$$\Omega（2012）$$Ω（2012）共振的产生中的耦合通道动力学资源-CSDN文库

Open

Access

64 浏览量 2020-03-30 08:15:11 上传评论收藏 992KB PDF 举报

资源推荐

资源详情

资源评论

Eur. Phys. J. C (2018) 78:857

https://doi.org/10.1140/epjc/s10052-018-6329-4

Regular Article - Theoretical Physics

Coupled channels dynamics in the generation of the (2012)

resonance

R. Pavao

,E.Oset

Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Aptdo.22085,

46071 Valencia, Spain

Received: 31 August 2018 / Accepted: 10 October 2018 / Published online: 25 October 2018

Abstract We look into the newly observed (2012) state

from the molecular perspective in which the resonance is

generated from the

K 

∗

, η and

K  channels. We ﬁnd that

this picture provides a natural explanation of the properties of

the (2012) state. We stress that the molecular nature of the

resonance is revealed with a large coupling of the (2012)

to the

K 

∗

channel, that can be observed in the (2012) →

K πdecay which is incorporated automatically in our chiral

unitary approach via the use of the spectral function of 

∗

the evaluation of the

K 

∗

loop function.

1 Introduction

The recent observation of an excited  state, 

∗

, by the Belle

collaboration in the K

−

 and K



−

decay channels [1] has

stirred a new wave of theoretical papers aiming at explaining

the nature of the state and its decay channels.

The existence of excited  states, like for any other

baryon, is predicted in the quark models by means of the

excitations of the quarks [2–6]. Large N

considerations [7],

QCD sum rules [8,9], the Skyrme model [10] and lattice

QCD simulations [11] have also added information to this

subject. Extensions of quark models which would accom-

modate ﬁve quark components [12–14] lead to more binding

than the original ones of Refs. [2,3]. Another extension of

the quark model is done in Ref. [15] using the chiral quark

model.

We investigate the state from the molecular point of view

with coupled channels and a chiral unitary approach. Work

along these lines was done in Refs. [16,17] and more recently

in Ref. [18]. Since the state is close to the

K 

∗

threshold

(

∗

of the  decuplet), the channel

K 

∗

is the essential

one, but the coupled channels require to consider simultane-

ously the η channel. This system is, however, peculiar since

e-mail: rpavao@iﬁc.uv.es

the

K 

∗

→

K 

∗

interaction with the dominant Weinberg-

Tomozawa interaction is zero (and so is the direct η → η

one). This means that the

K 

∗

system by itself does not

bind. It is the interaction with the η channel that ﬁnally

leads to a bound state. This peculiar behavior has, however,

an undesired side effect since the predictions of the model

are very sensitive to the way the loops are regularized. It suf-

ﬁces to mention that in Ref. [16] the binding can be obtained

around 1950 MeV, in Ref. [17] using dimensional regular-

ization with a subtraction constant a −2 a state around

2142 MeV was found, while the same model with a sub-

traction constant around −3.4 leads to a mass around 1785

MeV [18]. It is clear that the model allows much ﬂexibility,

as a consequence of the null diagonal matrix elements of the

interaction. The observation of the (2012) state close to the

K 

∗

threshold has provided us with vital information to con-

trol the chiral unitary approach. One can use the experimental

data to constrain the regulator of the loop functions and then

make further predictions to be contrasted with experiment.

After the experimental observation, work along this chiral

unitary model was done in Refs. [19–22]. All those works

coincide in the idea that support for the molecular

K 

∗

state

should come from the decay 

∗

→

K π, which actually

comes from 

∗

→

K 

∗

(virtual), 

∗

→ π.InRefs.[18,

22] the evaluation is done for this decay leading to a partial

width of about 3 MeV. In Refs. [20,22] the coupled channels

problem is solved to evaluate the couplings of the 

∗

K 

∗

and from there the decay width of 

∗

→

K π is

evaluated. In Ref. [21] the coupling is obtained using the

Weinberg compositeness condition [23,24] and the results

for this coupling between [21,22] vary by about 20%.

Apart from the 

∗

→

K π decay channel, the 

∗

→

K  channel is also evaluated in Refs. [20–22]. In Ref. [20]

SU(3) arguments are invoked to relate this decay to the  →

π N, although the 

∗

is in a

−

state and  in

, which

requires d-wave in the 

∗

case and p-wave in the  case. In

123

857 Page 2 of 8 Eur. Phys. J. C (2018) 78 :857

Ref. [21] a triangle diagram with 

∗

→

K 

∗

exchanging

vector mesons is used to make the transition to the ﬁnal

K 

state. In Ref. [22] vector mesons and baryons are allowed

to be exchanged in the triangle diagram and the contribution

of the vector mesons is found negligible. In Ref. [20]the

transition is estimated using a naive dimensional analysis

from Ref. [25].

In the present work we follow the lines of Refs. [17,20–

22] and as a novelty we use the

K 

∗

, η and

K  channels

as coupled channels, with

K 

∗

and η in s-wave and

K  in

d-wave. The formalism in this case follows closely the one

of Ref. [26]. Also, given the fact that some channels are in

s-wave and the

K  in d-wave, and in view of the different

subtraction constants required in Ref. [26] for those channels,

we found more instructive to use cutoff regularization, since

the idea of the cutoff is more intuitive, and, as we shall see,

one can use the same cutoff in the s- and d-wave channels.

One of the outcomes of the full coupled channel is that the

decay width for the 

∗

→

K π is provided directly from

the model without the need to study it explicitly. Indeed, the



∗

→

K π comes from 

∗

→

K 

∗

with the posterior

decay 

∗

→ π. This is incorporated automatically in our

scheme by making a convolution of the

K 

∗

loop function

with the spectral function of the 

∗

which incorporates the

width for the πchannel. The other output of the approach is

that, given the sensitivity of the model to the input due to the

zero diagonal transition matrix elements of the interaction,

the inclusion of the

K  channel into the coupled channels

has some effect, producing a shift in the position of the pole

(although small) and some diversionin thecouplingsfromthe

perturbative approach to 

∗

→

K  done in Refs. [21,22].

Another new output of the work is the determination of the

wave function at the origin for the

K 

∗

and η channels

that comes to support the dominance of the

K 

∗

compo-

nent in the molecular wave function of the 

∗

. With these

differences with respect to the former models, our approach

comes to support the conclusions of Refs. [20–22]astothe

natural interpretation of the recent (2012) state in terms of

a dynamically generated resonance from the

K 

∗

, η and

K  channels, with the largest overlap to the

K 

∗

channel.

2 Formalism

The new 

∗

state has been observed mainly in the ϒ(1S),

ϒ(2S) and ϒ(3S) decays where the search was made for the

decay of 

∗

into

K . Since the quantum numbers of the 

∗

are more likely to be J

−

[1], the coupling of

K  to



∗

is, in this case, in d-wave. And given the spin and ﬂavor

structure of the 

∗

, it will couple in s-wave to

K 

∗

and η,

and the decay to

K  will proceed via these channels.

Fig. 1 Flavor structure of the 

∗−

decay

If we assume that in the decays of ϒ(1S), ϒ(2S) and

ϒ(3S) an sss state is formed, then the decay of 

∗

to the

available channels will happen as shown in Fig. 1. For this

amplitude to be in s-wave one needs an excited s quark in

L = 1, which is plotted as the upper s-quark in the ﬁgure.

In terms of the ﬂavor states the hadronization goes as

sss →



i=1

s ¯q

ss ≡ H. (1)

Then, deﬁning the matrix

M =

⎛

⎝

u ¯uu

du¯s

d ¯ud

dd¯s

s ¯us

ds¯s

⎞

⎠

, (2)

we get

H =



i=1

ss. (3)

We then rewrite the q ¯q matrix, M, in terms of the meson

components, φ,as:

φ =

⎛

⎜

⎝

√



√

−

√



√

−

√





⎞

⎟

⎠

(4)

where the standard η, η



mixing is assumed [27], and we get

H = K

−

uss +

dss +



−

√







sss. (5)

As usual, we omit the η



because of its large mass.

We want to write the three quark states in terms of the

baryon states which belong to the SU(3) decuplet represen-

tation:



∗0

√

(uss +sus + ssu), (6a)

123

剩余7页未读，继续阅读

评论收藏

内容反馈

weixin_38667849

粉丝: 7
资源: 895

$$ \ Omega（2012）$$Ω（2012）共振的产生中的耦合通道动力学

最新资源

$$ \ Omega（2012）$$Ω（2012）共振的产生中的耦合通道动力学

$$ \ Omega（2012）$$Ω（2012）的性质通过其强烈衰减

对新观察到的$$ \ Omega _b $$Ωb状态的可能解释

新近观察到的$$ \ Omega _b $$Ωb结构的强烈衰减

可能的五夸克候选人：新的兴奋的$$ \ Omega _c $$Ωc状态

介子-重子相互作用的分子$$ \ Xi _ {bc} $$Ξbc状态

重新讨论了分支比率$$ \ omega \ rightarrow \ pi ^ + \ pi ^-$$ω→π+π-

使用KLOE检测器研究$ \ omega $介子

双重子的弱衰变：W交换

标量场非最小耦合曲率的带电dester空间时空的强大宇宙检查

宇宙学筛选和幻影世界模型

具有现象学势模型的双重质重子的质量和衰变特性

大型强子对撞机在固定目标碰撞中的独家矢量介子光产生

双重子的弱衰变：$$ \ mathcal {B} _ {cc} \ rightarrow \ mathcal {B} _c V $$ Bcc→BcV

勘误表至：分支比率$$ \ omega \ rightarrow \ pi ^ + \ pi ^-$$ω→π+π-

Sagnac频率变化的识别和纠正：GINGERINO数据分析的实现

太阳系实验会限制标量-张量重力吗？

用爱因斯坦望远镜的引力波标准警报器限制全息暗能量的前景

Qt 5实现串口调试助手 （源工程文件、0积分下载）

【SystemVerilog】路科验证V2学习笔记（全600页）.pdf

AutoSAR标准协议4.2.2

光伏-储能并网系统仿真.rar

XCP协议的规范文档

GD32替换STM32注意事项.pdf

NPPJSONViewer.zip

蓝牙BLE协议中文版.pdf

CANoe通过CAPL脚本实现自动测试

AD20官方中文教程.pdf

最新资源

Qt 5实现串口调试助手（源工程文件、0积分下载）