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Andrew J. Larkoski - One of the best experts on this subject based on the ideXlab platform.
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Circumnavigating Collinear Superspace
Journal of High Energy Physics, 2020Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:In this paper, we extend the Collinear superspace formalism to include the full range of $\mathcal{N} = 1$ supersymmetric interactions. Building on the effective field theory rules developed in a companion paper - "Navigating Collinear Superspace" - we construct Collinear superspace Lagrangians for theories with non-trivial $F$- and $D$-term auxiliary fields. For (massless) Wess-Zumino models, the key ingredient is a novel type of Grassmann-valued supermultiplet whose lowest component is a (non-propagating) fermionic degree of freedom. For gauge theories coupled to charged chiral matter, the key ingredient is a novel type of vector superfield whose lowest component is a non-propagating gauge potential. This unique vector superfield is used to construct a gauge-covariant derivative; while such an object does not appear in the standard full superspace formalism, it is crucial for modeling gauge interactions when the theory is expressed on a Collinear slice. This brings us full circle, by showing that all types of $\mathcal{N} = 1$ theories in four dimensions can be constructed in Collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with $\mathcal{N} > 1$ could also be implemented using similar Collinear superspace constructions.
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navigating Collinear superspace
Journal of High Energy Physics, 2020Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:We introduce a new set of effective field theory rules for constructing Lagrangians with $$ \mathcal{N} $$ = 1 supersymmetry in Collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $$ \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) $$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F- and D-term components. By contrast, Collinear superspace depends on a smaller set of coordinates (xμ, η, η†), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct Collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with $$ \mathcal{N} $$ = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.
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navigating Collinear superspace
arXiv: High Energy Physics - Theory, 2018Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:We introduce a new set of effective field theory rules for constructing Lagrangians with $\mathcal{N} = 1$ supersymmetry in Collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $(x^\mu,\theta^\alpha, \theta^{\dagger \dot{\alpha}})$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary $F$- and $D$-term components. By contrast, Collinear superspace depends on a smaller set of coordinates $(x^\mu,\eta,\eta^\dagger)$, where $\eta$ is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct Collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing interacting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with $\mathcal{N} = 1$. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.
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Soft-Collinear Supersymmetry
Journal of High Energy Physics, 2017Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. LarkoskiAbstract:Soft-Collinear Effective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and Collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the effective Lagrangian for $\mathcal{N} = 1$ SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the effective Lagrangian for chiral SUSY theories with Yukawa couplings, specifically the single flavor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian -- to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding fields along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. Defining the theory with respect to a specific frame obfuscates Lorentz invariance -- given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: Collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang-Mills in "Collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of superfields. As a byproduct, bootstrapping up to the full theory yields the first algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. This work paves the way toward discovering the effective theory for the Collinear limit of $\mathcal{N} = 4$ SUSY Yang-Mills.
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Collinear Superspace
Physical Review D, 2016Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. LarkoskiAbstract:This paper provides a superfield based approach to constructing a Collinear slice of N=1 superspace. The strategy is analogous to integrating out antiCollinear fermionic degrees-of-freedom as was developed in the context of soft-Collinear effective theory. The resulting Lagrangian can be understood as an integral over Collinear superspace, where half the supercoordinates have been integrated out. The application to N=1 super Yang-Mills is presented. Collinear superspace provides the foundation for future explorations of supersymmetric soft-Collinear effective theory.National Science Foundation (U.S.) (PHY–0969510)National Science Foundation (U.S.) (PHY–1419008)National Science Foundation (U.S.) (PHY–1066293
Raoul Rontsch - One of the best experts on this subject based on the ideXlab platform.
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analytic results for color singlet production at nnlo qcd with the nested soft Collinear subtraction scheme
arXiv: High Energy Physics - Phenomenology, 2019Co-Authors: Kirill Melnikov, Fabrizio Caola, Raoul RontschAbstract:We present analytic formulas that describe fully-differential production of color-singlet final states in $q\bar q$ and $gg$ annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-Collinear scheme which allows for fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and Collinear poles and present formulas for finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the nested soft-Collinear subtraction scheme.
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analytic results for color singlet production at nnlo qcd with the nested soft Collinear subtraction scheme
European Physical Journal C, 2019Co-Authors: Kirill Melnikov, Fabrizio Caola, Raoul RontschAbstract:We present analytic formulas that describe the fully-differential production of color-singlet final states in $$q{\bar{q}}$$ and gg annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-Collinear scheme, which allows the fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and Collinear poles and present formulas for the finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the nested soft-Collinear subtraction scheme.
H.Ş. Mert - One of the best experts on this subject based on the ideXlab platform.
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Spin configurations on a decorated square lattice
2016Co-Authors: Gülistan Mert, H.Ş. MertAbstract:Spin configurations on a decorated square lattice are investigated using Bertaut’s microscopic method. We have obtained Collinear and non-Collinear (canted) modes for the given wave vectors in the ground state. We have found ferromagnetic and antiferromagnetic commensurate spin configurations. We have found canted incommensurate spin configurations.
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Spin configurations of the four-sublattice model on rectangular lattice
Journal of Magnetism and Magnetic Materials, 2014Co-Authors: Gülistan Mert, H.Ş. MertAbstract:Abstract The spin configurations of the four-sublattice model with seven exchange interaction parameters (four of them are taken as direct-exchange interactions, the other three as super-exchange interactions) on a two-dimensional rectangular lattice have been investigated using a matrix method. For the four sublattices, using the two sets of the exchange parameters, we obtain Collinear and non-Collinear spin configurations for the given propagation vectors in the ground and the first excited states. When k = 0 , spin configuration is Collinear ferromagnetic mode in the ground state and Collinear antiferromagnetic mode in the first excited state. When k =[0.5, 0.5], spin configurations are non-Collinear, that is, canted structures.
Timothy Cohen - One of the best experts on this subject based on the ideXlab platform.
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Circumnavigating Collinear Superspace
Journal of High Energy Physics, 2020Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:In this paper, we extend the Collinear superspace formalism to include the full range of $\mathcal{N} = 1$ supersymmetric interactions. Building on the effective field theory rules developed in a companion paper - "Navigating Collinear Superspace" - we construct Collinear superspace Lagrangians for theories with non-trivial $F$- and $D$-term auxiliary fields. For (massless) Wess-Zumino models, the key ingredient is a novel type of Grassmann-valued supermultiplet whose lowest component is a (non-propagating) fermionic degree of freedom. For gauge theories coupled to charged chiral matter, the key ingredient is a novel type of vector superfield whose lowest component is a non-propagating gauge potential. This unique vector superfield is used to construct a gauge-covariant derivative; while such an object does not appear in the standard full superspace formalism, it is crucial for modeling gauge interactions when the theory is expressed on a Collinear slice. This brings us full circle, by showing that all types of $\mathcal{N} = 1$ theories in four dimensions can be constructed in Collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with $\mathcal{N} > 1$ could also be implemented using similar Collinear superspace constructions.
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navigating Collinear superspace
Journal of High Energy Physics, 2020Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:We introduce a new set of effective field theory rules for constructing Lagrangians with $$ \mathcal{N} $$ = 1 supersymmetry in Collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $$ \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) $$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F- and D-term components. By contrast, Collinear superspace depends on a smaller set of coordinates (xμ, η, η†), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct Collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with $$ \mathcal{N} $$ = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.
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navigating Collinear superspace
arXiv: High Energy Physics - Theory, 2018Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. Larkoski, Jesse ThalerAbstract:We introduce a new set of effective field theory rules for constructing Lagrangians with $\mathcal{N} = 1$ supersymmetry in Collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates $(x^\mu,\theta^\alpha, \theta^{\dagger \dot{\alpha}})$, and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary $F$- and $D$-term components. By contrast, Collinear superspace depends on a smaller set of coordinates $(x^\mu,\eta,\eta^\dagger)$, where $\eta$ is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct Collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing interacting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with $\mathcal{N} = 1$. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.
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Soft-Collinear Supersymmetry
Journal of High Energy Physics, 2017Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. LarkoskiAbstract:Soft-Collinear Effective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and Collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the effective Lagrangian for $\mathcal{N} = 1$ SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the effective Lagrangian for chiral SUSY theories with Yukawa couplings, specifically the single flavor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian -- to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding fields along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. Defining the theory with respect to a specific frame obfuscates Lorentz invariance -- given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: Collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang-Mills in "Collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of superfields. As a byproduct, bootstrapping up to the full theory yields the first algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. This work paves the way toward discovering the effective theory for the Collinear limit of $\mathcal{N} = 4$ SUSY Yang-Mills.
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Collinear Superspace
Physical Review D, 2016Co-Authors: Timothy Cohen, Gilly Elor, Andrew J. LarkoskiAbstract:This paper provides a superfield based approach to constructing a Collinear slice of N=1 superspace. The strategy is analogous to integrating out antiCollinear fermionic degrees-of-freedom as was developed in the context of soft-Collinear effective theory. The resulting Lagrangian can be understood as an integral over Collinear superspace, where half the supercoordinates have been integrated out. The application to N=1 super Yang-Mills is presented. Collinear superspace provides the foundation for future explorations of supersymmetric soft-Collinear effective theory.National Science Foundation (U.S.) (PHY–0969510)National Science Foundation (U.S.) (PHY–1419008)National Science Foundation (U.S.) (PHY–1066293
Fabrizio Caola - One of the best experts on this subject based on the ideXlab platform.
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analytic results for color singlet production at nnlo qcd with the nested soft Collinear subtraction scheme
arXiv: High Energy Physics - Phenomenology, 2019Co-Authors: Kirill Melnikov, Fabrizio Caola, Raoul RontschAbstract:We present analytic formulas that describe fully-differential production of color-singlet final states in $q\bar q$ and $gg$ annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-Collinear scheme which allows for fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and Collinear poles and present formulas for finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the nested soft-Collinear subtraction scheme.
-
analytic results for color singlet production at nnlo qcd with the nested soft Collinear subtraction scheme
European Physical Journal C, 2019Co-Authors: Kirill Melnikov, Fabrizio Caola, Raoul RontschAbstract:We present analytic formulas that describe the fully-differential production of color-singlet final states in $$q{\bar{q}}$$ and gg annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-Collinear scheme, which allows the fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and Collinear poles and present formulas for the finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the nested soft-Collinear subtraction scheme.
