arXiv 1209.04742012-09hep-ph

希格斯质量符合问题：为什么希格斯质量是$m_H^2=m_Z m_t$？

The Higgs mass coincidence problem: why is the higgs mass $m_H^2=m_Z m_t$?

E. Torrente-Lujan

备注：: Major changes. figures added

摘要：

根据最近LHC玻色子的发现，我们给出了$ρ_t=m_Z m_t/m_H^2$比值的唯象估计，由LHC组合的$m_H$值，我们得到（$ (1σ)$）$$ρ_t^{(exp)}= 0.9956\pm 0.0081.$$。类似地，我们评估比率$ρ_{Wt}=(m_W + m_t)/(2 m_H)$。从最新的质量值，我们得到$ρ_{Wt}^{(exp)}= 1.0066\pm 0.0035\; (1σ).$希格斯质量是数字接近（在$1\%$水平）的$m_H\sim (m_W+m_t)/2$。从这些关系式中，我们可以将任何两个质量比写成温伯格角的函数（精确度为$1\%$或更高）：\begin{eqnarray} \frac{m_i}{m_j}&\simeq & f_{ij}(θ_W),\quad i,j=W,Z,H,t. \end{eqnarray}例如：$m_H/m_Z \simeq 1+\sqrt{2} s_{θ_W/2}^2$，$m_H/m_t c_{θ_W} \simeq 1-\sqrt{2}s_{ θ_W/2}^2$。在极限$\cosθ_W\to 1$中，所有的质量将变为相等的$m_Z=m_W=m_t=m_H$。我们回顾了这一比例在SM和超越的理论情况。在SM中，这些关系在RGE下相当稳定，指出一些潜在的UV对称性。在SM中，这样的比率暗示了$λ\simeq κ\left (g^2+{g'}{}^2\right )$与$κ\simeq 1+o(g/g_t)$类型的非因果关系。此外，关系$m_i/m_j \simeq f_{ij}(θ_W)$的存在可以解释为一个提示的作用$SU(2)_c$保管对称性，连同其他未知的机制。如果没有对称性来解释，那么在SM中，就会出现希格斯质量符合问题，为什么$ρ_t,ρ_{Wt}$的比率如此接近1，我们能找到一种机制，自然地给出$m_H^2=m_Z m_t$，$2m_H= m_W+m_t$？

英文摘要：

On the light of the recent LHC boson discovery, we present a phenomenological evaluation of the ratio $ρ_t=m_Z m_t/m_H^2$, from the LHC combined $m_H$ value, we get ($ (1σ)$) $$ρ_t^{(exp)}= 0.9956\pm 0.0081.$$ This value is close to one with a precision of the order $\sim 1\%$. Similarly we evaluate the ratio $ρ_{Wt}=(m_W + m_t)/(2 m_H)$. From the up-to-date mass values we get $ρ_{Wt}^{(exp)}= 1.0066\pm 0.0035\; (1σ).$ The Higgs mass is numerically close (at the $1\%$ level) to the $m_H\sim (m_W+m_t)/2$. From these relations we can write any two mass ratios as a function of, exclusively, the Weinberg angle (with a precision of the order of $1\%$ or better): \begin{eqnarray} \frac{m_i}{m_j}&\simeq & f_{ij}(θ_W),\quad i,j=W,Z,H,t. \end{eqnarray} For example:$m_H/m_Z \simeq 1+\sqrt{2} s_{θ_W/2}^2$, $m_H/m_t c_{θ_W} \simeq 1-\sqrt{2}s_{ θ_W/2}^2$. In the limit $\cosθ_W\to 1$ all the masses would become equal $m_Z=m_W=m_t=m_H$. We review the theoretical situation of this ratio in the SM and beyond. In the SM these relations are rather stable under RGE pointing out to some underlying UV symmetry. In the SM such a ratio hints for a non-casual relation of the type $λ\simeq κ\left (g^2+{g'}{}^2\right )$ with $κ\simeq 1+o(g/g_t)$. Moreover the existence of relations $m_i/m_j \simeq f_{ij}(θ_W)$ could be interpreted as a hint for a role of the $SU(2)_c$ custodial symmetry, together with other unknown mechanism. % Without a symmetry at hand to explain then in the SM, it arises a Higgs mass coincidence problem, why the ratios $ρ_t,ρ_{Wt}$ are so close to one, can we find a mechanism that naturally gives $m_H^2=m_Z m_t$, $2m_H= m_W+m_t$?.

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