高能质子-质子散射的空洞性：热点与动力学解释

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"这篇文章是Physics Letters B 770 (2017) 149–153的一部分，由Javier L. Albacete和Alba Soto-Ontoso共同撰写，研究了高能质子-质子相互作用中的空洞性现象。文章在2017年1月25日提交，经过修订后于4月13日被接受，并于4月26日在线发布。编辑是J.-P. Blaizot。" 这篇研究论文探讨了在7 TeV质子-质子散射中发现的空心效应，这是一个在较低能量下未观察到的现象。空心效应指的是在碰撞零冲击参数下非弹性密度的减少。研究者通过三个关键要素来解释这一现象： 1. **质子内的胶子热点**：他们将质子内部的胶子热点视为描述散射过程的有效自由度。胶子是强相互作用的基本粒子，是夸克之间相互作用的媒介。在高能碰撞中，质子内部的胶子可以形成局部密集区域，即胶子热点。 2. **热点之间的相关性**：作者假设这些热点在质子内部的横向位置之间存在非平凡的相关性。这意味着热点的位置不是完全独立的，它们可能以某种方式相互影响或关联。 3. **多重散射和Glauber近似**：论文采用类似于Glauber理论的方法来构建散射振幅。Glauber理论是一种处理高能核碰撞的近似方法，它考虑了粒子间的多次无干扰散射，以计算整体的散射概率。在该模型中，随着碰撞能量的增加，热点在横向平面上的扩散或增长自然地解释了空心效应的出现。这表明，随着能量增加，质子内部的胶子热点在空间分布上变得更加广泛，导致在零冲击参数处的非弹性散射事件减少。研究结果对理解高能粒子碰撞的复杂性质，特别是质子结构和强相互作用的细节，具有重要意义。这种理解有助于推进我们对基本粒子物理学，尤其是量子色动力学（QCD）的理解，这是描述强相互作用的标准理论。此外，这些发现对于未来粒子加速器实验的设计和解释，如大型强子对撞机（LHC）的数据分析，也是至关重要的。

Physics Letters B 770 (2017) 149–153

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Hot spots and the hollowness of proton–proton interactions at high

energies

Javier L. Albacete, Alba Soto-Ontoso

∗

CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada E-18071 Campus de Fuentenueva, Granada, Spain

a r t i c l e i n f o a b s t r a c t

Article history:

Received

25 January 2017

Received

in revised form 12 April 2017

Accepted

13 April 2017

Available

online 26 April 2017

Editor:

J.-P. Blaizot

We present a dynamical explanation of the hollowness effect observed in proton–proton scattering at

√

s = 7TeV. This phenomenon, not observed at lower energies, consists in a depletion of the inelasticity

density at zero impact parameter of the collision. Our analysis is based on three main ingredients: we rely

gluonic hot spots inside the proton as ef fective degrees of freedom for the description of the scattering

process. Next we assume that some non-trivial correlation b etween the transverse positions of the hot

spots inside the proton exists. Finally we build the scattering amplitude from a multiple scattering,

Glauber-like series of collisions between hot spots. In our approach, the onset of the hollowness ef fect

is naturally explained as due to the dif fusion or growth of the hot spots in the transverse plane with

increasing collision energy.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

The analysis of experimental data on the elastic proton–proton

differential cross-section at collision energy

√

s = 7TeVmeasured

by the TOTEM Collaboration [1] has revealed a new, intriguing

feature of hadronic interactions: at high energies, the inelasticity

density of the collision does not reach a maximum at zero im-

pact

parameter. Rather, peripheral collisions, where the effective

geometric overlap of the colliding protons is smaller, are more

inelastic or, equivalently, are more effective in the production of

secondary particles than central ones. This phenomenon, not ob-

served

before at lower collision energies, has been referred to as

hollowness [2] or grayness [3–5] of proton–proton collisions by the

authors of the ﬁrst analyses where it was identiﬁed. Our own in-

dependent

analysis of LHC and ISR data, to be described below,

conﬁrms that the inelasticity density of the collision

(s,



b ) ≡

inel



=2Im



(s,



b) −|



(s,



b)|

, (1)

where



(s,



b) is the scattering amplitude in the impact parameter

representation, reaches a maximum at b =0for a collision energy

√

s = 7TeV, as shown in Fig. 1 for different parametrisations of

(s, t) as explained below. In the following we use the notation

t ≡|t|.

The hollowness effect challenges the standard geometric inter-

pretations

of proton–proton collisions. In particular, it precludes

Corresponding author.

E-mail

addresses: albacete@ugr.es (J.L. Albacete), ontoso@ﬁas.uni-frankfurt.de

(A. Soto-Ontoso).

models where the scattering amplitude includes only terms with

a positive dependence on the convolution of the density proﬁles

of the two colliding protons. Indeed, it can be shown that the

inelasticity density associated to any elastic scattering amplitude

thus constructed presents a maximum at zero impact parameter,

regardless how intricate the internal structure of one individual

proton may be [2]. These observations suggest that the scattering

problem may be best formulated in terms of sub nucleonic de-

grees

of freedom which internal dynamics and correlations should

be non-trivial with increasing collision energy. Such is the view

adopted in this work, where we consider hot spots to be the effec-

tive

degrees of freedom in terms of which to discuss the properties

of the scattering amplitude.

The

idea that the gluon content of the proton is concentrated

in domains of small radius R

, much smaller than the proton

electromagnetic radius that controls the valence quark distribution

 R

, is strongly supported by theoretical and phenomeno-

logical

arguments. Further , lattice QCD calculations conﬁrm the

smallness of the correlation length of the gluon ﬁeld strengths in-

side

hadrons [6]. Such domains of high gluonic density have been

dubbed gluonic drops or hot spots in the literature. While the ex-

istence

of hot spots inside hadrons is widely accepted, the debate

on their ultimate dynamical origin remains open. It is commonly

assumed that the gluon content of the proton is radiatively gen-

erated

from valence quarks in DGLAP or BFKL-like cascades. In

this view hot spots relate directly to the Fock space of valence

partons, for which they would provide an effective description.

However, the question arises of how and why the resulting glue

http://dx.doi.org/10.1016/j.physletb.2017.04.055

0370-2693/

SCOAP

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