手性费米子新模型：规范相互作用、狄拉克中微子与暗物质的关联

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"这篇研究论文探讨了一种新的理论框架，其中所有轻费米子，包括标准模型（SM）中的粒子和可能存在的超越标准模型的轻粒子，都具有手性，这意味着它们与自发破缺的阿贝尔规范对称性有关。论文提出了一种新的对称性U（1）ν，适用于所有新的轻费米子状态。为了消除异常，必须存在带有非平凡U（1）ν电荷的新费米子场。通过构建具体的模型，作者展示了在U（1）ν对称性破缺后，一部分费米子可以保持无质量，类似于SM中的中微子。此外，一种意外的全局对称性转变为稳定的块状粒子，这些粒子可能作为暗物质候选者，同时解决中微子质量和稳定暗物质的问题。论文中描述的中微子质量机制导致参数化的Dirac中微子质量变小，模型还要求至少存在四个Dirac无菌中微子。此外，作者还提供了一种通用方法，用于构建只有手性费米子的模型，这些模型在U（1）规范对称性下没有异常。" 这篇学术文章发表在JHEP10(2015)046上，由Springer代表SISSA发布。作者Andrè de Gouvêa和Daniel Hernández来自美国西北大学物理与天文学系。他们于2015年9月提交，同年9月接受，并在10月7日发表。研究的核心是将手性费米子与新的规范相互作用关联起来，以及它们如何在解释中微子性质和暗物质方面发挥作用。通过这个理论框架，研究人员不仅提出了一个新的物理模型，还提供了一种技术来处理只包含手性费米子的模型，这些模型在特定规范对称性下是异常自由的。这些发现对于理解基本粒子物理学中的未解之谜，如中微子质量起源和暗物质的性质，具有重要意义。

JHEP10(2015)046

where

= ∂

− ig

, (2.4)

µν

is the U(1)

ﬁeld strength and

the U(1)

gauge ﬁeld. i = 0, 1, 2, k = 1, 2. Note

that, here,

(which has charge −1) represents the complex-conjugated, right-handed

Weyl ﬁeld associate to the 1

left-handed Weyl ﬁeld, etc.

The Yukawa interacti ons in the DS are given by:

− L

DS−Yuk

= f

−

φ + h

−

φ + h

−

∗

+ h.c., (2.5)

where f, h are 2 × 3 and 3 × 3 Yukawa matrices respectively. In what follows t he indices

i, k will be omitted whenever there can be no confusion.

After U(1)

breaking, the 3

−

, 5

−

and 4

ﬁelds “pair up” into three Di r ac fe r mi ons,

labelled from here on χ

, thei r masses-squared associat ed to the eigenvalues of t he 3 × 3

mass-squared matrix M

†

, where

)

= h

, i, j = 0, 1, 2. (2.6)

In ge ne r al , M

is exp ec t ed to have three nonvanishing eigenvalues and hence describe three

massive Dirac fermions.

Similarly, the two 2

−

ﬁelds pair up with two linear combinations of the three 1

ﬁelds

into two Dirac fermions that we label N

. Note that there is n o 2

−

ﬁeld. Hence, there is

a massless chiral linear combination of 1

ﬁelds, that we call ν

. All the masses-squared,

including the vanishing one, can be obtai ne d from the eigenvalues of the 3×3 mass-squared

matrix M

νN

†

νN

, where

νN

)

= f

, i, j = 0, 1, 2 , (2.7)

and where we deﬁne f

≡ 0 for all i = 0, 1, 2. In summary, in the absence of ﬁelds that

connect the DS to the SM , after sy mme t ry breaking, the model contains 3 + 2 = 5 massive

Dirac fermions N

1,2

, χ

1,2,3

, and one massless left-handed Weyl fermion, ν

The unitary rotation of the ﬁelds 1

and 2

−

that renders M

νN

diagonal has no ef-

fect in eq. (

2.3) since these rotations operate independently on ﬁelds of the same charge.

Performing a similar change of basis on the 3

−

, 4

and 5

−

ﬁelds in order to render M

diagonal is diﬀerent since, in this case, the 5

−

and 3

1,2

−

ﬁelds must be grouped together as

components of a 3-vector. If M

is diagonalized by the transformation

†

= diag{M

, M

}, (2.8)

where U, V are 3 × 3 unitary matrices, “mixing” appears among the χ ﬁelds. The U(1)

couplings to the χ

mass eigenstates are oﬀ-diagonal which indicates the presence of “ﬂavor-

changing neutral currents” within each DS generation. Explicitly, in the mass basis, the

couplings are given by



¯σ

−

− 2

− 4¯χ

+ ¯χ



, (2.9)

The Dirac fermions are (ignoring i, k indexes), N

= (2

−

), χ

= (3

−

) , (5

−

), where the

comma indicates that χ are linear combinations of those two Dirac fermions.

– 4 –

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