COMPUTER ALGEBRA CALCULATIONS IN SUPERSYMMETTIC LECTRODYNAMICS

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

We propose a new symbolic algorithm and a C++ program for generating and calculating supersymmetric Feynman diagrams for N=1 supersymmetric electrodynamics regularized by higher derivatives in four dimensions. According to standard rules, the program generates all diagrams that are necessary to calculate a specific contribution to the two-point Green function of matter superfields in the needed order, and then reduces the answer to the sum of Euclidean momentum integrals. At the moment, the program was used to calculate the anomalous dimension in N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives, in the three-loop approximation.

Sobre autores

I. SHIROKOV

Moscow State University, Faculty of Physics

Autor responsável pela correspondência
Email: shi95@yandex.ru
Moscow, Russia

Bibliografia

  1. Campbell J.A., Hearn A.C. Symbolic analysis of feynman diagrams by computer // J. Comput. Phys. 1970. V. 5. P. 280.
  2. Гердт В.П., Тарасов О.В., Ширков Д.В. Аналитические вычисления на ЭВМ в приложении к физике и математике // УФН, 1980. Т. 130. С. 113–147.
  3. Nogueira P. Automatic Feynman graph generation // J. Comput. Phys. 1993. V. 105. P. 279–289.
  4. Kublbeck J., Bohm M., Denner A. Feyn Arts: Computer Algebraic Generation of Feynman Graphs and Amplitudes // Comput. Phys. Commun. 1990. V. 60. P. 165–180. a8 citations counted in INSPIRE as of 04 Feb 2022
  5. Papadopoulos C.G. PHEGAS: A Phase space generator for automatic cross-section computation // Comput. Phys. Commun., 2001. V. 137. P. 247–254.
  6. Moretti M., Ohl T., Reuter J. O’Mega: An Optimizing matrix element generator // [arXiv:hep-ph/0102195 [hep-ph]].
  7. Maltoni F., Stelzer T. MadEvent: Automatic event generation with MadGraph // JHEP. 2003. V. 02. P. 027.
  8. Wang J.X. Progress in FDC project // Nucl. Instrum. Meth. A, 2004. V. 534. P. 241–245.
  9. Boos E. et al. [CompHEP] CompHEP 4.4: Automatic computations from Lagrangians to events // Nucl. Instrum. Meth. A. 2004. V. 534. P. 250–259.
  10. Belyaev A., Christensen N.D., Pukhov A. CalcHEP 3.4 for collider physics within and beyond the Standard Model // Comput. Phys. Commun. 2013. V. 184. P. 1729–1769.
  11. Kilian W., Ohl T., Reuter J. WHIZARD: Simulating Multi-Particle Processes at LHC and ILC // Eur. Phys. J. C. 2011. V. 71. P. 1742.
  12. Bahr M., Gieseke S., Gigg M.A., Grellscheid D., Hamilton K., Latunde-Dada O., Platzer S., Richardson P., Seymour M.H., Sherstnev A., et al. Herwig++ Physics and Manual // Eur. Phys. J. C. 2008. V. 58. P. 639–707.
  13. Gleisberg T., Hoeche S., Krauss F., Schonherr M., Schumann S., Siegert F., Winter J. Event generation with SHERPA 1.1 // JHEP. 2009. V. 02. P. 007.
  14. Cullen G., van Deurzen H., Greiner N., Heinrich G., Luisoni G., Mastrolia P., Mirabella E., Ossola G., Peraro T., Schlenk J., et al. GOSAM-2.0: a tool for automated one-loop calculations within the Standard Model and beyond // Eur. Phys. J. C. 2014. V. 74. № 8. P. 3001.
  15. Alwall J., Frederix R., Frixione S., Hirschi V., Maltoni F., Mattelaer O., Shao H.S., Stelzer T., Torrielli P., Zaro M. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations // JHEP. 2014. V. 07. P. 079.
  16. Hahn T. Generating Feynman diagrams and amplitudes with FeynArts 3 // Comput. Phys. Commun. 2001. V. 140. P. 418–431.
  17. Wolfram Wolfram Mathematica, 2022. https://www.wolfram.com/mathematica/
  18. Maplesoft, a division of Waterloo Maple Inc. Maple, 2022. https://www.maplesoft.com/products/maple/
  19. Veltman M.J.G., Williams D.N. Schoonschip’91 // [arXiv:hep-ph/9306228 [hep-ph]].
  20. Ruijl B., Ueda T., Vermaseren J. FORM version 4.2 // [arXiv:1707.06453 [hep-ph]].
  21. Vollinga J. GiNaC: Symbolic computation with C++ // Nucl. Instrum. Meth. A. 2006. V. 559. P. 282–284.
  22. Peeters K. A Field-theory motivated approach to symbolic computer algebra // Comput. Phys. Commun. 2007. V. 176. P. 550–558.
  23. Bolotin D.A., Poslavsky S.V. Introduction to Redberry: a computer algebra system designed for tensor manipulation // [arXiv:1302.1219 [cs.SC]].
  24. Shtabovenko V., Mertig R., Orellana F. FeynCalc 9.3: New features and improvements // Comput. Phys. Commun. 2020. V. 256. P. 107478.
  25. Chetyrkin K.G., Tkachov F.V. Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops // Nucl. Phys. B. 1981. V. 192. P. 159–204.
  26. Anastasiou C., Lazopoulos A. Automatic integral reduction for higher order perturbative calculations // JHEP. 2004. V. 07. P. 046.
  27. Smirnov A.V., Chuharev F.S. FIRE6: Feynman Integral REduction with Modular Arithmetic // Comput. Phys. Commun. 2020. V. 247. P. 106877.
  28. Lee R.N. LiteRed 1.4: a powerful tool for reduction of multiloop integrals // J. Phys. Conf. Ser. 2014. V. 523. P. 012059.
  29. Studerus C. Reduze-Feynman Integral Reduction in C++ // Comput. Phys. Commun. 2010. V. 181. P. 1293–1300.
  30. Maierhöfer P., Usovitsch J., Uwer P. Kira–A Feynman integral reduction program // Comput. Phys. Commun. 2018. V. 230. P. 99–112.
  31. Dubovyk I., Gluza J., Riemann T., Usovitsch J. Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions // PoS. 2016. V. LL2016. P. 034.
  32. Smirnov A.V. FIESTA4: Optimized Feynman integral calculations with GPU support // Comput. Phys. Commun. 2016. V. 204. P. 189–199.
  33. Borowka S., Heinrich G., Jones S.P., Kerner M., Schlenk J., Zirke T. SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop // Comput. Phys. Commun. 2015. V. 196. P. 470–491.
  34. Gorishnii S.G., Larin S.A., Surguladze L.R., Tkachov F.V. Mincer: Program for Multiloop Calculations in Quantum Field Theory for the Schoonschip System // Comput. Phys. Commun. 1989. V. 55. P. 381–408.
  35. Gorishnii S.G., Kataev A.L., Larin S.A., Surguladze L.R. The Analytical four loop corrections to the QED Beta function in the MS scheme and to the QED psi function: Total reevaluation // Phys. Lett. B. 1991. V. 256. P. 81–86.
  36. Lorca A., Riemann T. Automated calculations for massive fermion production with aITALC // Nucl. Phys. B Proc. Suppl. 2004. V. 135. P. 328–332.
  37. Fontes D., Romão J.C. FeynMaster: a plethora of Feynman tools // Comput. Phys. Commun. 2020. V. 256. P. 107311.
  38. Feng F., Xie Y.F., Zhou Q.C., Tang S.R. HepLib: A C++ library for high energy physics // Comput. Phys. Commun. 2021. V. 265. P. 107982.
  39. Gerlach M., Herren F., Lang M. tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions // [arXiv:2201.05618 [hep-ph]].
  40. Hahn T., Schappacher C. The Implementation of the minimal supersymmetric standard model in FeynArts and FormCalc // Comput. Phys. Commun. 2002. V. 143. P. 54–68.
  41. Kreuzberger T., Kummer W., Schweda M. SUSYCAL: A PROGRAM FOR SYMBOLIC COMPUTATIONS IN SUPERSYMMETRIC THEORIES // Comput. Phys. Commun. 1990. V. 58. P. 89–104.
  42. Ferrari A.F. SusyMath: A Mathematica package for quantum superfield calculations // Comput. Phys. Commun. 2007. V. 176. P. 334–346.
  43. Степаньянц К.В. Классическая теория поля. М.: ФИЗМАТЛИТ, 2009. 540 с.
  44. Боголюбов Н.Н., Ширков Д.В. Введение в теорию квантованных полей. М.: Наука, 1973. 416 с.
  45. Уэст П. Введение в суперсимметрию и супергравитацию. Пер. с англ. М.: Мир, 1989. 328 с.; West P.C. Introduction to supersymmetry and supergravity. Singapore: World Scientific, 1990. 425 p.
  46. Tarasov O.V., Vladimirov A.A. Three Loop Calculations in Non-Abelian Gauge Theories // Phys. Part. Nucl. 2013. V. 44. P. 791–802.
  47. OpenMP ARB OpenMP 5.2 Reference Guide, 2021. https://www.openmp.org/wp-content/uploads/OpenMPRefCard-5-2-web.pdf
  48. Gates S.J., Grisaru M.T., Rocek M., Siegel W. Superspace Or One Thousand and One Lessons in Supersymmetry // Front. Phys. 1983. V. 58. P. 1–548.
  49. Buchbinder I.L., Kuzenko S.M. Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Su-perspace, IOP, Bristol, UK, 1998. 656 p.
  50. Slavnov A.A. Invariant regularization of nonlinear chiral theories // Nucl. Phys. B. 1971. V. 31. P. 301–315.
  51. Славнов A.A. Инвариантная регуляризация калибровочных теорий // ТМФ. 1972. Т. 13:2. С. 174–177.
  52. Кривощеков В.К. Инвариантная регуляризация для суперсимметричных калибровочных теорий // ТМФ. 1978. Т. 36. С. 291.
  53. West P.C. Higher Derivative Regulation Of Supersymmetric Theories // Nucl. Phys. B. 1986. V. 268. P. 113.
  54. Славнов А.А. Регуляризация Паули–Вилларса для неабелевых калибровочных групп // ТМФ. 1977. Т. 33:2. С. 210–217.
  55. Катаев А.Л., Степаньянц К.В. -Функция Новикова–Шифмана–Вайнштейна–Захарова в суперсимметричных теориях при различных регуляризациях и перенормировочных предписаниях // ТМФ. 2014. Т. 181:3. С. 475–486.
  56. Aleshin S.S., Durandina I.S., Kolupaev D.S., Korneev D.S., Kuzmichev M.D., Meshcheriakov N.P., Novgorodtsev S.V., Petrov I.A., Shatalova V.V., Shirokov I.E. et al. Three-loop verification of a new algorithm for the calculation of a -function in supersymmetric theories regularized by higher derivatives for the case of SQED // Nucl. Phys. B. 2020. V. 956. P. 115020.
  57. Shirokov I.E., Stepanyantz K.V. The three-loop anomalous dimension and the four-loop -function for SQED regularized by higher derivatives // JHEP. 2022. V. 2204. P. 108.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
2.

Baixar (28KB)

Declaração de direitos autorais © И.Е. Широков, 2023

Este site utiliza cookies

Ao continuar usando nosso site, você concorda com o procedimento de cookies que mantêm o site funcionando normalmente.

Informação sobre cookies