Implications of a Higgs field for the spontaneously broken pure R^2 gravity: magnetic monopoles, new interactions and dark radiation

希格斯场对自发破裂的纯 R^2 引力的影响：磁单极子、新相互作用和暗辐射

• 批准号: SAPIN-2019-00034
• 负责人: Edery, Ariel
• 金额: $ 1.09万
• 依托单位: Bishop's University
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=739416
• 关键词: Implications; Higgs; field; spontaneously; broken

Pure R^2 gravity (R^2 gravity alone with no additional R term where R is the Ricci scalar) has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and an extra massless scalar field. This equivalence occurs via the spontaneous breaking of its scale symmetry (it actually possesses a larger symmetry called restricted Weyl symmetry). The massless scalar field is identified as the Goldstone boson of the broken sector. The non-zero cosmological constant implies that in the Einstein action the vacuum or background spacetime have non-zero Ricci scalar and can be either de Sitter (dS) or anti-de Sitter (AdS) but not Minkowski spacetime. In the unbroken sector, the vacuum solution has R=0 and Minkowski spacetime is a background solution. However, it was shown by previous authors that linearized R^2 gravity about Minkowski spacetime does not yield gravitons but only a propagating scalar. Simply put, Minkowski does not "gravitate" at the linearized level in this theory. One of the objectives of our program is to study the implications of adding a Higgs field that is non-minimally coupled to the Ricci scalar in the original action. The Higgs field must be originally massless to preserve the restricted Weyl symmetry but it acquires a mass in the Einstein action after the symmetry is spontaneously broken. There are two crucial consequences to adding the Higgs field. First, in the Einstein action, there is a new interaction term that arises between the Higgs and the extra massless scalar field. Secondly, though the original pure R^2 theory without Higgs field has no viable Minkowski background, it does have one when the Higgs field acquires a non-zero vacuum expectation value. If the Higgs is a triplet of scalar fields, one can study magnetic monopoles under Einstein gravity. My collaborator and I already obtained numerically Einstein-Yang-Mills-Higgs (EYMH) magnetic monopoles with non-minimal coupling in Minkowski, dS and AdS backgrounds. We would now like to study the EYMH magnetic monopoles with the interaction term, something which has never been carried out to date. We can include all the Standard Model fields in our original action with a massless Higgs doublet. After spontaneous symmetry breaking we would recover the usual Standard Model with a massive Higgs but with a novel interaction between the scalar field and the Higgs doublet. This would be of great interest to study as part of physics beyond the Standard Model.

纯r^2重力（仅r^2重力，没有其他r项，其中r是ricci标量）已被证明等同于爱因斯坦重力，具有非零宇宙学常数和一个额外的无质量标量场。这种同等的是通过赞助量表对称性的打破（实际上具有称为限制的Weyl对称性的较大对称性）。无质量标量场被确定为破碎扇形的戈德石玻色子。非零宇宙常数意味着在爱因斯坦动作中，真空或背景时空具有非零ricci标量，并且可以是de Sitter（DS）或反DE保姆（ADS），而不是Minkowski SpaceTime。在不间断的扇区中，真空解决方案具有r = 0，而Minkowski时空是背景解决方案。然而，以前的作者表明，关于Minkowski时空的线性化R^2重力不会产生重力，而仅产生一个传播标量。简而言之，在该理论中，Minkowski不会在线性化的水平上“吸引”。我们程序的目标之一是研究添加HIGGS字段的含义，该字段是在原始动作中与RICCI标量无关的。 Higgs场最初必须无质量来保留受限的Weyl对称性，但是在赞助对称性后，它在爱因斯坦动作中获得了质量。添加希格斯字段有两个至关重要的后果。首先，在爱因斯坦动作中，希格斯和额外的无质量标量场之间出现了一个新的相互作用项。其次，尽管没有希格斯字段的原始纯r^2理论没有可行的Minkowski背景，但是当希格斯字段获得非零真空期望值时，它确实具有一个。如果希格斯是标量场的三胞胎，则可以在爱因斯坦重力下研究磁单脚。我和我的合作者已经在Minkowski，DS和ADS背景中获得了具有非最小耦合的数值爱因斯坦Yang-Mills-higgs（EYMH）磁单磁单极。现在，我们想使用相互作用项研究EYMH磁性单极管，这是从未进行过的。我们可以将所有标准模型字段与无质量的Higgs Doublet一起包含在我们的原始动作中。在赞助对称性破裂之后，我们将用大量的希格斯恢复通常的标准模型，但是标量场和希格斯双峰之间存在新的相互作用。作为标准模型以外的物理学的一部分，研究将是非常有趣的。