Measurement of stopping beam distributions in the PIBETA detector

Precise calculation of the geometrical acceptance of a large solid angle detector with an integrated stopping target relies on precise knowledge of the beam geometry. We describe four alternative methods that we used to measure the beam stopping distributions in the PIBETA detector active target: (i) light response of segmented target elements to incident beam particles, (ii) back-tracking of charged particles from pi+ and mu+ decays using multi-wire proportional chambers, (iii) volume distribution of the Dalitz decay (pi0->gamma e+e-) event vertices, and (iv) the opening angle distribution of two pi0 photons originating from the beta decay of pi+ at rest. We demonstrate consistent results obtained by these four independent approaches and show how particular beam stopping distributions affect the detector's geometrical acceptance.Comment: 38 pages, 16 postscript figures, 2 tables, LaTeX, submitted to Nucl. Instrum. Meth.

Twisted supersymmetric 5D Yang-Mills theory and contact geometry

We extend the localization calculation of the 3D Chern-Simons partition function over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on a five sphere for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90's, and in a way it is covariantization of their ideas for a contact manifold.Comment: 28 pages; v2: minor mistake corrected; v3: matches published versio

Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as $N^{5/2}$ for $U(N)$ gauge groups with large values of the Chern-Simons 't\,Hooft coupling, $\tilde\lambda\equiv N/k$. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the $N^{5/2}$ behavior parallels other fixed points which have known supergravity duals. We also demonstrate that $SU(N)$ gauge groups cannot have this $N^{5/2}$ scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of $\tilde\lambda$, although the details differ between small and large values of $\tilde\lambda$. For pure Chern-Simons theories we present evidence for a chain of phase transitions as $\tilde\lambda$ is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops.Comment: 40 pages, 17 figures, Minor corrections, Published versio

PT-symmetric interpretation of double-scaling

The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its PT-symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the PT-symmetric analog is calculated explicitly in the double-scaling limit.Comment: 11 pages, 2 figure

Improved α4\alpha^4 Term of the Electron Anomalous Magnetic Moment

We report a new value of electron $g-2$, or $a_e$, from 891 Feynman diagrams of order $\alpha^4$. The FORTRAN codes of 373 diagrams containing closed electron loops have been verified by at least two independent formulations. For the remaining 518 diagrams, which have no closed lepton loop, verification by a second formulation is not yet attempted because of the enormous amount of additional work required. However, these integrals have structures that allow extensive cross-checking as well as detailed comparison with lower-order diagrams through the renormalization procedure. No algebraic error has been uncovered for them. The numerical evaluation of the entire $\alpha^4$ term by the integration routine VEGAS gives $-1.7283 (35) (\alpha/\pi)^4$, where the uncertainty is obtained by careful examination of error estimates by VEGAS. This leads to $a_e = 1 159 652 175.86 (0.10) (0.26) (8.48) \times 10^{-12}$, where the uncertainties come from the $\alpha^4$ term, the estimated uncertainty of $\alpha^5$ term, and the inverse fine structure constant, $\alpha^{-1} = 137.036 000 3 (10)$, measured by atom interferometry combined with a frequency comb technique, respectively. The inverse fine structure constant $\alpha^{-1} (a_e)$ derived from the theory and the Seattle measurement of $a_e$ is $137.035 998 83 (51)$.Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added after Eq.(40

A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics

We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are non-perturbative and mathematically rigorous.Comment: 18 pages, 3 figure

Partition Functions for Maxwell Theory on the Five-torus and for the Fivebrane on S1XT5

We compute the partition function of five-dimensional abelian gauge theory on a five-torus T5 with a general flat metric using the Dirac method of quantizing with constraints. We compare this with the partition function of a single fivebrane compactified on S1 times T5, which is obtained from the six-torus calculation of Dolan and Nappi. The radius R1 of the circle S1 is set to the dimensionful gauge coupling constant g^2= 4\pi^2 R1. We find the two partition functions are equal only in the limit where R1 is small relative to T5, a limit which removes the Kaluza-Klein modes from the 6d sum. This suggests the 6d N=(2,0) tensor theory on a circle is an ultraviolet completion of the 5d gauge theory, rather than an exact quantum equivalence.Comment: v4, 37 pages, published versio

Breit Hamiltonian and QED Effects for Spinless Particles

We describe a simplified derivation for the relativistic corrections of order $\alpha^4$ for a bound system consisting of two spinless particles. We devote special attention to pionium, the bound system of two oppositely charged pions. The leading quantum electrodynamic (QED) correction to the energy levels is of the order of $\alpha^3$ and due to electronic vacuum polarization. We analyze further corrections due to the self-energy of the pions, and due to recoil effects, and we give a complete result for the scalar-QED leading logarithmic corrections which are due to virtual loops involving only the scalar constituent particles (the pions); these corrections are of order $\alpha^5 \ln \alpha$ for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press

First-principles calculations of the phonon dispersion curves of H on Pt(111)

We have calculated the surface phonon dispersion curves for H on Pt(111), using first-principles, total energy calculations based on a mixed-basis set and norm-conserving pseudopotentials. Linear response theory and the harmonic approximation are invoked. For one monolayer of H in the preferred adsorption site (fcc hollow) vibrational modes polarized parallel and perpendicular to the surface are found, respectively, at 73.5 meV and 142.6 meV, at the Γ point of the surface Brillouin zone. The degeneracy of the parallel mode is lifted at the zone boundaries, yielding energies of 69.6 meV and 86.3 meV at the M point and 79.4 meV and 80.8 meV at the K point. The dispersion curves for H adsorption at the hcp hollow site differ only slightly from the above. In either case, H adsorption has considerable impact on the substrate modes; in particular the surface mode in the gap in the bulk phonon spectrum (around M point) is pushed into the bulk band. For on-top H adsorption, modes polarized parallel and perpendicular to the surface have respective energies of 47.4 meV and 277.2 meV, at the Γ point. The former disperses to 49.1 meV and 59.5 meV at the M point and to 56 meV and 56.7 meV at the K point. The H vibrational mode polarized perpendicular to the surface shows little dispersion, in all three cases considered. Insights are obtained from the hybridization of the H and Pt electronic states.Comment: 26 pages, 6 figure