The Experts below are selected from a list of 105 Experts worldwide ranked by ideXlab platform
Wen Chen - One of the best experts on this subject based on the ideXlab platform.
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reduction of feynman integrals in the parametric representation iii integrals with cuts
arXiv: High Energy Physics - Phenomenology, 2020Co-Authors: Wen ChenAbstract:Cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. by directly parametrizing theta functions and constructing Integration-by-Part (IBP) identities in the parametric representation, we provide a systematic method to reduce integrals with cuts. Since IBP method is available, it becomes possible to evaluate integrals with cuts by constructing and solving differential equations.
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reduction of feynman integrals in the parametric representation
Journal of High Energy Physics, 2020Co-Authors: Wen ChenAbstract:In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the Integration-by-Part (IBP) method in the momentum space. Tensor integrals can directly be parametrized without performing tensor reductions. The integrands of parametric integrals are functions of Lorentz scalars, instead of four momenta. The complexity of a calculation is determined by the number of propagators that are present rather than the number of all the linearly independent propagators. Furthermore, the symmetries of Feynman integrals under permutations of indices are transparent in the parametric representation. Since all the indices of the propagators are nonnegative, an algorithm to solve those identities can easily be developed, which can be used for automatic calculations.
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reduction of feynman integrals in the parametric representation ii reduction of tensor integrals
arXiv: High Energy Physics - Phenomenology, 2019Co-Authors: Wen ChenAbstract:In a recent paper by the author [arXiv:1902.10387], the reduction of Feynman integrals in the parametric representation was considered. Tensor integrals were directly parametrized by using a generator method. The resulting parametric integrals were reduced by constructing and solving parametric Integration-by-Part (IBP) identities. In this paper, we further show that polynomial equations for the operators that generate tensor integrals can be derived. Basing on these equations, two methods to reduce tensor integrals are developed. In the first method, by introducing some auxiliary parameters, tensor integrals are parametrized without shifting the spacetime dimension. The resulting parametric integrals can be reduced by using the standard IBP method. In the second method, tensor integrals are (Partially) reduced by using the technique of Grobner basis.
P. Njionou Sadjang - One of the best experts on this subject based on the ideXlab platform.
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On the Fundamental Theorem of $$\varvec{(p,q)}$$ ( p , q ) -Calculus and Some $$\varvec{(p,q)}$$ ( p , q ) -Taylor Formulas
Results in Mathematics, 2018Co-Authors: P. Njionou SadjangAbstract:In this paper, the (p, q)-derivative and the (p, q)-Integration are investigated. Two suitable polynomial bases for the (p, q)-derivative are provided and various properties of these bases are given. As application, two (p, q)-Taylor formulas for polynomials are given, the fundamental theorem of (p, q)-calculus is included and the formula of (p, q)-Integration by Part is proved.
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On the fundamental theorem of $(p,q)$-calculus and some $(p,q)$-Taylor formulas
arXiv: Quantum Algebra, 2013Co-Authors: P. Njionou SadjangAbstract:In this paper, the $(p,q)$-derivative and the $(p,q)$-Integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor formulas for polynomials are given, the fundamental theorem of $(p,q)$-calculus is included and the formula of $(p,q)$-Integration by Part is proved.
Zheng Yu-hui - One of the best experts on this subject based on the ideXlab platform.
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Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
2021Co-Authors: Li Hao-lin, Ren Zhe, Shu Jing, Xiao Ming-lei, Yu Jiang-hao, Zheng Yu-huiAbstract:We present a complete list of the dimension 8 operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way. We adopt a new form of operators in terms of the irreducible representations of the Lorentz group, and identify the Lorentz structures as states in a $SU(N)$ group. In this way, redundancy from equations of motion is absent and that from Integration-by-Part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields. For the first time, we provide the explicit form of independent flavor-specified operators in a systematic way. Our algorithm can be easily applied to higher dimensional standard model effective field theory and other effective field theories, making these studies more approachable.Comment: 72 pages, 1 figure, 4 tables, minor revision on monomial operators with desymmetrization procedur
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Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
2020Co-Authors: Li Hao-lin, Ren Zhe, Xiao Ming-lei, Yu Jiang-hao, Zheng Yu-huiAbstract:We present a complete and independent list of the dimension 9 operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis (y-basis) is first constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and Integration-by-Part redundancies all removed. In the presence of repeated fields, another basis (p-basis) with explicit flavor symmetries among them is derived from the y-basis, which further induces a basis of independent monomial operators through a systematic process called de-symmetrization. Our form of operators have advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $\Delta B = 2$ and $\Delta L = 3$, which only appear at the dimensions $d \ge 9$.Comment: 58 pages, 1 figure, 10 table
Li Hao-lin - One of the best experts on this subject based on the ideXlab platform.
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Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
2021Co-Authors: Li Hao-lin, Ren Zhe, Shu Jing, Xiao Ming-lei, Yu Jiang-hao, Zheng Yu-huiAbstract:We present a complete list of the dimension 8 operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way. We adopt a new form of operators in terms of the irreducible representations of the Lorentz group, and identify the Lorentz structures as states in a $SU(N)$ group. In this way, redundancy from equations of motion is absent and that from Integration-by-Part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields. For the first time, we provide the explicit form of independent flavor-specified operators in a systematic way. Our algorithm can be easily applied to higher dimensional standard model effective field theory and other effective field theories, making these studies more approachable.Comment: 72 pages, 1 figure, 4 tables, minor revision on monomial operators with desymmetrization procedur
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Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
2020Co-Authors: Li Hao-lin, Ren Zhe, Xiao Ming-lei, Yu Jiang-hao, Zheng Yu-huiAbstract:We present a complete and independent list of the dimension 9 operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis (y-basis) is first constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and Integration-by-Part redundancies all removed. In the presence of repeated fields, another basis (p-basis) with explicit flavor symmetries among them is derived from the y-basis, which further induces a basis of independent monomial operators through a systematic process called de-symmetrization. Our form of operators have advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $\Delta B = 2$ and $\Delta L = 3$, which only appear at the dimensions $d \ge 9$.Comment: 58 pages, 1 figure, 10 table
Roman N. Lee - One of the best experts on this subject based on the ideXlab platform.
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Group structure of the Integration-by-Part identities and its application to the reduction of multiloop integrals
Journal of High Energy Physics, 2008Co-Authors: Roman N. LeeAbstract:The excessiveness of Integration-by-Part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI) identities do not bring any information additional to that contained in the IBP identities, and therefore, can be discarded.