2018 Vol. 42, No. 6
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2018, 42(6): 063001. doi: 10.1088/1674-1137/42/6/063001
Abstract:
To investigate the nature of the ψ(3770) resonance and to measure the cross section for e+e-→DD, a cross-section scan data sample, distributed among 41 center-of-mass energy points from 3.73 to 3.89 GeV, was taken with the BESⅢ detector operated at the BEPCⅡ collider in the year 2010. By analyzing the large angle Bhabha scattering events, we measure the integrated luminosity of the data sample at each center-of-mass energy point. The total integrated luminosity of the data sample is 76.16±0.04±0.61 pb-1, where the flrst uncertainty is statistical and the second systematic.
To investigate the nature of the ψ(3770) resonance and to measure the cross section for e+e-→DD, a cross-section scan data sample, distributed among 41 center-of-mass energy points from 3.73 to 3.89 GeV, was taken with the BESⅢ detector operated at the BEPCⅡ collider in the year 2010. By analyzing the large angle Bhabha scattering events, we measure the integrated luminosity of the data sample at each center-of-mass energy point. The total integrated luminosity of the data sample is 76.16±0.04±0.61 pb-1, where the flrst uncertainty is statistical and the second systematic.
2018, 42(6): 063101. doi: 10.1088/1674-1137/42/6/063101
Abstract:
We calculate the D0-D0 mixing parameter y in the factorization-assisted topological-amplitude (FAT) approach,considering contributions from D0→PP,PV,and VV modes,where P (V) stands for a pseudoscalar (vector) meson.The D0→PP and PV decay amplitudes are extracted in the FAT approach,and the D0→VV decay amplitudes with flnal states in the longitudinal polarization are estimated via the parameter set for D0→PV.It is found that the VV contribution to y,being of order of 10-4,is negligible,and that the PP and PV contributions amount only up to yPP+PV=(0.21±0.07)%,a prediction more precise than those previously obtained in the literature, and much lower than the experimental data yexp=(0.61±0.08)%.We conclude that D0 meson decays into other two-body and multi-particle flnal states are relevant to the evaluation of y,so it is difficult to understand it fully in an exclusive approach.
We calculate the D0-D0 mixing parameter y in the factorization-assisted topological-amplitude (FAT) approach,considering contributions from D0→PP,PV,and VV modes,where P (V) stands for a pseudoscalar (vector) meson.The D0→PP and PV decay amplitudes are extracted in the FAT approach,and the D0→VV decay amplitudes with flnal states in the longitudinal polarization are estimated via the parameter set for D0→PV.It is found that the VV contribution to y,being of order of 10-4,is negligible,and that the PP and PV contributions amount only up to yPP+PV=(0.21±0.07)%,a prediction more precise than those previously obtained in the literature, and much lower than the experimental data yexp=(0.61±0.08)%.We conclude that D0 meson decays into other two-body and multi-particle flnal states are relevant to the evaluation of y,so it is difficult to understand it fully in an exclusive approach.
2018, 42(6): 063102. doi: 10.1088/1674-1137/42/6/063102
Abstract:
We propose a strategy to access the qq component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the qq component is derived at difierent valence quark masses, and shows a linear dependence on mπ2. The slope is determined to be c1=0.505(3)GeV-1, from which the valence πρ sigma term is extracted to be σπρ(val)=9.82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the qq component is interpolated to be mρ=775.9±6.0±1.8 MeV, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the qq component to be fρ-=208.5±5.5±0.9 MeV, which can be compared with the experimental value fρexp≈221 MeV through the relation fρexp=√Zρfρ±, with Zρ≈1.13 being the on-shell wavefunction renormalization of ρ owing to the ρ-π interaction. We emphasize that mρ and fρ of the qq component, which are obtained for the flrst time from QCD, can be taken as the input parameters of ρ in efiective fleld theory studies where ρ acts as a fundamental degree of freedom.
We propose a strategy to access the qq component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the qq component is derived at difierent valence quark masses, and shows a linear dependence on mπ2. The slope is determined to be c1=0.505(3)GeV-1, from which the valence πρ sigma term is extracted to be σπρ(val)=9.82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the qq component is interpolated to be mρ=775.9±6.0±1.8 MeV, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the qq component to be fρ-=208.5±5.5±0.9 MeV, which can be compared with the experimental value fρexp≈221 MeV through the relation fρexp=√Zρfρ±, with Zρ≈1.13 being the on-shell wavefunction renormalization of ρ owing to the ρ-π interaction. We emphasize that mρ and fρ of the qq component, which are obtained for the flrst time from QCD, can be taken as the input parameters of ρ in efiective fleld theory studies where ρ acts as a fundamental degree of freedom.
2018, 42(6): 063103. doi: 10.1088/1674-1137/42/6/063103
Abstract:
Over the last few years LHCb found some discrepancies in b→sl+l- FCNC transitions, including anomalies in the angular observables of B→K*μ+μ-, particularly in P5', in the low dimuon mass region. Recently, these anomalies have been confirmed by Belle, CMS and ATLAS. As direct evidence of physics beyond the Standard Model is absent so far, these anomalies are being interpreted as indirect hints of new physics. In this context, we study the implications of the family non-universal Z' model for the angular observables P1,2,3, P4,5,6' and newly proposed lepton flavor universality violation observables, Q4,5, in the B→K*(→Kπ)μ+μ- decay channel in the low dimuon mass region. To see the variation in the values of these observables from their Standard Model values, we have chosen different scenarios for the Z' model. It is found that these angular observables are sensitive to the values of the parameters of the Z' model. We have also found that with the present parametric space of the Z' model, the P5'-anomaly could be accommodated. However, more statistics on the anomalies in the angular observables are helpful to reveal the status of the considered model and, in general, the nature of new physics.
Over the last few years LHCb found some discrepancies in b→sl+l- FCNC transitions, including anomalies in the angular observables of B→K*μ+μ-, particularly in P5', in the low dimuon mass region. Recently, these anomalies have been confirmed by Belle, CMS and ATLAS. As direct evidence of physics beyond the Standard Model is absent so far, these anomalies are being interpreted as indirect hints of new physics. In this context, we study the implications of the family non-universal Z' model for the angular observables P1,2,3, P4,5,6' and newly proposed lepton flavor universality violation observables, Q4,5, in the B→K*(→Kπ)μ+μ- decay channel in the low dimuon mass region. To see the variation in the values of these observables from their Standard Model values, we have chosen different scenarios for the Z' model. It is found that these angular observables are sensitive to the values of the parameters of the Z' model. We have also found that with the present parametric space of the Z' model, the P5'-anomaly could be accommodated. However, more statistics on the anomalies in the angular observables are helpful to reveal the status of the considered model and, in general, the nature of new physics.
2018, 42(6): 063104. doi: 10.1088/1674-1137/42/6/063104
Abstract:
In this paper, the ρ meson impact parameter dependent parton distributions and the impact parameter dependent form factors are introduced and discussed. By employing a Gaussian form wave packet, we calculate the impact parameter distributions of the ρ meson based on a light-cone constituent quark model.
In this paper, the ρ meson impact parameter dependent parton distributions and the impact parameter dependent form factors are introduced and discussed. By employing a Gaussian form wave packet, we calculate the impact parameter distributions of the ρ meson based on a light-cone constituent quark model.
2018, 42(6): 063105. doi: 10.1088/1674-1137/42/6/063105
Abstract:
We derive the solution for a spherically symmetric string cloud configuration in a d-dimensional spacetime in the framework of f(R) theories of gravity. We also analyze some thermodynamic properties of the joint black hole-cloud of strings solution. For its Hawking temperature, we found that the dependence of the mass with the horizon is significantly different in both theories. For the interaction of a black hole with thermal radiation, we found that the shapes of the curves are similar, but shifted. Our analysis generalizes some known results in the literature.
We derive the solution for a spherically symmetric string cloud configuration in a d-dimensional spacetime in the framework of f(R) theories of gravity. We also analyze some thermodynamic properties of the joint black hole-cloud of strings solution. For its Hawking temperature, we found that the dependence of the mass with the horizon is significantly different in both theories. For the interaction of a black hole with thermal radiation, we found that the shapes of the curves are similar, but shifted. Our analysis generalizes some known results in the literature.
2018, 42(6): 064001. doi: 10.1088/1674-1137/42/6/064001
Abstract:
The accuracy of dielectronic recombination (DR) data for astrophysics related ions plays a key role in astrophysical plasma modeling. The absolute DR rate coefficient of Fe17+ ions was measured at the main cooler storage ring at the Institute of Modern Physics, Lanzhou, China. The experimental electron-ion collision energy range covers the first Rydberg series up to n=24 for the DR resonances associated with the 2P1/2→2P3/2Δn=0 core excitations. A theoretical calculation was performed by using FAC code and compared with the measured DR rate coefficient. Overall reasonable agreement was found between the experimental results and calculations. Moreover, the plasma rate coefficient was deduced from the experimental DR rate coefficient and compared with the available results from the literature. At the low energy range, significant discrepancies were found, and the measured resonances challenge state-of-the-art theory at low collision energies.
The accuracy of dielectronic recombination (DR) data for astrophysics related ions plays a key role in astrophysical plasma modeling. The absolute DR rate coefficient of Fe17+ ions was measured at the main cooler storage ring at the Institute of Modern Physics, Lanzhou, China. The experimental electron-ion collision energy range covers the first Rydberg series up to n=24 for the DR resonances associated with the 2P1/2→2P3/2Δn=0 core excitations. A theoretical calculation was performed by using FAC code and compared with the measured DR rate coefficient. Overall reasonable agreement was found between the experimental results and calculations. Moreover, the plasma rate coefficient was deduced from the experimental DR rate coefficient and compared with the available results from the literature. At the low energy range, significant discrepancies were found, and the measured resonances challenge state-of-the-art theory at low collision energies.
2018, 42(6): 064101. doi: 10.1088/1674-1137/42/6/064101
Abstract:
We calculate the shear viscosity (η) and bulk viscosity (ζ) to entropy density (s) ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg↔gg forward scattering and the inelastic soft gluon bremsstrahlung gg↔ggg processes. Due to the suppressed contribution to η and ζ in the gg↔gg forward scattering and the effective g↔gg gluon splitting, Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM) have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung gg↔ggg process with an analytic method. We find that the contribution of the collision term from the gg↔ggg soft gluon bremsstrahlung process is just a small perturbation to the gg↔gg scattering process and that the correction is at~5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula ζ∝(αs2T3)/(lnαs-1) in high-temperature gluon plasma.
We calculate the shear viscosity (η) and bulk viscosity (ζ) to entropy density (s) ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg↔gg forward scattering and the inelastic soft gluon bremsstrahlung gg↔ggg processes. Due to the suppressed contribution to η and ζ in the gg↔gg forward scattering and the effective g↔gg gluon splitting, Arnold, Moore and Yaffe (AMY) and Arnold, Dogan and Moore (ADM) have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung gg↔ggg process with an analytic method. We find that the contribution of the collision term from the gg↔ggg soft gluon bremsstrahlung process is just a small perturbation to the gg↔gg scattering process and that the correction is at~5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula ζ∝(αs2T3)/(lnαs-1) in high-temperature gluon plasma.
2018, 42(6): 064102. doi: 10.1088/1674-1137/42/6/064102
Abstract:
The decay widths of Υ(nS)→d*(2380)+X with n=1,2,3 are studied in a phenomenological way. With the help of crossing symmetry, the decay widths are obtained by investigating the imaginary part of the forward scattering amplitudes between d* and Υ(nS). The wave functions of m d* and deuteron obtained in previous studies are used for calculating the amplitude. The interaction between d* (d) and Υ is governed by the quark-meson interaction, where the coupling constant is determined by fitting the observed widths of Υ(nS)→d+X. The numerical results show that the decay widths of Υ(nS)→d*+X are about 2-10 times smaller than that of d+X. The calculated momentum of d* is in the range 0.3-0.8 GeV. Therefore, it is very likely that one can find d*(2380) in these semi-inclusive decay processes.
The decay widths of Υ(nS)→d*(2380)+X with n=1,2,3 are studied in a phenomenological way. With the help of crossing symmetry, the decay widths are obtained by investigating the imaginary part of the forward scattering amplitudes between d* and Υ(nS). The wave functions of m d* and deuteron obtained in previous studies are used for calculating the amplitude. The interaction between d* (d) and Υ is governed by the quark-meson interaction, where the coupling constant is determined by fitting the observed widths of Υ(nS)→d+X. The numerical results show that the decay widths of Υ(nS)→d*+X are about 2-10 times smaller than that of d+X. The calculated momentum of d* is in the range 0.3-0.8 GeV. Therefore, it is very likely that one can find d*(2380) in these semi-inclusive decay processes.
2018, 42(6): 064103. doi: 10.1088/1674-1137/42/6/064103
Abstract:
We investigate low-lying bound states of the neutron-rich nucleus 15B by assuming it is a three-body system made of an inert core 13B and two valence neutrons. The three-body wave functions are obtained using the Faddeev formalism. Special attention is paid to the excited state at 3.48(6) MeV observed in the 13C(14C,12N)15B reaction, whose properties are less clear theoretically. In our three-body model, besides the ground state 3/21-, a second 3/22- state is discovered at around 3.61 MeV, which might be identified with the excited state observed at 3.48(6) MeV. We study this 3/22- state in detail. It turns out to be a two-neutron halo state with a large matter radius rm≈4.770 fm.
We investigate low-lying bound states of the neutron-rich nucleus 15B by assuming it is a three-body system made of an inert core 13B and two valence neutrons. The three-body wave functions are obtained using the Faddeev formalism. Special attention is paid to the excited state at 3.48(6) MeV observed in the 13C(14C,12N)15B reaction, whose properties are less clear theoretically. In our three-body model, besides the ground state 3/21-, a second 3/22- state is discovered at around 3.61 MeV, which might be identified with the excited state observed at 3.48(6) MeV. We study this 3/22- state in detail. It turns out to be a two-neutron halo state with a large matter radius rm≈4.770 fm.
2018, 42(6): 064104. doi: 10.1088/1674-1137/42/6/064104
Abstract:
We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process. Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state (EOS). Each EOS is characterized by a particular symmetryenergy coefficient (asym) and a corresponding density-slope parameter L. The stepwise trends of the neutron (proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym= 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay, yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.
We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process. Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state (EOS). Each EOS is characterized by a particular symmetryenergy coefficient (asym) and a corresponding density-slope parameter L. The stepwise trends of the neutron (proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life Tα with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value asym= 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay, yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.
2018, 42(6): 064105. doi: 10.1088/1674-1137/42/6/064105
Abstract:
The relativistic mean-field models tested in previous works against nuclear matter experimental values, critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energy γ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate the γ values, a trend of linear correlation is observed between γ and the symmetry energy (S0) and a more clear linear relationship is established between γ and the slope of the symmetry energy (L0). These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of R1.0 and R1.4, in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely, IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤Mmax/M⊙≤2.05 and with the overlap band for the L0×S0 region, to present γ in the range of γ=0.25±0.05.
The relativistic mean-field models tested in previous works against nuclear matter experimental values, critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energy γ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate the γ values, a trend of linear correlation is observed between γ and the symmetry energy (S0) and a more clear linear relationship is established between γ and the slope of the symmetry energy (L0). These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of R1.0 and R1.4, in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely, IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤Mmax/M⊙≤2.05 and with the overlap band for the L0×S0 region, to present γ in the range of γ=0.25±0.05.
2018, 42(6): 064106. doi: 10.1088/1674-1137/42/6/064106
Abstract:
The density-dependent term in Skyrme forces is essential to simulate three-body and many-body correlations beyond the low-momentum two-body interaction. We speculate that a single density term may be insufficient and a higher-order density dependent term is added. The present work investigates the influence of higher-order density dependencies based on extended UNEDF0 and SkM* forces. Global descriptions of nuclear masses and charge radii are presented. The extended UNEDF0 force gives a global rms error on binding energies of 1.29 MeV. The influence on fission barriers and equation of state are also investigated. Perspectives to improve Skyrme forces are discussed, including global center-of-mass corrections and Lipkin-Nogami pairing corrections.
The density-dependent term in Skyrme forces is essential to simulate three-body and many-body correlations beyond the low-momentum two-body interaction. We speculate that a single density term may be insufficient and a higher-order density dependent term is added. The present work investigates the influence of higher-order density dependencies based on extended UNEDF0 and SkM* forces. Global descriptions of nuclear masses and charge radii are presented. The extended UNEDF0 force gives a global rms error on binding energies of 1.29 MeV. The influence on fission barriers and equation of state are also investigated. Perspectives to improve Skyrme forces are discussed, including global center-of-mass corrections and Lipkin-Nogami pairing corrections.
2018, 42(6): 065001. doi: 10.1088/1674-1137/42/6/065001
Abstract:
The ‘lithium problem’ in Big Bang nucleosynthesis (BBN) has recently focused on reactions involving 7Be. The 6Li(p, γ)7Be reaction can provide us not only with information about 6Li destruction but also with information about 7Be production. In the present work, the proton spectroscopic factor in 7Be is extracted to be 0.70±0.17 from the angular distribution of 7Be(d, 3He)6Li at Ec.m.=6.7 MeV. This value is then used to compute the direct component of the astrophysical 6Li(p, γ)7Beg.s. S(E) factors and determine the resonance parameters from the total S(E) factors.
The ‘lithium problem’ in Big Bang nucleosynthesis (BBN) has recently focused on reactions involving 7Be. The 6Li(p, γ)7Be reaction can provide us not only with information about 6Li destruction but also with information about 7Be production. In the present work, the proton spectroscopic factor in 7Be is extracted to be 0.70±0.17 from the angular distribution of 7Be(d, 3He)6Li at Ec.m.=6.7 MeV. This value is then used to compute the direct component of the astrophysical 6Li(p, γ)7Beg.s. S(E) factors and determine the resonance parameters from the total S(E) factors.
2018, 42(6): 065101. doi: 10.1088/1674-1137/42/6/065101
Abstract:
We elaborate on a toy model of matter bounce, in which the matter content is constituted by two fermion species endowed with four fermion interaction terms. We describe the curvaton mechanism that is thus generated, and then argue that one of the two fermionic species may realize baryogenesis, while the other (lighter) one is compatible with constraints on extra hot dark matter particles.
We elaborate on a toy model of matter bounce, in which the matter content is constituted by two fermion species endowed with four fermion interaction terms. We describe the curvaton mechanism that is thus generated, and then argue that one of the two fermionic species may realize baryogenesis, while the other (lighter) one is compatible with constraints on extra hot dark matter particles.
2018, 42(6): 065102. doi: 10.1088/1674-1137/42/6/065102
Abstract:
In this paper, we have investigated the structural properties of rotating neutron stars using the numerical RNS code and equations of state which have been calculated within the lowest order constrained variational (LOCV) approach. In order to calculate the equation of state of nuclear matter, we have used UV14 +TNI and AV18 potentials. We have computed the maximum mass of the neutron star and the corresponding equatorial radius at different angular velocities. We have also computed the structural properties of Keplerian rotating neutron stars for the maximum mass configuration, MK, RK, fK and jmax.
In this paper, we have investigated the structural properties of rotating neutron stars using the numerical RNS code and equations of state which have been calculated within the lowest order constrained variational (LOCV) approach. In order to calculate the equation of state of nuclear matter, we have used UV14 +TNI and AV18 potentials. We have computed the maximum mass of the neutron star and the corresponding equatorial radius at different angular velocities. We have also computed the structural properties of Keplerian rotating neutron stars for the maximum mass configuration, MK, RK, fK and jmax.
2018, 42(6): 065103. doi: 10.1088/1674-1137/42/6/065103
Abstract:
We investigate the constraints on the sum of neutrino masses (Σmν) using the most recent cosmological data, which combines the distance measurement from baryonic acoustic oscillation in the extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample with the power spectra of temperature and polarization anisotropies in the cosmic microwave background from the Planck 2015 data release. We also use other low-redshift observations, including the baryonic acoustic oscillation at relatively low redshifts, Type Ia supernovae, and the local measurement of the Hubble constant. In the standard cosmological constant Λ cold dark matter plus massive neutrino model, we obtain the 95% upper limit to be Σmν<0.129 eV for the degenerate mass hierarchy, Σmν<0.159 eV for the normal mass hierarchy, and Σmν<0.189 eV for the inverted mass hierarchy. Based on Bayesian evidence, we find that the degenerate hierarchy is positively supported, and the current data combination cannot distinguish between normal and inverted hierarchies. Assuming the degenerate mass hierarchy, we extend our study to non-standard cosmological models including generic dark energy, spatial curvature, and extra relativistic degrees of freedom, but find these models are not favored by the data.
We investigate the constraints on the sum of neutrino masses (Σmν) using the most recent cosmological data, which combines the distance measurement from baryonic acoustic oscillation in the extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample with the power spectra of temperature and polarization anisotropies in the cosmic microwave background from the Planck 2015 data release. We also use other low-redshift observations, including the baryonic acoustic oscillation at relatively low redshifts, Type Ia supernovae, and the local measurement of the Hubble constant. In the standard cosmological constant Λ cold dark matter plus massive neutrino model, we obtain the 95% upper limit to be Σmν<0.129 eV for the degenerate mass hierarchy, Σmν<0.159 eV for the normal mass hierarchy, and Σmν<0.189 eV for the inverted mass hierarchy. Based on Bayesian evidence, we find that the degenerate hierarchy is positively supported, and the current data combination cannot distinguish between normal and inverted hierarchies. Assuming the degenerate mass hierarchy, we extend our study to non-standard cosmological models including generic dark energy, spatial curvature, and extra relativistic degrees of freedom, but find these models are not favored by the data.
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