低温下软壁AdS/QCD中核子电磁特性和Roper共振研究

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本文探讨了在软壁AdS/QCD框架下，对核子在有限温度T下的电磁特性以及Roper共振的性质进行的研究。软壁AdS/QCD是一种基于AdS/CFT猜想的模型，它将强相互作用中的问题映射到AdS空间的引力理论中，从而简化计算并提供物理现象的粗略描述。作者们利用之前他们开发的软壁AdS/QCD方法的扩展版本，特别关注了在AdS Poincaré度量标准下的AdS几何。由于AdS-Schwarzschild几何带来的影响在低温下（即小温度T）相对较小，只在O(T^4)阶次级效应中起作用，因此在小温度范围内，研究者忽略了这种几何结构的温度依赖性。这一处理与Hawking-Page相变的概念相符，表明在临界温度附近，热AdS/QCD的物理行为会发生转换。核心内容是引入了一种有效电势，它与AdS空间中的全息坐标z成二次依赖，且受胶子和夸克冷凝物的影响。这种有效电势的温度依赖性主要体现在O(T^2)阶，这在低温条件下成为分析的关键因素。研究的重点在于通过这个有效电势来探讨核子的质量、电磁形状因子以及Roper共振的螺旋度振幅等特性。具体而言，文章详细分析了核子的电磁形貌，包括其电荷和磁矩分布，这些都是通过计算电磁形状因子来揭示的。同时，Roper共振，尽管在低能区通常被理论家用来解释对核子内部结构的复杂性，也被纳入了研究范围，其与核子的过渡过程得到了探究。总结起来，这篇研究利用了软壁AdS/QCD模型在高温背景下对基本粒子性质的预测，特别是在理解核子和Roper共振在有限温度下的行为，提供了新的见解。它不仅展示了AdS/QCD理论在量子色动力学领域内的应用潜力，也为实验物理学与理论计算之间的桥梁搭建了一定程度的桥梁。读者可以通过链接（Available online at www.sciencedirect.com 和 www.elsevier.com/locate/nuclphysb）访问全文，获取更深入的技术细节和结果。

4 T. Gutsche et al. / Nuclear Physics B 952 (2020) 114934

where  =|0|¯qq|0| is the quark condensate. The Ioffe formula gives reasonable agreement

with data. However, as stressed in Ref. [25], there is a puzzle, since this formula implies that a

large contribution to baryon masses comes from the quark condensate. In the overview to this

problem presented in Ref.

[25]it is mentioned that conceptually different theoretical approaches

(lattice QCD [26], chiral quark-soliton model [27], dilaton compensated model based on hidden

local symmetry [28], holographic QCD [29]) arrived at similar conclusions, which is that the

main source of the baryon mass is due to the quark condensate independent term m

plus a

correction due to the quark condensate. In particular, in Ref. [28]the following formula for the

baryon mass M

was proposed:

+() , (3)

where () is the correction due to the quark condensate. In Ref. [29]it was found that there are

two different regimes of low and large values of the quark condensate  = (N

/2π

) σ . At low

values of σ the baryon mass is saturated by the condensate independent term 887 MeV controlled

by the conﬁnement scale, while at large values of σ it is deﬁned by the scalar repulsion force and

linearly depends on the quark condensate [29]:

=max[887;−407 +940 (z

1/3

)] MeV , (4)

where z

= (323 MeV)

−1

is the position of the infrared hard wall in the holographic approach

that we are considering. Note that the physical explanation of the dominant term m

is different

in various approaches: constituent quark mass, qluon condensate, skyrmion, etc.

In our approach the baryon masses are proportional to the scale parameter κ occurring in the z

dependent holographic potential U

(z) = κ

. This corresponds to the square of the linearized

part of the Cornell potential, because the equation of motion (EOM) for the wave function with

corresponds to the square of the EOM with the Cornell potential, as proven in Refs. [30,31].

Here κ = 383 MeV is the dilaton scale parameter ﬁxed in the previous study. In order to get

explicit expressions for the baryon masses in terms of quark condensates we parametrize the

scale parameter as:

=κ

(1 −y) +



y, (5)

where y is the mixing parameter. The speciﬁc normalization of the condensate containing term is

chosen for convenience. The squared nucleon mass in the soft-wall AdS/QCD model, for leading

twist τ =3, is given by [6]:

=8 κ

, (6)

then one gets:

=8 κ

(1 −y) +

8 π



y. (7)

Next, using the Ioffe formula (2) one has

=8 κ

(1 −y) + M

y. (8)

This last relation has a very clear physical meaning. Here and in Eq. (5)the limits y =0 and y = 1

correspond to the cases of vanishing and fully dominating quark condensates in the expression

for the nucleon mass and κ

. In previous papers we consider the case y = 1. Here we vary the

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