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Register a new userForces inside hadrons: pressure, surface tension, mechanical radius, and all that
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The physics related to the form factors of the energy momentum tensor spans a wide spectrum of problems, and includes gravitational physics, hard exclusive reactions, hadronic decays of heavy quarkonia, and the physics of exotic hadrons described as hadroquarkonia. It also provides access to the last global unknown property: the D-term. We review the physics associated with the form factors of the energy-momentum tensor and the D-term, their interpretations in terms of mechanical properties, their applications, and the current experimental status.
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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.
In this work we discuss a novel approach to model the hadronic and nuclear matter equations of state using the induced surface tension concept. Since the obtained equations of state, classical and quantum, are among the most successful ones in describing the properties of low density phases of strongly interacting matter, they set strong restrictions on the possible value of the hard-core radius of nucleons. Therefore, we perform a detailed analysis of its value which follows from hadronic and nuclear matter properties and find the most trustworthy range of its values: the hard-core radius of nucleons is 0.30--0.36 fm. A comparison with the phenomenology of neutron stars implies that the hard-core radius of nucleons has to be temperature and density dependent.
Many textbooks dealing with surface tension favor the thermodynamic approach (minimization of some thermodynamic potential such as free energy) over the mechanical approach (balance of forces) to describe capillary phenomena, stating that the latter is flawed and misleading. Yet, mechanical approach is more intuitive for students than free energy minimization, and does not require any knowledge of thermodynamics. In this paper we show that capillary phenomena can be unmistakably described using the mechanical approach, as long as the system on which the forces act is properly defined. After reminding the microscopic origin of a tangential tensile force at the interface, we derive the Young-Dupr{e} equation, emphasizing that this relation should be interpreted as an interface condition at the contact line, rather than a force balance equation. This correct interpretation avoids misidentification of capillary forces acting on a given system. Moreover, we show that a reliable method to correctly identify the acting forces is to define a control volume that does not embed any contact line on its surface. Finally, as an illustration of this method, we apply the mechanical approach in a variety of ways on a classic example: the derivation of the equilibrium height of capillary rise (Jurins law).
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 2D vertex operator algebra (VOA) construction in 4D $mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 times S^1$, focusing both on old puzzles as well as new observations. The VOA lives on a two-torus $mathbb{T}^2subset S^3times S^1$, it is $frac12mathbb{Z}$-graded, and this torus is equipped with the natural choice of spin structure (1,0) for the $mathbb{Z} +frac12$-graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserve the VOA, we find that it admits discrete deformations, which allow access to the remaining spin structures (1,1), (0,1) and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle, the two-point functions, and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the $T$-transformation acts on our four partition functions and lifts to a large diffeomorphism on $S^3times S^1$. More interestingly, we generalize the four partition functions on the torus to an infinite family labeled both by the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the $S$-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the $Omega$-background.
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