Evidence for the saturation of the Froissart bound

It is well known that fits to high energy data cannot discriminate between asymptotic ln(s) and ln^2(s) behavior of total cross section. We show that this is no longer the case when we impose the condition that the amplitudes also describe, on average, low energy data dominated by resonances. We demonstrate this by fitting real analytic amplitudes to high energy measurements of the gamma p total cross section, for sqrt(s) > 4 GeV. We subsequently require that the asymptotic fit smoothly join the sqrt(s) = 2.01 GeV cross section described by Dameshek and Gilman as a sum of Breit-Wigner resonances. The results strongly favor the high energy ln^2(s) fit of the form sigma_{gamma p} = c_0 + c_1 ln(nu/m) + c_2 ln^2(nu/m) + beta_{P'}/sqrt(nu/m), basically excluding a ln(s) fit of the form sigma_{\gamma p} = c_0 + c_1 ln(nu/m) + beta_P'/sqrt(\nu/m), where nu is the laboratory photon energy. This evidence for saturation of the Froissart bound for gamma p interactions is confirmed by applying the same analysis to pi p data using vector meson dominance.Comment: 7 pages, Latex2e, 4 postscript figures, uses epsf.st

The Elusive p-air Cross Section

For the \pbar p and $pp$ systems, we have used all of the extensive data of the Particle Data Group[K. Hagiwara {\em et al.} (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. We then subject these data to a screening process, the ``Sieve'' algorithm[M. M. Block, physics/0506010.], in order to eliminate ``outliers'' that can skew a $\chi^2$ fit. With the ``Sieve'' algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high \delchi, the individual i$^{\rm th}$ point's contribution to the total $\chi^2$. The $\chi^2$ fits are then made to the sieved data. We demonstrate that we cleanly discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of total hadronic cross sections when we require that these amplitudes {\em also} describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to the ``sieved'' high energy measurements of $\bar p p$ and $pp$ total cross sections and $\rho$-values for $\sqrt s\ge 6$ GeV, while requiring that their asymptotic fits smoothly join the the $\sigma_{\bar p p}$ and $\sigma_{pp}$ total cross sections at $\sqrt s=$4.0 GeV--again {\em both} in magnitude and slope. Our results strongly favor a high energy $\ln^2s$ fit, basically excluding a $\ln s$ fit. Finally, we make a screened Glauber fit for the p-air cross section, using as input our precisely-determined $pp$ cross sections at cosmic ray energies.Comment: 15 pages, 6 figures, 2 table,Paper delivered at c2cr2005 Conference, Prague, September 7-13, 2005. Fig. 2 was missing from V1. V3 fixes all figure

Predicting Proton-Air Cross Sections at sqrt s ~30 TeV, using Accelerator and Cosmic Ray Data

We use the high energy predictions of a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near \sqrt s \approx 30 TeV. The parameterization of the proton-proton cross section incorporates analyticity and unitarity, and demands that the asymptotic proton is a black disk of soft partons. By comparing with the p-air cosmic ray measurements, our analysis results in a constraint on the inclusive particle production cross section.Comment: 9 pages, Revtex, uses epsfig.sty, 5 postscript figures. Minor text revisions. Systematic errors in k included, procedure for extracting k clarified. Previously undefined symbols now define

Adaptive Ising Model and Bacterial Chemotactic Receptor Network

We present a so-called adaptive Ising model (AIM) to provide a unifying explanation for sensitivity and perfect adaptation in bacterial chemotactic signalling, based on coupling among receptor dimers. In an AIM, an external field, representing ligand binding, is randomly applied to a fraction of spins, representing the states of the receptor dimers, and there is a delayed negative feedback from the spin value on the local field. This model is solved in an adiabatic approach. If the feedback is slow and weak enough, as indeed in chemotactic signalling, the system evolves through quasi-equilibrium states and the ``magnetization'', representing the signal, always attenuates towards zero and is always sensitive to a subsequent stimulus.Comment: revtex, final version to appear in Europhysics Letter

The utilisation of health research in policy-making: Concepts, examples, and methods of assessment

Chapter 1: Introduction and Background • The importance of utilising health research in policy-making, and therefore the need to understand the mechanisms involved, is increasingly recognised. Recent reports calling for more resources to improve health in developing countries, and global pressures for accountability, draw greater attention to research-informed policy-making. • For at least twenty years there has been recognition of the multiple meanings or models of research utilisation in policy-making. It has similarly been long recognised that a range of factors is involved in the interactions between health research and policy-makers. • The emerging focus on Health Research Systems (HRS) has identified additional mechanisms through which greater utilisation of research could be achieved. Assessment of the role of health research in policy-making is best undertaken as part of a wider study that also includes the utilisation of health research by industry, medical practitioners, and the public. Chapter 2: The Nature of Policy-Making, Types of Research and Utilisation Models • Policy-making broadly interpreted includes national health policies made by government ministers and officials, policies made by local health service managers, and clinical guidelines from professional bodies. In this report, however, the main focus is on public policy-making rather than that conducted by professional bodies. The utilisation of health research in policy-making should eventually lead to desired outcomes, including health gains. Research can make a contribution in at least three phases of the policy-making process: agenda setting; policy formulation; and implementation. Descriptions of these processes, however, can over-estimate the degree of rationality in policy-making. Therefore, the analysis is informed by a review of the full range of policy-making models. These include rational and incrementalist models. • Various categories of research are likely to be used differently in health policy-making. Applied research might be more readily useable by a policy system than basic research, but health policy-makers tend to relate more willingly to natural sciences than social sciences. When research is based on the priorities of potential users, and/or is research of proven quality, this increases the possibility that it will be translated into policies. There also appears to be a greater chance of research being used in clinical policies about delivering care to patients, than in national policies on the structures of the health service. • Models of research utilisation in policy-making start with a link to rational or instrumental views of policy-making, and include descriptions of how commissioned research can help to find solutions to problems. Other models relate to an incrementalist view in which policy-making involves a series of small steps over a long period; research findings might gradually cause a shift in perceptions about an issue in a process of ‘enlightenment’. Interactive models of research utilisation stress the way in which policy-makers and researchers might develop links over a long period. Research can also be used symbolically to support decisions already taken. Chapter 3: Examples from Previous Studies • A study of health policy-making in two southern African countries illustrates how policy-making processes can be analysed. It addresses agenda setting, policy formulation and implementation. The methods used included documentary analysis and key informant interviews. • Many previous studies of research utilisation can provide lessons for future assessments. Two broad approaches can be identified. Some studies start with pieces, or programmes, of research and examine their impact. Others consider policy on a particular topic and assess the role of research in the policy-making. There are advantages and drawbacks in each approach, and overlaps between them. • To facilitate comparison, studies of research utilisation are best organised around a conceptual framework. Despite that, the influence of contextual factors in different settings makes it difficult to generalise. • The two methods used most frequently, and usually together, come from the qualitative tradition: documentary analysis and in-depth interviews. Questionnaires, bibliometric analysis, insider knowledge and historical approaches have all been applied. A few recent studies have attempted to score or scale the level of utilisation. • The examples suggest there is a greater level of utilisation and final outcomes in terms of health, health equity, and social and economic gain than is often assumed, whilst still showing much underutilisation. There is considerable variation in the degree of utilisation, both within and between studies. Chapter 4: Key Issues in the Analysis of Research Utilisation in Policy-Making • Increasing attention is focusing on the concept of interfaces between researchers and the users of research. This incorporates the idea that there are likely to be different values and interests between the two communities. • In relation to utilisation, the prioritisation debate revolves around two key aspects: whether priorities are being set that will produce research that policy-makers and others will want to use, and whether priorities are being set that will engage the interests and commitment of the research community. • Interactions across the interface between policy-makers and researchers are important in transferring research to policy-makers. This fits especially well with the interactive model of utilisation. Actions by individual researchers can be useful in generating interaction, but it is desirable to consider the role of the HRS in encouraging or facilitating interactions, networks and mechanisms at a system-wide level. The HRS could provide funding and organisational support for various items including: long-term research centres; research brokerage/translator mechanisms; the creation of official committees of policy-makers and researchers; and mechanisms for review and synthesis of research findings. • There is increased recognition of the significance of policy-makers in their role as the receptors of research. In relation to the perspective of policy-makers there is a spectrum of key questions. These range from whether relevant research is available and effectively being brought to their attention, to whether they are able to absorb it and willing to use it. The HRS has a responsibility, especially in the early parts of the spectrum, but the wider health system also has a responsibility to create appropriate institutional mechanisms and ensure there are staff willing and able to incorporate relevant research. • More attention should be given to the role of incentives, both for researchers to produce utilisable research, and for policy-makers, at the system or individual level, to use it. The assessment of utilisation becomes a key issue if rewards are to focus on relevance as well as research excellence. • An appropriate model for assessing research utilisation in policy-making combines analysis of two issues: the role of receptors and the importance of actions at the interfaces. An emphasis on the role of the receptor is necessary because ultimately it is up to the policy-maker to make the decisions. Any assessment of the success of the HRS in relation to utilisation must accept that the wider political context is beyond the control of the HRS, but consider the activities of the HRS, within its given context, to enhance the utilisation of research by increasing the permeability of the interfaces. Chapter 5: Assessment of Research Utilisation in Health Policy-Making • The reasons for assessing the utilisation of research in policy-making include: advocacy, accountability, and increased understanding. For the World Health Organization there could be a role in conducting such assessments with the aim of providing evidence of the effective use of research resources. This could support advocacy for greater resources to be made available for health research. It is important that the purposes of any assessment are taken into account in planning the methods to be used. • Previous studies demonstrated the difficulties of making generalisations about specific factors associated with high levels of utilisation. To address this in any cross-national WHO initiative involving a series of studies in a range of countries, it would be desirable to structure all the studies around a conceptual framework (such as the interfaces and receptor framework considered here) and base the studies in each country on common themes. These could include policies for the adoption of multi-drug therapy for treating leprosy, and for the equitable access to health services. • Analysis of documents and semi-structured interviews would be appropriate methods in each study assessing the role of research in policy-making on a specific policy theme. Questionnaires could also have a role. These approaches would provide triangulation of methods and data-sources and should also provide material to help identify the relative importance, in relation to the level of utilisation recorded, of the HRS mechanisms described in the previous analysis. The types and sources of research used, and reasons for their use, should also be recorded and attempts made to correlate them with the previous priority setting approaches. It is expected that each study will produce its own narrative or story of what caused utilisation in the particular context, but the data gathered could also be applied to descriptive scales of the level research utilisation. The four scales could cover the consistency of policy with research findings, and the degree of influence of research on agenda setting, policy formulation, and implementation. • The findings from the assessments in each participating country should be collated. For each policy theme or topic the analysis would compare two sets of data: the scales for level of research utilisation in each country, and the contextualised lists of the HRS activities and other mechanisms and networks thought to be important. Although the account here has focused on research impact on policy-making, the evaluations would be stronger as part of a wider analysis covering research utilisation and interactions with practitioners, industry and the public. • Given appropriate and targeted topic and country selection, this approach is likely to meet the purpose of using structured methods to provide examples of effective research utilisation. The approach should contribute towards enhanced understanding of the issues and could provide the basis of an assessment tool which, if used widely in countries, could lead to greater utilisation of health research.Research Policy and Co-operation (RPC) Department of the World Health Organization, Geneva; UK Department of Health’s Policy Research Programme; Alliance for Health Policy and Systems Research from the governments of Norway and Sweden; World Bank and International Development Research Council of Canad

New physics, the cosmic ray spectrum knee, and pppp cross section measurements

We explore the possibility that a new physics interaction can provide an explanation for the knee just above $10^6$ GeV in the cosmic ray spectrum. We model the new physics modifications to the total proton-proton cross section with an incoherent term that allows for missing energy above the scale of new physics. We add the constraint that the new physics must also be consistent with published $pp$ cross section measurements, using cosmic ray observations, an order of magnitude and more above the knee. We find that the rise in cross section required at energies above the knee is radical. The increase in cross section suggests that it may be more appropriate to treat the scattering process in the black disc limit at such high energies. In this case there may be no clean separation between the standard model and new physics contributions to the total cross section. We model the missing energy in this limit and find a good fit to the Tibet III cosmic ray flux data. We comment on testing the new physics proposal for the cosmic ray knee at the Large Hadron Collider.Comment: 17 pages, 4 figure

A new numerical method for obtaining gluon distribution functions G(x,Q2)=xg(x,Q2)G(x,Q^2)=xg(x,Q^2), from the proton structure function F2γp(x,Q2)F_2^{\gamma p}(x,Q^2)

An exact expression for the leading-order (LO) gluon distribution function $G(x,Q^2)=xg(x,Q^2)$ from the DGLAP evolution equation for the proton structure function $F_2^{\gamma p}(x,Q^2)$ for deep inelastic $\gamma^* p$ scattering has recently been obtained [M. M. Block, L. Durand and D. W. McKay, Phys. Rev. D{\bf 79}, 014031, (2009)] for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate $G(x,Q^2)$, and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire $x$ and $Q^2$ spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of $F_2^{\gamma p}(x,Q^2)$.Comment: 9 pages, 2 figure

Analytic models and forward scattering from accelerator to cosmic-ray energies

Analytic models for hadron-hadron scattering are characterized by analytical parametrizations for the forward amplitudes and the use of dispersion relation techniques to study the total cross section $\sigma_{tot}$ and the $\rho$ parameter. In this paper we investigate four aspects related to the application of the model to $pp$ and $\bar{p}p$ scattering, from accelerator to cosmic-ray energies: 1) the effect of different estimations for $\sigma_{tot}$ from cosmic-ray experiments; 2) the differences between individual and global (simultaneous) fits to $\sigma_{tot}$ and $\rho$; 3) the role of the subtraction constant in the dispersion relations; 4) the effect of distinct asymptotic inputs from different analytic models. This is done by using as a framework the single Pomeron and the maximal Odderon parametrizations for the total cross section. Our main conclusions are the following: 1) Despite the small influence from different cosmic-ray estimations, the results allow us to extract an upper bound for the soft pomeron intercept: $1 + \epsilon = 1.094$; 2) although global fits present good statistical results, in general, this procedure constrains the rise of $\sigma_{tot}$; 3) the subtraction constant as a free parameter affects the fit results at both low and high energies; 4) independently of the cosmic-ray information used and the subtraction constant, global fits with the odderon parametrization predict that, above $\sqrt s \approx 70$ GeV, $\rho_{pp}(s)$ becomes greater than $\rho_{\bar{p}p}(s)$, and this result is in complete agreement with all the data presently available. In particular, we infer $\rho_{pp} = 0.134 \pm 0.005$ at $\sqrt s = 200$ GeV and $0.151 \pm 0.007$ at 500 GeV (BNL RHIC energies).Comment: 16 pages, 7 figures, aps-revtex, wording changes, corrected typos, to appear in Physical Review

Survival Probability of Large Rapidity Gaps in pbar p, pp, gamma p and gamma gamma Collisions

Using an eikonal analysis, we simultaneously fit a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, together with cosmic ray data (using Glauber theory), to predict proton-air and proton-proton cross sections at energies near \sqrt s \approx 30 TeV. The p-air cosmic ray measurements greatly reduce the errors in the high energy proton-proton and proton-air cross section predictions--in turn, greatly reducing the errors in the fit parameters. From this analysis, we can then compute the survival probability of rapidity gaps in high energy pbar p and pp collisions, with high accuracy in a quasi model-free environment. Using an additive quark model and vector meson dominance, we note that that the survival probabilities are identical, at the same energy, for gamma p and gamma gamma collisions, as well as for nucleon-nucleon collisions. Significantly, our analysis finds large values for gap survival probabilities, \approx 30% at \sqrt s = 200 GeV, \approx 21% at \sqrt s = 1.8 TeV and \approx %%13% at \sqrt s = 14 TeV.Comment: 9 pages, Latex2e, uses epsfig.sty, 4 postscript figure