Chinese Physics C

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays

Jun Cao, Guo-yuan Huang, Yu-Feng Li, Yifang Wang, Liang-Jian Wen, Zhi-zhong Xing, Zhen-hua Zhao, Shun Zhou

2020, 44(3): 031001. doi: 10.1088/1674-1137/44/3/031001

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Abstract:
We emphasize that it is extremely important for future neutrinoless double-beta (

\begin{document}$0\nu\beta\beta$\end{document}

) decay experiments to reach the sensitivity to the effective neutrino mass

\begin{document}$|m_{\beta\beta}| \approx 1\;{\rm {meV}}$\end{document}

. With such a sensitivity, it is highly possible to discover the signals of

\begin{document}$0\nu\beta\beta$\end{document}

decays. If no signal is observed at this sensitivity level, then either neutrinos are Dirac particles or stringent constraints can be placed on their Majorana masses. In this paper, assuming the sensitivity of

\begin{document}$|m_{\beta\beta}| \approx 1\;{\rm {meV}}$\end{document}

for future

\begin{document}$0\nu\beta\beta$\end{document}

decay experiments and the precisions on neutrino oscillation parameters after the JUNO experiment, we fully explore the constrained regions of the lightest neutrino mass

\begin{document}$m_1$\end{document}

and two Majorana-type CP-violating phases

\begin{document}$\{\rho, \sigma\}$\end{document}

. Several important conclusions in the case of normal neutrino mass ordering can be made. First, the lightest neutrino mass is severely constrained to a narrow range

\begin{document}$m_1 \in [0.7, 8]\;{\rm {meV}}$\end{document}

, which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum

\begin{document}$m_2 \in [8.6, 11.7]\;{\rm {meV}}$\end{document}

and

\begin{document}$m_3 \in [50.3, 50.9]\;{\rm {meV}}$\end{document}

. Second, one of the two Majorana CP-violating phases is limited to

\begin{document}$\rho \in [130^\circ, 230^\circ]$\end{document}

, which cannot be obtained from any other realistic experiments. Third, the sum of three neutrino masses is found to be

\begin{document}$\Sigma \equiv m_1 + m_2 + m_3 \in [59.2, 72.6]\;{\rm {meV}}$\end{document}

, while the effective neutrino mass for beta decays turns out to be

\begin{document}$m_\beta \equiv (|U_{e1}|^2 m^2_1 + |U_{e2}|^2 m^2_2 + |U_{e3}|^2 m^2_3)^{1/2}\in [8.9, 12.6]\;{\rm {meV}}$\end{document}

. These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.

Drawing insights from pion parton distributions

Minghui Ding, Khépani Raya, Daniele Binosi, Lei Chang, C. D. Roberts, S. M. Schmidt

2020, 44(3): 031002. doi: 10.1088/1674-1137/44/3/031002

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Abstract:
A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale

\begin{document}$\zeta_2:=2\,{\rm{GeV:}}\langle x_{\rm valence} \rangle = 0.48(3)$\end{document}

,

\begin{document}$\langle x_{\rm glue} \rangle = 0.41(2)$\end{document}

,

\begin{document}$\langle x_{\rm sea} \rangle = 0.11(2)$\end{document}

; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function,

\begin{document}$q^\pi(x)$\end{document}

, exhibits the

\begin{document}$x\simeq 1$\end{document}

behaviour predicted by quantum chromodynamics (QCD). After evolution to

\begin{document}$\zeta=5.2\,{\rm{GeV}}$\end{document}

, the prediction for

\begin{document}$q^\pi(x)$\end{document}

matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

Hunting potassium geoneutrinos with liquid scintillator Cherenkov neutrino detectors

Zhe Wang, Shaomin Chen

2020, 44(3): 033001. doi: 10.1088/1674-1137/44/3/033001

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Abstract:
The research on geoneutrinos is a new interdisciplinary subject involving particle experiments and geo-science. Potassium-40 (⁴⁰K) decays contribute roughly to 1/3 of the radiogenic heat of the Earth, which is not yet accounted for by experimental observation. Solar neutrino experiments with liquid scintillators have observed uranium and thorium geoneutrinos and are the most promising experiments with regard to low-background neutrino detection. In this study, we present the new concept of using liquid-scintillator Cherenkov detectors to detect the neutrino-electron elastic scattering process of ⁴⁰K geoneutrinos. Liquid-scintillator Cherenkov detectors using a slow liquid scintillator achieve this goal with both energy and direction measurements for charged particles. Given the directionality, we can significantly suppress the dominant intrinsic background originating from solar neutrinos in conventional liquid-scintillator detectors. We simulated the solar- and geo-neutrino scatterings in the slow liquid scintillator detector, and implemented energy and directional reconstructions for the recoiling electrons. We found that ⁴⁰K geoneutrinos can be detected with three-standard-deviation accuracy in a kiloton-scale detector.

Neutron-antineutron oscillations in the deuteron studied with NN and ${{\bar NN}}$ interactions based on chiral effective field theory

Johann Haidenbauer, Ulf-G. Meißner

2020, 44(3): 033101. doi: 10.1088/1674-1137/44/3/033101

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Abstract:
Neutron-antineutron (

\begin{document}$ n-\bar n $\end{document}

) oscillations in the deuteron are considered. Specifically, the deuteron lifetime is calculated in terms of the free-space

\begin{document}$ n-\bar n $\end{document}

oscillation time

\begin{document}$ \tau_{n-\bar n} $\end{document}

based on

\begin{document}$ NN $\end{document}

and

\begin{document}$ \bar NN $\end{document}

interactions derived within chiral effective field theory (EFT). This results in

\begin{document}$ (2.6\pm 0.1) \times 10^{22}\,\tau^2_{n-\bar n} $\end{document}

s, which is close to the value obtained by Dover and collaborators more than three decades ago, but disagrees with recent EFT calculations that were performed within the perturbative scheme proposed by Kaplan, Savage, and Wise. Possible reasons for the difference are discussed.

Extended projection method for massive fermions

Yefan Wang, Zhao Li

2020, 44(3): 033102. doi: 10.1088/1674-1137/44/3/033102

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Abstract:
Tensor reduction is of considerable importance in calculations of multi-loop amplitudes, and the projection method is one of the most popular approaches for tensor reduction. However, the projection method can be problematic when applied to amplitudes with massive fermions, due to the inconsistency between helicity and chirality. We propose an extended projection method for reducing the loop amplitude which contains a fermion chain with two massive spinors. The extension is achieved by decomposing one of the massive spinors into two massless spinors, the “null spinor” and the “reference spinor”. The extended projection method can be effectively applied in all processes, including the production of massive fermions. We present the tensor reduction for a virtual Z boson decaying into a top-quark pair as a demonstration of our approach.

Analysis of the excited bottom and bottom-strange states B₁(5721), ${{ B_{2}^{*}(5747) }}$, ${{ B_{s1}(5830)}} $, $ {{B_{s2}^{*}(5840) }}$, ${{ B_{J}(5840) }}$ and $ {{B_{J}(5970) }}$ of the B meson family

Guo-Liang Yu, Zhi-Gang Wang

2020, 44(3): 033103. doi: 10.1088/1674-1137/44/3/033103

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Abstract:
In order to make a further confirmation of the assignments of the excited bottom and bottom-strange mesons

\begin{document}$ B_{1}(5721) $\end{document}

,

\begin{document}$ B_{2}^{*}(5747) $\end{document}

,

\begin{document}$ B_{s1}(5830) $\end{document}

and

\begin{document}$ B_{s2}^{*}(5840) $\end{document}

and identify possible assignments of

\begin{document}$ B_{J}(5840) $\end{document}

and

\begin{document}$ B_{J}(5970) $\end{document}

, we study the strong decay of these states with the

\begin{document}$ ^{3}P_{0} $\end{document}

decay model. Our analysis supports the assignments of

\begin{document}$ B_{1}(5721) $\end{document}

and

\begin{document}$ B_{2}^{*}(5747) $\end{document}

as the

\begin{document}$ 1P_{1}' $\end{document}

and

\begin{document}$ 1^{3}P_{2} $\end{document}

states, and

\begin{document}$ B_{s1}(5830) $\end{document}

and

\begin{document}$ B_{s2}^{*}(5840) $\end{document}

as the strange partners of

\begin{document}$ B_{1}(5721) $\end{document}

and

\begin{document}$ B_{2}^{*}(5747) $\end{document}

. Besides, we tentatively identify the recently observed

\begin{document}$ B_{J}(5840) $\end{document}

and

\begin{document}$ B_{J}(5970) $\end{document}

as the

\begin{document}$ 2^{3}S_{1} $\end{document}

and

\begin{document}$ 1^{3}D_{3} $\end{document}

states. It is noted that these conclusions need further confirmation by measurements of the decay channels

\begin{document}$ B_{J}(5840)\rightarrow B\pi $\end{document}

and

\begin{document}$ B_{J}(5970)\rightarrow B\pi $\end{document}

.

Calculation of disconnected quark loops in lattice QCD

Zhen Cheng, Jian-Bo Zhang, Guang-Yi Xiong

2020, 44(3): 033104. doi: 10.1088/1674-1137/44/3/033104

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Abstract:
Calculation of disconnected quark loops in lattice QCD is very time consuming. Stochastic noise methods are generally used to estimate these loops. However, stochastic estimation gives large errors in the calculations of disconnected diagrams. We use the symmetric multi-probing source (SMP) method to estimate the disconnected quark loops, and compare the results with the

\begin{document}$Z(2)$\end{document}

noise method and the spin-color explicit (SCE) method on a quenched lattice QCD ensemble with lattice volume

\begin{document}$12^{3}\times24$\end{document}

and lattice spacing

\begin{document}$a\approx0.1$\end{document}

fm. The results show that the SMP method is very suitable for the calculation of pseudoscalar disconnected quark loops. However, the SMP and SCE methods do not have an obvious advantage over the

\begin{document}$Z(2)$\end{document}

noise method in the evaluation of the scalar disconnected loops.

Measurement of ⁸⁵Rb (n, 2n) ⁸⁴Rb reaction cross-section from 12 MeV up to 19.8 MeV

Chuanxin Zhu, Jia Wang, Li Jiang, Pu Zheng

2020, 44(3): 034001. doi: 10.1088/1674-1137/44/3/034001

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Abstract:
The cross-section data of the ⁸⁵Rb(n, 2n)⁸⁴Rb reaction have been measured with the neutron energies of 12 MeV to 19.8 MeV using the activation technique and the relative method. The ⁸⁵Rb samples were irradiated on the surface of a two-ring orientation assembly with neutrons produced from the ³H(d, n)⁴He reaction at the 5SDH-2 1.7-MV Tandem accelerator in China. Theoretical model calculations were performed with the TALYS-1.9 code. The present data were compared with previously obtained experimental data and the available evaluated data.

Applicability of ⁹Be global optical potential to description of ^8,10,11B elastic scattering

Yong-Li Xu, Yin-Lu Han, Hai-Ying Liang, Zhen-Dong Wu, Hai-Rui Guo, Chong-Hai Cai

2020, 44(3): 034101. doi: 10.1088/1674-1137/44/3/034101

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Abstract:
We achieved a set of ⁹Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209. The obtained ⁹Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of ^8,10,11B projectiles. The predictions are made by performing a detailed analysis comparing with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range, and reasonable results are obtained. Possible physical explanations for the observed differences are also discussed.

Nuclear chart in covariant density functional theory with dynamic correlations: From oxygen to tin

Yi-Long Yang, Ya-Kun Wang

2020, 44(3): 034102. doi: 10.1088/1674-1137/44/3/034102

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Abstract:
Nuclear masses of even-even nuclei with the proton number

\begin{document}$8\leqslant Z\leqslant 50$\end{document}

(O to Sn isotopes) from the proton drip line to neutron drip line are investigated using the triaxial relativistic Hartree-Bogoliubov theory with the relativistic density functional PC-PK1. Further, the dynamical correlation energies (DCEs) associated with the rotational motion and quadrupole-shaped vibrational motion are taken into account by the five-dimensional collective Hamiltonian (5DCH) method. The root-mean-square deviation with respect to the experimental masses reduces from 2.50 to 1.59 MeV after the consideration of DCEs. The inclusion of DCEs has little influence on the position of drip lines, and the predicted numbers of bound even-even nuclei between proton and neutron drip lines from O to Sn isotopes are 569 and 564 with and without DCEs, respectively.

Statistical method in quark combination model

Yang-Guang Yang, Jun Song, Feng-Lan Shao, Zuo-Tang Liang, Qun Wang

2020, 44(3): 034103. doi: 10.1088/1674-1137/44/3/034103

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Abstract:
We present a new method for solving the probability distribution for baryons, antibaryons, and mesons at the hadronization of the constituent quark and antiquark system. The hadronization is governed by the quark combination rule in the quark combination model developed by the Shandong Group. We employ the method of the generating function to derive the outcome of the quark combination rule, which is significantly simpler and easier to generalize than the original method. Furthermore, we use the formula of the quark combination rule and its generalization to study the property of the multiplicity distribution of net-protons. Taking a naive case of quark number fluctuations and correlations at hadronization, we calculate ratios of multiplicity cumulants of final-state net-protons and discuss the potential applicability of the quark combination model by studying hadronic multiplicity fluctuations and the underlying phase transition property in relativistic heavy-ion collisions.

Comparative study of the forward and backward methods for calculating jet properties in pp collisions at ${\sqrt{ s}}$=7 TeV

Yu-Liang Yan, Ayut Limphirat, Dai-Mei Zhou, Pornrad Srisawad, Yupeng Yan, Chunbin Yang, Xu Cai, Ben-Hao Sa

2020, 44(3): 034104. doi: 10.1088/1674-1137/44/3/034104

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Abstract:
We propose a forward method based on PYTHIA6.4 to study the jet properties in ultra-relativistic pp collisions. In the forward method, the partonic initial states are first generated with PYTHIA6.4 and then hadronized in the Lund string fragmentation model, and finally the hadronic jets are constructed from the created hadrons. Jet properties calculated with the forward method for pp collisions at

\begin{document}$\sqrt{s}$\end{document}

=7 TeV are comparable to those calculated with the usual anti-

\begin{document}$k_t$\end{document}

algorithm (backward method) in PYTHIA6.4. The comparison between the backward and forward methods may contribute to the understanding of the partonic origin of jets in the backward method.

Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density

Jingyi Chao, Mei Huang, Andrey Radzhabov

2020, 44(3): 034105. doi: 10.1088/1674-1137/44/3/034105

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Abstract:
The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu–Jona-Lasinio model. The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space, i.e. the charged pion. In this framework,

\begin{document}$\pi^{\pm}$\end{document}

are treated as bound states of quarks and not as point-like charged particles. The isospin chemical potential plays the role of a trigger for charged pion condensation. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition. The dependence of pion condensation on model parameters is investigated.

High-K multi-particle bands and pairing reduction in ²⁵⁴No

Xiao-Tao He, Shu-Yong Zhao, Zhen-Hua Zhang, Zhong-Zhou Ren

2020, 44(3): 034106. doi: 10.1088/1674-1137/44/3/034106

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Abstract:
The multi-particle states and rotational properties of the two-particle bands in

\begin{document}$^{254}{\rm{No}}$\end{document}

are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method. The rotational bands on top of the two-particle

\begin{document}$K^{\pi}=3^+, \;8^-$\end{document}

and

\begin{document}$10^+$\end{document}

states and the pairing reduction are studied theoretically in

\begin{document}$^{254}{\rm{No}}$\end{document}

for the first time. The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations. Better agreement with the data is achieved by including the high-order deformation

\begin{document}$\varepsilon_{6}$\end{document}

, which leads to enlarged

\begin{document}$Z=100$\end{document}

and

\begin{document}$N=152$\end{document}

deformed shell gaps. An increase of

\begin{document}$J^{(1)}$\end{document}

in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.

K* production in the ${{KN\to K \pi p}}$ reaction

Shao-Fei Chen, Bo-Chao Liu

2020, 44(3): 034107. doi: 10.1088/1674-1137/44/3/034107

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Abstract:
We investigate the

\begin{document}$ K^* $\end{document}

production in the

\begin{document}$ KN\to K \pi p $\end{document}

reaction using the effective Lagrangian approach and the isobar model. To describe this reaction, we first take into account the contributions from the

\begin{document}$ \pi $\end{document}

,

\begin{document}$ \rho $\end{document}

and

\begin{document}$ \omega $\end{document}

exchanges, as in previous studies. We find that although the experimental data can be generally described, there are some obvious discrepancies between the model and the experiments. To improve the model, we consider the contributions of the axial-vector meson and hyperon exchange. It is shown that a large contribution of the axial-vector meson exchange can significantly improve the results. This may indicate that the coupling of the axial-vector meson, e.g.

\begin{document}$ a_1(1260) $\end{document}

, is large in the

\begin{document}$ KK^* $\end{document}

channel. To verify our model, measurements of the angular distributions and spin density matrix elements of

\begin{document}$ K^{*0} $\end{document}

in the

\begin{document}$ K_{\rm L} p\to K^{*0} p $\end{document}

reaction would be helpful, and we make predictions for this reaction for a future comparison.

Phase diagram of two-color QCD matter at finite baryon and axial isospin densities

Jingyi Chao

2020, 44(3): 034108. doi: 10.1088/1674-1137/44/3/034108

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Abstract:
We study the two-color QCD matter with two fundamental quark flavors using the chiral perturbation theory and the Nambu-Jona-Lasinio (NJL) model. The effective Lagrangian is derived in terms of mesons and baryons, i.e. diquarks. The low lying excitations lie in the extended

\begin{document}$ {SU}(4)$\end{document}

flavor symmetry space. We compute the leading order terms of the Lagrangian as a function of the baryon and axial isospin densities. After numerically solving the gap equations in the two-color NJL model, the phase diagram is obtained in the

\begin{document}$\mu-\nu_{5}$\end{document}

plane.

Static fluid spheres admitting Karmarkar condition

Ksh. Newton Singh, Ravindra K. Bisht, S. K. Maurya, Neeraj Pant

2020, 44(3): 035101. doi: 10.1088/1674-1137/44/3/035101

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Abstract:
We explore a new relativistic anisotropic solution of the Einstein field equations for compact stars based on embedding class one condition. For this purpose, we use the embedding class one methodology by employing the Karmarkar condition. Employing this methodology, we obtain a particular differential equation that connects both the gravitational potentials

\begin{document}${\rm e}^{\lambda}$\end{document}

and

\begin{document}${\rm e}^{\nu}$\end{document}

. We solve this particular differential equation choosing a simple form of generalized gravitational potential

\begin{document}$g_{rr}$\end{document}

to describe a complete structure of the space-time within the stellar configuration. After determining this space-time geometry for the stellar models, we discuss thermodynamical observables including radial and tangential pressures, matter density, red-shift, velocity of sound, etc., in the stellar models. We also perform a complete graphical analysis, which shows that our models satisfy all the physical and mathematical requirements of ultra-high dense collapsed structures. Further, we discuss the moment of inertia and M-R curve for rotating and non-rotating stars.

Joule-Thomson expansion of the regular(Bardeen)-AdS black hole

Sen Guo, Jin Pu, Qing-Quan Jiang, Xiao-Tao Zu

2020, 44(3): 035102. doi: 10.1088/1674-1137/44/3/035102

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Abstract:
We study the Joule-Thomson expansion of the regular black hole in an anti-de Sitter background, and obtain the inversion temperature for the Bardeen-AdS black hole in the extended phase space. We investigate the isenthalpic and inversion curves for the Bardeen-AdS black hole in the T-P plane and find that the intersection points between them are exactly the inversion points discriminating the heating from the cooling process. The inversion curve for the regular(Bardeen)-AdS black hole is not closed and there is only a lower inversion curve, in contrast to the Van der Waals fluid. Most importantly, we find that the ratio between the minimum inversion temperature and the critical temperature for the regular(Bardeen)-AdS black hole is 0.536622, which is larger than any known ratio for the singular black hole. The large ratio for the Bardeen-AdS black hole may be due to the repulsive de Sitter core near the origin of the regular black hole.

2020 Vol. 44, No. 3