Skip to main content
Log in

Optimization of Monte Carlo Integration for Estimating of the Pion Damping Width

  • COMPUTER TECHNOLOGIES IN PHYSICS
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

This work presents algorithm and methods for numerical calculation of multidimensional collision integrals based on the Monte Carlo method. The source code was used for the calculation of the pion damping width in hot nuclear matter taking all possible pion-pion scattering modes into account. For optimization of the computation the parallel calculation algorithm is implemented in C++ programming language using OpenMP and NVIDIA CUDA technology. Calculations are performed on nodes with multicore CPUs and Intel Xeon Phi coprocessors and Nvidia Tesla K40 accelerator installed within heterogeneous cluster of the Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. I. Sobol, Numerical Monte-Carlo Methods (Nauka, Moscow, 1973) [in Russian].

    MATH  Google Scholar 

  2. S. P. Klevansky, “The Nambu–Jona-Lasinio model of quantum chromodynamics,” Rev. Mod. Phys. 64, 649 (1992). https://link.aps.org/doi/10.1103/RevModPhys.64.649.

    Article  ADS  MathSciNet  Google Scholar 

  3. Y. L. Kalinovsky and A. V. Friesen, “Properties of mesons and critical points in the Nambu–Jona-Lasinio model with different regularizations,” Phys. Part. Nucl. Lett. 12, 737 (2015).

    Article  Google Scholar 

  4. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (W. A. Benjamin, New York, 1962).

    MATH  Google Scholar 

  5. F. Wei-Jie and L. Yu-Xin, “Mesonic excitations and pi-pi scattering lengths at finite temperature in the two-flavor Polyakov–Nambu–Jona-Lasinio model,” Phys. Rev. D 79, 074011 (2009).

    Article  ADS  Google Scholar 

  6. E. Quak, P. Zhuang, Y. L. Kalinovsky, S. P. Klevansky, and J. Hüfner, “π–π scattering lengths at finite temperature,” Phys. Lett. B 348, 1 (1995).

    Article  ADS  Google Scholar 

  7. H. Bauke, Tina’s Random Number Generator Library, Version 4.24. https://www.numbercrunch.de/trng/ trng.pdf. Available March 27, 2021.

  8. A. S. Antonov, Parallel Programming Technologies MPI and OpenMP, A Textbook (Mosk. Gos. Univ., Moscow, 2012) [in Russian].

    Google Scholar 

  9. NVIDIA CUDA C++ Programming Guide v11.5.0 (2021).

  10. A. Wergieluk, D. Blaschke, Y. L. Kalinovsky, and A. Friesen, “Pion dissociation and Levinson’s theorem in hot PNJL quark matter,” Phys. Part. Nucl. Lett. 9, 660–668 (2012); arXiv: 1212.5245 [nucl-th].

    Google Scholar 

  11. A. V. Friesen, Yu. L. Kalinovsky, and V. D. Toneev, “Thermodynamics in NJL-like models,” hep-th/1102.1813 (2011).

  12. P. Rehberg and S. P. Klevansky, “One loop integrals at finite temperature and density,” Ann. Phys. 252, 422–457 (1996).

    Article  ADS  Google Scholar 

  13. A. S. Khvorostukhin, “Calculation of the one loop box integral at finite temperature and density,” arXiv: 2011.14596 [hep-ph] (2021).

  14. S. R. Cotanch and P. Maris, “QCD based quark description of π–π scattering up to the σ and ρ regions,” Phys. Rev. D 66, 116010 (2002).

    Article  ADS  Google Scholar 

  15. A. V. Friesen, Y. L. Kalinovsky, and V. D. Toneev, “Decay of a scalar σ-meson near the critical end-point in the PNJL model,” Phys. Part. Nucl. Lett. 9, 1 (2012); arXiv: 1104.2698 [nucl-th].

    Article  Google Scholar 

  16. The GSL Team GNU Scientific Library v2.7. https://www.gnu.org/software/gsl/doc/html/montecarlo.html.

  17. D. Blaschke, M. K. Volkov, and V. L. Yudichev, “Pion damping width from SU(2) X SU(2) NJL Model,” Phys. At. Nucl. 66, 1 (2003); arXiv: 0303034 [nucl-th].

  18. The Laboratory of Information Technologies Heterogeneous Computing Cluster HybriLIT. http://hybrilit.jinr.ru.

Download references

Funding

The work was supported by the RFBR, grant no. 18-02-40137.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to A. V. Friesen, D. Goderidze or Yu. L. Kalinovsky.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Friesen, A.V., Goderidze, D. & Kalinovsky, Y.L. Optimization of Monte Carlo Integration for Estimating of the Pion Damping Width. Phys. Part. Nuclei Lett. 19, 412–421 (2022). https://doi.org/10.1134/S1547477122040112

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477122040112

Navigation