernel in the quantum generalized Langevin equation is multiplicative, which broadens the applicability beyond Gaussian approximations. Given specific interactions, these equations are expected to be instrumental in investigating critical transport phenomena.

We elaborate on the application of on shell and unitarity-based methods for evaluating renormalization group coefficients, and generalize this framework to account for the mixing of operators with different dimensions and leading mass effects. We derive a master formula for anomalous dimensions stemming from the general structure of operator mixings, up to two-loop order, and show how the Higgs low-energy theorem can be exploited to include leading mass effects. A few applications on the renormalization properties of popular effective field theories showcase the strength of the proposed approach, which drastically reduces the complexity of standard loop calculations. Our results provide a powerful tool to interpret experimental measurements of low-energy observables, such as flavor violating processes or electric and magnetic dipole moments, as induced by new physics emerging above the electroweak scale.

The measurement of the magnetic field created in high-energy heavy-ion collisions is challenging, due to the fact that the magnetic field decays so drastically that in a thermalized quark-gluon plasma the field strength becomes rather weak. By incorporating the weak magnetic effect into the medium, and especially into the production formalism of dileptons from the quark-gluon plasma, the effect of dilepton polarization is studied through the dilepton angular distribution. We find that the anisotropic coefficients in the dilepton spectrum are quite sensitive to the orientation and strength of the weak field. Accordingly, these coefficients provide ideal probes for the magnetic field in realistic experiments.

Correlators of $\mathcal{N}=2$ hypermultiplets with two-derivative interactions in ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level four-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless ${\varphi }^4$ theory in ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$. This theory serves as a toy model for IIB string theory in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ and is interesting in its own right because ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ describes the near-horizon limit of extremal black holes in four dimensions. We argue that, after acting with an $SU(1,1)\times SU(2)$ Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a two-derivative interaction in ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ whose Witten diagrams should directly reproduce four-point correlators to all loops without acting with Casimirs.

The question of geodesic completeness of cosmological spacetimes has recently received renewed scrutiny. A particularly interesting result is the observation that the well-known Borde-Guth-Vilenkin (BGV) theorem may misdiagnose geodesically complete cosmologies. We propose a simple amendment to the BGV theorem which addresses such loopholes while retaining much of its generality. We give straightforward proofs of some recently offered conjectures concerning (generalized) Friedmann-Lemaître-Robertson-Walker spacetimes; geodesic completeness implies (i) the existence of a bounce, loitering phase or an emergent cosmology, and (ii) a phase of accelerated expansion with strictly increasing Hubble rate. Our results are purely kinematic and do not assume general relativity or energy conditions.