In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential (<span><svg height="9.39034pt" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.8797 9.39034" width="11.8797pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.89,3.132)"></path></g></svg>)</span> and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle (<svg height="9.49473pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g></svg>=<svg height="10.1628pt" style="vertical-align:-0.2064095pt" version="1.1" viewbox="-0.0498162 -9.95639 17.4724 10.1628" width="17.4724pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"></path></g><g transform="matrix(.013,0,0,-0.013,6.241,0)"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.481,-5.741)"></path></g></svg>) has been studied. The variation of differential scattering cross-section with scattering angle <svg height="9.49473pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-230"></use></g></svg> (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at <span><svg height="10.1628pt" style="vertical-align:-0.2064095pt" version="1.1" viewbox="-0.0498162 -9.95639 17.738 10.1628" width="17.738pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-230"></use></g><g transform="matrix(.013,0,0,-0.013,10.107,0)"></path></g></svg><span></span><span><svg height="10.1628pt" style="vertical-align:-0.2064095pt" version="1.1" viewbox="21.320183800000002 -9.95639 17.524 10.1628" width="17.524pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,21.37,0)"><use xlink:href="#g113-58"></use></g><g transform="matrix(.013,0,0,-0.013,27.611,0)"><use xlink:href="#g113-49"></use></g><g transform="matrix
{"title":"Study of Differential Scattering Cross-Section Using Yukawa Term of Medium-Modified Cornell Potential","authors":"Siddhartha Solanki, Manohar Lal, Vineet Kumar Agotiya","doi":"10.1155/2022/1456538","DOIUrl":"https://doi.org/10.1155/2022/1456538","url":null,"abstract":"In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential (<span><svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 11.8797 9.39034\" width=\"11.8797pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.89,3.132)\"></path></g></svg>)</span> and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle (<svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 6.59789 9.49473\" width=\"6.59789pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>=<svg height=\"10.1628pt\" style=\"vertical-align:-0.2064095pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.95639 17.4724 10.1628\" width=\"17.4724pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,6.241,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,12.481,-5.741)\"></path></g></svg>) has been studied. The variation of differential scattering cross-section with scattering angle <svg height=\"9.49473pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 6.59789 9.49473\" width=\"6.59789pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-230\"></use></g></svg> (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at <span><svg height=\"10.1628pt\" style=\"vertical-align:-0.2064095pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.95639 17.738 10.1628\" width=\"17.738pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-230\"></use></g><g transform=\"matrix(.013,0,0,-0.013,10.107,0)\"></path></g></svg><span></span><span><svg height=\"10.1628pt\" style=\"vertical-align:-0.2064095pt\" version=\"1.1\" viewbox=\"21.320183800000002 -9.95639 17.524 10.1628\" width=\"17.524pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,21.37,0)\"><use xlink:href=\"#g113-58\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.611,0)\"><use xlink:href=\"#g113-49\"></use></g><g transform=\"matrix","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" 10","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138514426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The space available to our perception is three-dimensional with full evidence. The development of physics led to the hypothesis of extra dimensions. It is believed that an important role in the unification of physics should play by the Planck units of mass, length and time, built on the universal constants c (the speed of light in a vacuum), G (the gravitational constant), and ħ (the reduced Planck constant). In August 2021, published work in which it is shown that the fundamental role in the unification of physics, in fact, was played by the Stoney units, built on the universal constants c − G − e or c − G − ħ and α (where e is the elementary electric charge, and α is the fine-structure constant). Using this result, the presented work offers a possible solution to the riddle of extra dimensions; it is shown that any additional spatial dimension can be expressed in terms of the fundamental length or the product of the fundamental time and the speed of light in a vacuum.
{"title":"Fundamental Units of Measurement and Extra Dimensions","authors":"A. Abdukadyrov","doi":"10.1155/2022/2655733","DOIUrl":"https://doi.org/10.1155/2022/2655733","url":null,"abstract":"The space available to our perception is three-dimensional with full evidence. The development of physics led to the hypothesis of extra dimensions. It is believed that an important role in the unification of physics should play by the Planck units of mass, length and time, built on the universal constants \u0000 \u0000 c\u0000 \u0000 (the speed of light in a vacuum), \u0000 \u0000 G\u0000 \u0000 (the gravitational constant), and \u0000 \u0000 ħ\u0000 \u0000 (the reduced Planck constant). In August 2021, published work in which it is shown that the fundamental role in the unification of physics, in fact, was played by the Stoney units, built on the universal constants \u0000 \u0000 c\u0000 −\u0000 G\u0000 −\u0000 e\u0000 \u0000 or \u0000 \u0000 c\u0000 −\u0000 G\u0000 −\u0000 ħ\u0000 \u0000 and \u0000 \u0000 α\u0000 \u0000 (where e is the elementary electric charge, and α is the fine-structure constant). Using this result, the presented work offers a possible solution to the riddle of extra dimensions; it is shown that any additional spatial dimension can be expressed in terms of the fundamental length or the product of the fundamental time and the speed of light in a vacuum.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49604169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics and providing a quantum mechanical framework for the minimal length uncertainty, at the Planck scale. We demonstrate that the GUP parameter, β 0 , could be best constrained by the gravitational wave observations, GW170817 event. To determine the difference between the group velocity of graviton and that of the light, we suggest another proposal based on the modified dispersion relations (MDRs). We conclude that the upper bound of β 0 reads ≃1060. Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant Λ (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, Λ ≃ 1 0 − 47 GeV4/ℏ3c3.
我们提出了广义不确定性原理(GUP)，并在弦理论和黑洞物理的驱动下增加了二次动量项，并为普朗克尺度下的最小长度不确定性提供了量子力学框架。我们证明GUP参数β 0可以最好地由引力波观测GW170817事件约束。为了确定引力子的群速度和光的群速度之间的差异，我们提出了另一种基于修正色散关系(mdr)的方法。我们得出β 0的上限为≃1060。利用紫外/红外光谱的对应特征和GUP的明显相似性(包括非重力和重力对海森堡测不准原理的影响)以及理论和观测到的宇宙常数Λ的差异(重力对真空能量密度的明显影响)，即非重力真空突变，我们提出了一个可能的解决方案Λ: 1 0−47 GeV4/ h 3c3。
{"title":"A Possible Solution of the Cosmological Constant Problem Based on GW170817 and Planck Observations with Minimal Length Uncertainty","authors":"A. Diab, Abdel Nasser Tawfik","doi":"10.1155/2022/9351511","DOIUrl":"https://doi.org/10.1155/2022/9351511","url":null,"abstract":"We propose generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics and providing a quantum mechanical framework for the minimal length uncertainty, at the Planck scale. We demonstrate that the GUP parameter, \u0000 \u0000 \u0000 \u0000 β\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 , could be best constrained by the gravitational wave observations, GW170817 event. To determine the difference between the group velocity of graviton and that of the light, we suggest another proposal based on the modified dispersion relations (MDRs). We conclude that the upper bound of \u0000 \u0000 \u0000 \u0000 β\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 reads ≃1060. Utilizing features of the UV/IR correspondence and the apparent similarities between GUP (including nongravitating and gravitating impacts on Heisenberg uncertainty principle) and the discrepancy between the theoretical and the observed cosmological constant \u0000 \u0000 Λ\u0000 \u0000 (obviously manifesting gravitational influences on the vacuum energy density), known as catastrophe of nongravitating vacuum, we suggest a possible solution for this long-standing physical problem, \u0000 \u0000 Λ\u0000 ≃\u0000 1\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 −\u0000 47\u0000 \u0000 \u0000 \u0000 GeV4/ℏ3c3.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64788172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Abu-shady, R. Luz, G. Petronilo, R. Amorim, A. Santana
Considering the formalism of symplectic quantum mechanics, we investigate a two-dimensional nonrelativistic strong interacting system, describing a bound heavy quark-antiquark state. The potential has a linear component that is analyzed in the context of generalized fractional derivatives. For this purpose, the Schrödinger equation in phase space is solved with the linear potential. The ground state solution is obtained and analyzed through the Wigner function for the meson c c ¯ . One basic and fundamental result is that the fractional quantum phase-space analysis gives rise to the confinement of quarks in the meson, consistent with experimental results.
{"title":"Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics","authors":"M. Abu-shady, R. Luz, G. Petronilo, R. Amorim, A. Santana","doi":"10.1155/2023/8366154","DOIUrl":"https://doi.org/10.1155/2023/8366154","url":null,"abstract":"Considering the formalism of symplectic quantum mechanics, we investigate a two-dimensional nonrelativistic strong interacting system, describing a bound heavy quark-antiquark state. The potential has a linear component that is analyzed in the context of generalized fractional derivatives. For this purpose, the Schrödinger equation in phase space is solved with the linear potential. The ground state solution is obtained and analyzed through the Wigner function for the meson \u0000 \u0000 c\u0000 \u0000 \u0000 c\u0000 \u0000 \u0000 ¯\u0000 \u0000 \u0000 \u0000 . One basic and fundamental result is that the fractional quantum phase-space analysis gives rise to the confinement of quarks in the meson, consistent with experimental results.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46671560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Yang-Mills-aether theory is considered. Implications of the non-Abelian aether-like term, which introduces violation of the Lorentz symmetry, are investigated in a thermal quantum field theory. The thermofield dynamics formalism is used to introduce the temperature effects and spatial compactification. As a consequence, corrections due to the non-Abelian aether term are calculated for the non-Abelian Stefan-Boltzmann law and for the non-Abelian Casimir energy and pressure at zero and finite temperature.
{"title":"Non-Abelian Aether-Like Term and Applications at Finite Temperature","authors":"A. F. Santos, F. Khanna","doi":"10.1155/2022/6703645","DOIUrl":"https://doi.org/10.1155/2022/6703645","url":null,"abstract":"The Yang-Mills-aether theory is considered. Implications of the non-Abelian aether-like term, which introduces violation of the Lorentz symmetry, are investigated in a thermal quantum field theory. The thermofield dynamics formalism is used to introduce the temperature effects and spatial compactification. As a consequence, corrections due to the non-Abelian aether term are calculated for the non-Abelian Stefan-Boltzmann law and for the non-Abelian Casimir energy and pressure at zero and finite temperature.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49327439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We have studied the transverse momentum ( p T ) spectra of the final-state strange particles, including K ± , ϕ , Ξ , and Ω , produced in high energy lead–lead (Pb–Pb), proton–lead ( p –Pb), xenon–xenon (Xe–Xe) collisions at the Large Hadron Collider (LHC). Taking into account the contribution of multiquark composition, whose probability density distribution is described by the modified Tsallis–Pareto-type function; we simulate the p T spectra of the final-state strange particles by a Monte Carlo method, which is shown to be in good agreement with the experimental data in most the cases. The kinetic freeze-out parameters are obtained. The present method provides a new tool for studying the spectra of various particles produced in high energy collisions, reflecting more realistically the collision process, which is of great significance to study the formation and properties of the produced particles.
{"title":"Random Statistical Analysis of Transverse Momentum Spectra of Strange Particles and Dependence of Related Parameters on Centrality in High Energy Collisions at the LHC","authors":"Xu-Hong Zhang, Fu-Hu Liu, K. Olimov, A. Deppman","doi":"10.1155/2022/5949610","DOIUrl":"https://doi.org/10.1155/2022/5949610","url":null,"abstract":"We have studied the transverse momentum (\u0000 \u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 T\u0000 \u0000 \u0000 \u0000 ) spectra of the final-state strange particles, including \u0000 \u0000 \u0000 \u0000 K\u0000 \u0000 \u0000 ±\u0000 \u0000 \u0000 \u0000 , \u0000 \u0000 ϕ\u0000 \u0000 , \u0000 \u0000 Ξ\u0000 \u0000 , and \u0000 \u0000 Ω\u0000 \u0000 , produced in high energy lead–lead (Pb–Pb), proton–lead (\u0000 \u0000 p\u0000 \u0000 –Pb), xenon–xenon (Xe–Xe) collisions at the Large Hadron Collider (LHC). Taking into account the contribution of multiquark composition, whose probability density distribution is described by the modified Tsallis–Pareto-type function; we simulate the \u0000 \u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 T\u0000 \u0000 \u0000 \u0000 spectra of the final-state strange particles by a Monte Carlo method, which is shown to be in good agreement with the experimental data in most the cases. The kinetic freeze-out parameters are obtained. The present method provides a new tool for studying the spectra of various particles produced in high energy collisions, reflecting more realistically the collision process, which is of great significance to study the formation and properties of the produced particles.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48979076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3 σ level of the recent global fit data of neutrino oscillations, the distribution of the scattered points of the angles between the vectors, which are constructed by the element of the leptonic mixing matrix, is analysed. We find that the scattered points are concentrated on several special regions. Using the data in these regions, correlations of the leptonic mixing angles and the Dirac CP violating phase are obtained. The implications of the correlations are shown through the predicted flavor ratio of high-energy astrophysical neutrinos (HANs) at Earth.
{"title":"The Geometric Correlations of Leptonic Mixing Parameters","authors":"Dingan Xu, Shu-Jun Rong","doi":"10.1155/2023/6057292","DOIUrl":"https://doi.org/10.1155/2023/6057292","url":null,"abstract":"Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3\u0000 \u0000 σ\u0000 \u0000 level of the recent global fit data of neutrino oscillations, the distribution of the scattered points of the angles between the vectors, which are constructed by the element of the leptonic mixing matrix, is analysed. We find that the scattered points are concentrated on several special regions. Using the data in these regions, correlations of the leptonic mixing angles and the Dirac CP violating phase are obtained. The implications of the correlations are shown through the predicted flavor ratio of high-energy astrophysical neutrinos (HANs) at Earth.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44470770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Oluwadare, E. O. Ilesanmi, T. O. Abiola, O. Olubosede, E. A. Odo, S. O. Ajibade, K. Oyewumi
We investigate the nonrelativistic magnetic effect on the energy spectra, expectation values of some quantum mechanical observables, and diamagnetic susceptibility for some diatomic molecules bounded by the isotropic oscillator plus inverse quadratic potential. The energy eigenvalues and normalized wave functions are obtained via the parametric Nikiforov-Uvarov method. The expectation values square of the position r 2 , square of the momentum p 2 , kinetic energy T , and potential energy V are obtained by applying the Hellmann-Feynman theorem, and an expression for the diamagnetic susceptibility X is also derived. Using the spectroscopic data, the low rotational and low vibrational energy spectra, expectation values, and diamagnetic susceptibility X for a set of diatomic molecules (I2, H2, CO, and HCl) for arbitrary values, Larmor frequencies are calculated. The computed energy spectra, expectation values, and diamagnetic susceptibility X were found to be more influenced by the external magnetic field strength and inverse quadratic potential strength g than the vibrational frequencies and the masses of the selected molecules.
{"title":"Investigating Some Diatomic Molecules Bounded by the Two-Dimensional Isotropic Oscillator plus Inverse Quadratic Potential in an External Magnetic Field","authors":"O. Oluwadare, E. O. Ilesanmi, T. O. Abiola, O. Olubosede, E. A. Odo, S. O. Ajibade, K. Oyewumi","doi":"10.1155/2022/6565048","DOIUrl":"https://doi.org/10.1155/2022/6565048","url":null,"abstract":"We investigate the nonrelativistic magnetic effect on the energy spectra, expectation values of some quantum mechanical observables, and diamagnetic susceptibility for some diatomic molecules bounded by the isotropic oscillator plus inverse quadratic potential. The energy eigenvalues and normalized wave functions are obtained via the parametric Nikiforov-Uvarov method. The expectation values square of the position \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 r\u0000 \u0000 \u0000 2\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 , square of the momentum \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 2\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 , kinetic energy \u0000 \u0000 \u0000 \u0000 T\u0000 \u0000 \u0000 \u0000 , and potential energy \u0000 \u0000 \u0000 \u0000 V\u0000 \u0000 \u0000 \u0000 are obtained by applying the Hellmann-Feynman theorem, and an expression for the diamagnetic susceptibility \u0000 \u0000 X\u0000 \u0000 is also derived. Using the spectroscopic data, the low rotational and low vibrational energy spectra, expectation values, and diamagnetic susceptibility \u0000 \u0000 X\u0000 \u0000 for a set of diatomic molecules (I2, H2, CO, and HCl) for arbitrary values, Larmor frequencies are calculated. The computed energy spectra, expectation values, and diamagnetic susceptibility \u0000 \u0000 X\u0000 \u0000 were found to be more influenced by the external magnetic field strength and inverse quadratic potential strength \u0000 \u0000 g\u0000 \u0000 than the vibrational frequencies and the masses of the selected molecules.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43856572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study pair production of particles in the presence of an external electric field in a large N non-supersymmetric Yang-Mills theory using the holographic duality. The dual geometry we consider is asymptotically AdS and is effectively parametrized by two parameters, u 0 and − 5 / 2 < δ ≤ 0 , both of which can be related to the effective mass of quark/antiquark for non-supersymmetric theories. We numerically calculate the interquark potential profile and the effective potential to study pair production and analytically find out the threshold electric field beyond which one gets catastrophic pair creation by studying rectangular Wilson loops using the holographic method. We also find out the critical electric field from DBI analysis of a probe brane. Our initial investigations reveal that the critical electric field necessary for spontaneous pair production increases or decreases w.r.t. its non-supersymmetric value depending on the parameter δ . Ultimately, we find out the pair production rate of particles in the presence of an external electric field by evaluating circular Wilson loops using perturbative methods. From the later investigation, we note the resemblance with our earlier prediction. However, we also see that for and below another certain value of the parameter δ , the pair production rate of particle/antiparticle pairs blows up as the external electric field is taken to zero. We thus infer that the vacuum of the non-SUSY gauge theory is unstable for a range of non-supersymmetric parameter δ and that the geometry/non-SUSY field theory under consideration has quite different characteristics than earlier reported.
{"title":"Schwinger-Type Pair Production in Non-SUSY AdS/CFT","authors":"U. Chowdhury","doi":"10.1155/2023/8685867","DOIUrl":"https://doi.org/10.1155/2023/8685867","url":null,"abstract":"We study pair production of particles in the presence of an external electric field in a large \u0000 \u0000 N\u0000 \u0000 non-supersymmetric Yang-Mills theory using the holographic duality. The dual geometry we consider is asymptotically AdS and is effectively parametrized by two parameters, \u0000 \u0000 \u0000 \u0000 u\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 and \u0000 \u0000 −\u0000 \u0000 \u0000 5\u0000 /\u0000 2\u0000 \u0000 \u0000 <\u0000 δ\u0000 ≤\u0000 0\u0000 \u0000 , both of which can be related to the effective mass of quark/antiquark for non-supersymmetric theories. We numerically calculate the interquark potential profile and the effective potential to study pair production and analytically find out the threshold electric field beyond which one gets catastrophic pair creation by studying rectangular Wilson loops using the holographic method. We also find out the critical electric field from DBI analysis of a probe brane. Our initial investigations reveal that the critical electric field necessary for spontaneous pair production increases or decreases w.r.t. its non-supersymmetric value depending on the parameter \u0000 \u0000 δ\u0000 \u0000 . Ultimately, we find out the pair production rate of particles in the presence of an external electric field by evaluating circular Wilson loops using perturbative methods. From the later investigation, we note the resemblance with our earlier prediction. However, we also see that for and below another certain value of the parameter \u0000 \u0000 δ\u0000 \u0000 , the pair production rate of particle/antiparticle pairs blows up as the external electric field is taken to zero. We thus infer that the vacuum of the non-SUSY gauge theory is unstable for a range of non-supersymmetric parameter \u0000 \u0000 δ\u0000 \u0000 and that the geometry/non-SUSY field theory under consideration has quite different characteristics than earlier reported.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46898454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1 + 1 and 2 + 1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2 + 1 and 3 + 1 dimensional spacetime, then the quantization of spatial length is possible in our approach.
{"title":"On the Quantization of Length in Noncommutative Spaces","authors":"Muthukumar Balasundaram, A. Rashid","doi":"10.1155/2022/8009789","DOIUrl":"https://doi.org/10.1155/2022/8009789","url":null,"abstract":"We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in \u0000 \u0000 1\u0000 +\u0000 1\u0000 \u0000 and \u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in \u0000 \u0000 2\u0000 +\u0000 1\u0000 \u0000 and \u0000 \u0000 3\u0000 +\u0000 1\u0000 \u0000 dimensional spacetime, then the quantization of spatial length is possible in our approach.","PeriodicalId":7498,"journal":{"name":"Advances in High Energy Physics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47681731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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