arXiv subjects
Publications and source records attributed to J. Gegelia.
Matrix elements of the energy-momentum tensor for one-particle states of the $Z$-boson are parameterized in terms of gravitational form factors. One-loop order electroweak corrections to these quantities are calculated. Renormalization and physical interpretation of the obtained results are discussed.
In a recent publication, Cirigliano {\it et al.} [Phys. Rev. Lett. 135, 022501 (2025)] argue that three-nucleon forces (3NFs) involving short-range operators that couple two pions with two nucleons are enhanced beyond what is expected in chiral effective field theory based on naive dimensional analysis. Here, we scrutinize the arguments and conclusions of that paper by taking into account renormalization scheme dependence of the corresponding low-energy constants. We gain further insights into the expected impact of these 3NFs by comparing them with contributions of similar type, induced by pion-exchange diagrams at lower orders in the chiral expansion. We also estimate the impact of these 3NFs on properties of nuclear matter. After removal of scheme-dependent short-distance components in pion loops, the 3NFs considered by Cirigliano {\it et al.} are shown to yield reasonably small contributions to the equation of state of neutron and symmetric nuclear matter in agreement with expectations based on Weinberg's power counting.
Recently the nucleon-nucleon interaction derived using time-ordered perturbation theory in manifestly Lorentz-invariant chiral effective field theory was shown to yield promising results for peripheral neutron-proton scattering. In this work we study low partial waves at next-to-leading order by treating the potential non-perturbatively in the scattering equation. Reasonable description of the phase shifts in the $S$ and $P$ waves as well as the deuteron properties is observed, which can be regarded as a feasibility study for the application of our formalism to the few- and many-body calculations.
We calculate the one-loop electroweak corrections to the gravitational form factors of the Higgs boson and discuss the interpretation of the obtained results.
It is shown to all orders of perturbation theory that in the effective field theory of general relativity the condition of vanishing of the vacuum energy leads to the same value of the cosmological constant, viewed as a parameter of the effective Lagrangian, as obtained by demanding the consistency of the effective field theory in Minkowski background. The resulting effective action is characterized by the cosmological constant term that vanishes exactly.
The gravitational form factors of the deuteron are calculated in the framework of non-relativistic chiral effective field theory. Non-relativistic reduction of the matrix element of the energy-momentum tensor operator for spin-one systems is worked out, and the gravitational form factors of the deuteron are extracted from the three-point function of the energy-momentum tensor using the LSZ reduction formula. The obtained form factors are compared to results of model calculations available in the literature.
We work out the spatial density distributions corresponding to the axial-vector charge density operator for spin-1/2 systems using states described by sharply localized wave packets in arbitrary Lorentz-frames. The static approximation, leading to the frequently assumed Breit-frame distributions, is also considered. We discuss the interpretation of the resulting spatial densities in terms of the axial charge density.
A consistency condition of general relativity as an effective field theory in Minkowskian background uniquely fixes the value of the cosmological constant. In two-loop calculations, including the interaction of gravitons with matter fields, it has been shown that this value of the cosmological constant leads to vanishing vacuum energy, under the assumption that the energy-momentum tensor of the gravitational field is given by the pseudotensor of Landau-Lifshitz's classic textbook. Here, we demonstrate that this result also holds when the self-interaction of a scalar field is taken into account. That is, our two-loop-order calculation suggests that in an effective field theory of metric and scalar fields, one arrives at a consistent theory with massless gravitons if the cosmological constant is fixed from the condition of vanishing vacuum energy. Vice versa, imposing the consistency condition in Minkowskian background leads to a vanishing vacuum energy.
The gravitational form factors of the transition from the proton to the $Δ^+$ resonance are calculated to leading one-loop order using a manifestly Lorentz-invariant formulation of chiral perturbation theory. We take into account the leading electromagnetic and strong isospin-violating effects. The loop contributions to the transition form factors are found to be free of power-counting violating pieces, which is consistent with the absence of tree-level diagrams at the considered order. In this sense, our results can be regarded as predictions of chiral perturbation theory.
We work out details of defining the spatial densities corresponding to the gravitational form factors of spin-0 and spin-1/2 systems using spherically symmetric sharply localized wave packets. The expressions for the spatial densities are provided in the frames with both zero and non-zero expectation values of the momentum operator.
The matrix elements of the electromagnetic current and the energy-momentum tensor for sharply localized states of spin-1 systems are considered. Their interpretation as local spatial densities of various characteristics of the considered system is discussed.
The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions of associated spatial distributions in terms of form factors are derived.
The leading one-loop corrections to the gravitational form factors of the delta resonance are calculated in the framework of chiral effective field theory. Various contributions to the energy-momentum tensor and the renormalization of the low-energy constants are worked out. Using the small scale expansion, expressions for static quantities are obtained and the real and imaginary parts of the gravitational form factors are calculated numerically.
We study the nucleon-nucleon interaction up to next-to-next-to-leading order using time-ordered perturbation theory in the framework of manifestly Lorentz-invariant chiral effective field theory. We present the two-pion exchange contribution at one-loop level, which is consistent with the corresponding non-relativistic expressions in the large-nucleon-mass limit. Using the Born series truncated at one-loop order, we calculate the phase shifts and mixing angles of the partial waves with the angular momentum $l\geq 2$. Comparing with the results of non-relativistic formulation, we find an improved description of the phase shifts for some $D$ waves such as the $^3D_3$ one. For the other partial waves, both approaches show the globally similar results.
An unambiguous definition of the electromagnetic spatial densities for a spin-1/2 system is proposed and worked out in the zero average momentum frame and in moving frames. The obtained results are compared with the traditional definition of the densities in terms of the three-dimensional Fourier transforms of the electromagnetic form factors in the Breit frame.
We show that the matrix element of a local operator between hadronic states gives rise to an unambiguous definition of the associated spatial density. As an explicit example, we consider the charge density of a spinless particle in the rest and moving frames and clarify its relationship to the electric form factor. Our results suggest that the interpretation of the spatial densities of local operators and their moments such as the mean square charge radius needs to be revised.
The low-energy chiral effective field theory of vector mesons and Goldstone bosons in external gravitational field is considered. The energy-momentum tensor is obtained and the gravitational form factors of the $ρ$-meson are calculated up to next-to-leading order in the chiral expansion. This amounts to considering tree-level and one-loop order diagrams. The chiral expansion of the form factors at zero momentum transfer as well as of the slope parameters is worked out. Also, the long-range behaviour of the energy and internal force distributions is obtained and analysed.
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.