Unitarity of the tree approximation to the Glauber AA amplitude for large A
M. A. Braun, A. V. Krylov
研究了树近似下重参与核的核-核Glauber振幅。结果表明，与以前的结果相反，它不是统一的实际值的核子-核子截面。
The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross-sections.
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Unitarity Corrections and Structure Functions
我们研究了描述深层非弹性过程的色偶极图象，主要是由胶子分布直接驱动的结构函数。这些函数的估计得到使用的有效偶极子截面给出的格劳伯-穆勒方法在QCD，编码的修正，由于与饱和现象相关的么正性效应。通过对实验数据的分析，在观测量的计算中验证了标架不变性。
Tree-level unitarity constraints in the most general 2HDM
我们得到了最一般的两个Higgs双重模型（2HDM）的显式CP破坏的树级么正性约束。我们简要地讨论了可能违反树级幺正性限制和物理内容的理论之间的对应关系。
Tree-level unitarity constraints in the 2HDM with CP-violation
我们得到了具有明确CP破坏的双Higgs模型（2HDM）的树级么正性约束。我们仅限于理论的离散Z_2对称性的软破坏的情况。2HDM拉格朗日量的重定相不变性起着关键作用。我们推导这些约束的简单方法可以很容易地转移到其他形式的希格斯部门。我们简要地讨论了可能违反树级么正性限制与理论物理内容之间的对应关系。
We study perturbative unitarity and electroweak oblique corrections in the electroweak symmetry breaking models including an arbitrary number of neutral Higgs bosons. Requiring the perturbative unitarity of the high energy scattering amplitudes of weak gauge bosons and the neutral Higgs bosons at tree level, we obtain a set of conditions among the Higgs coupling strengths (unitarity sum rules). It is shown that the unitarity sum rules require the tree level rho parameter to be 1 if there are only neutral Higgs bosons. Moreover, we find that the one-loop finiteness of the electroweak oblique co…
Quartic Gauge Boson Couplings and Tree Unitarity in the SU(3)_C X SU(3)_L X U(1)_N Models
给出了${SU(3)}_C \otimes {SU(3)}_L \otimes {U(1)}_N$模型中的四次规范玻色子耦合。我们发现四个{ \it不同}规范玻色子的耦合可能具有不寻常的Lorentz结构，并且在高能极限下满足树么正性要求.
Tree Level Unitarity Bounds for the Minimal B-L Model
本文通过对Higgs玻色子和Goldstone玻色子在树水平上的二对二散射的全类分析，导出了标准模型的最小B-L扩展在高能极限下的么正性界.此外，我们已经研究了这些限制如何在一些较低的能量临界值变化。
Tree FCNC and non-unitarity of CKM matrix
我们讨论了可能的签名的树级FCNC，这是由于CKM矩阵的非酉性。我们首先定义了一步一步的unitaity，并可能通过四值KM参数化的非unitaity的测试。然后，我们展示了在类矢量下夸克模型中幺正三角形的相位角是如何变化的。作为树FCNC的另一个例子，我们研究了疏脂$Z'$模型及其在最近的$B_s$混合测量中的应用。
Strong tree level unitarity violations in the extra dimensional Standard Model with scalars in the bulk
我们展示了如何树级酉侵犯紧额外的维度扩展的标准模型成为更强的标量部门时，包括在批量。这种效应发生时，耦合不抑制较大的卡鲁扎-克莱因水平，并可能有相关的后果，下一代对撞机的现象。我们还介绍了一个简单的和通用的形式主义，以获得有限能量的么正性界，考虑到耦合通道，包括塔卡鲁扎-克莱因激发。
Tree-level unitarity constraints for the SM-like 2HDM
本文考虑Z_2对称的双Higgs二重态模型（2HDM），其中两个二重态的真空期望值都是非零的。类SM的2HDM的幺正性约束进行了分析的质量最轻的希格斯玻色子的范围内[115，127] GeV。导出了tanβ的新的严格界：0.17<tanβ<6.10。这些限制的来源进行了讨论。
We extract the Glauber divergences from the spectator amplitudes for two-body hadronic decays $B \to M_1 M_2$ in the $k_T$ factorization theorem, where $M_2$ denotes the meson emitted at the weak vertex. Employing the eikonal approximation, the divergences are factorized into the corresponding Glauber phase factors associated with the $M_1$ and $M_2$ mesons. It is observed that the latter factor enhances the spectator contribution to the color-suppressed tree amplitude by modifying the interference pattern between the two involved leading-order diagrams. The first factor rotates the enhanced s…
Tree-unitarity bounds for THDM Higgs masses revisited
我们重新考虑了理论上的两个希格斯偶模型（THDM）内的标量玻色子质量的上限，采用著名的技术条件的树级么正性。我们的处理提供了一个适度的扩展和推广其他作者的一些先前的结果。我们提出了一个相当详细的讨论有关的不等式的解决方案，并提供了一些新的解析公式以及数值的Higgs质量边界的问题。与早期的结果，可以在文献中找到的主题进行比较。
Note on tree-level unitarity in the General Two Higgs Doublet Model
本文研究了一般双Higgs模型（THDM）中希格斯玻色子玻色子质量的树级么正性约束。我们首先考虑的情况下，希格斯势是不变的离散对称变换下，并推导出强约束的质量最轻的CP-甚至希格斯玻色子（$M_h$）作为一个功能的$\tanβ$。然后，我们表明，列入离散对称性破缺项大大削弱了质量边界。这表明，$M_h$和$\tanβ$的测量可能使两个希格斯势之间的歧视。
Tree-level unitarity in Gauge-Higgs Unification
我们数值估计的尺度$Λ_{uni}$树级么正性被违反的$SO(5)\times U(1)_X$规范希格斯统一模型通过评估纵向W玻色子的散射振幅。散射振幅在弯曲时空中比在平坦时空中取更大的值，并且在$θ_H=π/2$时取最大值，其中$θ_H$是沿着额外维度的威尔逊线相位。我们不仅考虑了弹性散射，而且还考虑了可能的非弹性散射，以估计$Λ_{\rm uni}$。我们发现在弯曲时空中存在$Λ_{\rm uni}\simeq 1.3m_{KK}$，在平坦时空中存在$Λ_{\rm uni}\simeq 140m_{KK}$，其中$m_{KK}$是卡鲁扎-克莱因质量标度。在前一种情况下，由于WWH耦合的消失，树级么正性在$O(1TeV)$处被违反，对于$θ_H=π/2$。
Non-local Higgs actions: Tree-level electroweak constraints and high-energy unitarity
我们考虑电弱对称性破缺的某一类非本地希格斯部门。扩展以前的研究，采用曼德尔森条件，一个直的威尔逊线被用来使希格斯作用规范不变。我们展示了一个广泛的非局部行动类的矢量玻色子散射的么正化，但发现威尔逊线模型导致树水平的修正电弱精密观测，这限制了模型的参数空间。我们还发现，Unhiggs模型不能解决的层次结构问题，一旦参数表示的低能量的可观测量。
Explicit Conditions for Diagnosing Tree-Level Unitarity
本文提出了一种基于粒子内容的树级单位性诊断方法，通过显式给出所有耦合条件，无需重构完整拉格朗日量即可判断系统是否满足树级单位性，并展示了如何通过递归构造四点幅来推导树级单位性条件。
The Abelian Higgs model forms an essential part of the electroweak standard model: it is the sector containing only Z and Higgs bosons. We present a diagram-based proof of the tree-level unitarity of this model inside the unitary gauge, where only physical degrees of freedom occur. We derive combinatorial recursion relations for off-shell amplitudes in the massless approximation, which allows us to prove the cancellation of the first two orders in energy of unitarity-violating high-energy behaviour for any tree-level amplitude in this model. We describe a deformation of the amplitudes by exten…
On Tree-Level Unitarity in Theories of Massive Spin-2 Bosons
我们在一个只有相关算子和边缘算子的理论中分析了大质量自旋2玻色子的树能级2->2散射，并提取了在非常高的能量下实现树能级么正性所需的耦合常数和质量的求和规则。我们这样做的四个说明性的情况。在第一种情况下，我们在理论中包含了质量为自旋1和自旋0的玻色子，但不要求规范不变性。对于这种情况，我们发现，它是，事实上，有可能构建一个理论，所有的2->2散射过程是树级酉非常高的能量。在第二种情况下，我们考虑一个理论，只包括大量的自旋2和自旋0玻色子。在没有自旋1玻色子的情况下，我们发现自旋2散射是不可能幺正化的。在第三和第四种情况下，我们重新引入自旋为1的玻色子作为规范玻色子，并要求所有的相互作用都是规范不变的。我们取自旋为2的玻色子在一个或两个规范群的伴随表象下进行变换。对于这两种情况，我们发现，unitarization是无法实现的。
From Tree Unitarity to Top Quark Physics in 5D Higgsless Models
在五维无Higgs电弱对称破缺模型中，通过交换规范玻色子Kaluza-Klein模而不是交换希格斯玻色子，恢复了规范玻色子散射的树能级么正性.涉及顶夸克的散射振幅的么正性也需要第三族夸克的卡鲁扎-克莱因模。结果表明，相应的么正性抵消与边界条件引起的规范对称性破缺是一致的。这些结果被用来约束耦合的顶夸克卡鲁扎-克莱因模式和对撞机现象的影响进行了讨论。
A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
单圈散射振幅的么正性技术的最新进展使得该方法的数值实现成为可能。我们提出了一个四维么正性方法来计算振幅的截可构造部分，并在数值程序中实现了该方法。我们的技术可以应用于任何一个循环的散射振幅，并提供了一个循环的计算可以自动进行的可能性，树级振幅目前完成。我们的单回路评估的成分不是单个费曼图，而是树级振幅，这通常是已知的。为了研究这种方法的实用性，我们使用解析已知的4，5和6胶子树级振幅，数值计算了4，5和6胶子单圈振幅的可切构造部分。与解析解进行比较，以确定该方法的数值精度。
The tree-loop duality relation is used as a starting point to derive the constraints of causality and unitarity. Specifically, the Bogoliubov causality condition is ab initio derived at the individual graph level. It leads to a representation of a graph in terms of lower order cut graphs. Extracting the absorptive part gives then the general unitarity relation (Cutkosky rule). The derivation, being carried out directly in momentum space, holds for any local (polynomial) hermitian interaction vertices. This is in contrast to the technical difficulties arising from contact terms in the spacetime…
Gamma^* - Gamma^* Scattering: Saturation and Unitarization in the BFKL approach
本文用BFKL动力学方法讨论了两个光子具有大的但几乎相等的虚度的$γ^* - γ^*$散射，着重讨论了偶极-偶极振幅的大碰撞参量行为（$b_t$）。结果表明，非微扰贡献是必不可少的，以满足区域的$b_t > 1/2 m_π$，其中$m_π$是π质量的幺正性约束。在Glauber-Mueller方法的框架内考虑了偶极-偶极振幅的饱和和么正化。主要结果是，我们可以满足的幺正性约束，引入非微扰修正只有在初始条件（玻恩振幅）。
Unitarity In An Alternative Electroweak Theory
研究了一个电弱模型（Moffat），其中能量为$E < μ=\sqrtλM_W$，其中$λ$是规范参数，$M_W$是$W$玻色子质量.对于足够大的$λ$，标量玻色子质量$μ=\sqrtλM_W$可以足够重，以避免在大型强子对撞机实验中被检测到。对于解耦的标量相互作用，该理论是微扰重整化的。通过假设有效耦合常数$g_{\rm eff}(s)$随$1/\sqrt{s}$或$s\rightarrow\infty$的消失而消失，预测EW相互作用在高能时变弱，纵向极化$W_L W_L\rightarrow W_L W_L$散射不违反Born近似树图么正性，可以保证Born近似树图么正性.
Weighted Power Counting and Perturbative Unitarity
我们考虑在d维Lifshitz点的可重整化性和么正性之间的关系。我们测试树的理论只包含标量和费米子，纯规范理论的么正性。在这两种情况下，我们发现加权幂计数重正化的要求是等价的树么正性。
Tree-level Unitarity in SU(2)$_L\times$U(1)$_Y \times$U(1)$_{Y'}$ Models
该研究推导了SU(2)$_L\times$U(1)$_Y \times$U(1)$_{Y'}$规范理论的树阶幺正性耦合求和规则，阐明了最小扩展模型中弱混合角与$\rho$参数的定义，提出了实用的广义$\rho^\prime$参数，为暗物质等扩展规范模型研究提供支撑。
We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy growing behavior at most of $\mathcal{O} (E)$. This is the special case of the requirement of tree unitarity, which states that the $N$-particle scattering amplitudes at tree-level should grow at most as $\mathcal{O} (E^{4-N})$ in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-…
We present the first comprehensive analysis of the unitarity thresholds and anomalous thresholds of scattering amplitudes at two loops and beyond based on the loop-tree duality, and show how non-causal unphysical thresholds are locally cancelled in an efficient way when the forest of all the dual on-shell cuts is considered as one. We also prove that soft and collinear singularities at two loops and beyond are restricted to a compact region of the loop three-momenta, which is a necessary condition for implementing a local cancellation of loop infrared singularities with the ones appearing in r…
Unitarity-violation in Generalized Higgs Inflation Models
么正性破坏对基于弱尺度粒子物理的非最小耦合暴胀模型提出了挑战。本文研究了具有多个标量场的广义模型散射过程中树能级么正性破坏的能量尺度，其中暴胀子是单重标量场或希格斯粒子。在非最小耦合都相等的限制下（例如在希格斯或其他复杂暴胀子的情况下），树级么正性破坏的尺度与现有结果相匹配。然而，如果暴胀子是一个单线态，并且如果它比模型中的其他标量具有更大的非最小耦合，那么这种层次结构会增加树级幺正性破坏的规模。一个足够强的层次结构将树级幺正性破坏的尺度推到普朗克尺度之上。我们还讨论了试图解决希格斯暴胀中的幺正性破坏问题的模型。
We calculate the tree-level amplitudes for electrically neutral $2\to2$ scattering for the Standard Model Higgs doublet non-minimally coupled to the Ricci scalar. We consider both the metric and the Palatini formulation of gravity. We find the partial wave unitarity limit for a general background field value. Our results are in agreement with previous work. In the electroweak vacuum, tree-level unitarity is violated at $\sim M_\text{Planck}/ξ$ in the metric formulation, and at $\sim M_\text{Planck}/\sqrtξ$ in the Palatini formulation. In the inflationary large field background, the unitarity l…
Self-healing unitarity is an optical illusion
本文检验希格斯暴胀中通过求和真空极化圈修正实现“自愈”树级幺正性的方案，发现其潜在约束仍给出相同的微扰幺正性界限，故并未真正恢复幺正性。
Tree-level unitarity constraints on heavy neutral leptons
本研究通过分析分波矩阵的树级幺正性，探讨了远超电弱标度的重中性轻子约束，发现J=1过程给出最严格耦合限制，并确定了type-I seesaw模型中HNL的最大质量。
Unitarity Method with Spurious Pole
在幺正割方法中，壳层上树能级振幅的紧凑输入是简化计算的关键。虽然BCFW在壳递归关系给出了非常紧凑的树级振幅，但它们通常包含伪极点。在本文中，我们提出了一种方法来处理这个问题，并提供了明确的简单代数函数的各种系数的存在虚假极点。作为应用，我们首次给出了单圈五胶子A（-+）带标量传播子的解析结果（不只是有理项）。
Littlest Higgs Model and Unitarity Constraints
最小希格斯模型的约束使用树级微扰参数，类似于那些用来获得希格斯质量约束。发现微扰幺正性破坏发生在能量标度$\sim 1.5χf$上，其中$f$是π衰变常数的模拟，它决定了理论中的质量标度和强相互作用标度，而$χ$是一个无量纲参数，它和$f$一起决定了理论中重标量的质量标度.
Any loop QCD amplitude at full colour is constructed from kinematic and gauge-group building blocks. In a unitarity-based on-shell framework, both objects can be reconstructed from their respective counterparts in tree-level amplitudes. This procedure is at its most powerful when aligned with flexible colour decompositions of tree-level QCD amplitudes. In this note we derive such decompositions for amplitudes with an arbitrary number of quarks and gluons from the same principle that is used to bootstrap kinematics - unitarity factorisation. In the process we formulate new multi-quark bases and…
Scattering of massive W bosons into gravitinos and tree unitarity in broken supergravity
本文利用规范和质量本征态，研究了破缺相中WW散射到引力子和高吉诺的过程。接着，我们在规范对称性未破缺的情况下，发现了散射振幅的新结构，这种新结构在一定尺度上可以导致么正性的破坏。这是因为在湮灭图中，由于SUGRA顶点的存在，规范玻色子传播子的纵向自由度从振幅中消失了。我们表明，在壳层W的纵向极化成为强烈的相互作用在高能量极限，并列入图表与壳层标量的MSSM不取消的分歧。
Electroweak radiative corrections and unitarity of Standard Model
计算了纵向规范和希格斯玻色子散射振幅的电弱修正。由于Sudakov双曲线，其效果是抑制随着质心能量增加而快速增长的振幅，导致与树级结果相比截面显著减小。例如，由于这些校正，$W^+_{\text{L}}W^-_{\text{L}}$散射的截面的抑制因子从$100\text{TeV}$的质心能量处的0.3变化到$10^{13}\text{TeV}$的质心能量处的因子$10^{-12}$。得到了这些修正对SM么正性界的修正。
Multiscalar production amplitudes beyond threshold
我们提出了精确的树级振幅$H^* \to n~H$，包含一个或两个粒子与非零的三个动量的最终状态，为各种相互作用势。我们发现，有潜力导致树的振幅，满足么正性，不仅在阈值，但也在上述运动学配置，并可能超越。作为一个副产品，我们还计算了$2\to n$树振幅在阈值，并表明，对于不间断的$ϕ^4$理论，他们消失的$n>4~$，标准模型希格斯粒子，他们消失的$n\ge 3~$和模型潜力，尊重树阶么正性，$n$甚至和$n>4~$。最后，我们计算了对称和自发破缺$ϕ^4$理论中单圈$1\to n$振幅的虚部。
Full one-loop amplitudes from tree amplitudes
基于广义$D$维酉性，我们建立了一个有效的多项式复杂度单圈计算算法。它允许从壳上树振幅自动计算可切割构造的{ \it和}单回路散射振幅的有理部分。我们通过（重新）计算QCD中所有四、五和六胶子散射振幅来说明这种方法。
We describe the unitarity approach for the numerical computation of two-loop integral coefficients of scattering amplitudes. It is well known that the leading propagator singularities of an amplitude's integrand are related to products of tree amplitudes. At two loops, Feynman diagrams with doubled propagators appear naturally, which lead to subleading pole contributions. In general, it is not known how these contributions can be directly expressed in terms of a product of on-shell tree amplitudes. We present a universal algorithm to extract these subleading pole terms by releasing some of the…
Calculation of QCD loops using tree-level matrix elements
本文简要讨论了基于广义么正性和参数积分技术的半数值算法中，将颜色和其他量子数一样处理在单圈振幅计算中的可能性。给出了多胶子散射虚修正的数值计算结果。
Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
本文在重顶夸克极限下，利用四维单位性切割方法，构建了自对偶希格斯玻色子与最多四个正螺旋胶子的双环幅度，通过多项式对数部分和有限域积分减少提取出理性的模糊性。
Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
SAMURAI是一种自动数值评估工具，用于对维度正则化方案内的任何散射振幅进行单循环校正。它是基于分解的被积函数根据OPP的方法，扩展到适应的广义d维酉切割技术的实施，并使用多项式插值利用离散傅立叶变换。SAMURAI可以处理被积函数，被积函数既可以是费曼图的分子，也可以是三级振幅的乘积。本文讨论了量子电动力学中的六光子和八光子散射以及量子色动力学中的六夸克散射。SAMURAI已被实施为一个Fortran 90库，公开提供，它可能是一个有用的模块，面向自动化下一个领先的顺序计算相关的LHC现象学的虚拟校正的系统评估。
A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity of this model in the unitary gauge, i.e. employing only physical fields. A new Ward-like identity is used to show that the high-energy behaviour of all amplitudes cannot be more than quadratic; the use of generating functions for all off-shell amplitudes then leads to the unitarity proof.
Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
我们提出了一种替代减少主积分的单圈振幅在任意尺寸使用的么正切割方法。我们分两步进行还原。第一步是一个纯粹的四维切割集成树振幅与质量参数，第二步是应用维位移恒等式的主积分。这种简化是在被积函数级进行的，因此系数可以用代数方法读出。
Maximal Unitarity at Two Loops
我们展示了如何计算系数的双盒基积分在一个无质量的四点振幅的树振幅。我们将展示如何选择合适的多维轮廓进行所需的削减，并从要求的总导数消失的积分推导出一致性方程。我们的系数公式既可以解析地使用，也可以数值地使用。
Partial-Wave Unitarity Bounds on Higher-Dimensional Operators from 2-to-$N$ Scattering
本文提出一种方法，用于推导高维算符在2到N散射中的单元性界限，通过构造正交幅度基并解析计算相空间积分，应用于标准模型有效场论中的维度7和8算符。
We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in $d$ dimensions. We then show that divergent wavefunction cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in $4-2ε$ dimensions and ultraviolet poles in $6-2ε$ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-lev…
One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
本文提出了一种利用么正性和共线极限构造单圈振幅的规范理论解的方法。作为一个例子，我们得到了在具有Parke-Taylor树振幅的螺旋度位形的$N=4$超对称Yang-Mills理论中，$n$胶子散射振幅的单圈贡献.我们证明了我们的$N=4$的猜测是正确的使用相关的单圈$n$ -点积分的一般性质。我们还给出了支配规范理论中单圈螺旋度振幅共线行为的“分裂振幅”。
Tree amplitudes and color decomposition in broken SU(2)
我们提出了SU（2）规范理论中一般树振幅的颜色分解，该理论通过Higgs机制自发破缺.在幺正规范下，我们通过显式地给出一组色序费曼规则来构造色序振幅。这些原始振幅是规范不变的，并且它们在高能极限下保持微扰么正性。作为积木的颜色装饰树振幅，他们允许有效的评估树级散射振幅涉及规范玻色子和希格斯玻色子通过颜色有序电流的Berends-Giele递归关系。我们证明了这种计算方案的效率，通过计算壳层上的振幅为5，6和9个W玻色子在消失的温伯格角的限制。
We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the $D$-dimensional decomposition of integrands of scattering amplitudes into master and surface terms, the computation of tree-level amplitudes in floating point or finite-field arithmetic, the numerical computation of one- and two-loop amplitudes in QCD and Einstein gravity, and functional reconstruction tools. We provide programs that showcase Caravel's main functionaliti…
Global Bases for Nonplanar Loop Integrands, Generalized Unitarity, and the Double Copy to All Loop Orders
本文提出一种基于图的全局圈积分基底构造方法，可同时处理平面与非平面贡献，并直接读出广义幺正性系数，从而将树级双拷贝推广到任意圈阶引力振幅。
Here we discuss color-kinematics duality for higher-derivative QCD-like amplitudes. We explicitly show that the duality still holds in this case and it can be instrumental in constructing the associated quadratic-gravity amplitudes by using the double-copy prescription. This allows one to drastically simplify calculations. We also evaluate some tree-level Compton scattering amplitudes in higher-derivative Yang-Mills and quadratic gravity coupled with matter. Furthermore, we illustrate the application of generalized unitarity method for both cases by studying a specific one-loop amplitude.
The pion - nucleon scattering phase shifts in $s$ and $p$ waves are analyzed using PKU unitarization approach that can separate the phase shifts into different contributions from poles and branch cuts. It is found that in $S_{11}$ and $P_{11}$ channels, there exist large and positive missing contributions when one compares the phase shift from known resonances plus branch cuts with the experimental data, which indicates that those two channels may contain sizable effects from $N^*(1535)$ and $N^*(1440)$ shadow poles. Those results are obtained using tree level results of the $πN$ amplitude.
We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract th…
Relations of loop partial amplitudes in gauge theory by Unitarity cut method
众所周知，在色分解下，胶子的单圈振幅包含单迹结构和双迹结构的振幅，特别是所有双迹结构的振幅都可以表示为单迹结构的振幅的线性组合。利用酉割方法证明了该结果是树级Kleiss-Kuijf关系的自然结果。将酉割方法推广到双环（在这种情况下是三重割），我们表明，与单环情况不同，双和三重迹结构的部分振幅不能表示为主导色单迹结构的部分振幅的线性组合。对于亚铅色单迹结构的分振幅，我们给出了六点和七点振幅的非平凡Kleiss-Kuijf关系，这是本文的一个新结果，用U（1）-解耦方法不能得到。当考虑八点情况时，对于次铅色单道分振幅，Kleiss-Kuijf关系必须修正。
We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the ob…
Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
我们确定了一个大类的单圈振幅的无质量粒子，可以通过从树振幅幺正性构建，没有任何歧义。无质量超对称规范理论的单圈振幅属于这一类;此外，许多非超对称振幅可以重新排列以利用这一结果。作为应用，我们构造了具有Parke-Taylor树振幅的螺旋位形的$N=1$超对称理论中$n$ -胶子散射的单圈振幅，以及$N=4$超杨-米尔斯理论中六胶子散射的单圈振幅.
We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-$R^2$ inflation models by including an additional $R^2 |Φ|^2$-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corr…
Unitarity in Dirichlet Higgs Model
我们表明，一个五维的通用额外的维度模型，紧凑的线段，一贯制定即使规范对称性被打破，完全由非零Dirichlet边界条件的散装希格斯场，没有任何四次相互作用。我们发现，在没有Higgs零模的情况下，由于KK希格斯玻色子玻色子的无限塔的交换，纵向W+W弹性散射振幅被归一化.合成振幅与散射能量成线性比例，表现出五维性质。对于KK标度430（500）GeV，在6.7（5.7）TeV以下满足树能级分波么正性条件，在90%CL内的电弱数据支持该条件。
The UT plots played already for three decades an important role in the tests of the SM and the determination of the CKM parameters. As of 2022, among the four CKM parameters, $V_{us}$ and $β$ are already measured with respectable precision, while this is not the case of $|V_{cb}|$ and $γ$. In the case of $|V_{cb}|$ the main obstacle are the significant tensions between its inclusive and exclusive determinations from tree-level decays. The present uncertainty in $γ$ of $4^\circ$ from tree-level decays will be reduced to $1^\circ$ by the LHCb and Belle II collaborations in the coming years. Unfo…
We compute the $2\rightarrow 2$ gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass $m_{3/2}$) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $κ^2 E^4/m_{3/2}^2$, signaling a potential breakdown of unitarity at a scale $Λ^2\sim m_{3/2}/κ\sim M_{\mathrm{SUSY}}^2$. As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (s…
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