arXiv subjects

M. M. Block

Publications and source records attributed to M. M. Block.

At least 19 recordsLinked to original sources

arXiv2014

Cross Section to Multiplicity Ratios at Very High Energy

Recent data from the LHC makes it possible to examine an old speculation that at very high energy the total multiplicity and the cross section in elementary particle interactions vary in parallel with energy. Using fits incorporating the new data, it appears that the ratios of the total, elastic, and inelastic cross sections to the average multiplicity N can in fact approach constants at very high energy. The approach to the limit is however quite slow for the total and inelastic cross sections and is not yet reached at LHC energies. The elastic ratio sigma^{el}/N at 7 TeV, however, is not far from its asymptotic value.

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arXiv2011

Ultra-high Energy Predictions of Proton-Air Cross Sections from Accelerator Data: an Update

At $\sqrt s = 57\pm 7$ TeV, the Pierre Auger Observatory (PAO) collaboration has recently measured the proton-air inelastic production cross section $σ_{\rm p-air}$. Assuming a helium contamination of 25%, they subtracted 30 mb from their measured value, resulting in a p-air inelastic production cross section, $σ_{\rm p-air}=475 \pm 22\ ({\rm stat.})\pm^{20}_{15} \ ({\rm syst.})$ mb, exclusive of helium contamination. Using this result in a Glauber calculation to obtain the $pp$ inelastic cross section, they found the inelastic $pp$ cross section $σ_{\rm inel}= 90\pm 7\ ({\rm stat.}) \pm^9_{11} ({\rm syst.}) \pm 1.5 {\rm \ (Glaub.})$ mb. Parameterization of the $\bar pp$ and $pp$ cross sections incorporating analyticity constraints and unitarity has allowed us to make accurate extrapolations to ultra-high energies, and using Glauber calculations, accurately predict cosmic ray results for $\spai$. In this update for 57 TeV, we predict i) a $pp$ total cross section, $σ_{\rm tot}=133.4\pm 1.6$ mb, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar pp$ and $pp$ scattering amplitudes and ii) a p-air inelastic production cross section, $σ_{\rm p-air}=483\pm 3 $ mb, by using $σ_{\rm tot}$ together with Glauber theory, allowing us to determine independently that the helium contamination was 19%, in reasonable agreement with their estimate of 25%. Our predictions agree with all available cosmic ray extensive air shower measurements, both in magnitude and in energy dependence. By using our value for the $pp$ total cross section at 57 TeV, Block and Halzen \cite{blackdisk} have predicted that the $pp$ inelastic cross section is $σ_{\rm inel}= 92.9\pm 1.6$ mb, in agreement with the measured POA value.

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arXiv2007

Ultra-high Energy Predictions of proton-air Cross Sections from Accelerator Data

We predict $σ_{p{-}\rm air}^{\rm prod}$, the proton--air inelastic production cross section, at $pp$ center-of-mass energies $2\le\sqrt s \le 100000$ TeV, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar pp$ and $pp$ scattering amplitudes, together with Glauber theory. The parameterization of the $\bar pp$ and $pp$ cross sections incorporates analyticity constraints and unitarity, allowing accurate extrapolations to ultra-high energies. Our predictions are in excellent agreement with cosmic ray extensive air shower measurements, both in magnitude and in energy dependence

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arXiv2007

Analytic Expression for the Joint x and Q^2 Dependences of the Structure Functions of Deep Inelastic Scattering

We obtain a good analytic fit to the joint Bjorken-x and Q^2 dependences of ZEUS data on the deep inelastic structure function F_2(x, Q^2). At fixed virtuality Q^2, as we showed previously, our expression is an expansion in powers of log (1/x) that satisfies the Froissart bound. Here we show that for each x, the Q^2 dependence of the data is well described by an expansion in powers of log Q^2. The resulting analytic expression allows us to predict the logarithmic derivatives {({\partial}^n F_2^p/{(\partial\ln Q^2})^n)}_x for n = 1,2 and to compare the results successfully with other data. We extrapolate the proton structure function F_2^p(x,Q^2) to the very large Q^2 and the very small x regions that are inaccessible to present day experiments and contrast our expectations with those of conventional global fits of parton distribution functions.

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arXiv2006

Small x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep Inelastic Scattering Cross Section

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln^2 s fit, A + beta ln^2 (s/s_0), where s= [Q^2/x] (1-x) + m^2, and Q^2 is the virtuality of the exchanged photon. Over a wide range in Q^2 (0.11 < Q^2 < 1200 GeV^2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x -- well beyond the range accessible experimentally. As Q^2 --> infinity, the structure function F_2^p(x, Q^2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.

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arXiv2006

Implications from analyticity constraints used in a Landshoff-Donnachie fit

Landshoff and Donnachie[hep-ph/0509240, (2005)] parametrize the energy behavior of pp and p\bar p scattering cross sections with five parameters, using: σ^+=56.08 s^{-0.4525}+21.70s^{0.0808} for pp, σ^-=98.39 s^{-0.4525}+21.70s^{0.0808} for p\bar p. Using the 4 analyticity constraints of Block and Halzen[M. M. Block and F. Halzen, Phys. Rev. D {\bf 72}, 036006 (2005)], we simultaneously fit the Landshoff-Donnachie form to the same ``sieved'' set of pp and p\bar p cross section and ρdata that Block and Halzen used for a very good fit to a ln^2 s parametrization. We show that the satisfaction of the analyticity constraints will require complicated modifications of the Landshoff-Donnachie parametrization for lower energies, greatly altering its inherent appeal of simplicity and universality.

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arXiv2006

Analyticity as a Robust Constraint on the LHC Cross Section

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as $\ln^2s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a Finite Energy Sum Rule.

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arXiv2006

New analyticity constraints on the high energy behavior of hadron-hadron cross sections

We here comment on a series of recent papers by Igi and Ishida[K. Igi and M. Ishida, Phys. Lett B 622, 286 (2005)] and Block and Halzen[M. M. Block and F. Halzen, Phys. Rev D 72, 036006 (2005)] that fit high energy $pp$ and $\bar pp$ cross section and $ρ$-value data, where $ρ$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. These authors used Finite Energy Sum Rules and analyticity consistency conditions, respectively, to constrain the asymptotic behavior of hadron cross sections by anchoring their high energy asymptotic amplitudes--even under crossing--to low energy experimental data. Using analyticity, we here show that i) the two apparently very different approaches are in fact equivalent, ii) that these analyticity constraints can be extended to give new constraints, and iii) that these constraints can be extended to crossing odd amplitudes. We also apply these extensions to photoproduction. A new interpretation of duality is given.

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arXiv2005

New evidence for the saturation of the Froissart bound

Fits to high energy data alone cannot cleanly discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of total hadronic cross sections. We demonstrate that this is no longer true when we require that these amplitudes also describe, on average, low energy data dominated by resonances.

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arXiv2004

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_{γp} = c_0 + c_1 ln(nu/m) + beta_P'/sqrt(ν/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.

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arXiv2004

A global test of factorization for nucleon-nucleon, gamma p and gamma gamma scattering

The purpose of this note is to show that the cross section factorization relation $σ_{nn}(s)/σ_{γp}(s) = σ_{γp}(s)/ σ_{γγ}(s)$ is satisfied experimentally in the energy domain $8\le\sqrt s\le 2000$ GeV, where the $σ$'s are total cross sections and $nn$ denotes the even portion of the $pp$ and $\pbar p$ total cross section. A convenient phenomenological paramaterization for a global simultaneous fit to the $pp$, $\pbar p$, $γp$ and $γγ$ total cross section data together with the $ρ$-value data for $pp$ and $\pbar p$ is provided by using real analytic amplitudes. Within experimental errors, we show that factorization is satisfied when we unfold the published $γγ$ data which had averaged the cross sections obtained by using the two different PHOJET and PYTHIA Monte Carlo results. Our analysis clearly favors the PHOJET results and suggests that the additive quark model, together with vector meson dominance, allows one to compute $σ_{γp}(s)$ and $σ_{γγ}(s)$ from $σ_{nn}(s)$ with essentially no free parameters. The universal $ρ$-value predicted by our fit, {\em i.e.,} $ρ_{nn} = ρ_{γp} = ρ_{γγ}$, is compared to the $ρ$-value obtained by a QCD-inspired analysis of $\pbar p$ and $pp$ data, including the p-air cross sections from cosmic rays. The $ρ$-values obtained from the two techniques are essentially indistinguishable in the energy region $8\le\sqrt s\le 2000$ GeV, giving us increased confidence in our parameterization of the cross sections needed for the factorization relation.

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arXiv2003

Factorization Theorems for High Energy nn, gamma p and gamma gamma Scattering

The robustness of the factorization theorem for total cross sections, $σ_{nn}/σ_{γp}=σ_{γp}/σ_{γγ}$, originally proved by Block and Kaidalov\cite{bk} for $nn$ (the even portion of $pp$ and $\pbar p$ scattering), $γp$ and $γγ$ scattering, is demonstrated. Factorization theorems for the nuclear slope parameter $B$ and $ρ$, the ratio of the real to the imaginary portion of the forward scattering amplitude, are derived under very general conditions, using analyticity and the optical theorem.

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arXiv2002

Forward Elastic Scattering of Light on Light, γ+γ\toγ+γ

The forward elastic scattering of light on light, {\em i.e.,} the reaction $γ+γ\to γ+γ$ in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate $ρ_{γγ}$, the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total $γγ$ cross section data in the high energy region $5 GeV \le \sqrt s \le 130 $ GeV, assuming a cross section that rises asymptotically as $\ln^2 s$. We then compare $ρ_{γγ}$ to $ρ_{nn}$, the ratio of the even portions of the $pp$ and $\pbar p$ forward scattering amplitudes, as well as to $ρ_{γp}$, the $ρ$ value for Compton scattering. Within errors, we find that the three $ρ$-values in the c.m.s. energy region $5 GeV \le \sqrt s \le 130$ GeV are the same, as predicted by a factorization theorem of Block and Kadailov.

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arXiv2002

Forward Compton Scattering, using Real Analytic Amplitudes

We analyze forward Compton scattering, using real analytic amplitudes. By fitting the total γp scattering cross section data in the high energy region 5 GeV < \sqrt s < 20 GeV, using a cross section rising as \ln^2 s, we calculate ρ_{γp}, the ratio of the real to the imaginary portion of the the forward Compton scattering amplitude, and compare this to ρ_{nn}, the ratio of the even portions of the pp and p-bar p forward scattering amplitudes. We find that the two ρ-values are, within errors, the same in the c.m.s. energy region 5 GeV < \sqrt s < 200 GeV, as predicted by a factorization theorem of Block and Kadailov.

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arXiv2001

On Factorization, Quark Counting, and Vector Dominance

Using an eikonal structure for the scattering amplitude, Block and Kaidalov have derived factorization theorems for nucleon-nucleon, $γp$ and $γγ$ scattering at high energies, using only some very general assumptions. We present here an analysis giving experimental confirmation for factorization of cross sections, nuclear slope parameters B and $ρ$-values (ratio of real to imaginary portion of forward scattering amplitudes), showing that: i) the three factorization theorems hold, ii) the additive quark model holds to ~1%, and iii) vector dominance holds to better than ~4%.

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arXiv2001

Consequences of the Factorization Hypothesis in pbar p, pp, gamma p and gamma gamma Collisions

Using an eikonal analysis, we examine the validity of the factorization theorem for nucleon-nucleon, gamma p and gamma gamma collisions. As an example, using the additive quark model and meson vector dominance, we directly show that for all energies and values of the eikonal, that the factorization theorem sigma_{nn}/sigma_{gamma p} = sigma_{gamma p}/sigma_{gamma gamma} holds. We can also compute the survival probability of large rapidity gaps in high energy pbar p and pp collisions. We show that the survival probabilities are identical (at the same energy) for gamma p and gamma gamma collisions, as well as for nucleon-nucleon collisions. We further show that neither the factorization theorem nor the reaction-independence of the survival probabilities depends on the assumption of an additive quark model, but, more generally, depends on the opacity of the eikonal being independent of whether the reaction is n-n, gamma p or gamma gamma.

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arXiv2001

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.

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arXiv2000

Extending the Frontiers - Reconciling Accelerator and Cosmic Ray p-p Cross Sections

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 provide a strong constraint on the inclusive particle production cross section, as well as greatly reducing the errors on the fit parameters---in turn, greatly reducing the errors in the high energy proton-proton and proton-air cross section predictions.

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