Rising total cross sections and the flavoring of the pomeron

The relationship of the non-diffractive renormalization of the bare pomeron via$\text{K}\text{K}$ and $\text{B}\text{B}$ production - or its “flavoring” by λ quark loops and di-quark loops - and the shape of the NN total cross section is studied in some detail. The “unflavored” bare pomeron P? generated by non-strange quark loops with intercept $\text{α}\text{=0.85}$ is non-diffractively renormalized into the “flavored” (Gribov) bare pomeron P with intercept α above one (α = 1.06 here). We utilize inclusive data on $\text{K}\text{K}\text{and}\text{B}\text{B}$ production as well as inelastic diffraction to constrain parameters, and we fit the combination $\text{1}\text{2}\text{(σ}{}_{\mathrm{<mtext>pp</mtext>}}\text{+ σ}{}_{\mathrm{<mtext>p</mtext><mtext>p</mtext>}}\text{)}$ from s = 10 GeV² through ISR energies, including the new Fermilab data, to high accuracy. No pronounced long wavelength oscillations are observed. We suggest that these data favor the Chew-Rosenzweig realization of the topological expansion over that of Harari-Freund. We show that our scheme is consistent with the rising behavior of 2σ_KN ? σ_πN.     

Non-vanishing of the bare triple-Pomeron coupling from s-channel unitarity

In the crossing symmetric Reggeon calculus based on the $\text{1}\text{N}$ expansion, s-channel unitarity sum rules are written down explicitly to each order in $\text{1}\text{N}$. Some of the lowest order sum rules are shown to imply a non-vanishing bare triple-Pomeron coupling at t = 0, irrespectively of the bare Pomeron intercept.     

Unitarity,phenomenology, and the bare Pomeron

The possibility of utilizing the multifireball expansion and a bare Pomeron at $\text{α}\text{?}{}_{\mathrm{o}}\text{=0.85}$ as an approximation to a solution of the s-channel unitarity equations explicitly connecting 2-body and inelastic phenomenology is discussed. A scale for Pomeron renormalization effects is inferred.     

Fragmentation and multiperipheral dynamics: A connection through unitarity

A rapidity space decomposition of s-channel unitarity implies interdependence between production mechanisms. The presence of a low multiplicity diffractive production channel shadows the multiperipheral mechanism while the high multiplicity multiperipheral channel shadows the diffractive mechanism in the high produced mass region. The first effect results in negative contributions to the effective two-pomeron cut. Pomeron couplings to elastic and inelastic channels then require a cut structure which evades decoupling theorems. For hard cuts there is a connection between the relative amount of diffractive production and the dip in $\text{d}\text{σ}{}_{\mathrm{<mtext>el</mtext>}}{}^{\mathrm{<mtext>PP</mtext>}}\text{/}\text{d}\text{t}\text{at}\text{?t = 1,}\text{2}\text{GeV}{}^2\text{c}{}^2$ at ISR. The consequent cut to pole strength is 10–20%. It is conjectured that the situation described here resembles the approach to a phase transition in the multiperipheral gas.     

Topological cross sections in hadron-nucleon and hadron-nucleus collisions at very high energies

We apply our microscopic model for the topological cross section σ_n to produce n charged particles in hadron-proton interactions to hadron-nucleus scattering. The model is based on a stochastic branching process for hadronization. We calculate multiplicity distributions of hadron-nucleus collisions for 50 GeV ? E_L ? 400 GeV based on a multiple collision model. The production of “grey” $\text{(0.3 <}\text{ν}\text{c}\text{< 0.7)}$ particles is considered together with the shower $\text{(}\text{ν}\text{c}\text{> 0.7)}$ particles in order to test the model for higher number of collisions. The joint probability distribution of numbers of shower and grey particles F(n_s, n_g) is calculated. Finally, we critically compare the results to experimental data.     

Elastic and inelastic φ photoproduction

The differential cross section of the reaction (γp → pφ) has been measured in the t range 0 ? t ? 0.4 GeV² and for photon energies from 3.0 to 6.7 GeV. In particular for the small t region the measurement accuracy was better than 10%. We obtained for the slope parameter B in an exponential parametrization of the differential cross section dσ/dt = Ae^?Bt values of $\text{B ? 6 ± 0.5}\text{GeV}{}^{\mathrm{?2}}$ which are significantly larger than the slopes obtained by most other experiments at higher t values. This indicates a t dependence of B particularly in the small t region.An energy dependence of the optical point (dσ/dt)_t=0, observed in our measurements, has been explained as a kinematic effect due to the VDM relation. A fit of our measurements is in excellent agreement with all other published values of (dσ/dt)_t=0(γp → φp), this implies that σ_tot(φp) must be essentially energy independent in this energy range.Spin density matrix elements of the φ have been evaluated and an analysis of the helicity amplitudes has been carried out. This analysis confirmed s-channel helicity conservation. Moments of spherical harmonics of the $\text{K}\text{K}$ angular decay distribution have been computed for 10 MeV $\text{K}\text{K}$ mass-bins from threshold to 1.3 GeV. The mass dependence of the normalized moments is generally smooth. Contributing amplitudes have essentially only even moments. The moment 〈Y₂⁰〉/〈Y₀⁰〉 changes sign above the φ mass.Differential cross sections for the inelastic φ production γp → φX have been evaluated for the first time both with respect to t?t_min and M_K. The integrated inelastic cross sections are comparable in size with the elastic ones. The slopes of the differential cross sections dσ/dt appear to become flatter with increasing M_X.     

Prong cross-sections from a realistic two-component model

The inclusive pp → pX data, supporting a large triple Pomeron contribution, is invoked to predict the diffractive multiplicity distributions. Poisson decay is assumed for the excited cluster. The predicted diffractive prong cross-sections agree with the empirical estimates at 200 $\text{GeV}\text{c}$ and suggest a significant broadening at 1500 $\text{GeV}\text{c}$ (giving a rise in σ_T ～ 2.5 mb). Consequently the full prong distribution should develop no dip.     

Scaling function for two-point correlations with long-range interactions to order 1/η

The two-point correlation function ? (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as $\text{|}\text{R}\text{/a|}{}^{\mathrm{?(d\; +\; \sigma )}}$, for $\text{|}\text{R}\text{/a|}\text{a}\text{?}\text{1}$, where a is the spacing on a d-dimensional lattice, σ < d < 2σ and 0 < σ ? 2 ? η_SR. The calculations are done in zero field for T ? T_c. Explicit expansions for long-range propagators are developed for $\text{σ « 1}$ and for the neighborhood of σ ? 2 ? η_SR, in terms of which a universal, cut-off independent scaling function is obtained over the whole range of $\text{x = |}\text{q}\text{| ξ}$, and it is shown that the amplitude of the correlation-length dependence of the susceptibility becomes a universal parameter. Both the exponents and the coefficients of the expansion for fixed q as $\text{(T ? T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{→0}$ are calculated explicitly. The former are shown to require the validity of the operator-product expansion and explicit logarithmic correction terms are obtained for $\text{d = d}{}^1\text{= 3σ/2}$. For these and other dimensionalities, the coefficients are shown to be finite functions of d and σ. The correction to the Ornstein-Zernike form is given explicitly, with non-integer powers of x that have finite coefficients.     

Critical scaling function for long-range interactions to order 1/n

A universal scaling function of the order-parameter correlation function for an n-vector system in d dimensions, with long-range interactions $\text{～1/z.sfnc}\text{r}\text{z.sfnc}{}^{\mathrm{d+\sigma }}$, is discussed on the basis of explicit zero-field calculations to order 1/n, for T?T_c and σ<d<2σ.     

A one-dimensional approximation for the pomeron in the dual unitarity scheme

Using a one-dimensional approximation, the pomeron in the dual unitarity scheme is examined analytically in a multiperipheral cluster model. Clusters have negative short range correlations due to the t_min effect. In dual models, the pomeron has a crossing odd part, especially in B$\text{B}$ and BB scattering. By taking all reggeon loops into account, we show explicitly in our approximation that the crossing-odd part has only lower-lying singularities in the j-plane (typically complex poles with $\text{Re}\text{α?0.2}$) whereas the crossing-even part has the leading singularity at j = α_P (we imposed α_P = 1). The dual unitarity scheme leads to a modified version of the f-dominance of the pomeron. We calculate the SU(3) breaking of the pomeron due to the SU(3) breaking among Regge trajectories without additional assumptions on the SU(3) property of the pomeron.     

Study of the (α, 2α) reaction at 700 MeV

The results of a measurement of the cross section $\text{d}{}^3\text{σ/}\text{d}\text{Ω}{}_{\mathrm{\alpha 1}}\text{d}\text{Ω}{}_{\mathrm{\alpha 2}}\text{d}\text{E}$ for the (α, 2α) reaction on ⁶Li, ¹⁰B, C, O, Na, Al, Fe, Cu and Pb, are presented. Values for the effective cluster number n_0eff are deduced for these targets excluding lead, using the PWIA. It is observed that the PW1A value of n_eff is strongly dependent upon the theoretical shape assumed for the internal momentum distribution of the α-cluster. Using a S-state pole approximation for the momentum distribution leads to a value of the virtual decay amplitude g for A → α + (A ? 4) which is the same from ⁶Li to Fe.     

Temperature variation of the magnetic cluster structures in an iron-nickel invar alloy

Small-angle scattering of long wavelength neutrons $\text{(λ = 6.42}\text{A}\text{?}\text{)}$ from an Fe₆₅Ni₃₅ single crystal has been measured with the applied magnetic field (6.2 kG) parallel and perpendicular to the scattering vector $\text{K}$ of the elastic scattering over the temperature range from 25 to 422°C (T_c = 227°C). The scattering cross sections due to the longitudinal spin fluctuation have been analyzed by means of Guinier's approximation $\text{(dσ/dω)}{}_0\text{exp}\text{(?κ}{}^2\text{R}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{3}\text{)}$, where the forward cross section (dσ/dω)₀ is proportional to n, which is the number of atoms in a paramagnetic cluster, and R_g is the radius of gyration of the cluster. The empirical relation between n and R_g is = 0.298 × R_g^2.34 to be compared with that calculated for a simple spherical cluster model n = 1.274 R_g³.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Polarization transfer in the 2H(d,n)3He reaction at θ = 0°

The vector polarization transfer coefficient K_y^y′ and the tensor analyzing power A_zz have been measured for the ²H($\text{d}$$\text{n}$)³He reaction at θ = 0° over an incident deuteron energy range from 1 to 15 MeV in 0.5 MeV steps. The results agree with the previous ²H($\text{d}$$\text{n}$)³He measurements of Simmons et al. and are nearly identical to the ²H($\text{d}$$\text{n}$)³H measurements of Clegg et al. in the region of overlap. The present results provide an accurate and complete set of the observables necessary to use the ²H($\text{d}$,$\text{n}$)³He reaction as a source of polarized neutrons.     

On the separation of the direct reaction contribution in fluctuating cross sections by the use of polarized particles

A method to determine the direct reaction contribution y_D to the differential cross section in the presence of Ericson fluctuations is proposed. For the scattering of polarized $\text{spin}\text{-}\text{1}\text{2}$ particles from spinless nuclei the statistical analysis of the differential cross section dσ/dΩ and of the differential analyzing power $\text{(}\text{d}\text{σ/}\text{d}\text{Ω)A}$ allows an unambiguous and model independent extraction of y_D. The method is applied to the elastic scattering of polarized protons from ²⁶Mg, ⁸⁸Sr and ⁹⁰Zr; the results are in agreement with Hauser-Feshbach calculations.     

Does the enhancement mechanism work in non-leptonic decays of heavy pseudoscalar mesons with new flavors (b and t)?

We show that the enhancement mechanism proposed for non-leptonic decays of charmed mesons (D⁰, F⁺) is still important for decays of pseudoscalar mesons with b flavor, while its effect is small for mesons with t flavor. For the semi-leptonic branching ratios of B^? (b$\text{u}$), B⁰(b$\text{d}$) and B_S⁰(b$\text{s}$) we predict BR (B^? → evX ～' 9%, BR(B⁰ → evX) ～' BR(B_s⁰ → evX) ～' 5%. We can also derive the enhancement of the branching ratios of uncharmed final states in B decays, i.e. $\text{BR}\text{(}\text{B}{}^{\mathrm{?}}\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext>}}\text{)}$ ～' 20 %, $\text{BR}\text{(}\text{B}{}^0\text{→}\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>d</mtext>}}\text{)}$ ≈ 10%, where $\text{X}{}_{\mathrm{<mtext>s</mtext><mtext>u</mtext><mtext>(</mtext><mtext>s</mtext><mtext>d</mtext><mtext>)</mtext>}}$ = $\text{K}$π + ... + $\text{K}$K$\text{K}$ + ... .     

Membrabe models and generalized Z2 gauge theories

We consider models of (d?n)-dimensional membranes fluctuating in a d-dimensional space under the action of surface tension. We investigate the renormalization properties of these models perturbatively and in $\text{1}\text{n}$ expansion. The potential relationships of these models to generalized Z₂ gauge theories are indicated.