A hypergeometric function is proposed to calculate the scalar integrals of Feynman diagrams. In this study, we verify the equivalence between the Feynman parametrization and the hypergeometric technique for the scalar...A hypergeometric function is proposed to calculate the scalar integrals of Feynman diagrams. In this study, we verify the equivalence between the Feynman parametrization and the hypergeometric technique for the scalar integral of the three-loop vacuum diagram with four propagators. The result can be described in terms of generalized hypergeometric functions of triple variables. Based on the triple hypergeometric functions, we establish the systems of homogeneous linear partial differential equations (PDEs) satisfied by the scalar integral of three-loop vacuum diagram with four propagators. The continuation of the scalar integral from its convergent regions to entire kinematic domains can be achieved numerically through homogeneous linear PDEs by applying the element method.展开更多
In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（p, k） ...In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（p, k） for b → sγ transition even after we sum up the contributions from four related Feynman diagrams; （b） for an on-shell photon, such terms do not contribute et al.; （c） for off-shell photon, these terms will be canceled when the contributions from both vertex ^sγb and ^sZb are taken into account simultaneously, and therefore the finite and gauge-independent function Zo（xt） = Co（xt） ＋ Do（xt）/4, which governs the semi-leptonic decay b → sl^- l^＋, is derived in the unitary gauge.展开更多
We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams.We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the inte...We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams.We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases,including that of Feynman diagrams with symmetry factors.展开更多
The Feynman diagram theory with the state-space formalism is adopted to study the multifrequency nonlinear acoustics effects. By establishing the relation between the strain magnitude corresponding to any final state ...The Feynman diagram theory with the state-space formalism is adopted to study the multifrequency nonlinear acoustics effects. By establishing the relation between the strain magnitude corresponding to any final state S(m1,…,mn; x) and the number of paths from the initial state of the interactingphonons to the final state, not only the complete perturbation solutions but also the corresponding analytical expressions of the acoustic harmonics and intermodulation products have been obtained. For a few special cases, results of our theory is consistent with those obtained by conventional methods. While the general solution for any number of frequencies can easily be obtained by our theory, this is impossible by using conventional methods.展开更多
A sizable difference in top quark pair forward backward asymmetry （AFB） is observed at Tevatron. The discrepancy triggers many new physics beyond the standard model （SM） and then constrains the parameter spaces in...A sizable difference in top quark pair forward backward asymmetry （AFB） is observed at Tevatron. The discrepancy triggers many new physics beyond the standard model （SM） and then constrains the parameter spaces in them. In this article we calculate the AFB of the top-pair production at Tevatron up to next to leading order （NLO） in the little Higgs model （LHM）. We find that the contribution of ZH can be large enough to make up the gap between SM prediction and experimental data. Then, the parameter space for the couplings between ZH and quarks are constrained. Thus, this model can fulfill the experimental data, both in AFB and in cross section.展开更多
A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO inter...A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO interactions. The method is based on counting the number of allowable Feynman diagrams. Some important assertions have been proved rigorously in this paper.展开更多
A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO inter...A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO interactions. The method is based on counting the number of allowable Feynman diagrams. The following important assertion has been proved rigorously in this paper. The ratios of the numbers of Feynman diagrams allowable in various Bragg diffractions (isotropic, nondegenerate birefringent, and degenerate birefringent) to that in Raman-Nath diffraction are independent of the number of different acoustic frequencies, being a function only of the order of the Feynman diagram and the diffraction order of the final state. General expressions for these ratios are obtained. Based on this, complete perturbation solutions for the scattering amplitudes and intensities are obtained for any kind of AO interactions, any number of acoustic frequencies, and any final state. This theory gives all results obtained previously by the theory of coupled-wave equation. The theory is also verified by comparing with experiments.展开更多
基金Supported partly by the National Natural Science Foundation of China(NNSFC)(11535002,11705045)the youth top-notch talent support program of the Hebei Province
文摘A hypergeometric function is proposed to calculate the scalar integrals of Feynman diagrams. In this study, we verify the equivalence between the Feynman parametrization and the hypergeometric technique for the scalar integral of the three-loop vacuum diagram with four propagators. The result can be described in terms of generalized hypergeometric functions of triple variables. Based on the triple hypergeometric functions, we establish the systems of homogeneous linear partial differential equations (PDEs) satisfied by the scalar integral of three-loop vacuum diagram with four propagators. The continuation of the scalar integral from its convergent regions to entire kinematic domains can be achieved numerically through homogeneous linear PDEs by applying the element method.
基金The project supported by National Natural Science Foundation of China under Grant No. 10575052 and the Specialized Research Fund for the Doctoral Program of Higher Education （SRFDP） under Grant No. 20050319008
文摘In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（p, k） for b → sγ transition even after we sum up the contributions from four related Feynman diagrams; （b） for an on-shell photon, such terms do not contribute et al.; （c） for off-shell photon, these terms will be canceled when the contributions from both vertex ^sγb and ^sZb are taken into account simultaneously, and therefore the finite and gauge-independent function Zo（xt） = Co（xt） ＋ Do（xt）/4, which governs the semi-leptonic decay b → sl^- l^＋, is derived in the unitary gauge.
基金Supported by the National Natural Science Foundation of China(11805152,10575080,11947301)the Natural Science Basie Research Program of Shaanxi Province(2019JQ-107)Shaanxi Key Laboratory for Theoretical Physics Frontiers in China。
文摘We study the relation between the symmetry group of a Feynman diagram and its reduced diagrams.We then prove that the counterterms in the BPHZ renormalization scheme are consistent with adding counterterms to the interaction Hamiltonian in all cases,including that of Feynman diagrams with symmetry factors.
基金The project was supported by National Natural Science Foundation of China
文摘The Feynman diagram theory with the state-space formalism is adopted to study the multifrequency nonlinear acoustics effects. By establishing the relation between the strain magnitude corresponding to any final state S(m1,…,mn; x) and the number of paths from the initial state of the interactingphonons to the final state, not only the complete perturbation solutions but also the corresponding analytical expressions of the acoustic harmonics and intermodulation products have been obtained. For a few special cases, results of our theory is consistent with those obtained by conventional methods. While the general solution for any number of frequencies can easily be obtained by our theory, this is impossible by using conventional methods.
基金Supported by National Natural Science Foundation of China(10975027,11275036,11047002)Natural Science Foundation of Hebei Province(A2013201277,A2011201118)+2 种基金Natural Science Fund of Hebei University(2011JQ05,2007113)open project of State Key Laboratory of Mathematics-Mechanization(Y3KF311CJ1)Natural Science Fund of Hebei University(2011JQ05,2012-242)
文摘A sizable difference in top quark pair forward backward asymmetry （AFB） is observed at Tevatron. The discrepancy triggers many new physics beyond the standard model （SM） and then constrains the parameter spaces in them. In this article we calculate the AFB of the top-pair production at Tevatron up to next to leading order （NLO） in the little Higgs model （LHM）. We find that the contribution of ZH can be large enough to make up the gap between SM prediction and experimental data. Then, the parameter space for the couplings between ZH and quarks are constrained. Thus, this model can fulfill the experimental data, both in AFB and in cross section.
基金This work was partly supported by the National Natural Science Foundation of China
文摘A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO interactions. The method is based on counting the number of allowable Feynman diagrams. Some important assertions have been proved rigorously in this paper.
基金This work was partly supported by the National Natural Science Foundation of Chinasupported by the Joint Service Electronics Program under contract number DAAL03-87-K-0059.
文摘A Feynman diagram theory for acousto-optic (AO) interactions is established, which provides a general method to calculate the scattering amplitudes and intensities for both single-frequency and multifrequency AO interactions. The method is based on counting the number of allowable Feynman diagrams. The following important assertion has been proved rigorously in this paper. The ratios of the numbers of Feynman diagrams allowable in various Bragg diffractions (isotropic, nondegenerate birefringent, and degenerate birefringent) to that in Raman-Nath diffraction are independent of the number of different acoustic frequencies, being a function only of the order of the Feynman diagram and the diffraction order of the final state. General expressions for these ratios are obtained. Based on this, complete perturbation solutions for the scattering amplitudes and intensities are obtained for any kind of AO interactions, any number of acoustic frequencies, and any final state. This theory gives all results obtained previously by the theory of coupled-wave equation. The theory is also verified by comparing with experiments.
