Kl3衰变：电弱辐射校正的新理论方法

160 浏览量更新于2024-07-16 收藏 976KB PDF 举报

"K l3衰变中电弱辐射校正的新理论框架" 这篇研究论文提出了一种新的理论框架，旨在深入理解K l3衰变中的电弱辐射校正。K l3衰变是粒子物理学中一个重要的过程，涉及到K介子向一个轻子（通常是电子或缪子）和一个中微子的转变。在这个过程中，电弱相互作用——即弱力和电磁力的组合——起着关键作用。辐射校正则是对基本粒子过程进行精确计算时必须考虑的量子效应，这些效应通常在高能物理实验中变得显著。传统的电流代数方法在处理这些校正时遇到了挑战，而新框架则将这种方法与有效场论（EFT）相结合。有效场论允许研究人员在特定能量尺度上忽略高能细节，从而简化计算。在新的框架下，O $$ \mathcal{O} $$（GFα）级别的辐射校正被一个称为Tμν的张量所描述，这个张量包含了带电弱电流和电磁电流的时间乘积。这样的表示法使得复杂的过程变得更为有序和可解。文章进一步指出，在K l3 0 $$ {K} _ {l3} ^ 0 $$通道中，由于受到的低能量常数的约束最少，因此该衰变过程特别适合于进行精确分析。这意味着K l3衰变可以作为一个理想的平台，用于更准确地提取V us这一CKM（Cabibbo-Kobayashi-Maskawa）矩阵元的值。CKM矩阵是描述夸克之间弱相互作用的重要工具，对于理解粒子物理学的标准模型至关重要。研究团队包括Chien-Yeah Seng、Daniel Galviz和Ulf-G. Meißner，他们分别来自德国波恩大学的赫尔姆霍茨核物理研究所和贝特理论物理中心，以及 Forschungszentrum Jülich的研究机构和第比利斯州立大学。他们的工作展示了如何通过创新理论方法改进粒子衰变过程的理解，并为未来实验提供了理论基础，以提高测量的精度和可靠性。这篇论文是在JHEP（Journal of High Energy Physics）发表的，表明了其在高能物理领域的专业性和开放获取的特性，这使得全球的研究者都能免费访问并利用这些研究成果。该研究于2019年11月提交，经过修订后于2020年初被接受，并在同年的2月11日正式发布，反映了科研界快速发展的动态和对精确理论计算的需求。

JHEP02(2020)069

are two types of K

decays:

: K

(p) → π

−

)ν

)

: K

(p) → π

)ν

), (2.3)

where l = e, µ. We may deﬁne the momentum transfer q = p − p

. At low energy, the

charged weak interaction between leptons and quarks is described by Fermi’s theory, with

the following eﬀective Lagrangian:

= −

√

lγ

(1 − γ

)ν

+ h.c. . (2.4)

Therefore, the decay amplitude at tree level is given by:

(0)

= −

√

Kπ

, p)¯u

)γ

(1 − γ

), (2.5)

where the charged weak form factor is deﬁned as F

Kπ

, p) = hπ(p

)|J

µ†

(0) |K(p)i. One

could in general parameterize it in terms of two invariant functions:

Kπ

, p) = V

∗



Kπ

)(p + p

)

+ f

Kπ

−

)(p − p

)



. (2.6)

By Lorentz covariance, it is obvious that only the vector component of J

µ†

contributes

to the form factor. It is also a standard procedure to explicitly factor out the q

= 0

component of f

Kπ

by deﬁning:

Kπ

) =

Kπ

)

Kπ

(0)

Kπ

−

) =

Kπ

−

)

Kπ

(0)

, (2.7)

as the overall factor f

Kπ

(0) can then be studied with non-perturbative methods such as

lattice QCD.

We further deﬁne the following kinematic quantities:

y =

2p.p

, z =

2p.p

, r

, (2.8)

with M

and m

the pion and the lepton mass, in order. With these, the K

decay rate

at tree level is given by:

(0)

Kπ

128π



Kπ

(0)



dydz ¯ρ

(0)

Kπ

(y, z), (2.9)

where

¯ρ

(0)

Kπ

(y, z) = A

(0)

(y, z)



Kπ

)



+ A

(0)

(y, z)

Kπ

)

Kπ

−

) + A

(0)

(y, z)



Kπ

−

)



(0)

(y, z) = 4(1 − y)(y + z − 1) + r

(4y + 3z − 3) − 4r

+ r

− r

)

(0)

(y, z) = 2r

(3 − 2y − z + r

− r

)

(0)

(y, z) = r

(1 − z + r

− r

). (2.10)

It is customary to isolate an isospin factor C

out of the invariant functions f

Kπ

, but we do not do

it here because in the current algebra formalism, the most important pieces of the radiative corrections to

δf

Kπ

will be expressed as momentum integrals, and it would look weird to have a factor C

−1

in front.

– 5 –

JHEP02(2020)069

The physical domain D

of the three-body ﬁnal state can be expressed in two equivalent

ways:

c(z) − d(z) < y < c(z) + d(z), 2

√

< z < 1 + r

− r

c(z) =

(2 − z)(1 + r

+ r

− z)

2(1 + r

− z)

, d(z) =

√

− 4r

(1 + r

− r

− z)

2(1 + r

− z)

(2.11)

a(y) − b(y) < z < a(y) + b(y), 2

√

< y < 1 + r

− r

a(y) =

(2 − y)(1 + r

+ r

− y)

2(1 + r

− y)

, b(y) =

− 4r

(1 + r

− r

− y)

2(1 + r

− y)

(2.12)

depending on whether y or z is ﬁrst integrated.

An important observation from this analysis is that the contribution from f

Kπ

−

)

to the decay rate, which is always attached to A

(0)

2,3

, is suppressed by r

= m

, even

for the muon, this factor still reads ∼ 0.04  1 so the suppression is signiﬁcant. This

also implies the following: the eﬀect of any theoretical uncertainty in the electromagnetic

radiative correction to f

Kπ

−

is suppressed in the total error budget of the K

decay rate.

3 General formalism for radiative corrections in semi-leptonic beta de-

cays, and its application to K

To start our discussions on electroweak radiative corrections, we ﬁrst review the known

results of muon decay which serves as an important reference point. The Fermi constant

= 1.1663787(6)×10

−5

GeV

−2

[3] is deﬁned through the muon lifetime after the inclusion

of O(G

α) electromagnetic radiative corrections calculated in the Fermi theory [19]:

192π

F (x)



1 +

2π



− π

+ O(m

)



, (3.1)

where F (x) = 1 −8x −12x

ln x + 8x

− x

and x = m

In connection to the full SM calculation, it is useful to follow Sirlin’s approach that

splits the full photon propagator in the fermion self-energy diagrams into two pieces [18]:

− M

− k

− M

. (3.2)

Here we have introduced a small photon mass M

as an infrared (IR) regulator. The ﬁrst

term at the right hand side (r.h.s.) of eq. (3.2) describes a “massive photon”, whereas the

second term describes a massless photon with an extra Pauli-Villars (PV) regulator [20]

with Λ = M

. The beneﬁt of such a separation is evident: fermion self-energy corrections

involving the PV-regulated photon propagator, together with the γW box diagram, give

exactly the PV-regulated electromagnetic radiative corrections to the Fermi theory as de-

scribed in eq. (3.1), up to O(G

) discrepancies which may be safely neglected. Meanwhile,

– 6 –

剩余30页未读，继续阅读

weixin_38606169

粉丝: 4
资源: 957

Kl3衰变：电弱辐射校正的新理论方法

重弱希格斯态的费米离子衰变的电弱校正

η（'）Dalitz衰变的辐射校正

基于“放射性物质衰变”建立一个详细的数学模型

geant4如何模拟阿尔法衰变

基于“放射性物质衰变”建立一个详细的微分方程数学模型

geant4如何模拟镭源的阿尔法衰变

least-squares approximation求未知原子衰变的半衰期c++

geant4模拟阿尔法衰变代码

python 用随机方法模拟213Bi衰变为209Bi的级联过程。 画出反应链中各原子的数量随时间的变化过程。

用euler 解决 radioactive decay用python

最新资源

python 用随机方法模拟213Bi衰变为209Bi的级联过程。画出反应链中各原子的数量随时间的变化过程。