AdS/CFT与Froissart界限的改进：高能截面研究

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"AdS / CFT对Froissart边界的改进" 在这篇文章中，作者探讨了Froissart边界的高能行为问题，这是一个在强子截面总截面上的重要理论约束。Froissart边界是基于散射振幅的解析性质推导出来的，并且已经被所有可用的强子截面实验数据验证。文章特别关注在强耦合情况下的这一边界，因为在这种情况下，量规/重力对偶（AdS/CFT对应）提供了一种深入理解这种行为的方法。 AdS/CFT对应是弦理论的一个重要成果，它建立了一个联系：在高维Anti-de Sitter（AdS）空间中的量子场论（CFT）与低维边界上的引力理论。通过这个对偶，我们可以从一个理论领域获得另一个领域的信息，即便在强耦合条件下，这通常难以用传统方法处理。在本研究中，作者使用AdS/CFT对应找到了Froissart边界的次主导项。Froissart边界限制了总截面随着能量增加的增长率，即总截面不能无限制地增长，而必须以不超过ln²(s/s₀)的速度增长，其中s是中心-of-mass能量的平方，s₀是一个常数。作者发现了ln(s/s₀)项的负系数，这意味着在AdS/CFT框架下，总截面的增长受到更严格的约束。文章指出，添加这个次主导项以及相应的负系数，对于拟合现有的实验数据是有益的。这表明，利用AdS/CFT对应改进后的Froissart边界能够更好地解释和适应现有的强子截面观测数据，从而提供了更精确的理论预测。此外，研究还讨论了文章的接收和接受日期，以及编辑的信息。这表明，该工作经过同行评审并被物理学杂志《Physics Letters B》接收，反映了其在学术界的重要性和质量。这篇论文展示了如何运用AdS/CFT对应来深化对强相互作用中总截面高能行为的理解，特别是在Froissart边界上进行的次主导项的计算，这对于粒子物理和量子场论的研究具有重要意义。通过这种方式，理论预测可以更加准确地与实验结果相吻合，进一步推动了我们对基本粒子相互作用本质的理解。

Physics Letters B 746 (2015) 285–292

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Improvements to the Froissart bound from AdS/CFT

Verónica Errasti Díez

a,b,∗

, Rohini M. Godbole

, Aninda Sinha

Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012, India

Physics Department, McGill University, 3600 University St, Montréal, QC H3A 2T8, Canada

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

Article history:

Received

5 May 2015

Accepted

7 May 2015

Available

online 13 May 2015

Editor: L.

Alvarez-Gaumé

In this paper we consider the issue of the Froissart bound on the high energy behaviour of total cross

sections. This bound, originally derived using principles of analyticity of scattering amplitudes, is seen

to be satisﬁed by all the available experimental data on total hadronic cross sections. At strong cou-

pling,

gauge/gravity duality has been used to provide some insights into this behaviour. In this work,

we ﬁnd the subleading terms to the so-derived Froissart bound from AdS/CFT. We ﬁnd that a (ln

)

term is obtained, with a negative coeﬃcient. We see that the ﬁts to the currently available data conﬁrm

improvement in the ﬁts due to the inclusion of such a term, with the appropriate sign.

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

1. Introduction

The high energy behaviour of the total cross sections for the

scattering of any two high energy particles has been a subject

of great theoretical interest over many decades, beginning from

Heisenberg [1]. The various bounds one obtains on the rate of

the rise of these cross sections are based just on the analyticity

properties of scattering amplitudes and do not use any knowledge

of the underlying dynamics of the interaction responsible for the

scattering. The most important of all these has been the Froissart

bound [2,3], which states that at high energies, the total cross sec-

tion

for a scattering process 1 +2 → f ( f =any ﬁnal state) has an

upper bound ∼ (ln

). Here

√

s is the centre of mass energy and

√

is an energy scale. Since the bound can be derived from very

general physical arguments, such as the unitarity of the S matrix

and certain analytical properties of the scattering amplitude, it has

to be true in any quantum ﬁeld theory. However, to derive this

in the context of theories of strong interactions, like QCD, one re-

quires

to handle the theory in the non-perturbative regime. As a

result, there exist only models and these usually try to incorporate

known properties of QCD, the modelling aspect involving assump-

tions

and ansaetze about the non-perturbative regime [4–11]. In

fact, analyses of [9,12] in the framework of the Bloch–Nordsiek

improved eikonalised mini jet model [13] indicate a direct relation-

ship

between the Froissart bound at high energy and the dynamics

Corresponding author at: Physics Department, McGill University, 3600 Univer-

sity St,

Montréal, QC H3A 2T8, Canada.

E-mail

addresses: vediez@physics.mcgill.ca (V. Errasti Díez),

rohini@cts.iisc.ernet.in (R.M. Godbole), asinha@cts.iisc.ernet.in (A. Sinha).

of ultra soft gluons, i.e., the behaviour of QCD in the far infrared.

An analysis of the high energy behaviour of the available data on

total hadronic cross sections, while being completely consistent

with the bound, seems to need in the ﬁts the presence of a sub-

leading

(ln

) term to the Froissart bound. Various QCD (inspired)

models use such a subleading term, though there is no theory with

a proper explanation of this subleading behaviour [8,14–16].

In this article, we attempt to seek a theoretical understanding

of this subleading behaviour shown by the data on total cross sec-

tions

at high energies, using the AdS/CFT correspondence [17]. It

is known that the leading term (Froissart bound) can be derived

using AdS/CFT [18–20]. The model based on [21] describes high

energy scattering in a large-N, large-λ gauge theory with broken

conformal symmetry which is achieved by putting a cut-off in the

infra-red (IR). Here N is the number of colours and λ is the ’t Hooft

coupling. When a point mass m is placed on the IR boundary,

the perturbations in the AdS space can be big enough to create

a black hole. The geometrical cross section of such a black hole,

whose radius is equal to the AdS radius, is the gravity dual of the

maximum possible scattering cross section in the ﬁeld theory. In

order to have a more realistic model, which takes into account

ﬁnite coupling corrections (in 1/N and 1/λ), we can incorporate

higher curvature corrections in the dual gravity description. If we

are working perturbatively in the couplings, then the leading cor-

rection

of this type will be at four-derivative order [22]. Such terms

can be redeﬁned into a single Gauss–Bonnet term whose coeﬃ-

cient

describes a 1/N correction – see e.g. [23] for the dictionary

relating the ﬁeld theory to gravity in such a theory. As we will ar-

gue

below, this result will in fact hold for any higher curvature

gravity dual based on the results in [24]. In [19,20] it is argued

http://dx.doi.org/10.1016/j.physletb.2015.05.016

0370-2693/

SCOAP

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