Open Physics Journal




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ISSN: 1874-8430 ― Volume 5, 2019

Diffractive Cross Sections Implemented in PYTHIA8-MBR vs LHC Results§



Konstantin Goulianos*
The Rockefeller University, 1230 York Avenue, New York, NY 10065, USA

Abstract

We review the predictions of diffractive cross sections implemented in the PYTHIA8-MBR Monte Carlo simulation and compare them to recent LHC results.

PACS Number(s): 12.40.Nn, 12.39.St, 13.85.Lg, 13.85.Fb.

Keywords: Diffractive, inelalstic, soft, total.


Article Information


Identifiers and Pagination:

Year: 2014
Volume: 1
Issue: Suppl 1: M11
First Page: 72
Last Page: 74
Publisher Id: PHY-1-72
DOI: 10.2174/1874843001401010072

Article History:

Received Date: 25/11/2013
Revision Received Date: 24/01/2014
Acceptance Date: 25/1/2014
Electronic publication date: 31/12/2014
Collection year: 2014

© Konstantin Goulianos; Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.


* Address correspondence to this author at The Rockefeller University, 1230 York Avenue, New York, NY 10065, USA; Tel:+1.212.3278817; Fax: +1.212.327.7786; E-mail: dino@rockefeller.edu§ This paper is an essentially identical update of [3Goulianos K. Predictions of Diffractive, Elastic, Total, and Total-Inelastic pp Cross Sections vs LHC Measurements 2013 Marseilles France. -DIS2013 22-26 April.; Marseilles, France. Chicago: Proceedings of XXI International Workshop on Deep-Inelastic Scattering and Related Subject 2013.], which in itself is a more substantial update of [7Ciesielski R, Goulianos K. MBR Monte Carlo Simulation in PYTHIA8 Proc Sci 2013; 00: 301-5.].






1. INTRODUCTION

Measurements at the LHC have shown that there are sizable disagreements among Monte Carlo (MC) implementations of “soft” processes based on cross sections proposed by various physics models, and that it is not possible to reliably predict all such processes, or even all aspects of a given process, using a single model [1Goulianos K, Ed. Predictions of Diffractive Cross Sections in Proton-Proton Collisions In: 1st AMA National Conference on Child Abuse and Neglect; 1984 Mar 30-31; Chicago. Chicago: American Medical Association 1985; Goulianos K. Predictions of Diffractive Cross Sections in Proton-Proton Collisions Proceedings of Diffraction 2012 International Workshop on Diffraction in High Energy Physics 10-15 September. 2012 AIP Conf Proc 2013; 1523: 107-16.-3Goulianos K. Predictions of Diffractive, Elastic, Total, and Total-Inelastic pp Cross Sections vs LHC Measurements 2013 Marseilles France. -DIS2013 22-26 April.; Marseilles, France. Chicago: Proceedings of XXI International Workshop on Deep-Inelastic Scattering and Related Subject 2013.]. In the CDF studies of diffraction at the Tevatron, all processes are well modeled by the MBR (Minimum Bias Rockefeller) MC simulation, which is a stand-alone simulation based on a unitarized Regge-theory model, RENORM [4Goulianos K. Hadronic Diffraction Where do we Stand? Proceedings of Les Rencontres de Physique de la Vallee d'Aoste Results and Perspectives in Particle Physics [arXiv: hep-ph/0407035]. In: Frascati Physics Series, Special 34 Issue, edited by Mario Greco; February 27 - March 6; La Thuile, Italy. 2004.], employing inclusive nucleon parton distribution functions (PDF’s) and QCD color factors. The RENORM model was updated in a presentation at EDS-2009 [5Mario D, Ed. Goulianos K. Diffractive and Total pp Cross Sections at LHC In: Mario D, Ed. [arXiv: 10023527v2]. In: 13th International Conference on Elastic and Diffractive Scattering (Blois Workshop) Moving Forward into the LHC Era; June 29-July 3, 2009; CERN, Geneva, Switzerland. 2010.] to include a unique unitarization prescription for predicting the total  cross section at high energies, and that update has been included as an MBR option for simulating diffractive processes in PYTHIA8 since version PYTHIA8.165 [6(a) Sjöstrand T, Mrenna S, Skands P. PYTHIA 6. A brief introduction to PYTHIA 81. Physics and Manual J High Energ Phys 2006; 05: 026.], to be referred here-forth as PYTHIA8-MBR. In this paper, we briefly review the cross sections [7Ciesielski R, Goulianos K. MBR Monte Carlo Simulation in PYTHIA8 Proc Sci 2013; 00: 301-5.] implemented in this option of PYTHIA8 and compare them with LHC measurements.

The PYTHIA8-MBR option includes a full simulation of the hadronization of the implemented diffraction dissociation processes: single, double, and central diffraction. In the MBR simulation used at CDF, the hadronization of the final state(s) was based on a data-driven phenomenological model of multiplicities and  (transverse momentum) distributions calibrated using SS and Fermilab fixed-target results. Later, the model was successfully tested against Tevatron minimum bias (MB) and diffraction data. However, only  and  particles were produced in the final state, with multiplicities obeying a statistical model of a modified Gamma distribution function that provided good fits to experimental data [8Goulianos K. A new statistical description of hardonic and e+e- multiplicity distributions Phys Lett B 1987; 193: 151-6.]. This model could not be used to predict specific-particle final states. In the PYTHIA8-MBR implementation, hadronization is perfor-med by PYTHIA8 tuned to reproduce final-state distribut-ions in agreement with MBR's, with hadronization done in the PYTHIA8 framework. Thus, all final-state particles are now automatically produced, greatly enhancing the horizon of applicability of PYTHIA8-MBR.

2. CROSS SECTIONS

The following diffraction dissociation processes are considered in PYTHIA8-MBR:

SD                       (1)

or             

DD                  (2)

CD/DPE              (3)

The RENORM predictions are expressed as unitarized Regge-theory formulas, in which the unitarization is achi-eved by a renormalization scheme where the Pomeron (IP) flux is interpreted as the probability for forming a diffractive (non-exponentially suppressed) rapidity gap and thereby its integral over all phase space saturates at the energy where it reaches unity. Differential cross sections are expressed in terms of the  IP-trajectory, , the IP-p coupling, , and the ratio of the triple-IP to the IP- couplings, . For large rapidity gaps, , for which IP -exchange dominates, the cross sections may be written as,

         (4)

   (5)

  (6)

where  is the 4-momentum-transfer squared at the proton vertex,  the rapidity-gap width, and  the center of the rapidity gap. In Eq. (6), the subscript  enumerates Pomerons in a DPE event,  is the total rapidity gap (sum of two gaps) in the event, and  is the center in  of the centrally-produced hadronic system.

The total cross section () is expressed as:

  (7)

  (8)

where  and  are energy and the Pomeron flux saturation scales, respectively [7Ciesielski R, Goulianos K. MBR Monte Carlo Simulation in PYTHIA8 Proc Sci 2013; 00: 301-5.]. For  TeV, where there are Reggeon contributions, we use the global fit expression [9Covolan RJM, Montanha J, Goulianos K. A new determination of the soft pomeron intercept. Phys Lett B 1996; 389: 176-80.], while for  TeV, where Reggeon contributions are negligible, we employ the Froissart-Martin formula [10Martin A. Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity I II Nuovo Cimento 1966; 42: 930-53.-12Deile M. (TOTEM Collaboration). Measurements of Proton-Proton and Total Cross Section at the LHC by TOTEM Proceedings of diffraction 2012 (figure from talk presented at the Conference) ]. The two expressions are smoothly matched at  TeV.

The elastic cross section is obtained from the global fit [9Covolan RJM, Montanha J, Goulianos K. A new determination of the soft pomeron intercept. Phys Lett B 1996; 389: 176-80.] for  TeV, while for  TeV we use an extrapolation of the global-fit ratio of , which is slowly varying with  multiplied by . The total non-diffractive cross section is then calculated as .

3. RESULTS

In this section, we present as examples of the predictive power of the RENORM model some results reported by the TOTEM, CMS, and ALICE collaborations for pp collisions at  TeV, which can be directly compared with RENORM formulas without using the PYTHIA8-MBR simulation.

Fig. (1, left) shows a comparison of the TOTEM total, elastic, and total-inelastic cross sections, along with results from other experiments fitted by the COMPETE Collaboration [13Abelev B, Adam J , Adamová D, et al. ALICE collaboration. Measurement of Inelastic, Single-and Double-Diffraction Cross Sections in Proton-Proton Collisions at the LHC with ALICE Eur Phys J C 2013; 73: 2456. [arXiv:1208.4968]]; the RENORM predictions, displayed as filled (green) squares, are in excellent agreement with the TOTEM results. Similarly, in Fig. (1, right), good agreement is observed between the ALICE [14Chatrchyan S, Khachatryan V, Sirunyan AM, et al. (CMS Collaboration) Measurement of the inelastic proto-proton cross section at TeV Phys Lett B 2013; 722(5): 2456.] and CMS [15Albrow MG, Coughlin TD, Forshaw JR, et al. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.] total-inelastic cross sections and the RENORM prediction.

Fig. (1)

(left) TOTEM measurements of the total, total-inelastic, and elastic pp cross sections at s = 7 TeV shown along with best COMPETE fits [13Abelev B, Adam J , Adamová D, et al. ALICE collaboration. Measurement of Inelastic, Single-and Double-Diffraction Cross Sections in Proton-Proton Collisions at the LHC with ALICE Eur Phys J C 2013; 73: 2456. [arXiv:1208.4968]], with RENORM predictions added as filled squares; (right) ALICE [14Chatrchyan S, Khachatryan V, Sirunyan AM, et al. (CMS Collaboration) Measurement of the inelastic proto-proton cross section at TeV Phys Lett B 2013; 722(5): 2456.] and CMS [15Albrow MG, Coughlin TD, Forshaw JR, et al. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.] measurements of the total inelastic cross section at s = 7 TeV show good agreement with the RENORM prediction (PYTHIA8-MBR).



Fig. (2)

Measured SD (left) and DD (right) cross sections for ξ < 0.05 compared with theoretical predictions; the model embedded in PYTHIA8-MBR provides a good description of all data.



The uncertainty shown in the RENORM prediction of  in Fig. (1, left) is dominated by that in the scale parameter . The latter can be reduced by a factor of ~4 if  is interpreted as the mean value of the glue-ball-like object discussed in [16Albrow MG, Coughlin TD, Forshaw Jr. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.] and the data shown in figure 8 of [16Albrow MG, Coughlin TD, Forshaw Jr. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.] are used to determine its value. Work is in progress to finalize the details of this interpretation.

Another example of the predictive power of RENORM is shown in Fig. (2), which displays the total SD (left) and total DD (right) cross sections for , after extrapolation into the low mass region from the measured CMS cross sections at higher mass regions, presented in [17Ciesielski R. (CMS Collaboration). Measurements of diffraction in p-p collisions in CMS Proceedings of XXI International Workshop on Deep-Inelastic Scattering and Related Subject-DIS April 2013 Marseilles France 2013 2013; 22-6.], using RENORM.

4. SUMMARY

We reviewed our pre- LHC predictions for the total, elastic, total-inelastic, and diffractive components of the proton-proton cross section at high energies, which are based on a special parton-model approach to diffraction employing inclusive proton parton distribution functions and QCD color factors. We discuss single diffraction/dissociation, double diffraction/dissociation, and central diffraction or double-Pomeron exchange, comparing predictions with LHC measurements. Agreement between data and PYTHIA8-MBR predictions is found in all cases.

CONFLICT OF INTEREST

The author confirms that this article content has no conflicts of interest.

ACKNOWLEDGEMENTS

I would like to thank Robert Ciesielski, my colleague at Rockefeller and collaborator in the implementation of the MBR simulation into PYTHIA8, and the Office of Science of the Department of Energy for supporting the Rockefeller experimental diffraction physics programs at Fermilab and LHC on which this research is anchored.

REFERENCES

[1] Goulianos K, Ed. Predictions of Diffractive Cross Sections in Proton-Proton Collisions In: 1st AMA National Conference on Child Abuse and Neglect; 1984 Mar 30-31; Chicago. Chicago: American Medical Association 1985; Goulianos K. Predictions of Diffractive Cross Sections in Proton-Proton Collisions Proceedings of Diffraction 2012 International Workshop on Diffraction in High Energy Physics 10-15 September. 2012 AIP Conf Proc 2013; 1523: 107-16.
[2] See models presented by various authors in proceedings of Diffraction 2012 AIP Conf Proc 2012; 1523: 107-37.
[3] Goulianos K. Predictions of Diffractive, Elastic, Total, and Total-Inelastic pp Cross Sections vs LHC Measurements 2013 Marseilles France. -DIS2013 22-26 April.; Marseilles, France. Chicago: Proceedings of XXI International Workshop on Deep-Inelastic Scattering and Related Subject 2013.
[4] Goulianos K. Hadronic Diffraction Where do we Stand? Proceedings of Les Rencontres de Physique de la Vallee d'Aoste Results and Perspectives in Particle Physics [arXiv: hep-ph/0407035]. In: Frascati Physics Series, Special 34 Issue, edited by Mario Greco; February 27 - March 6; La Thuile, Italy. 2004.
[5] Mario D, Ed. Goulianos K. Diffractive and Total pp Cross Sections at LHC In: Mario D, Ed. [arXiv: 10023527v2]. In: 13th International Conference on Elastic and Diffractive Scattering (Blois Workshop) Moving Forward into the LHC Era; June 29-July 3, 2009; CERN, Geneva, Switzerland. 2010.
[6] (a) Sjöstrand T, Mrenna S, Skands P. PYTHIA 6. A brief introduction to PYTHIA 81. Physics and Manual J High Energ Phys 2006; 05: 026.
[7] Ciesielski R, Goulianos K. MBR Monte Carlo Simulation in PYTHIA8 Proc Sci 2013; 00: 301-5.
[8] Goulianos K. A new statistical description of hardonic and e+e- multiplicity distributions Phys Lett B 1987; 193: 151-6.
[9] Covolan RJM, Montanha J, Goulianos K. A new determination of the soft pomeron intercept. Phys Lett B 1996; 389: 176-80.
[10] Martin A. Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity I II Nuovo Cimento 1966; 42: 930-53.
[11] Martin A. Froissart bound for inelastic cross sections Phys Rev D 2009; 50: 065013.
[12] Deile M. (TOTEM Collaboration). Measurements of Proton-Proton and Total Cross Section at the LHC by TOTEM Proceedings of diffraction 2012 (figure from talk presented at the Conference)
[13] Abelev B, Adam J , Adamová D, et al. ALICE collaboration. Measurement of Inelastic, Single-and Double-Diffraction Cross Sections in Proton-Proton Collisions at the LHC with ALICE Eur Phys J C 2013; 73: 2456. [arXiv:1208.4968]
[14] Chatrchyan S, Khachatryan V, Sirunyan AM, et al. (CMS Collaboration) Measurement of the inelastic proto-proton cross section at TeV Phys Lett B 2013; 722(5): 2456.
[15] Albrow MG, Coughlin TD, Forshaw JR, et al. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.
[16] Albrow MG, Coughlin TD, Forshaw Jr. Central Exclusive Particle Production at High Energy Hadron Colliders Prog Part Nucl Phys 2010; 65: 149-84.
[17] Ciesielski R. (CMS Collaboration). Measurements of diffraction in p-p collisions in CMS Proceedings of XXI International Workshop on Deep-Inelastic Scattering and Related Subject-DIS April 2013 Marseilles France 2013 2013; 22-6.

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