arXiv subjects
Publications and source records attributed to R. L. Jaffe.
In hep-ph/0404212 Diakonov, Petrov, and Polyakov respond to my recent comments on their 1997 paper, ``Exotic anti-decuplet of baryons: prediction from chiral solitons''. Their responses do not address the basic issues or alter the conclusions in my paper.
We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates and agree over a wide range of parameters with a recent numerical treatment of the sphere and plate with Dirichlet boundary conditions. Our approach improves upon proximity force approximation. It can be generalized easily to other geometries, other boundary conditions, to the computation of Casimir energy densities and to many other situations.
In 1997 Diakonov, Petrov, and Polyakov, calculated the width of the exotic baryon that they called $Θ^{+}$. The prediction, $Γ(Θ^{+})\lesssim$ 15 MeV, has received considerable attention, especially in light of the narrowness of the experimentally reported $Θ^{+}$ resonance. However, there is an arithmetic error in their work: when corrected, the width estimate quoted in that paper should have been $\lesssim$~30 MeV.
We propose that the recently discovered Θbaryon is a bound state of four quarks and an antiquark, containing two highly correlated ud-pairs. If so, the Θbaryon has positive parity, and it lies in an near-ideally mixed SU(3)_{f} \mathbf{\bar{10}}_{f} oplus \mathbf{8}_{f}. The Roper resonance and the P_{11}(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of Ξ's (S=-2) with J^Π=\half^{+} around 1750 MeV. A search for manifestly exotic Ξ^{+} and Ξ^{--} in this mass range could provide a sharp test of our proposal. We predict that charm and bottom analogues of the Θbaryon are stable against strong decays.
Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all energies. We study the vacuum polarization energy of renormalizable, continuum quantum field theory in the presence of a background field, designed to impose a Dirichlet boundary condition in a particular limit. We show that in two and three space dimensions, as a background field becomes concentrated on the surface on which the Dirichlet boundary condition would eventually hold, the Casimir energy diverges. This result implies that the energy depends in detail on the properties of the material, which are not captured by the idealized boundary conditions. This divergence does not affect the force between rigid bodies, but it does invalidate calculations of Casimir stresses based on idealized boundary conditions.
We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a ``Dirac spike'') and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.
We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the classical field equations. We unambiguously implement standard perturbative renormalization using phase shifts and the Born approximation. We illustrate our method by calculating the quantum energy of a soliton/antisoliton pair as a function of their separation. This energy includes an imaginary part that gives a quantum decay rate and is associated with a level crossing in the solutions to the classical field equation in the presence of the source that maintains the soliton/antisoliton pair.
We demonstrate an unambiguous and robust method for computing fermionic corrections to the energies of classical background field configurations. We consider the particular case of a sequence of background field configurations that interpolates continuously between the trivial vacuum and a widely separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum, we use phase shifts, the Born approximation, and Levinson's theorem to avoid ambiguities of renormalization procedure and boundary conditions. We carry out the calculation analytically at both ends of the interpolation and numerically in between, and show how the relevant physical quantities vary continuously. In the process, we elucidate properties of the fermionic phase shifts and zero modes.
I examine the effect of trying to impose a Dirichlet boundary condition on a scalar field by coupling it to a static background. The zero point -- or Casimir -- energy of the field diverges in the limit that the background forces the field to vanish. This divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of a surface on which a Dirichlet boundary condition is imposed, and other quantities like the surface tension, which are obtained by deforming the surface, depend on the physical cutoffs that characterize the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and forces between rigid surfaces are finite and independent of these complications
I describe some insight obtained from a lattice calculation on the possibility that the light scalar mesons are \qbar^2 q^2 states rather than \qbar q. First I review some general features of \qbar^2 q^2 states in QCD inspired quark models. Then I describe a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, which finds indications that for sufficiently heavy quarks there is a stable four-quark bound state with JPC=0{++} and non-exotic flavor quantum numbers.
We explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable.
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when confinement is implemented by forces that act normal to the surface. We review this confining potential formalism applied to the confinement of a particle to an arbitrary manifold embedded in a higher dimensional Euclidean space. We devote special attention to the geometrically induced gauge potential that appears in the effective Hamiltonian for motion on the surface. We emphasize that the gauge potential is only present when the space of states describing the degrees of freedom normal to the surface is degenerate. We also distinguish between the effects of the intrinsic and extrinsic geometry on the effective Hamiltonian and provide simple expressions for the induced scalar potential. We discuss examples including the case of a 3-dimensional manifold embedded in a 5-dimensional Euclidean space.
We study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of the surface and other quantities like the surface tension, which are obtained by deforming the surface, cannot be defined independently of the details of the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and the force between rigid surfaces are finite and independent of these complications.
The Casimir problem is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions. In reality, however, no interaction is strong enough to enforce a boundary condition on all frequencies of a fluctuating field. We construct a more physical model of the situation by coupling the fluctuating field to a smooth background potential that implements the boundary condition in a certain limit. To study this problem, we develop general new methods to compute renormalized one--loop quantum energies and energy densities. We use analytic properties of scattering data to compute Green's functions in time--independent background fields at imaginary momenta. Our calculational method is particularly useful for numerical studies of singular limits because it avoids terms that oscillate or require cancellation of exponentially growing and decaying factors. To renormalize, we identify potentially divergent contributions to the Casimir energy with low orders in the Born series to the Green's function. We subtract these contributions and add back the corresponding Feynman diagrams, which we combine with counterterms fixed by imposing standard renormalization conditions on low--order Green's functions. The resulting Casimir energy and energy density are finite functionals for smooth background potentials. In general, however, the Casimir energy diverges in the boundary condition limit. This divergence is real and reflects the infinite energy needed to constrain a fluctuating field on all energy scales; renormalizable quantum field theories have no place for ad hoc surface counterterms. We apply our methods to simple examples to illustrate cases where these subtleties invalidate the conclusions of the boundary condition approach.
I describe a few of the most exciting open questions in high energy spin physics. After a brief look at (g-2)_μand the muon electric dipole moment, I concentrate on QCD spin physics. Pressing questions include the interpretation of new asymmetries seen in semi-inclusive DIS, measuring the polarized gluon and quark transversity distributions in the nucleon, testing the DHGHY Sum Rule, measuring the orbital angular momentum in the nucleon, and many others which go beyond the space and time allotted for this talk.
The nucleon's axial vector charge, g_A, becomes delocalized in the chiral limit. When m_π= 0, and SU(2)_L x SU(2)_R is exact, 1/3 of the nucleon's axial charge is to be found at infinite distance from the nucleon. For finite m_πthis result is approached smoothly as m_π-> 0. We illustrate this effect by considering the lepton-proton spin-spin interaction arising from Z^0 exchange as a function of m_π. Delocalization may have implications for lattice calculations of g_A and in nuclei.
We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model.
We present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.