AI 中文总结
该研究通过将B-L对称性局域化并添加右手中微子与额外希格斯场，扩展了标准模型，数值求解场方程发现宇宙弦轮廓，并揭示高缠绕数下的过冲与同轴奇特现象。
AI 中文摘要
标准模型的一个不自然特征是重子数$B$与轻子数$L$之差是守恒的，这暗示了一个精确的全局对称性。我们通过将差值$B-L$耦合到一个阿贝尔规范场，将其提升为一个自然精确的局域对称性。通过添加右手中微子$\ u_{R}$来消除规范反常。在这种情况下，它们不是惰性的，这禁止了马约拉纳项，但我们通过添加一个希格斯型的单分量复标量场来安排$\ u_{R}$的质量。因此，我们得到了一个动机良好、适度的标准模型（SM）扩展。我们研究了相应的规范-希格斯扇区中的场方程，其中涉及两个希格斯场和非标准U(1)规范场。这导致了一组耦合的非线性微分方程，我们对其进行了数值求解。我们使用柱坐标，从而专注于宇宙弦的结构。对于大量参数，我们确定了弦轮廓和能量密度。这些轮廓取决于每个希格斯场的缠绕数。对于我们的参数，特征弦半径低于$10^{-3}~{\ m fm}$，并且弦张力没有被宇宙微波背景或引力波的观测所排除。作为一个惊人的特殊性，我们发现了——对于高缠绕数——“过冲”和“同轴”轮廓函数。在后一种情况下，标准希格斯场的轮廓在宇宙弦核心附近改变其符号。
英文摘要
It is an unnatural feature of the Standard Model that the difference between the baryon number $B$ and the lepton number $L$ is conserved, which implies an exact, global symmetry. We promote it to a naturally exact, local symmetry by coupling the difference $B-L$ to an Abelian gauge field. Gauge anomalies are cancelled by adding right-handed neutrinos $ν_{R}$. They are not sterile in this case, which forbids the Majorana term, but we arrange for a $ν_{R}$-mass by adding a Higgs-type 1-component complex scalar field. Thus we arrive at a well-motivated, modest extension of the Standard Model (SM). We investigate the field equations in the corresponding gauge-Higgs sector, involving both Higgs fields and the non-standard U(1) gauge field. This leads to a set of coupled, non-linear differential equations, which we solve numerically. We use cylindrical coordinates, thus focusing on the structures of cosmic strings. For a large variety of parameters, we identify the string profiles and energy densities. These profiles depend on the winding number of each of the Higgs fields. For our parameters, the characteristic string radii are below $10^{-3}~{\rm fm}$, and the string tension is not ruled out by observations of the Cosmic Microwave Background or gravitational waves. As an amazing peculiarity, we discover - for high winding numbers - ``overshooting'' and ``co-axial'' profile functions. In the latter case, the profile of the standard Higgs field changes its sign near the core of the cosmic string.
Comments6 pages, 5 figures, talk presented at the 43rd International Conference on High Energy Physics (ICHEP 2026), 30 July to 5 August , 2026 in Natal, Brazil
