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Register a new userQuadrupole pressure and shear forces inside baryons in the large $N_c$ limit
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We derive number of relations between quadrupole energy, elastic pressure, and shear force distributions in baryons using the large $N_c$ picture of baryons as chiral solitons. The obtained large $N_c$ relations are independent of particular dynamics and should hold in any picture in which the baryon is the chiral soliton. One of remarkable qualitative predictions of the soliton picture is the nullification of the tangential forces acting on the radial area element for any tensor polarisation of the baryon. The derived relations provide a powerful tool to check the hypothesis that the baryons are chiral solitons, say using lattice QCD.
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The distributions of pressure and shear forces inside the proton are investigated using lattice Quantum Chromodynamics (LQCD) calculations of the energy momentum tensor, allowing the first model-independent determination of these fundamental aspects of proton structure. This is achieved by combining recent LQCD results for the gluon contributions to the energy momentum tensor with earlier calculations of the quark contributions. The utility of LQCD calculations in exploring, and supplementing, the assumptions in a recent extraction of the pressure distribution in the proton from deeply virtual Compton scattering experiments is also discussed. Based on this study, the target kinematics for experiments aiming to determine the pressure and shear distributions with greater precision at Thomas Jefferson National Accelerator Facility and a future Electron Ion Collider are investigated.
We study the electromagnetic form factors of the lowest-lying singly heavy baryons in a pion mean-field approach, which is also known as the SU(3) chiral quark-soliton model. In the limit of the heavy-quark mass, the dynamics inside a singly heavy baryon is governed by the $N_c-1$ valence quarks, while the heavy quark remains as a mere static color source. In this framework, a singly heavy baryon is described by combining the colored soliton with the singly heavy quark. In the infinitely heavy-quark mass limit, we can compute the electric quadrupole form factors of the baryon sextet with spin 3/2 with the rotational $1/N_c$ and linear corrections of the explicit flavor SU(3) symmetry breaking taken into account. We find that the sea-quark contributions or the Dirac-sea level contributions dominate over the valence-quark contributions in lower $Q^2$ region. We examined the effects of explicit flavor SU(3) symmetry breaking in detail. The numerical results are also compared with the recent data from the lattice calculation with the unphysical value of the pion mass considered, which was used in the lattice calculation.
In the light of recent experimental progress in determining the pressure and shear distributions in the proton, these quantities are calculated in a model with confined quarks supplemented by the pion field required by chiral symmetry. The incorporation of the pion contributions is shown to account for the long-range distributions, in general agreement with the experimentally extracted quark contributions. The results of the model are also compared with lattice QCD results at unphysically large quark mass.
While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon $(g-2)_mu$ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from $pi^0$, $eta$, $eta$. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the $pi^0$ the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by $Delta a_mu^text{LSDC}=13(6)times 10^{-11}$. This number does not include the contribution from the charm quark, for which we find $a_mu^{ctext{-quark}}=3(1)times 10^{-11}$.
We have investigated the electromagnetic decays of the antitriplet and sextet charmed baryon systems with $J^P= frac{1}{2}^+, frac{3}{2}^+$ in the framework of the heavy baryon chiral perturbation theory. We first construct the chiral Lagrangians at $O(p^2)$ and $O(p^3)$. Then we calculate the electromagnetic (EM) decay amplitudes of the charmed baryon systems up to $O(p^3)$. With the help of the quark model, we estimate the low energy constants. The numerical results of the EM decay widths show good convergence of the chiral expansion. We notice that the two neutral EM decay processes $Xi_c^0rightarrowgamma+Xi_c^0$ and ${Xi_c^*}^0rightarrowgamma+Xi_c^0$ are strongly suppressed by the SU(3) U-spin flavor symmetry. With the same formalism, we also estimate the EM decay widths of the bottomed baryons. The EM decay widths of the heavy baryons may be measured at facilities such as LHCb and JPARC. The explicit chiral structures of the heavy baryon decay amplitudes derived in this work may be useful to the possible chiral extrapolations of the future lattice simulations of these EM decay amplitudes.
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