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arXiv 0707.3446hep-phhep-th
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高斯背景下夸克和轻子质量的统计理解

Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes

Lawrence J. Hall, Michael P. Salem, Taizan Watari

摘要:

自然的基本理论可能允许一个大的真空景观。即使理论包含统一的规范对称性,标准模型的22个味参数,包括中微子质量,可能在很大程度上取决于这个景观的统计,而不是任何对称性。那么风味参数的测量值不会导致任何基本对称性,而是统计偶然性;它们的精确值并不能提供对基本理论的任何见解,而是风味的整体模式反映了潜在的景观。我们调查是否从一个简单的景观统计随机选择可以解释夸克,带电轻子,中微子的质量和混合的广泛模式。我们提出高斯景观作为简化模型的景观Yukawa耦合结果从重叠积分的零模波函数在高维超对称规范理论。仅用五个自由参数,这样的景观就可以解释味道的所有总体特征,包括:夸克和带电轻子质量的层次结构;小夸克混合角,13混合小于12和23混合;非常轻的马约拉纳中微子质量,太阳与大气中微子质量比与数据一致;轻子12和23混合的分布在大值处达到峰值,而13混合的分布在低值处达到峰值;以及夸克和轻子扇区中的序统一CP违反相位。虽然风味参数的统计分布是广泛的,但分布对额外维度的几何形状的变化是鲁棒的。通过对观测值的松散切割来约束分布,导致中微子13混合、CP破坏和无中微子双β衰变测量的分布变窄。

英文摘要:

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the Standard Model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wavefunctions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including: the hierarchy of quark and charged lepton masses; small quark mixing angles, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic 12 and 23 mixings that are peaked at large values, while the distribution for 13 mixing is peaked at low values; and order unity CP violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of 13 mixing, CP violation, and neutrinoless double beta decay.

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