Supersymmetric pure spinor theory

A theory based solely on a 2×(N=2)-component Weyl spinor field χ(x) of subcanonical dimension $\text{1}\text{2}$ allows the local construction (without derivatives) of effective fermi and bose fields with spins up to N=2. It is demonstrated that the lagrangian $\text{～:}\text{det}\text{xx}{}^1\text{: (x)}$ studied earlier is invariant under a global N=2 supersymmetry transformation and can be cast into a form $\text{～(}\text{det DD}{}^1\text{):ππ}{}^1\text{:}$ involving the scalar chiral superfield $\text{π=}\text{exp}\text{[θ}{}_{\mathrm{x}}\text{(x + iθσθ}{}^1\text{)]}$ the components of which are finite part products of the basic field. The theory can be generalized to an N-supersymmetric theory in a 2N-dimensional space-time yielding the Thirring model as special case for N=1.     

A nucleon-nucleon potential that includes the effect of the N1(1236)

The transition potentials for the reaction $\text{N}\text{+}\text{N}\text{?}\text{N}\text{+}\text{N}{}^1\text{(1236)}$ and $\text{N}\text{+}\text{N}\text{?}\text{N}{}^1\text{(1236) +}\text{N}{}^1\text{(1236)+}\text{N}{}^1\text{(1236)}$ are derived in the case of the π and ? exchange using the quark model. The nucleon-nucleon scattering in the T=1, ¹S₀ state is treated as a coupled channel $\text{N}\text{+}\text{N}\text{?}\text{N}\text{+}\text{N}{}^1$ system.     

Opto-galvanic spectroscopy of broadening and shift of two-photon thallium transitions by N2 and He

This paper reports the first measurements of pressure broadening and shift of thallium 6 ${}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?8}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$$\text{3}\text{2}$ transitions by N₂ and He perturbers. Ion-detection with box-car integration was used for data collection. The number of the perturbating gases ranged from $\text{(1.1?4.7)×10}{}^{19}\text{cm}{}^3$. The red shift to N₂ and the shift due to He are found to vary linearly with pressure. The value of the effective cross section for the impact broadening was determined and van der Waals constants obtained.     

The Dyson instability and asymptotics of the perturbation series in QED

The probability of the ground state decay at e² < 0 is calculated by the steepest descent method in fermionic electrodynamics. The saddle points are the solution of some equations which have been obtained by calculating the asymptotic of the Dirac operator determinant in a very strong external field. The SO(3) × O(2) solutions are found explicitly. The main contribution from them to the Nth coefficient of perturbation theory is proportional to $\text{(?α)}{}^{\mathrm{<mtext>N</mtext><mtext>2</mtext>}}\text{Γ(}\text{N}\text{2}\text{)}$, where $\text{S = 2}{}^2\text{3}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}\text{π}{}^3$.     

N2+ bound quartet and sextet state potential energy curves

Potential energy curves for the ${}^4\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{u}}$, ${}^4\text{Π}{}_{\mathrm{g}}$ and ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ states of N⁺₂ that dissociate to N (${}^4\text{S}{}^0$) and $\text{N}{}^{\mathrm{+}}\text{(}{}^3\text{P)}$, have been determined from a complete active space self-consistent field calculation. The ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ state is found to be significantly bound (D_e = 2.68 eV) with a minimum at 1.72 Å.     

The energy of a system of relativistic massless bosons bound by oscillator pair potentials

We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian $\text{H=}\text{∑}\text{i=1}\text{N}\text{p}{}_{\mathrm{i}}{}^2\text{+}\text{∑}\text{j>i=1}\text{N}\text{γ|}\text{r}{}_{\mathrm{i}}\text{−}\text{r}{}_{\mathrm{j}}\text{|}{}^2\text{,}\text{γ>0.}$ We prove $\text{A}\text{γN}{}^2\text{(N−1)}{}^2{}^{\mathrm{1/3}}\text{⩽E⩽B}\text{γN}{}^2\text{(N−1)}{}^2{}^{\mathrm{1/3}}\text{,}$ where A=2.33810741 and $\text{B=}\text{81}\text{2π}{}^{\mathrm{1/3}}\text{=2.3447779}$. The average of these bounds determines E with an error less than 0.15% for all N⩾2.     

General theory of virtual heavy-particle effects in renormalizable field theories (I)

We develop a systematic method of isolating the effects of virtual heavy particles in renormalizable field theories. With a φ⁴-type field-theory model involving two real scalar fields (one with a heavy mass M, and the other light), we show in detail, that up to order $\text{1}\text{M}{}^2$ (but to all orders in renormalized coupling), effects of virtual heavy particles can be completely incorporated into pure light-particle theory via effective local vertices which involve operators of canonical dimension at most six. All the coupling strengths for such effective local interactions are of order $\text{1}\text{M}{}^2$ (the decoupling theorem) and are systematically calculable in renormalized perturbation theory. We also derive a closed set of Callan-Symanzik equations which are satisfied by these coupling strengths. Using these equations, we explicitly sum all the leading logarithms (i.e., log M ～ O(1)) which appear in the perturbative calculations of the effective coupling strengths.     

Isospin analysis of NN → NNπ reactions at 5.7 GeV/c

A cross-channel isospin analysis has been performed on the channels $\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}\text{and}\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}$ in terms of three isospin amplitudes $\text{M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^0\text{, M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$, and $\text{M}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^1$ where the upper index is the isospin of the exchanged “object” in the t-channel and the lower index is the isospin of the $\text{(}\text{N}\text{π)}\text{or}\text{(}\text{N}\text{π)}$ system. Enhancements are observed in the low Nπ) invariant mass region for an $\text{I =}\text{1}\text{2}$ final state when the isospin of the exchanged object in cross channel is I_E = 0 and 1.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

Two theorems on the level order in potential models

We study the potentials of the form U(r)=?r^?1+λV(r), $\text{(}\text{d}\text{d}\text{r}\text{)(}\text{r}{}^2\text{d}\text{V}\text{d}\text{r}\text{)?0}$, and show that the energy levels satisfy the inequalities $\text{E(N}{}_{\mathrm{c}}\text{, l)?E(N}{}_{\mathrm{c}}\text{, l+1)}$ to first order in λ, where N_c denotes the coulombic principal quantum number and l the angular momentum. Similarly for potentials $\text{U(r)=r}{}^2\text{+λV(r), (}\text{d}\text{d}\text{r}{}^2\text{)}{}^2\text{V(r)?0}$, we prove to first order in λ that $\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{)?}\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{+2)}$, where NH denotes the harmonic oscillator quantum number. In the latter case, we give also quantitative restrictions on the relative positions at the lth and (l+1)th states.     

Neutral pion production by weak neutral currents in neutrino and antineutrino reactions

A study is presented of single π^o production in neutrino and antineutrino interactions in Gargamelle filled with freon CF₃Br. Limits on the neutral to charged current cross-section ratios $\text{R}{}_{\mathrm{v}}\text{=σ(v}\text{N}\text{→v}\text{N}\text{′π}{}^{\mathrm{o}}\text{)/2 σ(v}\text{N}\text{→ μ}{}^{\mathrm{-}}\text{N}\text{′π}{}^{\mathrm{o}}\text{)}$ and $\text{R}{}_{\mathrm{<mtext>\nu </mtext>}}\text{= σ(}\text{ν}\text{N}\text{→}\text{ν}\text{N}\text{′π}{}^{\mathrm{o}}\text{)/2 σ(}\text{ν}\text{N}\text{→ ω}{}^{\mathrm{+}}\text{N}\text{′π}{}^{\mathrm{o}}\text{)}$ are found to be $\text{0.10 < R}{}_{\mathrm{\nu }}\text{< 0.20}\text{and}\text{0.26 < R}{}_{\mathrm{<mtext>\nu </mtext>}}\text{< 0.44}$ at 68% confidence level.     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.     

Valence band parameters and free exciton reduced mass of zinc telluride derived from free exciton magnetoreflectance

Reflectance spectra were measured on ZnTe in magnetic fields up to 18 T for B ? [100] and B ? [110]. The experiments yield renormalized valence band parameters $\text{γ}{}^1{}_2\text{= 0.83 ± 0.08}$ and $\text{γ}{}^1{}_3\text{= 1.30 ± 0.12}$, corresponding to bare parameters γ₂ = 0.95 ± 0.09 and γ₃ = 1.48 ± 0.14. From the free exciton Rydberg energy $\text{R}{}^1{}_0\text{= 12.8}\text{meV}$ we derive a reduced exciton polaron mass m₀ 0.080 ± 0.005 and a bare reduced mass m₀ 0.074 ± 0.005, corresponding to $\text{γ}{}^1{}_1\text{= 3.9 ± 0.7}$ and γ₁ = 4.4 ± 0.7 for an electron effective polaron mass $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.116 m}{}_0$. We further calculate the exciton diamagnetic shift rate according to existing low-field theories modified by a variational calculation taking into account polaron effects and valid up to γ ? 1. The difference between experiment and theory is 10% and the agreement is considered satisfactory.     

Propagation of ion acoustic solitons in plasma density gradients

Experimental observations of propagation of ion acoustic solitons in a plasma with density gradients are presented. Soliton amplitude and velocity change as $\text{N}\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{N}\text{x}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$ respectively where Nx is the local density.     

Nonorthogonality corrections in the method of correlated basis functions

A set of normalized linearly independent basis functions φ₁, φ₂, …, φ_j, … generates matrix representatives $\text{H}$ and $\text{N}$ of the Hamiltonian operator and the identity. An orthonormal basis $\text{φ}{}_1$, $\text{φ}{}_2$, …, $\text{φ}{}_{\mathrm{j}}$, … generated by a Löwdin transformation is characterized by the distance in Hilbert space between $\text{φ}{}_{\mathrm{j}}$ and φ_j. The choice of positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ minimizes these distances and maximizes the diagonal elements of $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Again for positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a finite basis, 1 ? j ? p, the analysis yields a general theorem on Trace $\text{N}$${}^{\mathrm{<mtext>?n</mtext><mtext>2</mtext>}}$ (? p for all positive and negative integral values of n except n = ?1 and ? p for n = ?1).Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of $\text{H}$. Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas.     

Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.     

Transition magnetic moments of hadrons and sidewise dispersion relations

Systems of linear relations for the magnetic moments of the nucleon and transition moments μ_ωπγ, μ_?πγ and ${}^{\mathrm{\mu }}\text{N}{}^1{}_{1470}\text{N}\text{γ}$ are obtained on the basis of sidewise dispersion relations in the one-pion approximation. In such an approach the magnetic moments of the transition ω(?)→ πγ and $\text{N}{}^1{}_{1470}\text{→Nγ}$ are expressed in terms of the anomalous magnetic moments of the nucleon and the strong interaction coupling constants.     

Index theorems and supersymmetry in the soliton sector: (II). Magnetic monopoles in 3+1 dimensions

For supersymmetric Yang-Mills theories with Bogomolny-Prasad-Sommerfield monopoles, we use an open-space trace theorem on $\text{R}{}^3$ to calculate the O(?) correction to the monopole mass. For the N = 2 theory, the unrenormalized mass correction is non-vanishing (and divergent). To the same order, we calculate the quantum corrections to the central charges, and demonstrate explicitly that the Bogomolny bound is saturated. We also show that the mass correction for the N = 4 theory vanishes to O(?). Finally we discuss the renormalization of the mass correction for the N = 2 theory. This requires the parameters of the theory to be renormalized in the monopole background-field gauge, although there is no simple way known to do this. We exhibit calculations in standard gauges to show explicitly that they give gauge-dependent answers. Physical arguments based on the Dirac quantization condition suggest that the renormalized mass correction vanishes.     

Intensity measurements and self-broadening coefficients in the γ band of O2 at 628 nm using intracavity laser-absorption spectroscopy (ICLAS)

Quantitative measurements of intensities and widths were made for individual rotational lines of the atmospheric oxygen $\text{b}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(ν′ = 2) ← X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}\text{(ν″ = 0)}$ γ band by using a recently developed, highly sensitive, intracavity laser-absorption spectroscopic technique (ICLAS) at 300 torr m. The total band intensity derived from the line intensities is $\text{1.26 ± 0.05}\text{cm}{}^{\mathrm{?1}}\text{km}{}^{\mathrm{?1}}\text{atm}{}^{\mathrm{?1}}$ (STP). Self-broadening collision coefficients for the ^PP and ^PQ branch lines have been determined from the absorption line width and were found to vary from 0.055 cm^?1 atm^?1 at N″ = 1 to 0.037 cm^?1 atm^?1 at N″ = 27.