Tractors,mass, and Weyl invariance

Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describe massive and gauge invariant theories using Weyl invariance. The key idea is to introduce a new scalar field which is constant when evaluated at the scale corresponding to the metric of physical interest. This technique relies on being able to efficiently construct Weyl invariant theories. This is achieved using tractor calculus—a mathematical machinery designed for the study of conformal geometry. From a physics standpoint, this amounts to arranging fields in multiplets with respect to the conformal group but with novel Weyl transformation laws. Our approach gives a mechanism for generating masses from Weyl weights. Breitenlohner–Freedman stability bounds for Anti-de Sitter theories arise naturally as do direct derivations of the novel Weyl invariant theories given by Deser and Nepomechie. In constant curvature spaces, partially massless theories—which rely on the interplay between mass and gauge invariance—are also generated by our method. Another simple consequence is conformal invariance of the maximal depth partially massless theories. Detailed examples for spins s?2$s?2$ are given including tractor and component actions, on-shell and off-shell approaches and gauge invariances. For all spins s?2$s?2$ we give tractor equations of motion unifying massive, massless, and partially massless theories.     

Massless composites with massive constituents

We construct model field theories in which a confining gauge interaction binds massive elementary fermions into massless composite particles. The massless composites are either Goldstone bosons or $\text{spin}\text{-}\text{1}\text{2}$ fermions. In these models, the manner in which exact chiral symmetries are realized changes at a critical value of the elementary fermion mass of order (e²/16π²)Λ, where Λ is the confinement scale and e is a weak gauge coupling.     

Parity-nonconservation effect in the helicities of conversion electrons accompanying the (5/2)− → (5/2)+ nuclear transition in the 229Pa nucleus

The ground state of the ²²⁹Pa nucleus is a 5/2^± doublet with a splitting energy of 220±50 eV. Such levels are peculiar to nuclei in the mass region around A=225 that are characterized by octupole deformations. A direct observation of P-odd effects in this system is of great interest because this can furnish information about the parity-nonconserving nucleon-nucleon potential. The transition between the two doublet states of opposite parities proceeds predominantly through internal conversion; therefore, P-odd mixing can be explored by studying the helicities of the conversion electron. It is shown that the helicities of the 6s _1/2, 6p _1/2, and 6p _3/2 conversion electrons are about 1%, which makes it possible to perform experiments aimed at determining the parameters of the effective parity-nonconserving nuclear potential.     

Covariant representations in a fibre bundle framework

Canonical and covariant representations of Lie groups of the semidirect product form G = N⊙K with N Abelian, are analyzed in a fibre bundle framework. We exhibit first the relationship between both kinds of representations in such framework. Two complementary methods of selecting irreducible representations from the covariant ones are developed. The first one proceeds by restriction to an invariant subspace and is exemplified in the case of massive integer spin representations of the Poincaré group. The second method takes quotients and is particularly useful when we deal with reducible but indecomposable representations. A family of stepped gauge transformations is generated when the method is used to obtain the covariant massless integer helicity representations of the Poincaré group; the electromagnetic and gravitational gauge transformations are just the first two cases of such a family.     

A spin dependent droplet model for high energy pion-nucleon elastic scattering

The Chou-Yang droplet model of hadron-hadron diffractive scattering is reinterpreted in a way that allows the spin structure of the amplitudes to be incorporated. The model is developed in the particular case of pion-nucleon elastic collisions, in which theA ⁽⁺⁾ andA′⁽⁺⁾ amplitudes are related respectively to theF ₂ andF ₁ Dirac form factors of the nucleon. A version of the model, which does not conserves-channel helicities, is first considered and its predictions compared with the high energy π±p elastic data, including polarization. Finally an interpretation of asymptotic helicity conservation is provided in terms of the model.     

SU(3) lattice Monte Carlo calculation of the glueball mass spectrum

We have calculated the glueball masses of various spins and parities in SU(3) gauge theory. Our first results give m_M(0⁺⁺)=(3.6±0.2)Λ_mom, m_E(0⁺⁺)=(4.3±0.3)Λ_mom, m(0^?+)=(7.2_?0.9^+1.6)Λ_mom, m_M(2⁺⁺)=(8.1±1.1)Λ_mom and m_E(2⁺⁺)=(8.3_?1.0^+1.6)Λ_mom as well as information on the glueball wave functions.     

ΛN and ΣN Interactions from Lattice QCD

We present our recent study on ΛN and ΣN (isospin I = 3/2) interactions by measuring Nambu–Bethe–Salpeter wave functions on the Lattice QCD. The lattice QCD calculation is performed by using the N _f  = 2 + 1 gauge configurations generated by PACS-CS collaboration together with employing an improved method to obtain potentials in lattice QCD simulations. For the ¹ S ₀ channel, the central ΣN (I = 3/2) potential and the central ΛN (¹ S ₀) potential are found to be very similar. For the spin triplet (³ S ₁?³ D ₁) channels, the central ΛN(³ S ₁?³ D ₁) potential is attractive while the central ΣN(I = 3/2, ³ S ₁?³ D ₁) potentials is repulsive. Tensor potentials, on the other hand, are rather weak in both ΛN and ΣN(I = 3/2) systems.     

On the uniqueness of the smooth zero mass limit for invariant amplitudes

The behavior of the invariant amplitudes for processes involving massive vector mesons is investigated in the limit as the mass goes to zero. The constraints of gauge invariance impose a definite structure on the amplitudes at k² = 0, and the question of the uniqueness of this structure is examined. It is shown that if the limit is smooth, the consequent relations between the massive and massless helicity amplitudes are unique, provided only that any additional dynamical assumptions are made consistently. Some of the implications of this result are discussed, with particular reference to the unambiguous covariant formulation of vector meson dominance for scattering amplitudes.     

The onset of deconfinement inSU(2) lattice gauge theory

InSU(2) lattice gauge theory, we study deviations from ideal gas behaviour near the deconfinement point. On lattices of sizeN _σ ³ ×4,N _σ=8, 12, 18 and 26, we calculate the quantityΔ≡(ε?3P)/T ⁴. It increases sharply just aboveT _c , peaks atT/T _c =1.15 ±0.05 and then drops quickly. This form of behaviour is shown to be the consequence of a second order phase transition. Dynamically it could arise because just aboveT _c , the low momentum states of the system are remnant massive modes rather than deconfined massless gluons.     

Study of proton dissociation into ΛK+ in 3-body final states at 10 and 16 GeV/c

Results are presented for p → (ΛK⁺) dissociation in the reactions K^?p → ΛK⁺K^? and and π^±p → ΛK⁺π^±at 10 and 16 GeV/c. The cross sections for the low-mass ΛK⁺ enhancement are compatible with the energy dependence σ ∝ p_lab^?0.3. The t′ spectra or the (ΛK⁺) threshold enhancement are exponential in shape. Its decay angular distribution reveals neither s-channel nor t-channel helicity conservation. The relative probabilities of the processes $\text{p}\text{→}\text{p, p}\text{→ (}\text{N}\text{π)}{}_{\mathrm{<mtext>I=</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{and p}\text{→ (Λ}\text{K}{}^{\mathrm{+}}\text{)}$ dissociation are in the ratios 100 : 10 : 0.2, independent of the nature of the incident particle.     

μ-capture and ortho-para transitions in the muonic molecule ppμ

The capture of a muon by protons at different hydrogen densities is considered. More precise values of γ-factors for ortho- and para-states of the muonic molecule ppμ are obtained: 2γ_o = 1.009±0.001 and 2γ_p = 1.143±0.001. Relativistic effects are taken into account in the muonic molecule, and the rate of ortho-para transitions λ_op = (7.1±1.2) × 10⁴s^?1, caused by these effects, is calculated. With this value of λ_op the μ-capture rate in liquid hydrogen is found to be Λ_c = (490±10)s^?1 that is in agreement with the value Λ_c = 460±20 s^? recently measured by the Saclay-CERN-Bologna collaboration.     

On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux Y(s ₁, ..., s _k ) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2k) algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.     

Inclusive Λ, Λ and Σ±(1385) production in 405 GeV/c pp interactions

We have investigated inclusive Λ, $\text{Λ}$ and Σ^±(1385) productions in 405 GeV/c pp interactions. The observed cross sections are σ(Λ)=4.05±0.39 mb, $\text{σ(}\text{Λ}\text{=0.63±0.17}$ mb, σ(Σ⁺(1385))=0.74±0.17 mb and σ(Λ^?(1385))=0.56±0.17 mb. $\text{Λ}$ production is dominant in a central region of ∣x∣≤0.4. The $\text{Λ/}\text{Λ}$ production ratio at ∣x∣≈0 is found to be 1.2±0.5. The excess, about 0.2 mb, of σ(Λ⁺(1385)) over σ(Λ^?(1385)) is most likely attributed to proton fragmentations (∣x∣≥0.4), and gives an evidence for scaling.     

The glueball mass spectrum in QCD: First results of a lattice Monte Carlo calculation

We perform a variational calculation of the masses of glueballs of various spins and parities in SU(2) gauge theory. The quantum vacuum we use is generated by the lattice Monte Carlo technique. Our first results, obtained on medium sized lattices give m(0⁺) = (3.6 ± 0.35) Λ_mom, m(0^? = (6.0 ± 1.0)Λ_mom, m(2⁺) = (6.5^+1.8_?1.1)Λ_mom, various mass upper bounds and information on glueball wave functions.     

Effective field theory for massive gravitons and gravity in theory space

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_Pl and a mass m_g, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m_g. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ∼(m_g⁴M_Pl)^1/5 for the Fierz-Pauli theory, but can be raised to Λ∼(m_g²M_Pl)^1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.     

Diffraction dissociation in the reaction p+p→Λ°+K++p at the CERN ISR

The exclusive reaction pp→Λ°K⁺p has been studied at 0.1<?t_pp<0.6 GeV² and energies √s=45 GeV and 53 GeV at the CERN ISR. Diffractive excitation p→Λ°K⁺ occurs predominantly in the mass range M(Λ°K⁺)≈2.1 GeV and peaks at 1.7 GeV. The cross section for pp→Λ°K⁺p is 10±3μb for M(Λ°K⁺)<2.5 GeV, and the t_pp dependence is exp (bt) with b=7.0±0.5 GeV^?2.     

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2⁺ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2⁺ and 2⁻ particles of equal mass, as well as a massive pseudoscalar.     

Phase transition ofSU(3) gauge theory at finite temperature

We present evidence for the presence of a phase transition inSU(3) lattice gauge theory at finite temperature using Monte-Carlo methods. An extrapolation to the continuum limit leads to the valueT _c =Λ_mom±15% for the critical temperature separating the two phases.     

s-and t-channel helicity conservation of pion induced nucleon diffraction dissociation at 3.9 GeV/c and the implications of a two-component model

A study of schannel and t-channel helicity conservation has been carried out on a prism plot separated sample of 3.9 GeV/cπ^±p → π (Nπ)_dd diffraction dissociation events. s-channel helicity conservation is found to be strongly violated while t-channel helicity conservation is found to be mildly violated. These results are similar to that found at 11.7 GeV/c. We explain these violations on the basis of a “two-component model” of which the first component is a single exchange amplitude. We postulate that this amplitude is the generalization of the pomeron exchange amplitude which may conserve s-channel helicity. The second component of the model is a double exchange mechanism which strongly violates s-channel helicity. The predictions of this model agree with the experimental data.     

A two-component model definition of two-body nucleon diffraction dissociation in πp → π(Nπ)reactions at 3.9 GeV/c and comparison with other experiments

Four low-mass “diffractive like” reactions π^±p → π^±(pπ⁰) and π^±p → π^±(nπ⁺) have been studied at 3.9 GeV/c incident pion momentum. These channels have been studied in the framework of a two-component model and we have proposed a definition of the diffraction dissociation amplitude. The following three features of the data are discussed: (1) an apparent violation of the predictions of isospin invariance for the cross section ratios, (2) the marked anisotropy of the s-channel helicity distributions and (3) the absence of the cross-over effect in the differential cross sections. The predictions of a two-component model previously used to explain the low mass $\text{I =}\text{1}\text{2}\text{(}\text{N}\text{π)}$ enhancement [1] and s- and t-channel helicity non-conservation [2] are seen to be in agreement with these observations. Predictions are also made for higher energy incident pions and incident K, p, and $\text{p}$ projectiles. These predictions are compared with available data including recent results at Fermilab and ISR energies.