重子手性扰动理论下Roper共振宽度的NLO计算与实验验证

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在《物理快报B》(Physics Letters B, Vol. 760, Issue 2, 2016)的一篇文章中，Jambul Gegelia、Ulf-G. Meißner、De-Liang Yao等人探讨了重子手性扰动理论（Baryon Chiral Perturbation Theory, BChPT）中的一个重要课题——Roper共振的宽度。BChPT是一种在低能量强相互作用领域广泛应用的有效理论框架，它基于量子色动力学（Quantum Chromodynamics, QCD）的对称性和破缺，用于描述强子间的相互作用，特别是在轻子和胶子的低能行为。研究者们在这个工作里扩展了BChPT，将介子（如π介子）、核子（nucleon）、δ（即N*(1232)或Delta resonance）和Roper共振（N*(1440)或Roper state）视为动态的自由度，这些共振是量子数类似于核子但质量较高的粒子，它们在描述粒子间非线性相互作用时起到关键作用。理论计算是在次主导阶（next-to-leading order, NLO）进行的，这意味着考虑了比基本项更复杂且包含更高阶修正的效应。文章的核心内容涉及到三个未知的低能量常数（low-energy constants, LECS），这些参数在BChPT中起到了调节理论预测与实验观测之间关系的作用。通过对Roper共振衰变宽度的实验数据进行比较，其中一个LECS被确定下来。接下来，作者假设Roper相互作用的其他两个耦合系数保持与核子相似的值，这样能够使理论预言与实验测量的Roper宽度相吻合。这项工作的重要意义在于，它不仅验证了BChPT在描述Roper共振这类高能态粒子方面的有效性，而且还提供了对低能常数的进一步理解，有助于推动对强相互作用本质的深入探索。通过这样的计算，理论家们能够更好地预测尚未被精确测量的物理现象，并为实验设计提供指导，特别是在核物理学和粒子物理的交叉领域。这篇文章展示了理论与实验的密切结合，以及BChPT在解释和预测重子谱特性方面的重要作用。

Physics Letters B 760 (2016) 736–741

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

The width of the Roper resonance in baryon chiral perturbation theory

Jambul Gegelia

a,b

, Ulf-G. Meißner

a,c

, De-Liang Yao

a,∗

Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany

Tbilisi State University, 0186 Tbilisi, Georgia

Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany

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

Article history:

Received

17 June 2016

Received

in revised form 26 July 2016

Accepted

26 July 2016

Available

online 29 July 2016

Editor: W.

Haxton

We calculate the width of the Roper resonance at next-to-leading order in a systematic expansion of

baryon chiral perturbation theory with pions, nucleons, and the delta and Roper resonances as dynamical

degrees of freedom. Three unknown low-energy constants contribute up to the given order. One of them

can be ﬁxed by reproducing the empirical value for the width of the Roper decay into a pion and a

nucleon. Assuming that the remaining two couplings of the Roper interaction take values equal to those

of the nucleon, the result for the width of the Roper decaying into a nucleon and two pions is consistent

with the experimental value.

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

1. Introduction

At low energies, chiral perturbation theory [1,2] provides a suc-

cessful

description of the Goldstone boson sector of QCD. It turns

out that a systematic expansion of loop diagrams in terms of small

parameters in effective ﬁeld theories (EFTs) with heavy degrees

of freedom is a rather complicated issue. The problem of power

counting in baryon chiral perturbation theory [3] may be solved

by using the heavy-baryon approach [4–6] or by choosing a suit-

able

renormalization scheme [7–10]. The  resonance and (axial)

vector mesons can also be included in EFT (see e.g. Refs. [11–20]).

On the other hand, the inclusion of heavier baryons such as the

Roper resonance is more complicated.

Despite

the fact that the Roper resonance was found a long

time ago in a partial wave analysis of pion–nucleon scattering data

[21], a satisfactory theory of this state is still missing. The Roper

is particularly interesting as it is the ﬁrst nucleon resonance that

exhibits a decay mode into a nucleon and two pions, besides the

decay into a nucleon and a pion. Also, the Roper appears unexpect-

edly

low in the spectrum, below the ﬁrst negative parity nucleon

resonance, the S

(1535). It is therefore timely to address this

state in a chiral EFT. First steps in this direction have been made

in Refs. [22–26]. In particular, the pion mass dependence of the

pole mass and the width of the Roper resonance has been stud-

ied

in Refs. [22,23] and the magnetic moment was investigated in

Corresponding author.

E-mail

addresses: j.gegelia@fz-juelich.de (J. Gegelia), meissner@hiskp.uni-bonn.de

(U.-G. Meißner),

d.yao@fz-juelich.de, yaodeliang@pku.edu.cn (D.-L. Yao).

Ref. [24]. The authors of Ref. [25] studied the impact of the ex-

plicit

inclusion of the Roper resonance in chiral EFT on the P

pion–nucleon scattering phase shift, and Ref. [26] presented new

ideas on the extension of the range of applicability of chiral EFT

beyond the low-energy region.

this work we calculate the width of the Roper resonance in a

systematic expansion in the framework of baryon chiral perturba-

tion

theory with pions, nucleons, the delta and Roper resonances

as explicit degrees of freedom.

The

paper is organized as follows: in Section 2 we specify the

effective Lagrangian, in Section 3 the pole mass and the width

of the Roper resonance are deﬁned and the perturbative calcula-

tion

of the width is outlined in Section 4. In Section 5 we discuss

the renormalization and the power counting applied to the decay

amplitude of the Roper resonance, while Section 6 contains the

numerical results. We brieﬂy summarize in Section 7.

2. Effective Lagrangian

We start by specifying the elements of the chiral effective La-

grangian

which are relevant for the calculation of the width of the

Roper at next-to-leading order in the power counting speciﬁed be-

low.

We consider pions, nucleons, the delta and Roper resonances

as dynamical degrees of freedom. The corresponding most general

effective Lagrangian can be written as

eff

= L

ππ

π N

π

π R

π N

π NR

πR

, (1)

where the subscripts indicate the dynamical ﬁelds contributing to

a given term. From the purely mesonic sector we need the follow-

ing

structures [2,27]

http://dx.doi.org/10.1016/j.physletb.2016.07.068

0370-2693/

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