大倾角下B→ππℓν衰变的QCD解析重构与新预测

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本文主要探讨的是大倾角下B介子衰变为两个π介子和一个轻子ν的量子色动力学(QCD)分解问题。在这个高阶物理过程中，B→ππℓν的形状因子是关键，它们反映了强相互作用在衰变过程中的动态。作者们利用解析性质的新约束，重新审视了大π介子质量区间的B→ππ形貌因子，这是之前研究中较少探索的领域。作者们基于解析性分析的理论基础，特别是QCD的主导旋度因子分解公式，提出了一种形状因子的参数化方法。这种方法综合考虑了所有已知的分析特性，包括B*极点的影响，这在处理大π介子质量下的衰变行为时尤为重要。这种参数化策略使得他们在计算上能够更加准确地连接QCD因子分解的结果与B*共振区域的特性。通过这种参数化插值，他们得以预测出比以往研究覆盖更广泛的相空间区域中的B→ππℓν衰减率。特别值得注意的是，他们计算得到的部分积分分支比高达约\( \mathcal{B} \sim 10^{-6} \)，这表明非共振半轻子衰变在Belle II实验中是可测量的，对实验数据的贡献不容忽视。这篇发表于《Journal of High Energy Physics》(JHEP)的开放获取文章，展示了理论物理学家们在精确计算和实验观测之间的桥梁作用，为深入理解B介子的衰变机制提供了重要的理论支持。作者们的成果不仅提升了我们对B→ππℓν过程的理解，也为未来的实验计划提供了有价值的数据预测，对于推动高能物理领域的前沿研究具有重要意义。

JHEP10(2018)030

Due to the large number of independent kinematic variables in the four-body decay

B → ππ`ν, the analytic structure of the B → ππ form factors is somewhat more compli-

cated than for the B → π or B → ρ form factors. Following [10, 13] we assign the momenta

as follows:

−

(p) → π

)π

−

)¯ν(q

−

) , (1.1)

and deﬁne

q = q

+ q

, k = k

+ k

¯q = q

− q

k = k

− k

(1.2)

In the following we use k

, q

, and

ˆq

≡ (p − k

)

= (q + k

)

(1.3)

as the independent kinematic variables, with q

≤ (M

−

√

)

and ˆq

≤ M

− k

. The

variable ˆq

can be exchanged for the dipion helicity angle θ

[10, 13]

q ·

k =

√

cos θ

for k

 M

, (1.4)

with λ

= λ(q

, k

, M

) the K¨all´en function. We use both representations; particularly,

we use the variable ˆq

to make the analytic structure of the form factors more readily

understandable. Hadronic intermediate states, which may contribute to the B → ππ`ν

decay in a dual way compared to the LO partonic picture, include:

B → R

(→ ππ)`ν. The R

= ρ, f

, ρ

, . . . are the light resonances arising from a branch

cut in the variable k

. For a point-wise description of the k

spectrum detailed

knowledge of the cut is required. However, in this work we focus on more inclu-

sive observables far above the ππ threshold, which do not resolve the individual R

resonances.

B → X

(→ `ν)ππ. Here, the X

= B

∗

, B

, B is either the vector, axialvector or pseu-

doscalar resonance, respectively, that contributes to the q

spectrum of the individual

form factors.

B → B

∗

(→ π

`ν)π

. The heavy vector meson B

∗

contributes here as a resonance in

the ˆq

≡ (p − k

)

= (q + k

)

spectrum. The aim of this article is to improve our

description of the B → ππ form factors by including this resonant contribution and

to thereby extend the form factors’ reach.

Our parametrization makes use of two conformal maps to accelerate convergence. The use

of residues to improve our understanding of the form factors is an approach known from

prior phenomenological studies, such as those deriving unitarity bounds for b → c form

factors [19, 20] and b → u form factors [21].

In the phase space of interest — i.e. the phase space for the semileptonic B decay —

the amplitudes are thus analytic functions of q

and ˆq

, while they exhibit a branch cut

– 2 –

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大倾角下B→ππℓν衰变的QCD解析重构与新预测

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