解决中子寿命问题：暗物质衰变与β衰变关联系数的研究

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本文主要探讨了中子暗物质衰变（n→χ+anything）的概念，这一现象被提出以解决标准模型（Standard Model, SM）中关于中子寿命τn=888.0（2.0）秒的长期存在的矛盾。SM的标准预测在实验测量如PERKEO II和UCNA合作的实验中未能得到验证，因为它们报告的轴向耦合常数λ与理论值λ= -1.2690不一致。这意味着中子的超标准行为可能源于SM之外的新物理效应，特别是Fierz干扰项，这些项在b~10^-2的精度级别上依赖于标量和张量耦合常数。作者们详细研究了中子β-衰变的所有相关系数，特别关注了这些额外的标量和张量相互作用对Fierz干扰项的影响。他们指出，考虑到这些新物理成分，中子的衰变模式不仅包括传统的SM过程n→p + anything，还包括暗物质衰变模式n→χ+ anything。他们的分析结果显示，这种暗物质衰变模式与当前的实验数据相吻合，即尽管存在束流实验测量到的中子衰变，但并不排除暗物质衰变的可能性。论文发表在《核物理学B》(Nuclear Physics B)杂志的938期，2019年卷，页码114-130。该研究是开放获取的，可以在ScienceDirect网站（www.sciencedirect.com）以及Elsevier的期刊定位服务nuclphysb（www.elsevier.com/locate/nuclphysb）上找到。作者们的工作不仅深化了我们对基本粒子相互作用的理解，而且也为暗物质搜索和超出标准模型的新物理提供了新的研究方向。他们强调，虽然实验数据目前并未直接证实暗物质衰变的存在，但这并不意味着这一理论可以轻易排除，而是激发了进一步实验探索和理论研究的热情。

A.N. Ivanov et al. / Nuclear Physics B 938 (2019) 114–130 117

b =−1.44 × 10

−2

calculated at the neglect of the quadratic contributions of scalar and tensor

coupling constants of interactions beyond the SM [5]. Thus, in order to conﬁrm a possibility

for the neutron to have any dark matter decay modes n →χ +anything we have to show that

a tangible inﬂuence of the Fierz interference term b =−1.44 × 10

−2

is restricted only by the

rate 1/τ

= 1/888.0 s

−1

= 1.126 × 10

−3

−1

of the neutron decay modes n → p + anything,

measured in beam experiments, and such a term does not affect the correlation coefﬁcients of the

electron-energy and angular distributions of the neutron β

−

-decay.

This paper is addressed to the analysis of the contrib

utions of scalar and tensor interactions

beyond the SM to the rate of the neutron decay modes n →p + anything, measured in beam

experiments, and correlation coefﬁcients of the neutron β

−

-decay with polarized neutron, polar-

ized electron and unpolarized proton. We take into account the contributions of the SM, including

a complete set of corrections of order 10

−3

, caused by the weak magnetism and proton recoil,

calculated to next-to-leading order in the large nucleon mass M expansion [53,54](see also [36]

and [23,55]), and radiative corrections of order O(α/π), calculated to leading order in the large

nucleon mass expansion [56–59](see also [36] and [23,55]). We search an

yone solution for the

values of scalar and tensor coupling constants of interactions beyond the SM allowing to ﬁt the

rate 1/τ

=1.126 ×10

−3

−1

of the neutron decay modes n →p +anything, measured in beam

experiments, and the experimental data on the correlation coefﬁcients of the neutron β

−

-decay

under consideration. The existence of such a solution for the values of scalar and tensor coupling

constants of interactions beyond the SM should imply an allowance for the neutron to have the

dark matter decay modes n →χ +anything.

The paper is or

ganized as follows. In section 2 we give the electron-energy and angular dis-

tribution of the neutron β

−

-decay with polarized neutron, polarized electron and unpolarized

proton. We write down the expressions for the correlation coefﬁcients including the contribu-

tions of the SM corrections of order 10

−3

, caused by the weak magnetism and proton recoil

to next-to-leading order in the large nucleon mass expansion of order O(E

/M) and radiative

corrections of order O(α/π), and the contributions of scalar and tensor interactions beyond the

SM, calculated to leading order in the large nucleon mass M expansion. In section 3 we analyse

the rate 1/τ

= 1.126 × 10

−3

−1

of the neutron decay modes n → p + anything, measured

in beam experiments, and ﬁt it by the contribution of the Fierz interference term by taking into

account the quadratic contributions of scalar and tensor interactions beyond the SM. In sec-

tion 4 we analyse possible solutions for the values of scalar and tensor coupling constants. On

this wa

y for a search of one of possible solutions we follow [46,52] and assume that the scalar

and tensor coupling constants are real, and set

=−C

and C

=−

. Such a solution

implies also that in scalar and tensor interactions beyond the SM the neutron and proton cou-

ple to right-handed electron and antineutrino only. We take into account the constraints on the

scalar coupling constant C

, i.e. |C

| = 0.0014(13) and |C

| = 0.0014(12) obtained by Hardy

and Towner [60] and González-Alonso et al. [61], respectively, from the superallowed 0

→0

transitions. Since in the superallowed 0

→ 0

transitions the scalar coupling constant C

commensurable with zero we propose the solution

=−C

= 0. For real scalar and tensor

coupling constants and for

=−C

= 0 and C

=−

we solve Eq. (6) and obtain the so-

lution Eq. (10). In the linear approximation we get C

=−

= 1.11 × 10

−2

and the Fierz

interference term equal to b =−1.44 × 10

−2

. We deﬁne the correlation coefﬁcients in terms of

the coupling constant C

=1.11 ×10

−2

and the Fierz interference term b =−1.44 ×10

−2

. We

show that the contributions of quadratic terms C

are of the standard order 10

−4

. In turn, the con-

tributions of linear terms are of order 10

−2

−10

−3

. In section 5 we analyse i) the contributions of

the Fierz interference term to the electron and antineutrino asymmetries, deﬁned by the neutron

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