arXiv subjects
Publications and source records attributed to P V Landshoff.
It is fundamental that the phase of an elastic scattering amplitude is related to its energy variation. We repeat a previous fit to proton-proton and proton-antiproton elastic scattering data from 13 to 13000 GeV, taking better account of the very high accuracy of the 13 TeV data. The conclusion remains that there is no evidence for the existence of an odderon in the small-t data
A simple application of Regge theory, with 9 free parameters, provides a good fit to elastic scattering data at small t from 13.76 GeV to 13 TeV. It yields a value for rho, the ratio of the real part of the forward amplitude to its imaginary part, close to 0.14 at 13 TeV. Although the exact value obtained for rho is sensitive to what functional form is chosen for the fit, there is no strong case for the presence of an odderon contribution to forward scattering.
We propose an approach to DGLAP evolution at small x that circumvents the usual problem that a perturbation expansion is not valid there. The data for the charm structure function are important to motivate the method, and it describes them much more successfully than the conventional approach.
Common beliefs about unitarity are not reliable, and we do not know how to apply DGLAP evolution at small x. Together with the big discrepancy between the measurements of the total cross section at the Tevatron, a consequence is that the cross section at the LHC could be anywhere between 90 and 160 mb.
Independently of any theory, the possibility that the large value of the Tevatron cross section claimed by CDF is correct suggests that the total cross section at the LHC may be large. Because of the experimental and theoretical uncertainities, the best prediction is $125\pm 35$ mb.
I review the formalism for gauge-field perturbation theory in noncovariant gauges, particularly the temporal axial gauge. I show that, even at zero temperature, there are complications and it is not known whether a formalism exists for handling these that is correct for all calculations. For thermal field theory in the imaginary time formalism, there are different difficulties, whose solution so far is known only up to lowest order in the coupling $g$.
The hard pomeron first came to light in deep inelastic lepton scattering, but evidence that it contributes also to soft hadronic collisions is reinforced by the fact that it seems to obey a factorisation similar to that of other Regge exchanges. Including a hard-pomeron term in a fit to data for sigma(pp) and sigma(p\bar p) leads to a large total cross section at the LHC. An exact prediction is not possible because of the uncertaintities arising from screening corrections; the best estimate is 125 \pm 25 mb.
We refute past suggestions that the data on soft diffraction dissociation demand modifications to conventional Regge theory.
The gluon distribution is dominated by the hard pomeron at small $x$ and all $Q^2$, with no soft-pomeron contribution. This describes well not only the DGLAP evolution of the hard-pomeron part of $F_2(x,Q^2)$, but also charm photoproduction and electroproduction, and the longitudinal structure function, all calculated in leading-order pQCD.
I review various theoretical questions that arise from data from HERA and the Tevatron, and which are relevant for the LHC. They range from soft physics, such as the total cross section, to hard physics, such as Higgs production. In particular, I argue that the proton's gluon density is somewhat larger at small $x$ than is currently accepted.
We explain how Regge theory and perturbative evolution may be made compatible at small x. The result not only gives striking support to the two-pomeron description of small-x behaviour, but gives a rather clean test of perturbative QCD itself. When x is very small, or Q^2 is very large, the proton's gluon distribution function is significantly larger than is commonly believed. Perturbative evolution is invalid below Q^2\approx 5 GeV^2.
The conventional approach to perturbative evolution is illegal because the expansion in powers of $α_s$ of the the DGLAP splitting matrix ${\bf P(z,α_s)}$ breaks down at small $z$. The small-$x$ data for the proton structure function $F_2(x,Q^2)$ and its charm component $F^c_2(x,Q^2)$ show that a hard pomeron, with intercept close to 1.4, must be added to the familar soft pomeron. Conventional perturbative evolution may be applied to the hard-pomeron component and provides a striking test of perturbative QCD.
The known analytic properties of the Compton amplitude at small $Q^2$ place significant constraints on its behaviour at large $Q^2$. This calls for a re-evaluation of the role of perturbative evolution in past fits to data.
New structure-function data are in excellent agreement with the existence of a hard pomeron, with intercept about 1.4. It gives a very economical description of the data. Having fixed 2 parameters from the data for the real-photon cross section $σ^{γp}$, we need just 5 further parameters to fit the data for $F_2(x,Q^2)$ with $x\leq 0.001$. The available data range from $Q^2=0.045$ to 35 GeV$^2$. With guesses consistent with dimensional counting for the $x$ dependences of our three separate terms, the fit extends well to larger $x$ and to $Q^2=5000$ GeV$^2$. With no additional parameters, it gives a good description of data for the charm structure function $F_2^c(x,Q^2)$ from $Q^2=0$ to 130 GeV$^2$. The two pomerons also give a good description of both the $W$ and the $t$ dependence of $γp\to J/ψp$.
Key issues in pomeron physics include whether the hard and soft pomerons are distinct objects, and whether the hard pomeron is already present in amplitudes at $Q^2=0$. It is urgent to learn how to combine perturbative and nonperturbative concepts, and to construct a sound theory of perturbative evolution at small $x$. Other questions are whether screening corrections are small, and gap survival probabilities large. Finally, do diffractive processes present a good way to discover the Higgs?
Recent small-t ZEUS data for exclusive rho photoproduction are in excellent agreement with exchange of the classical soft pomeron with slope alpha'=0.25 GeV^{-2}. Adding in a flavour-blind hard-pomeron contribution, whose magnitude is calculated from the data for exclusive J/psi photoproduction, gives a good fit also to the ZEUS data for rho photoproduction at larger values of t, and to phi photoproduction.
The ZEUS data on the charm structure function F_2^c at small x fit well to a single power of x, corresponding to the exchange of a hard pomeron that is flavour-blind. When combined with the contribution from the exchange of a soft pomeron, the hard pomeron gives a good description of elastic $J/ψ$ photoproduction.