arXiv subjects

M. J. Menon

Publications and source records attributed to M. J. Menon.

At least 19 recordsLinked to original sources

arXiv2019

Forward elastic scattering: Dynamical gluon mass and semihard interactions

The role of low-$x$ parton dynamics in dictating the high-energy behavior of forward scattering observables at LHC energies is investigated using a QCD-based model with even-under-crossing amplitude dominance at high-energies. We explore the effects of different sets of pre- and post-LHC fine-tuned parton distributions on the forward quantities $σ_{tot}$ and $ρ$, from $pp$ and $\bar{p}p$ scattering in the interval 10 GeV - 13 TeV. We also investigate the role of the leading soft contribution, the low-energy cuttoff, and the energy dependence of the semihard form factor on these observables. We show that in all cases investigated the highly restrictive data on $ρ$ parameter at $\sqrt{s}=13$ TeV indicate that a crossing-odd component may play a crucial role in forward elastic scattering at the highest energies. In the Regge language an odd-under-crossing object is called Odderon.

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arXiv2019

Proton-proton forward scattering at the LHC

Recently the TOTEM experiment at the LHC has released measurements at $\sqrt{s} = 13$ TeV of the proton-proton total cross section, $σ_{tot}$, and the ratio of the real to imaginary parts of the forward elastic amplitude, $ρ$. Since then an intense debate on the $C$-parity asymptotic nature of the scattering amplitude was initiated. We examine the proton-proton and the antiproton-proton forward data above 10 GeV in the context of an eikonal QCD-based model, where nonperturbative effects are readily included via a QCD effective charge. We show that, despite an overall satisfactory description of the forward data is obtained by a model in which the scattering amplitude is dominated by only crossing-even elastic terms, there is evidence that the introduction of a crossing-odd term may improve the agreement with the measurements of $ρ$ at $\sqrt{s} = 13$ TeV. In the Regge language the dominant even(odd)-under-crossing object is the so called Pomeron (Odderon).

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arXiv2018

Forward Elastic Scattering and Pomeron Models

Recent data from LHC13 by the TOTEM Collaboration have indicated an unexpected decrease in the value of the $ρ$ parameter and a $σ_{tot}$ value in agreement with the trend of previous measurements at 7 and 8 TeV. These data at 13 TeV are not simultaneously described by the predictions from Pomeron models selected by the COMPETE Collaboration, but show agreement with the maximal Odderon dominance, as recently demonstrated by Martynov and Nicolescu. Here we present a detailed analysis on the applicability of Pomeron dominance by means of a general class of forward scattering amplitude, consisting of even-under-crossing leading contributions associated with single, double and triple poles in the complex angular momentum plane. We carry out fits to $pp$ and $\bar{p}p$ data in the interval 5 GeV - 13 TeV. The data set comprises all the accelerator data below 7 TeV and we consider two independent ensembles by adding either only the TOTEM data or TOTEM and ATLAS data at the LHC energy region. In the data reductions to each ensemble the uncertainty regions are evaluated with both one and two standard deviation ($\sim$ 68 \% and $\sim$ 95 \% CL, respectively). Besides the general analytic model, we investigate four particular cases of interest, three of them typical of outstanding models in the literature. We conclude that, within the experimental and theoretical uncertainties and both ensembles, the general model and three particular cases are not able to describe the $σ_{tot}$ and $ρ$ data at 13 TeV simultaneously. However, if the discrepancies between the TOTEM and ATLAS data are not resolved, one Pomeron model, associated with double and triple poles and with only 7 free parameters, seems not to be excluded by the complete set of experimental information presently available.

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arXiv2018

Soft Pomerons and the Forward LHC Data

Recent data from LHC13 by the TOTEM Collaboration on $σ_{tot}$ and $ρ$ have indicated disagreement with all the Pomeron model predictions by the COMPETE Collaboration (2002). On the other hand, as recently demonstrated by Martynov and Nicolescu (MN), the new $σ_{tot}$ datum and the unexpected decrease in the $ρ$ value are well described by the maximal Odderon dominance at the highest energies. Here, we discuss the applicability of Pomeron dominance through fits to the \textit{most complete set} of forward data from $pp$ and $\bar{p}p$ scattering. We consider an analytic parametrization for $σ_{tot}(s)$ consisting of non-degenerated Regge trajectories for even and odd amplitudes (as in the MN analysis) and two Pomeron components associated with double and triple poles in the complex angular momentum plane. The $ρ$ parameter is analytically determined by means of dispersion relations. We carry out fits to $pp$ and $\bar{p}p$ data on $σ_{tot}$ and $ρ$ in the interval 5 GeV - 13 TeV (as in the MN analysis). Two novel aspects of our analysis are: (1) the dataset comprises all the accelerator data below 7 TeV and we consider \textit{three independent ensembles} by adding: either only the TOTEM data (as in the MN analysis), or only the ATLAS data, or both sets; (2) in the data reductions to each ensemble, uncertainty regions are evaluated through error propagation from the fit parameters, with 90 \% CL. We argument that, within the uncertainties, this analytic model corresponding to soft Pomeron dominance, does not seem to be excluded by the \textit{complete} set of experimental data presently available.

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arXiv2018

Leading Pomeron Contributions and the TOTEM Data at 13 TeV

The recent data by the TOTEM Collaboration on $σ_{tot}$ and $ρ$ at 13 TeV, have shown agreement with a leading Odderon contribution at the highest energies, as demonstrated in the very recent analysis by Martynov and Nicolescu (MN). In order to investigate the same dataset by means of Pomeron dominance, we introduce a general class of forward scattering amplitude, with leading contributions even under crossing, associated with simple, double and triple poles in the complex angular momentum plane. For the lower energy region, we consider the usual non-degenerated Regge trajectories, with even and odd symmetry. The analytic connection between $σ_{tot}$ and $ρ$ is obtained by means of dispersion relations and we carry out fits to $pp$ and $\bar{p}p$ data in the interval $\sqrt{s}=5$ GeV - 13 TeV; following MN we consider only the TOTEM data at the LHC energy region. From the fits, we conclude that the general analytic model, as well as some particular cases representing standard parameterizations, are not able to describe satisfactorily the $σ_{tot}$ and $ρ$ data at 13 TeV. Further analyses in course and some perspectives are outlined.

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arXiv2017

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $σ_{tot}$ and the $ρ$ parameter. The standard picture indicates for $σ_{tot}$ a leading log-squared dependence at the highest c.m. energies, in accordance with the Froissart-Lukaszuk-Martin bound. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (L$γ$), with $γ$ as a real free fit parameter. In this case, analytic connections with $ρ$ can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmén-Lindelöff theorems). In this work we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the L$γ$ and L2 leading terms. We also develop new Regge-Gribov fits with updated dataset on $σ_{tot}$ and $ρ$ from $pp$ and $\bar{p}p$ scattering, in the region 5 GeV-8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly 8 TeV is considered in the data reductions. Our main conclusions are: (1) all fit results present agreement with the experimental data analyzed and the goodness-of-fit is slightly better in case of the DDR approach; (2) by considering only the TOTEM data at the LHC region, the fits with L$γ$ indicate $γ\sim 2.0\pm 0.2$ (AU) and $γ\sim 2.3\pm 0.1$ (DDR); (3) by including the ATLAS data the fits provide $γ\sim 1.9\pm 0.1$ (AU) and $γ\sim 2.2\pm 0.2$ (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A review on the analytic results for $σ_{tot}$ and $ρ$ from the Regge-Gribov, DDR and AU approaches is presented.

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arXiv2017

Analytic components for the hadronic total cross-section: Fractional calculus and Mellin transform

In high-energy hadron-hadron collisions, the dependence of the total cross-section ($σ_{tot}$) with the energy still constitutes an open problem for QCD. Phenomenological analyses usually relies on analytic parameterizations provided by the Regge-Gribov formalism and fits to the experimental data. In this framework, the singularities of the scattering amplitude in the complex angular momentum plane determine the asymptotic behavior of $σ_{tot}$ in terms of the energy. Usual applications connect simple and triple pole singularities with asymptotic power and logarithmic-squared functions of the energy, respectively. More restrict applications have considered as a leading component for $σ_{tot}$ an empirical function consisting of a logarithmic raised to a real exponent, which is treated as a free fit parameter. With this function, data reductions lead to good descriptions of the experimental data and real (not integer) values of the exponent. In this paper, making use of two independent formalisms (fractional calculus and Mellin transform), we first show that the singularity associated with this empirical function is a branch point and then we explore the mathematical consequences of the result and possible physical interpretations. After reviewing the determination of the singularities from asymptotic forms of interest through the Mellin transform, we demonstrate that the same analytic results can be obtained by means of the Caputo fractional derivative, leading, therefore, to fractional calculus interpretations. Besides correlating Mellin transform, non-local fractional derivatives and exploring the generalization from integer to real exponents and derivative orders, this fractional calculus result may provide insights for physical interpretations on the asymptotic rise of $σ_{tot}$.

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arXiv2017

Bounds on the rise of total cross section from LHC7 and LHC8 data

Recent measurements of the proton-proton total cross section $σ_{tot}$ at 7 and 8 TeV by the TOTEM and ATLAS Collaborations are characterized by some discrepant values: the TOTEM data suggest a rise of the cross section with the energy faster than the ATLAS data. Attempting to quantify these different behaviors, we develop new analytical fits to $σ_{tot}$ and $ρ$ data from $pp$ and $\bar{p}p$ scattering in the energy region 5 GeV - 8 TeV. The dataset comprises all the accelerator data below 7 TeV and we consider three ensembles by adding: either only the TOTEM data (T), or only the ATLAS data (A), or both sets (T+A). For the purposes, we use our previous RRPL$γ$ parametrization for $σ_{tot}(s)$, consisting of two Reggeons (RR), one critical Pomeron (P) and a leading log-raised-to-gamma (L$γ$) contribution (with $γ$ as a free fit parameter), analytically connected to $ρ(s)$ through singly-subtracted derivative dispersion relations and energy scale fixed at the physical threshold. The data reductions with ensembles T and A present good agreement with the experimental data analyzed and cannot be distinguished on statistical grounds. The quality of the fit is not as good with ensemble T+A. The fit results provide $γ\sim 2.3 \pm 0.1$ (T), $2.0 \pm 0.2$ (A), $2.1 \pm 0.2$ (T+A), with $χ^2/\mathrm{DOF} \sim 1.07$ (T), $1.09$ (A), $1.14$ (T+A), suggesting extrema bounds for $γ$ given by 1.8 and 2.4. Fits with $γ= 2$ (fixed) are also developed and discussed.

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arXiv2016

Exploring central opacity and asymptotic scenarios in elastic hadron scattering

In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio $X$ between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. energy interval 5 GeV - 8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for $X$, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio $\bar{X}$ = 0.30 $\pm$ 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for $X$ and physical aspects related to a change of curvature in this quantity at 80 - 100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.

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arXiv2015

Updating an empirical analysis on the proton's central opacity and asymptotia

We present an updated empirical analysis on the ratio of the elastic (integrated) to the total cross section in the c.m. energy interval from 5 GeV to 8 TeV. As in a previous work, we use a suitable analytical parametrization for that ratio (depending on only four free fit parameters) and investigate three asymptotic scenarios: either the black disk limit or scenarios above or below that limit. The dataset includes now the datum at 7 TeV, recently reported by the ATLAS Collaboration. Our analysis favors, once more, a scenario below the black disk, providing an asymptotic ratio consistent with the rational value 1/3, namely a gray disk limit. Upper bounds for the ratio of the diffractive (dissociative) to the inelastic cross section are also presented.

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arXiv2014

Asymptotic Scenarios for the Proton's Central Opacity: An Empirical Study

We present a model-independent analysis of the experimental data on the ratio $X$ between the elastic and total cross-sections from $pp$ and $\bar{p}p$ scattering in the c.m. energy interval 5 GeV - 8 TeV. Using a novel empirical parametrization for that ratio as a function of the energy and based on theoretical and empirical arguments, we investigate three distinct asymptotic scenarios: either the black-disk (BD) limit or scenarios above and below that limit. Our analysis favors a scenario below the BD, with asymptotic ratio $X = 0.36 \pm 0.08$.

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arXiv2013

A study on analytic parametrizations for proton-proton cross-sections and asymptotia

A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp and \bar{p}p scattering in the c.m energy interval 5 GeV-8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P) law, or a log-squared (L2) law or a log-raised-to-gamma (Lgamma) law, where the exponent gamma is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; the fit results with the P law, the L2 law (free scale) and the Lgamma law (fixed scale and exponent gamma above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV; once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem.

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arXiv2013

An updated analysis on the rise of the hadronic total cross-section at the LHC energy region

A forward amplitude analysis on $pp$ and $\bar{p}p$ elastic scattering above 5 GeV is presented. The dataset includes the recent high-precision TOTEM measurements of the $pp$ total and elastic (integrated) cross-sections at 7 TeV and 8 TeV. Following previous works, the leading high-energy contribution for the total cross-section ($σ_{tot}$) is parametrized as $\ln^γ(s/s_h)$, where $γ$ and $s_h$ are free \textit{real} fit parameters. Singly-subtracted derivative dispersion relations are used to connect $σ_{tot}$ and the rho parameter ($ρ$) in an analytical way. Different fit procedures are considered, including individual fits to $σ_{tot}$ data, global fits to $σ_{tot}$ and $ρ$ data, constrained and unconstrained data reductions. The results favor a rise of the $σ_{tot}$ faster than the log-squared bound by Froissart and Martin at the LHC energy region. The parametrization for $σ_{tot}$ is extended to fit the elastic cross-section ($σ_{el}$) data with satisfactory results. The analysis indicates an asymptotic ratio $σ_{el}/σ_{tot}$ consistent with 1/3 (as already obtained in a previous work). A critical discussion on the correlation, practical role and physical implications of the parameters $γ$ and $s_h$ is presented. The discussion confronts the 2002 prediction of $σ_{tot}$ by the COMPETE Collaboration and the recent result by the Particle Data Group (2012 edition of the Review of Particle Physics). Some conjectures on possible implications of a fast rise of the proton-proton total cross-section at the highest energies are also presented.

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arXiv2013

On the rise of proton-proton cross-sections at high energies

The rise of the total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, reproducing well the experimental information in the energy region 5 GeV - 7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elastic-slope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the log-squared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively, a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Ya. I. Azimov on the rise of the total cross section.

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arXiv2012

Reply to "Commentary on "Total Hadronic Cross Section Data and the Froissart-Martin Bound", by Fagundes, Menon and Silva"

A reply to the above mentioned commentary by M.M. Block and F. Halzen on our quoted work is presented. We answer to each point raised by these authors and argument that our data reductions, strategies and methodology are adequate to the nonlinear-fit-problem in focus. In order to exemplify some arguments, additional information from our subsequent analysis is referred to. A brief commentary on the recent results by Block and Halzen is also presented. We understand that this reply gives support to the results and conclusions presented in our quoted work.

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arXiv2012

Preliminary Results on the Empirical Applicability of the Tsallis Distribution in Elastic Hadron Scattering

We show that the proton-proton elastic differential cross section data at dip position and beyond can be quite well described by a parametrization based on the Tsallis distribution, with only five free fit parameters. Extrapolation of the results obtained at 7 TeV to large momentum transfer, suggests that hadrons may not behave as a black-disk at the asymptotic energy region.

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arXiv2012

Total Hadronic Cross Section Data and the Froissart-Martin Bound

The energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the TOTEM Collaboration at 7 TeV and the Froissart-Martin bound. On the basis of a class of analytical parametrization with the exponent $γ$ in the leading logarithm contribution as a free parameter, different variants of fits to $pp$ and $\bar{p}p$ total cross section data above 5 GeV are developed. Two ensembles are considered, the first comprising data up to 1.8 TeV, the second also including the data collected at 7 TeV. We shown that in all fit variants applied to the first ensemble the exponent is statistically consistent with $γ$ = 2. Applied to the second ensemble, however, the same variants yield $γ$'s above 2, a result already obtained in two other analysis, by U. Amaldi \textit{et al}. and by the UA4/2 Collaboration. As recently discussed by Ya. I. Azimov, this faster-than-squared-logarithm rise does not necessarily violate unitarity. Our results suggest that the energy dependence of the hadronic total cross section at high energies still constitute an open problem.

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arXiv2012

Hadronic Cross Sections, Elastic Slope and Physical Bounds

An almost model-independent parametrization for the ratio of the total hadronic cross section to elastic slope is discussed. Its applicability in studies of asymptotia and analyses of extensive air shower in cosmic-ray physics is also outlined.

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