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arXiv 0806.4628hep-ph
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具有2个Higgs二重态的电-弱相互作用幺正SU(2/1)模型的量子构造

Quantum construction of a unitary SU(2/1) model of the electro-weak interactions with 2 Higgs doublets

Jean Thierry-Mieg

摘要:

在电-弱相互作用的SU(2)U(1)标准模型中,相互作用甚至Higgs标量场的数目都不是固定的,因而也没有解释弱相互作用的内禀手征性质。将SU(2)U(1)嵌入到李超代数SU(2/1)中填补了这些空白。SU(2/1)的2个最小表示充分描述了电子、中微子、上夸克和下夸克,并将它们的手征性与它们的U(1)荷关联起来,Higgs场具有奇生成元的量子数。但到目前为止,它与么正性有明显的冲突,因为夸克表示不是厄米的,超基灵度规也不是正定的。我们通过假设存在两个复杂的希格斯偶极通过SU(2/1)的奇生成元的手征投影最小地耦合到费米子来解决这个悖论。我们发现,拉格朗日诱导的费米子环是幺正的,由于轻子和夸克之间的平衡需要取消三角形异常和超雅可比恒等式保证光子保持无质量后对称性破缺。此外,拉格朗日量有一个经典的几何解释,在相应的厄米代数的曲率。假设标量和矢量耦合的相对强度不依赖于族的数量,那么希格斯粒子的质量就被限制在$M^2_{H^0_1} + M^2_{H^0_2} = 32/9 M^2_W = 2 (107.2 GeV)^2$。与大统一模型或Wess-Zumino超对称模型相反,SU(2/1)内部超统一模型并没有预言除了2个Higgs二重态之外的任何未观测到的粒子。

英文摘要:

The interactions and even the number of the Higgs scalar fields are not fixed in the SU(2)U(1) standard model of the electro-weak interactions and the intrinsically chiral nature of the weak interactions is not explained. Embedding SU(2)U(1) into the Lie super-algebra SU(2/1) fills these gaps. The 2 smallest representations of SU(2/1) adequately describe the electron, neutrino, up and down quarks and correlate their chiralities with their U(1) charges, and the Higgs fields have the quantum numbers of the odd generators. But so far, there was an apparent conflict with unitarity, because the quark representation is not Hermitian and the super-Killing metric is not positive definite. We solve this paradox by assuming the existence of 2 complex Higgs doublets minimally coupled to the Fermions via the chiral projections of the odd generators of SU(2/1). We find that Lagrangian induced by the Fermion loops is unitary, thanks to the balance between the leptons and the quarks needed to cancel the triangle anomaly and that the super-Jacobi identity guarantees that the photon remains massless after symmetry breaking. In addition, the Lagrangian has a classical geometric interpretation in terms of the curvature of the corresponding Hermitian algebra. Assuming that the relative strength of the scalar and vector couplings does not depend on the number of families constrains the mass of the Higgs to $M^2_{H^0_1} + M^2_{H^0_2} = 32/9 M^2_W = 2 (107.2 GeV)^2$. Contrary to grand-unified or Wess-Zumino super-symmetric models, the SU(2/1) internal super-unification does not predict any unobserved particle besides the 2 Higgs doublets.

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