We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible ...Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. The beauty and simplicity of the Abel transformations allow us to derive a number of new relations for light front force distributions. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. Due to the positivity property of the Abel transformation we obtain an important result-the 2D local stability conditions are satisfied automatically if the corresponding 3D stability conditions are fulfilled. In this way we established not only mathematical equivalence of 2D and 3D forces distributions but also their physics equivalence in terms of stability. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large Nc nucleon as a chiral soliton.
A
bstract
Using the instanton picture of the QCD vacuum we compute the nucleon
c
¯
Q
t
form factor of the quark part of the energy momentum tensor (EMT). This form factor describes the ...non-conservation of the quark part of EMT and contributes to the quark pressure distribution inside the nucleon. Also it can be interpreted in terms of forces between quark and gluon subsystems inside the nucleon. We show that this form factor is parametrically small in the instanton packing fraction. Numerically we obtain for the nucleon EMT a small value of
c
¯
Q
t
c
¯
Q
0
≃
1.4
·
10
−
2
at the low normalisation point of ∼ 0
.
4 GeV
2
. This smallness implies interesting physics picture — the forces between quark and gluon mechanical subsystems are smaller than the forces inside each subsystem. The forces from side of gluon subsystem squeeze the quark subsystem — they are compression forces. Additionally, the smallness of
c
¯
Q
t
might justify Teryaev’s equipartition conjecture. We estimate that the contribution of
c
¯
Q
t
to the pressure distribution inside the nucleon is in the range of 1-20% relative to the contribution of the quark
D
-term.
We define the form factors of the quark and gluon symmetric energy-momentum tensor (EMT). The static EMT is related to the spatial distributions of energy, spin, pressure, and shear forces. They are ...obtained in the form of a multipole expansion. The relations between gravitational form factors and the generalized parton distributions are given.
Using dispersive representations of the nucleon gravitational form factors, the results for their absorptive parts from chiral effective field theory in curved space-time, and the mechanical ...stability conditions, we obtain a model independent inequality for the value of the gravitational D(t) form factor at zero momentum transfer (Druck-term). In particular, the obtained inequality leads to a conservative bound on the Druck-term in the chiral limit D≤−0.95(9). This bound implies the restriction on the low-energy constant c8 of the effective chiral action for nucleons and pions in the presence of an external gravitational field, c8≤−1.1(1) GeV−1. For the physical pion mass we obtain a model independent bound D≤−0.20(2).
The pentaquark Pc+(4450) recently discovered by the LHCb has been interpreted as a bound state of Ψ(2S) and a nucleon. The charmonium-nucleon interaction which provides the binding mechanism is ...given, in the heavy-quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor. In this work, we show in a model-independent way, by exploring general properties of the effective interaction, that Ψ(2S) can form bound states with a nucleon and Δ. Using the Skyrme model to evaluate the effective interaction in the large-Nc limit and estimate 1/Nc corrections, we confirm the results from prior work which were based on a different effective model (chiral quark soliton model). This shows that the interpretation of Pc+(4450) is remarkably robust and weakly dependent on the details of the effective theories for the nucleon energy-momentum tensor. We explore the formalism further and present robust predictions of isospin-32 bound states of Ψ(2S) and Δ with masses around 4.5 GeV and widths around 70 MeV. The approach also predicts broader resonances in the Ψ(2S)−Δ channel at 4.9 GeV with widths of the order of 150 MeV. We discuss in which reactions these new isospin-32 pentaquarks with hidden charm can be observed.
Using the soft pion theorem, crossing, and the dispersion relations for the two-pion distribution amplitude (DA), we argue that the second Gegenbauer moment, the ρ-meson DA(a(ρ)2), is most probably ...negative. This result is at variance with the majority of the model calculations for a(ρ)2. Using the instanton theory of the QCD vacuum, we computed a(ρ)2 at a low normalization point and obtain for the ratio a (ρ)2/M(π)3 a definitely negative value in the range of a(ρ)2/M(π)3∈ −2, −1. The range of values corresponds to a generous variation of the parameters of the instanton vacuum. The value of the second Gegenbauer moment of pion DA is positive in the whole range and is compatible with its the most advanced lattice measurement. It seems that the topologically nontrivial field configurations in the QCD vacuum (instantons) lead to qualitatively different shapes of the pion and the ρ-meson DAs.
We employ the chiral quark-soliton model to describe excited baryons with one heavy quark. Identifying known charmed baryons with multiplets allowed by the model, we argue that apart from regular ...excitations of the ground-state multiplets, two out of five narrow Ωc0 states, recently reported by the LHCb Collaboration, may correspond to the exotic pentaquarks. This interpretation can be easily verified experimentally, since exotic Ωc0 states-contrary to the regular excitations-form isospin triplets rather than singlets.
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