# The Production of NeutralN∗(11052) Resonance with Hidden Beauty from π-p Scattering

Authors: Chen Cheng; Xiao-Yun Wang
Journal: Advances in High Energy Physics
 (2017)

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## Abstract

We investigate the discovery potential of the predicted neutral hidden beautyN∗(11052) resonance through π-p scattering within an effective Lagrangian approach. Two reactions π-p→K-Σ+ and π-p→ηbn are studied in this work, with nucleon pole exchange as the background. It is found that the contributions of the N∗(11052) resonance give clear peak structures in the magnitude of 1 μb near the threshold of N∗(11052) in the total cross sections. The numerical results indicate that the center of mass energy W≃11–11.1 GeV would be the best energy window for searching the N∗(11052) resonance, where the N∗(11052) signal can be easily distinguished from the background. The COMPASS experiment at CERN’s Super Proton Synchrotron (SPS) with pion beam of ≃280 GeV will be an ideal platform for searching the super-heavy resonance with hidden beauty, which is promising for testing the theoretical results.


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## Body

## 1. Introduction

Searching and explaining the exotic states, which is beyond the scheme of conventional quark model of 3-quark(qqq) and quark-antiquark (qq¯), have become a very intriguing issue in hadron physics. It provides us with a good chance to better understand the strong interaction governed by quantum chromodynamics (QCD). While the conventional quark model [1, 2], first introduced by Gell-Mann and Zweig, gives a good description to various ground hadrons, it fails to be consistent with the observations of various excited hadron states.For example, many charmonium-like and bottomonium-like statesXYZ have been observed [3, 4] in recent years. Such states definitely cannot be accommodated by the frame of conventional cc¯ or bb¯ states; they are considered as promising multiquark states or molecular states. On the baryon side, the mass order reverse problem between N∗(1535) and N∗(1440) has been long standing in the conventional quark model [5], since the N∗(1535) resonance with parity (1/2)- being considered the lowest orbitally excited nucleon is expected to be lighter than the first radically excited nucleon N∗(1440). Moreover in the BES experiment the N∗(1535) resonance is observed to have a large coupling to KΛ and ηN channels with strangeness [6–10] in the J/ψ→p¯pη and J/ψ→p¯K+Λ+c.c. reaction. In order to solve the problems above, pentaquark models with hidden strangeness (qqqss¯) are introduced to describe the exotic state [11–14]. However, because of the mixture of pentaquark and 3-quark exists in baryons, and there are always some adjustable ingredients in each model, it will be difficult to pin down the nature of N∗(1535). One way to eliminate the ambiguity is to extend the study of hidden strangeness baryons to hidden charm and hidden beauty baryons; they can be easily distinguished from the conventional quark model for their super large mass.Actually, many works have been done in the hidden charm region. In [15, 16], the UχPT approach is used; several N∗ and Λ∗ resonances with hidden charm were dynamically generated in the PB and VB channels; all of them have masses above 4 GeV and widths smaller than 100 MeV. Here PB and VB stand for pseudoscalar meson-baryon and vector meson-baryon, respectively. Several possible reactions were proposed to look for these predicted resonances, including the γp→J/ψp reaction [15–17] and meson-proton collision [18, 19]. Fortunately and delightfully enough, two resonances consistent with pentaquark states were observed in Λb0→J/ψK-p decays by the LHCb collaboration [20] later in 2015. The two newly discovered resonances were named Pc(4380)+ and Pc(4450)+, which have masses of 4380 MeV and 4450 MeV and widths of 205 MeV and 39 MeV. They are probably the partners of the predicted Ncc¯∗ resonances in [15, 16]. Different methods were proposed to detect the newly observed Pc states for further confirmation, including photoproduction [21] and π-p scattering [22]. Since many works in the hidden charm region have been done, it motivates us to take a step further, searching for the hidden beauty resonances.Actually, two charged bottomonium-like resonances had been reported by the Belle collaboration [24] in Υ(5S) decays, with masses of 10607 ± 2.0 MeV and 10652.2 ± 1.5 MeV, and widths of 18.4 ± 2.4 MeV and 11.5 ± 2.2 MeV. Charged π meson in the final states suggests that the minimal quark content of the two newly reported bottomonium-like resonances is a four-quark combination, and their low widths are consistent with the properties of the super-heavy nucleon resonances predicted in [23]. In [23], the meson-baryon coupled channel unitary approach with local hidden gauge formalism is extended to the hidden beauty region. Two N∗ and four Λ∗ resonances were predicted, with masses all around 11 GeV and widths only a few MeV. Relevant information of the two N∗ are listed in Table 1. Their super large masses and very narrow widths result from the bb¯ components in the states, all decays involve the exchange of a heavy beauty vector and hence are suppressed. According to the information listed in Table 1, we found that it would be an ideal channel to search and study the neutral N∗(11052) resonances through the π-p scattering, with productions of K-Σ+ or ηbn because of their dominant decay branch ratios. And since K- and Σ+ are ground states with charge, it will be easier to detect them in experiments.Table 1
Masses and decay widths of the two predictedN∗ with hidden beauty [23].
P B → P B P V → P V N ∗ ( 11052 ) N ∗ ( 11100 ) M (MeV) 11052 11100 Γ (MeV) 1.38 1.33 π N: 0.10 ρ π: 0.09 η N: 0.21 ω N: 0.30 Γ i (MeV) η ′ N: 0.11 K ∗ Σ: 0.39 K Σ: 0.42 Υ N: 0.51 η b N: 0.52Within an effective Lagrangian approach and isobar model, the production of theN∗(11052) resonance is investigated in this work. The results will not only provide valuable information for searching the neutral N∗(11052) resonance but also enable us to have a more comprehensive understanding of the properties of the super-heavy resonance. The COMPASS (Common Muon and Proton Apparatus for Structure and Spectroscopy) experiment [25] at CERN’s Super Proton Synchrotron (SPS) with pion beam of ≃280 GeV will be a good platform for searching the super-heavy resonance with hidden beauty, which may substantiate our numerical results in the future.This paper is organized as follows. After the introduction, the main ingredients and formalism in the neutralN∗(11052) production processes are discussed in Section 2. In Section 3, numerical results are presented and discussed. Finally, a brief summary is given in Section 4.


## 2. Production of NeutralN∗(11052) via π-p Scattering

In the energy region of resonances, it is difficult to investigate the strong interaction at the quark-gluon level. Thus an effective Lagrangian approach in terms of hadrons is adopted, which is an important theoretical approach in investigating various processes [12, 17–19, 21, 22, 26–29]. In this section, we introduce the theoretical formalism and ingredients to calculate the production process of the predicted N∗(11052) resonance from two possible reactions, namely, the π-p→K-Σ+ reaction and the π-p→ηbn reaction.


### 2.1. Production from theπ-p→K-Σ+ Reaction

In Figure1, the basic tree-level Feynman diagrams for the production of N∗(11052) in the π-p→K-Σ+ reaction were shown, including background of nucleon pole. S-channel of N∗(11052) as an intermediate state is considered.Figure 1
Feynman diagrams for the production the ofN∗(11052) resonance through π-p→K-Σ+ reaction, including the background of nucleon pole. Kinematical variables (p1, p2, p3, and p4) used in our calculation are indicated in the figure.
(a)
Signal (b)
BackgroundTheN∗(11052) resonance, which is dynamically generated from the PB channels, favors its spin-parity quantum number Jp=(1/2)- [23]. The effective Lagrangian densities of the relevant interaction vertices can be written as follows [23, 30]:(1)LπNN∗=gπNN∗N-τ→·π→N∗+H.c.,LKΣN∗=gKΣN∗N-∗Kτ→·Σ→+H.c.,LπNN=gπNNN-γ5τ→·π→N+H.c.,LKΣN=gKΣNN-γ5Kτ→·Σ→+H.c.,where N∗ stands for the N∗(11052) resonance and τ→ stands for the Pauli matrix. The coupling constants gπNN∗ and gKΣN∗ in the Lagrangian densities above are determined by the partial decay widths listed in Table 1:(2)ΓN∗⟶πN=3gπNN∗24πEN+mNmN∗p1→c.m.,ΓN∗⟶KΣ=3gKΣN∗24πEΣ+mΣmN∗p2→c.m.,with (3)EN=p1→c.m.2+mN2,p1→c.m.=λ1/2mN∗2,mπ2,mN22mN∗,EΣ=p2→c.m.2+mΣ2,p2→c.m.=λ1/2mN∗2,mK2,mΣ22mN∗,where λ is the Källen function with λ(x,y,z)=(x-y-z)2-4yz. p1→c.m. and p2→c.m. are the three momenta of either outgoing particle in the center of mass (c.m.) frame, whereas EN and EΣ are the energy of N and Σ in c.m. frame.With the equations above, we obtain the coupling constantsgπNN∗=0.011 and gKΣN∗=0.024. For coupling constants of the background channel gπNN=13.45 (obtained from gπNN2/4π=14.4) as used in [31–33], while gKΣN is obtained by SU(3) symmetry gKΣN=gπNN(1-2α1)=2.69 with α1=0.4.In addition, due to the fact that hadrons are not point-like particles, form factors are introduced as used in [34–36]:(4)FN∗=ΛN∗4ΛN∗4+q2-MN∗22,(5)FN=ΛN4ΛN4+q2-MN22,where MN∗ (MN) and ΛN∗ (ΛN) correspond to the mass and cut-off parameter of the intermediate N∗(11052) resonance (nucleon pole).Finally, for propagatorGN∗(q), we adopt the Breit-Wigner formula:(6)GN∗q=iq+MN∗q2-MN∗2+iMN∗ΓN∗,where ΓN∗ stands for the full decay width of N∗(11052). For the background of nucleon pole, its form can be written as(7)GNq=iq+MNq2-MN2.With the ingredients above, the invariant amplitudes for theπ-p→K-Σ+ reaction, according to the contributions shown in Figure 1, can be written as(8)Mtot=MN∗+MN,MN∗=2gπNN∗gKΣN∗u¯p4,s4GN∗qsup2,s2FN∗qs2,MN=2gπNNgKΣNu¯p4γ5GNqsγ5up2FNqs2,where qs=p1+p2 and s2 and s4 are the polarization variables of the initial proton and the final Λ baryon.The unpolarized differential cross section in the center of mass frame for theπ-p→K-Σ+ reaction can be derived from the invariant amplitude square M2, read as(9)dσdcos⁡θ=4mpmΛ32π2sp3→c.m.p1→c.m.12∑s2,s4M2,where s=W2 is total energy squared in c.m. frame and θ denotes the angle of the outgoing K- meson relative to the π- beam direction in c.m. frame.


### 2.2. Production from theπ-p→ηbn Reaction

In Table1 there is another channel suitable for searching the N∗(11052) resonance: the ηbN decay channel because of its relatively big decay branch ratio. The tree-level Feynman diagrams of the π-p→ηbn reaction are shown in Figure 2, with s-channel and u-channel considered.Figure 2
Feynman diagrams for theπ-p→ηbn reaction including s-channel and u-channel, with background of nucleon pole considered. Kinematical variables (p1,p2,p3, and p4) used in our calculation are indicated in the figure.
(a)
s-channel signal (b)
u-channel signal (c)
s-channel background (d)
u-channel backgroundThe Lagrangians for the relevant vertices in Figure2 can be written as follows [23, 30]:(10)LπNN∗=gπNN∗N¯τ→·π→N∗,LηbNN∗=gηbNN∗N¯∗ηbN+H.c.,LπNN=gπNNN¯γ5τ→·π→N,LηbNN=gηbNNN¯γ5ηbN+H.c.The coupling constants are taken asgN∗Nπ2/4π=1.03×10-5, gN∗Nηb2/4π=1.81×10-3, gπNN=14.4, and gppηb=1×10-6 as used in [23].For form factors and propagators, we adopt the same form of (4), (5), (6), and (7). The total invariant amplitudes for the π-p→ηbn reaction can be written as(11)Mtot=MN∗+MN,MN∗=MN∗s+MN∗u,MN∗s=2gπNN∗gηbNN∗u¯p4,s4GN∗qs×up2,s2FN∗qs2,MN∗u=2gπNN∗gηbNN∗u¯p4,s4GN∗qu×up2,s2FN∗qu2,MN=MNs+MNu,MNs=2gπNNgηbNNu¯p4,s4γ5GNqs×γ5up2,s2FNqs2,MNu=2gπNNgηbNNu¯p4,s4γ5GNqu×γ5up2,s2FNqu2,where qs=p1+p2 and qu=p1-p3. s2 and s4 are the polarization variables of the initial proton and final neutron.The unpolarized differential cross section derived from the invariant amplitude square|M|2 can be written as(12)dσdcos⁡θ=4mpmn32π2sp3→c.m.p1→c.m.12∑s2,s4M2.


## 2.1. Production from theπ-p→K-Σ+ Reaction

In Figure1, the basic tree-level Feynman diagrams for the production of N∗(11052) in the π-p→K-Σ+ reaction were shown, including background of nucleon pole. S-channel of N∗(11052) as an intermediate state is considered.Figure 1
Feynman diagrams for the production the ofN∗(11052) resonance through π-p→K-Σ+ reaction, including the background of nucleon pole. Kinematical variables (p1, p2, p3, and p4) used in our calculation are indicated in the figure.
(a)
Signal (b)
BackgroundTheN∗(11052) resonance, which is dynamically generated from the PB channels, favors its spin-parity quantum number Jp=(1/2)- [23]. The effective Lagrangian densities of the relevant interaction vertices can be written as follows [23, 30]:(1)LπNN∗=gπNN∗N-τ→·π→N∗+H.c.,LKΣN∗=gKΣN∗N-∗Kτ→·Σ→+H.c.,LπNN=gπNNN-γ5τ→·π→N+H.c.,LKΣN=gKΣNN-γ5Kτ→·Σ→+H.c.,where N∗ stands for the N∗(11052) resonance and τ→ stands for the Pauli matrix. The coupling constants gπNN∗ and gKΣN∗ in the Lagrangian densities above are determined by the partial decay widths listed in Table 1:(2)ΓN∗⟶πN=3gπNN∗24πEN+mNmN∗p1→c.m.,ΓN∗⟶KΣ=3gKΣN∗24πEΣ+mΣmN∗p2→c.m.,with (3)EN=p1→c.m.2+mN2,p1→c.m.=λ1/2mN∗2,mπ2,mN22mN∗,EΣ=p2→c.m.2+mΣ2,p2→c.m.=λ1/2mN∗2,mK2,mΣ22mN∗,where λ is the Källen function with λ(x,y,z)=(x-y-z)2-4yz. p1→c.m. and p2→c.m. are the three momenta of either outgoing particle in the center of mass (c.m.) frame, whereas EN and EΣ are the energy of N and Σ in c.m. frame.With the equations above, we obtain the coupling constantsgπNN∗=0.011 and gKΣN∗=0.024. For coupling constants of the background channel gπNN=13.45 (obtained from gπNN2/4π=14.4) as used in [31–33], while gKΣN is obtained by SU(3) symmetry gKΣN=gπNN(1-2α1)=2.69 with α1=0.4.In addition, due to the fact that hadrons are not point-like particles, form factors are introduced as used in [34–36]:(4)FN∗=ΛN∗4ΛN∗4+q2-MN∗22,(5)FN=ΛN4ΛN4+q2-MN22,where MN∗ (MN) and ΛN∗ (ΛN) correspond to the mass and cut-off parameter of the intermediate N∗(11052) resonance (nucleon pole).Finally, for propagatorGN∗(q), we adopt the Breit-Wigner formula:(6)GN∗q=iq+MN∗q2-MN∗2+iMN∗ΓN∗,where ΓN∗ stands for the full decay width of N∗(11052). For the background of nucleon pole, its form can be written as(7)GNq=iq+MNq2-MN2.With the ingredients above, the invariant amplitudes for theπ-p→K-Σ+ reaction, according to the contributions shown in Figure 1, can be written as(8)Mtot=MN∗+MN,MN∗=2gπNN∗gKΣN∗u¯p4,s4GN∗qsup2,s2FN∗qs2,MN=2gπNNgKΣNu¯p4γ5GNqsγ5up2FNqs2,where qs=p1+p2 and s2 and s4 are the polarization variables of the initial proton and the final Λ baryon.The unpolarized differential cross section in the center of mass frame for theπ-p→K-Σ+ reaction can be derived from the invariant amplitude square M2, read as(9)dσdcos⁡θ=4mpmΛ32π2sp3→c.m.p1→c.m.12∑s2,s4M2,where s=W2 is total energy squared in c.m. frame and θ denotes the angle of the outgoing K- meson relative to the π- beam direction in c.m. frame.


## 2.2. Production from theπ-p→ηbn Reaction

In Table1 there is another channel suitable for searching the N∗(11052) resonance: the ηbN decay channel because of its relatively big decay branch ratio. The tree-level Feynman diagrams of the π-p→ηbn reaction are shown in Figure 2, with s-channel and u-channel considered.Figure 2
Feynman diagrams for theπ-p→ηbn reaction including s-channel and u-channel, with background of nucleon pole considered. Kinematical variables (p1,p2,p3, and p4) used in our calculation are indicated in the figure.
(a)
s-channel signal (b)
u-channel signal (c)
s-channel background (d)
u-channel backgroundThe Lagrangians for the relevant vertices in Figure2 can be written as follows [23, 30]:(10)LπNN∗=gπNN∗N¯τ→·π→N∗,LηbNN∗=gηbNN∗N¯∗ηbN+H.c.,LπNN=gπNNN¯γ5τ→·π→N,LηbNN=gηbNNN¯γ5ηbN+H.c.The coupling constants are taken asgN∗Nπ2/4π=1.03×10-5, gN∗Nηb2/4π=1.81×10-3, gπNN=14.4, and gppηb=1×10-6 as used in [23].For form factors and propagators, we adopt the same form of (4), (5), (6), and (7). The total invariant amplitudes for the π-p→ηbn reaction can be written as(11)Mtot=MN∗+MN,MN∗=MN∗s+MN∗u,MN∗s=2gπNN∗gηbNN∗u¯p4,s4GN∗qs×up2,s2FN∗qs2,MN∗u=2gπNN∗gηbNN∗u¯p4,s4GN∗qu×up2,s2FN∗qu2,MN=MNs+MNu,MNs=2gπNNgηbNNu¯p4,s4γ5GNqs×γ5up2,s2FNqs2,MNu=2gπNNgηbNNu¯p4,s4γ5GNqu×γ5up2,s2FNqu2,where qs=p1+p2 and qu=p1-p3. s2 and s4 are the polarization variables of the initial proton and final neutron.The unpolarized differential cross section derived from the invariant amplitude square|M|2 can be written as(12)dσdcos⁡θ=4mpmn32π2sp3→c.m.p1→c.m.12∑s2,s4M2.


## 3. Numerical Results and Discussion

With the formalism and ingredients given above, cross sections for the neutralN∗(11052) production processes can be evaluated. The results for two production processes are discussed in the following two subsections.


### 3.1.π-p→K-Σ+

In this subsection, we discuss the numerical results for theπ-p→K-Σ+ production process, with total and differential cross sections given.In Figure3(a), the signal cross section with variations of different cut-off parameters ΛN∗= 1.5, 2.0, and 3.0 GeV are shown. There is a significant enhancement at c.m. energy W=11.05 GeV. The cut-off parameters determine the widths of the peaks, but the positions of the peaks are independent of the cut-off parameters. These properties originate from form factors (4); form factors reach maximize value of 1 when q2=MN∗2.Figure 3
Total cross section versus c.m. energyW for the π-p→K-Σ+ reaction, where “nb” in the vertical axis represents nanobarn. (a) Signal with different cut-off parameters ΛN∗= 1.5, 2.0, and 3.0 GeV. (b) Background with different cut-off parameters ΛN= 1.0, 1.5, and 2.0 GeV. (c) Contributions from the signal and the background, with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.5 GeV. “Total” denotes the contributions from both the signal and the background.
(a) (b) (c)In Figure3(b), the background is shown, with different cut-off parameters ΛN= 1.0, 1.5, and 2.0 GeV. Although the values of the cut-off parameter ΛN have a considerable effect on the magnitude of the background cross section, it is still negligible when compared with the signal around c.m. energy W=11 GeV. Because this energy region W≃11 GeV is too far away from the mass of nucleon, form factor of the nucleon pole (5) is rather small, so the background is suppressed.In Figure3(c), with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.0 GeV, the comparison of the signal with the background, together with the total (including signal and background), channel are shown. The signal channel is absolutely dominant near c.m. energy W=11.05 GeV; we conclude that 11GeV≃W≃11.1GeV will be an ideal energy region for searching the N∗(11052) resonance through the π-p→K-Σ+ reaction. In the laboratory frame, the incident pion beam momentum that corresponds to such c.m. energy W=11 GeV is plab=64 GeV, which can be done by the COMPASS experiment [25]. It is worth mentioning that, beyond W=11.1 GeV, the interference of the signal and the background has a considerable cancelling effect; the total channel is smaller than the signal or the background.Figure4 shows the differential cross sections of the signal, background, and total channel, at center of mass energy W=10.5, 11.05, and 11.5 GeV. The contribution from signal is dominant at c.m. energies W=11.05 GeV, whereas when W deviate from the threshold of N∗(11052), for example, W=10.5 GeV or W=11.5 GeV, the contribution from the background becomes significant. Differential cross sections are independent of the outgoing angle θ, for these are s-channel reactions. All these properties can be tested by future experiment.Figure 4
The differential cross section for theπ-p→K-Σ+ reaction, at c.m. energies W= 10.5, 11.05, and 11.5 GeV, where “nb/sr” in the vertical axis represents nanobarn per steradian. Here “total” denotes the differential cross section including contributions from both the signal and the background. The red solid line stands for the signal, the black dotted line stands for the background, and the blue dashed line stands for the total contribution.
(a) (b) (c)


### 3.2.π-p→ηbN

In this subsection, we discuss the numerical results for theπ-p→ηbN production process, with total and differential cross sections given.Figure5(a) shows the total cross section of the signal channel, with variations of different cut-off parameters ΛN∗=1.5, 2.0 and 3.0 GeV. The comparison of the contributions from s-channel and u-channel are shown in Figure 5(b). Although the u-channel reaction is included in this production process, its contribution is rare as shown in Figure 5(b). Because the N∗(11052) resonance as an exchange particle is too heavy, the u-channel reaction is deeply suppressed. In Figure 5(c) the comparison of the signal and the background is shown; contribution from the background becomes significant when the c.m. energy goes beyond 11.5 GeV. But, in the energy region of 11GeV≲W≲11.1GeV, the signal is absolutely dominant, so we conclude that this is the best energy window for searching the N∗(11052) resonance in our calculation. And the peaks can reach up to the magnitude of 1 μb around c.m. energy W≃11.052 GeV. It is about the same magnitude as in the neutral pc pentaquark states production process in π-p→J/ψn reaction [22], which is appreciable to be observed and measured in experiment.Figure 5
(a) Total cross section of the signal channel, with cut-off parametersΛN∗=1.5, 2.0, and 3.0 GeV, where “nb” in the vertical axis represents nanobarn. (b) Comparison of s-channel with u-channel, with cut-off parameter sets at ΛN∗=2.0 GeV. Here “total” denotes the contributions from both s-channel and u-channel. (c) Comparison of the signal with the background, with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.5 GeV. “Total” denotes the contributions from both signal and background.
(a) (b) (c)The differential cross section of theπ-p→ηbN reaction is shown in Figure 6, at center of energy of W=10.5, 11.05, and 11.5 GeV. For the signal channel, differential cross section is independent of the outgoing angle θ since the u-channel rarely contributes. But for the background channel there is a relative large contribution from the backward angle. As shown in Figure 6, it originates from the u-channel contribution of nucleon pole exchange. These properties are expected to be tested by further experiments.Figure 6
The differential cross section of theπ-p→ηbN reaction at c.m. energies W=10.5, 11.05, and 11.5 GeV, where “nb/sr” in the vertical axis represents nanobarn per steradian. “Total” denotes the differential cross section including contributions from both the signal and the background. The red solid line stands for the signal, the black dotted line stands for the background, and the blue dashed line stands for the total contribution.
(a) (b) (c)


## 3.1.π-p→K-Σ+

In this subsection, we discuss the numerical results for theπ-p→K-Σ+ production process, with total and differential cross sections given.In Figure3(a), the signal cross section with variations of different cut-off parameters ΛN∗= 1.5, 2.0, and 3.0 GeV are shown. There is a significant enhancement at c.m. energy W=11.05 GeV. The cut-off parameters determine the widths of the peaks, but the positions of the peaks are independent of the cut-off parameters. These properties originate from form factors (4); form factors reach maximize value of 1 when q2=MN∗2.Figure 3
Total cross section versus c.m. energyW for the π-p→K-Σ+ reaction, where “nb” in the vertical axis represents nanobarn. (a) Signal with different cut-off parameters ΛN∗= 1.5, 2.0, and 3.0 GeV. (b) Background with different cut-off parameters ΛN= 1.0, 1.5, and 2.0 GeV. (c) Contributions from the signal and the background, with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.5 GeV. “Total” denotes the contributions from both the signal and the background.
(a) (b) (c)In Figure3(b), the background is shown, with different cut-off parameters ΛN= 1.0, 1.5, and 2.0 GeV. Although the values of the cut-off parameter ΛN have a considerable effect on the magnitude of the background cross section, it is still negligible when compared with the signal around c.m. energy W=11 GeV. Because this energy region W≃11 GeV is too far away from the mass of nucleon, form factor of the nucleon pole (5) is rather small, so the background is suppressed.In Figure3(c), with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.0 GeV, the comparison of the signal with the background, together with the total (including signal and background), channel are shown. The signal channel is absolutely dominant near c.m. energy W=11.05 GeV; we conclude that 11GeV≃W≃11.1GeV will be an ideal energy region for searching the N∗(11052) resonance through the π-p→K-Σ+ reaction. In the laboratory frame, the incident pion beam momentum that corresponds to such c.m. energy W=11 GeV is plab=64 GeV, which can be done by the COMPASS experiment [25]. It is worth mentioning that, beyond W=11.1 GeV, the interference of the signal and the background has a considerable cancelling effect; the total channel is smaller than the signal or the background.Figure4 shows the differential cross sections of the signal, background, and total channel, at center of mass energy W=10.5, 11.05, and 11.5 GeV. The contribution from signal is dominant at c.m. energies W=11.05 GeV, whereas when W deviate from the threshold of N∗(11052), for example, W=10.5 GeV or W=11.5 GeV, the contribution from the background becomes significant. Differential cross sections are independent of the outgoing angle θ, for these are s-channel reactions. All these properties can be tested by future experiment.Figure 4
The differential cross section for theπ-p→K-Σ+ reaction, at c.m. energies W= 10.5, 11.05, and 11.5 GeV, where “nb/sr” in the vertical axis represents nanobarn per steradian. Here “total” denotes the differential cross section including contributions from both the signal and the background. The red solid line stands for the signal, the black dotted line stands for the background, and the blue dashed line stands for the total contribution.
(a) (b) (c)


## 3.2.π-p→ηbN

In this subsection, we discuss the numerical results for theπ-p→ηbN production process, with total and differential cross sections given.Figure5(a) shows the total cross section of the signal channel, with variations of different cut-off parameters ΛN∗=1.5, 2.0 and 3.0 GeV. The comparison of the contributions from s-channel and u-channel are shown in Figure 5(b). Although the u-channel reaction is included in this production process, its contribution is rare as shown in Figure 5(b). Because the N∗(11052) resonance as an exchange particle is too heavy, the u-channel reaction is deeply suppressed. In Figure 5(c) the comparison of the signal and the background is shown; contribution from the background becomes significant when the c.m. energy goes beyond 11.5 GeV. But, in the energy region of 11GeV≲W≲11.1GeV, the signal is absolutely dominant, so we conclude that this is the best energy window for searching the N∗(11052) resonance in our calculation. And the peaks can reach up to the magnitude of 1 μb around c.m. energy W≃11.052 GeV. It is about the same magnitude as in the neutral pc pentaquark states production process in π-p→J/ψn reaction [22], which is appreciable to be observed and measured in experiment.Figure 5
(a) Total cross section of the signal channel, with cut-off parametersΛN∗=1.5, 2.0, and 3.0 GeV, where “nb” in the vertical axis represents nanobarn. (b) Comparison of s-channel with u-channel, with cut-off parameter sets at ΛN∗=2.0 GeV. Here “total” denotes the contributions from both s-channel and u-channel. (c) Comparison of the signal with the background, with cut-off parameters set at ΛN∗=2.0 GeV and ΛN=1.5 GeV. “Total” denotes the contributions from both signal and background.
(a) (b) (c)The differential cross section of theπ-p→ηbN reaction is shown in Figure 6, at center of energy of W=10.5, 11.05, and 11.5 GeV. For the signal channel, differential cross section is independent of the outgoing angle θ since the u-channel rarely contributes. But for the background channel there is a relative large contribution from the backward angle. As shown in Figure 6, it originates from the u-channel contribution of nucleon pole exchange. These properties are expected to be tested by further experiments.Figure 6
The differential cross section of theπ-p→ηbN reaction at c.m. energies W=10.5, 11.05, and 11.5 GeV, where “nb/sr” in the vertical axis represents nanobarn per steradian. “Total” denotes the differential cross section including contributions from both the signal and the background. The red solid line stands for the signal, the black dotted line stands for the background, and the blue dashed line stands for the total contribution.
(a) (b) (c)


## 4. Summary

In this work, we investigated the discovery potential of the predicted neutralN∗(11052) resonance through π-p scattering within an effective Lagrangian approach. Two possible reactions π-p→K-Σ+ and π-p→ηbn are studied, with the background of nucleon pole considered. The results showed that there is a significant enhancement for the production of N∗(11052) resonance around c.m. energy W=11.05 GeV. Moreover, it is found that in the π-p→ηbn reaction s-channel mediated by the N∗(11052) is absolutely dominant, whereas the contribution from the u-channel N∗(11052) exchange is negligible. The π-p→K-Σ+ reaction is especially ideal for searching the N∗(11052) resonance; for the final products K- and Σ+ are ground states with charge, it will be easier to detect them in experiment.It is worth mentioning that theN∗(11052) resonance is a predicted state [23] and have not been observed by experiments or confirmed by other evidence. Its existence and many properties remain in doubt; nevertheless, this work constitutes a first step in this direction, and more works concerning these exotic resonances with hidden beauty are needed. Although the model we employed in this work depends strongly on the cut-off parameters within the form factors, the magnitudes and the positions of the signal peaks do not vary with different parameter values. The background analysis is less than exhaustive, due to the fact that the experimental data and theoretical study are scarce in this hidden beauty energy region. We investigated the contribution from the nucleon pole background as an illumination; it is shown that near the threshold the contribution from the nucleon pole is negligible when compared with the signal’s. If this possible pentaquark candidate state really exists, according to our research in this work, it will be very likely to detect such resonance through the π-p scattering near the production threshold.The center of mass energyW≃11–11.1 GeV would be the best energy window for searching the N∗(11052) resonance in the π-p scattering discussed above. Total cross section can reach up to the magnitude of 1 μb near the threshold of the N∗(11052) resonance. The results will not only provide us with a feasible way for searching the super-heavy resonance N∗(11052) but also enable us to have a more comprehensive understanding of the properties of the super-heavy resonance. The COMPASS experiment will be a good platform for conducting such experiments. The estimated total cross sections, together with the angular distributions, can be checked by future COMPASS experiments.



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*Source: 9398732-2017-01-03.xml*