论文标题
Flatland：标准模型的Abelian扩展，具有半简单的完成
Flatland: abelian extensions of the Standard Model with semi-simple completions
论文作者
论文摘要
我们参数所有可能的风味非宇宙$ \ mathfrak {u}（1）_x $扩展标准模型的扩展的空间，该模型嵌入了无异常的半简化理论中，包括最多三个右手中微子。更一般而言，我们通过此类半简单完成的SM的所有$ \ Mathfrak {u}（1）$来参数所有Abelian扩展名（即）。 Abelian扩展的最终空间是尺寸$ \ leq 6 $的平面集合。从数值上讲，我们发现大约$ 2.5 \％$的无异常$ \ mathfrak {u}（1）_x $ SM的扩展，最大充电率为$ \ pm 10 $可以嵌入此类半简单量表理论中。 $ \ mathfrak {g} = \ mathfrak {su}（12）（12）\ oplus \ mathfrak {su}（2）_l \ oplus \ mathfrak \ mathfrak {su}（su}（su}（su}（su}（2）_r，我们还提供了一个简单的计算机程序，该程序测试是否给定的$ \ Mathfrak {u}（1）_ {X^1} \ oplus \ Mathfrak \ Mathfrak \ Mathfrak {u}（1）_ {x^2} \ oplus \ dots $ coluckement $ coluckement a puragements具有半含量的完成，如果它可以完成，如果它确实可以，如果它可以输出Maximal a Maximal a set a Maximal fut n set a set all fut n set all fut n set all ful n set。 $ \ mathfrak {sm} \ oplus \ mathfrak {u}（1）_ {x^1} \ oplus \ mathfrak {u}（1）_ {x^2} \ oplus \ dots $ dots $模型可以嵌入。我们希望这是一个有用的工具，可以指向从$ \ Mathfrak {sm} \ oplus \ Mathfrak {u}（1）_ {x^1} \ oplus \ mathfrak \ Mathfrak {u}（1）_ {x^2} \ oplus \ oplus \ dots $模型，这些模型都可以完成许多景观。
We parametrise the space of all possible flavour non-universal $\mathfrak{u}(1)_X$ extensions of the Standard Model that embed inside anomaly-free semi-simple gauge theories, including up to three right-handed neutrinos. More generally, we parametrise all abelian extensions (i.e.) by any number of $\mathfrak{u}(1)$'s) of the SM with such semi-simple completions. The resulting space of abelian extensions is a collection of planes of dimensions $\leq 6$. Numerically, we find that roughly $2.5\%$ of anomaly-free $\mathfrak{u}(1)_X$ extensions of the SM with a maximum charge ratio of $\pm 10$ can be embedded in such semi-simple gauge theories. Any vector-like anomaly-free abelian extension embeds (at least) inside $\mathfrak{g} = \mathfrak{su}(12)\oplus \mathfrak{su}(2)_L\oplus \mathfrak{su}(2)_R$. We also provide a simple computer program that tests whether a given $\mathfrak{u}(1)_{X^1}\oplus \mathfrak{u}(1)_{X^2}\oplus \dots$ charge assignment has a semi-simple completion and, if it does, outputs a set of maximal gauge algebras in which the $\mathfrak{sm}\oplus\mathfrak{u}(1)_{X^1}\oplus \mathfrak{u}(1)_{X^2}\oplus \dots$ model may be embedded. We hope this is a useful tool in pointing the way from $\mathfrak{sm} \oplus\mathfrak{u}(1)_{X^1}\oplus \mathfrak{u}(1)_{X^2}\oplus \dots$ models, which have many phenomenological uses, to their unified gauge completions in the ultraviolet.
