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arXiv 1610.09293hep-ph
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紫外-完全复合-Higgs模型中介子共振谱的非微扰分析

Non-perturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model

Nicolas Bizot, Michele Frigerio, Marc Knecht, Jean-Loïc Kneur

备注：
v1: 65 pages, 25 figures. v2: 70 pages, 29 figures; several references and clarifications included; two additional subsections on the S-parameter and on the spectral sum rules for mixed mesons
发表信息：
Phys. Rev. D 95, 075006 (2017)
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摘要：

我们考虑一个矢量类规范理论的费米子，限制在多TeV的规模，并实现了希格斯粒子作为一个复合戈德斯通玻色子。弱相互作用嵌入在自发破缺的$SU(4)$味群的未破缺子群$Sp(4)$中。介子共振在费米子双线性的两点算符中表现为极点，包括戈德斯通玻色子加上一个大质量赝标量$η'$，以及标量、矢量和轴矢量。我们计算这些介子的质量谱，以及它们的衰变常数，在手征极限，在近似的hypercolour $Sp(2N)$动力学描述的四个费米子运营商，La Nambu-Jona Lasinio。通过绘制$1/N$展开式中的主导图，我们发现自旋为1的状态超出了LHC的范围，而自旋为0的电弱单重态可能与Goldstone玻色子衰变常数$f\sim 1$ TeV一样轻。我们也面对我们的结果与一组可用的谱求和规则。为了提供复合的顶夸克伙伴，该理论包含了额外的费米子，它们同时带有超色和普通色，并带有相关的味色破坏模式$SU(6)/SO(6)$。我们确定和分析几个非平凡的功能，完整的两个部门规范理论：'t~Hooft异常匹配条件;高维运营商，其中包括超色轴单重态异常的影响;耦合质量间隙方程;单重介子的两个部门之间的混合，导致额外的戈德斯通玻色子$η_0$，和新的光谱求和规则。假设四费米子相互作用在两个扇区中的强度相同，我们发现色矢量和标量介子的质量为$\gtrsim 4 f$，而胶子环诱导的色赝Goldstone玻色子的质量为$\gtrsim 1.5f$ .

英文摘要：

We consider a vector-like gauge theory of fermions that confines at the multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone boson. The weak interactions are embedded in the unbroken subgroup $Sp(4)$ of a spontaneously broken $SU(4)$ flavour group. The meson resonances appear as poles in the two-point correlators of fermion bilinears, and include the Goldstone bosons plus a massive pseudoscalar $η'$, as well as scalars, vectors and axial vectors. We compute the mass spectrum of these mesons, as well as their decay constants, in the chiral limit, in the approximation where the hypercolour $Sp(2N)$ dynamics is described by four-fermion operators, à la Nambu-Jona Lasinio. By resumming the leading diagrams in the $1/N$ expansion, we find that the spin-one states lie beyond the LHC reach, while spin-zero electroweak-singlet states may be as light as the Goldstone-boson decay constant, $f\sim 1$ TeV. We also confront our results with a set of available spectral sum rules. In order to supply composite top-quark partners, the theory contains additional fermions carrying both hypercolour and ordinary colour, with an associated flavour symmetry-breaking pattern $SU(6)/SO(6)$. We identify and analyse several non-trivial features of the complete two-sector gauge theory: the 't~Hooft anomaly matching conditions; the higher-dimension operator which incorporates the effects of the hypercolour axial-singlet anomaly; the coupled mass-gap equations; the mixing between the singlet mesons of the two sectors, resulting in an extra Goldstone boson $η_0$, and novel spectral sum rules. Assuming that the strength of the four-fermion interaction is the same in the two sectors, we find that the coloured vector and scalar mesons have masses $\gtrsim 4 f$, while the masses of coloured pseudo-Goldstone bosons, induced by gluon loops, are $\gtrsim 1.5f$.

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