标题： 标准模型中的塔和层次从量子引力的涌现中得到 显示英文标题

标题： Towers and Hierarchies in the Standard Model from Emergence in Quantum Gravity

摘要： 基于量子引力的论点，有人提出，在紫外截断尺度以下轻粒子的所有动能项都可能通过量子（环）修正在红外区产生。这些环路修正涉及无限塔状状态变得轻量化（例如，Kaluza-Klein 或弦塔）。我们研究了这一“涌现提案”对标准模型（SM）基本尺度的影响。在这个框架下，所有 Yukawa 耦合在紫外区为一阶量级，较轻世代的小 Yukawa 值是由于由状态塔诱导出的大异常维度所致。因此，观测到的夸克和轻子质量层次反映了低于量子引力尺度（$\Lambda_{\text{QG}}$）的状态塔结构。与实验观测一致的小狄拉克中微子质量出现是因为存在一个质量为$m_{0}\simeq Y_{\nu_3}M_p\simeq 7\times 10^5$GeV 的 SM 奇异态塔，打开了一个新的额外维度，而紫外截断尺度则出现在$\Lambda_{\text{QG}}\lesssim 10^{14}$GeV。如果施加 Swamp 地带条件（$m_{\nu_1}\lesssim V_0^{1/4}$），其中最轻的中微子记为$\nu_1$，则会出现与电弱（EW）尺度和宇宙常数（c.c.）尺度（分别记为$M_{\text{EW}}$和$V_0$）相关的额外约束，这本身是通过对 SM 圆圈紧致化得到的 3D 真空应用 AdS 非 SUSY 猜想或 AdS/dS 距离猜想后产生的。 特别是，电弱标度与额外维度的标度满足关系式${m_0 \, M_{\text{EW}}\lesssim 10^{2}\, V_0^{1/4}M_p}$，从而将电弱层次问题与宇宙学常数问题联系起来。因此，所有基本标度都可以表示为宇宙学常数的幂，即$m_{\bullet}\sim V_0^\delta M_p^{1-4\delta}$。SUSY破缺的能量标度为$m_{3/2}\lesssim 7\times 10^5$GeV，这有利于一种可能在LHC和/或FCC上被测试的Mini-Split情形。 显示英文摘要

摘要： Based on Quantum Gravity arguments, it has been suggested that all kinetic terms of light particles below the UV cut-off could arise in the IR via quantum (loop) corrections. These loop corrections involve infinite towers of states becoming light (e.g. Kaluza-Klein or string towers). We study implications of this Emergence Proposal for fundamental scales in the Standard Model (SM). In this scheme all Yukawa couplings are of order one in the UV and small Yukawas for lighter generations appear via large anomalous dimensions induced by the towers of states. Thus, the observed hierarchies of quark and lepton masses are a reflection of the structure of towers of states that lie below the Quantum Gravity scale, $\Lambda_{\text{QG}}$. Small Dirac neutrino masses consistent with experimental observation appear due to the existence of a tower of SM singlet states of mass $m_{0}\simeq Y_{\nu_3}M_p\simeq 7\times 10^5$ GeV, opening up a new extra dimension, while the UV cut-off occurs at $\Lambda_{\text{QG}}\lesssim 10^{14}$ GeV. Additional constraints relating the Electro-Weak (EW) and cosmological constant (c.c.) scales (denoted $M_{\text{EW}}$ and $V_0$) appear if the Swampland condition $m_{\nu_1}\lesssim V_0^{1/4}$ is imposed (with $\nu_1$ denoting the lightest neutrino), which itself arises upon applying the AdS non-SUSY Conjecture or the AdS/dS Distance Conjecture to the 3d vacua from circle compactifications of the SM. In particular, the EW scale and that of the extra dimension fulfill ${m_0 \, M_{\text{EW}}\lesssim 10^{2}\, V_0^{1/4}M_p}$, thus relating the EW hierarchy problem to that of the c.c. Hence, all fundamental scales may be written as powers of the c.c., i.e. $m_{\bullet}\sim V_0^\delta M_p^{1-4\delta}$. The scale of SUSY breaking is $m_{3/2}\lesssim 7\times 10^5$ GeV, which favours a Mini-Split scenario that could be possibly tested at LHC and/or FCC.