Properties of upsilon meson based on the two intertwined spaces

Document Type : Original Article

Authors

1 Department of Physics and Engineering Sciences, Buein Zahra Technical University, Qazvin, Iran

2 Department of Physics, University of Agriculture and Environmental Sciences Umuagwo, Imo State, Nigeria

Abstract

This paper studies the important concepts in the fundamental optimization of mass and thermal properties of strong interactions based on quantum approximate operators. It explores and analytically calculates the radial part of the Schrödinger equation at finite temperature using the two intertwined spaces based on the Wick ordering method in the Bernoulli Potential. We provide analytical expressions for the ground state energy eigenvalues to define the zeroth approximation. Bernoulli potential refers to some of the potential types that are returned to the Bernoulli series. The method presented in this study allows us to rewrite some of the exponential potentials simply to even power levels in the Bernoulli series. Given that the Hulthen potential is a modified form of main hadronic interaction potentials, it is used to calculate the bound state mass and properties of hadronic atoms such as π-atoms, κ-atoms or various hadronic structures with positive/negative and heavy/light quark bound states such as 〖D_s〗^+,〖B_c〗^+,〖〖〖B_ 〗^+,D^+ ,D〗_ 〗^(*+) at finite temperatures. The main goal of this research is to the combined quantum operators and two intertwined spaces within the Bernoulli expansion to determine the best approximation of upsilon meson mass and thermal properties.

Keywords

Main Subjects

Article Title [Persian]

بررسی خصوصیات پیوند مقید مزون اوپسیلون در فضای دوگانه

Author [Persian]

  • آرزو جهانشیر 1

1 گروه فیزیک و علوم مهندسی، مرکز آموزش عالی فنی و مهندسی بویین زهرا، قزوین

2 گروه فیزیک، دانشگاه علوم محیطی و کشاورزی اومائگو، نیجریه

Abstract [Persian]

پتانسیل‌ برنولی به پتانسیل‌هایی اطلاق می‌شود که به سری برنولی برگردانده می‌شوند. روش ارائه شده در این پژوهش به ما این امکان را می‌دهد تا بتوانیم پتانسیل‌های نمایی از نوع هالثن را به سادگی تا درجات توانی زوج به شیوة سری برنولی بازنویسی نماییم. با توجه به این نکته که پتانسیل هالثن شکل اصلاح شده از پتانسیلهای اصلی برهم کنش هادرونی است، برای محاسبه جرم حالت مقید شبه اتم‌های هادرونی مانند π-اتم، κ-اتم و یا ساختارهای متنوع هادرونی با یک کوارک مثبت و سنگین و یک کوارک منفی سبک یا برابر مانندD^+ ،〖D_s〗^+،〖D_ 〗^(*+)، 〖B_c〗^+ و〖B_ 〗^+ در دمای بالا پیشنهاد شده است. از این رو مهمترین نکته در شیوة ذکر شده بسط برنولی پتانسیل نمایی-هالثن است که با روش تبدیل فضای همتافته، متغیرهای کانونیک را با درجات توانی مرتبه بالا برای طیف جرم مزون اوپسیلون بدست می‌آوریم. حذف توان‌های فرد بزرگتر از یک به ما این امکان را می‌دهد تا تقریب مناسب‌تری را با عبارات بیشتر بازنویسی کنیم و طیف جرم را نسبت به توان‌های بالاتر از روش‌های متعارف دیگر بدست آوریم.

Keywords [Persian]

  • پیوند مقید
  • اصلاحات نسبیتی
  • پتانسیل برنولی
  • برهمکنش قوی
[1] H. Mutuk, “Mass Spectra and Decay constants of Heavy-light Mesons: A case study of QCD sum Rules and Quark model.” Advances in High Energy Physics, 20 (2018) 8095653. doi.org/10.1155/2018/8095653
[2] L. Dong, Y. Guo et al., “Effective Debye screening mass in an anisotropic quark-gluon plasma.” Physical Review D, 104 (2021) 096017. doi.org/10.1103/PhysRevD.104.096017
[3] A. Mocsy, “Potential models for quarkonia.” The European Physical Journal C, 61 (2009) 710. doi.org/10.1140/epjc/s10052-008-0847-4
[4] A. N. Ikot et al., “Superstatistics of Schrodinger equation with pseudo-harmonic potential in external magnetic and Aharanov-Bohm fields.” Heliyon, 6 (2020) e03738. doi.org/10.1016/j.heliyon.2020.e03738
[5] P. Gubler, T. Song, S. Lee, “D-meson mass and heavy quark potential at finite temperature.” Physical Review D, 101 (2020) 114029-39. doi.org/ 10.1103/PhysRevD.101.114029
[6] H. Mansour, and A. Gamal, “Bound state of Heavy Quarks using a general polynomial potential.” Advances in High Energy Physics, 65 (2018) 1234. doi.org/10.1155/2018/7269657
[7] Abu-Shady, T. Abdel-Karim, E. Khokha, “Binding energies and dissociation temperatures of heavy quarkonia at finite temperature and chemical potential in the n-dimensional space.” Advances in High Energy Physics, 2018 (2018) 7356843. doi.org/10.1155/2019/4785615
[8] D. H. Lehmer, “On the Maxima and Minima of Bernoulli Polynomials.” American Mathematical Monthly, 47 (1940), 533–538. doi.org/10.1080/00029890.1940.11991015
[9] Zhi-Wei Sun, Hao Pan, “Identities concerning Bernoulli and Euler polynomials.” Acta Arithmetica, 125 (2006) 21–39.
[10] M. J. Ambrosio, et al., “Mathematical properties of generalized Sturmian functions.” Journal of Physics A, Mathematical and Theoretical, 45 (2012) 21. doi.org/101088/1751- 8113/45/1/015201
[11] B. R. Johnson, “On a connection between radial Schrödinger equations for different power law potentials.” Journal of Mathematical Physics, 21 2640 (1980). doi.org/10.1063/1.524378
[12] M. Dienykhan, G. Efimov, G. GanboldS, N.Nedelko, “Oscillator Representation in Quantum Physics.” first ed., Springer-Verlag, DE, (1995); W. Greiner, S. Schramm, E.Stein, Quantum chromodynamics, Springer Science & Business Media; 2007.
[13] R Rosenfelder, “Path Integrals in Quantum Physics.” arXiv:1209.1315v2 [nucl-th], (2012).
[14] R. P. Feynman, A.R. Hibbs, “Quantum Mechanics and Path Integrals.” Dover Publications Inc, (2010).
[15] J. Kelley, J. Leventhal, “Ladder Operators for the Harmonic Oscillator:Problems in classical and quantum mechanics.” first ed., Publishing Springer- Verlag, DE, (2017)
[16] M. E. Peskin, D. V. Schroeder, “An Introduction To Quantum Field Theory.” CRC Press; 1st edition (2019)
[17] P. A. Zyla et al., Particle Data Group, Progress of Theoretical and Experimental Physics, 2020 (2020) 083C0.
[18] G. Boyd, J. Engels, F. Karsch et al., “Thermodynamics of SU(3) lattice gauge theory.” Nuclear Physics B, 469 (1996) 419. doi.org/10.1016/0550-3213(96)00170-8
[19] Bernard, T. Burch, E. Gregory et al., “QCD thermodynamics with three flavors of improved staggered quarks,” Physical Review D, 71 (2005) 034504.
[20] R. N. Faustov, V. O. Galkin, A. V. Tatarintsev, A. S. Vshivtsev, “Spectral problem of the radial Schrödinger equation with confining power potentials.” Theoretical and Mathematical Physics, 113 (1997) 1530. doi.org/10.1007/BF02634513
[21] R. Kumar, F. Chand, “Series solutions to the Ndimensional radial Schrödinger equation for the quark-antiquark interaction potential.” Physica  Scripta, 85 (2012) 055008.
 
doi.org/10.1088/0031-8949/86/02/027002
[22] F. Al-Jamel and H. Widyan, “Heavy quarkonium mass spectra in a Coulomb field plus quadratic potential using Nikiforov-Uvarov method.” Applied Physics Research, 4 (2012) 94. doi.org/10.5539/apr.v4n3p94
[23] I. Ahmadov, C. Aydin, and O. Uzun, “Bound state solution of the Schrödinger equation at finite temperature.” Journal of Physics Conference Series, 1194 (2019) 012001. doi.org/10.1088/1742-6596/1194/1/012001