P-wave States Research Articles

Investigation on the Ω(2012) from QCD sum rules

We investigate the recently observed Ω(2012) baryon using QCD sum rules. By constructing P-wave Ω baryon currents and performing spin projection and parity projection, we obtain the masses of the JP=1/2− and 3/2− states as M1/2−=2.07−0.07+0.07GeV and M3/2−=2.05−0.10+0.09GeV, in good agreement with experiment. This suggests that Ω(2012) is likely to be a negative parity P-wave excited state, though its spin remains undetermined and requires further study of its decay properties.

Measurements of the branching fractions of the P -wave charmonium spin-singlet state hc(P11)→h+h−π0/η

Based on (2712.4±14.3)×106 ψ(3686) events, we investigate four hadronic decay modes of the P-wave charmonium spin-singlet state hc(1P1)→h+h−π0/η (h=π or K) via the process ψ(3686)→π0hc at BESIII. The hc→π+π−π0 decay is observed with a significance of 9.6σ after taking into account systematic uncertainties. Evidences for hc→K+K−π0 and hc→K+K−η are found with significances of 3.5σ and 3.3σ, respectively, after considering the systematic uncertainties. The branching fractions of these decays are measured to be B(hc→π+π−π0)=(1.36±0.16±0.14)×10−3, B(hc→K+K−π0)=(3.26±0.84±0.36)×10−4, and B(hc→K+K−η)=(3.13±1.08±0.38)×10−4, where the first uncertainties are statistical and the second are systematic. No significant signal of hc→π+π−η is found, and the upper limit of its decay branching fraction is determined to be B(hc→π+π−η)<4.0×10−4 at the 90% confidence level. Published by the American Physical Society 2024

Investigation on the Ω(2012) from QCD sum rules

We study the recently observed Ω(2012) baryon in quantum chromodynamics (QCD) sum rules. We construct the P-wave Ω baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin 1/2 and 3/2. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of JP=1/2− and 3/2− states to be M1/2−=2.07−0.07+0.07 GeV and M3/2−=2.05−0.10+0.09 GeV. Both results are in good agreement with the experimental result. Therefore, it is likely that the Ω(2012) is a negative parity state, which is interpreted as a P-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties. Published by the American Physical Society 2024

FKS subtraction for quarkonium production at NLO

We extend the local infrared-divergence subtraction formalism, originally proposed by Frixione, Kunszt and Signer (FKS), to calculate short-distance (differential) cross section for any inclusive process involving a quarkonium particle in non-relativistic QCD (NRQCD) factorisation at next-to-leading order (NLO) accuracy in the strong coupling constant αs. The new formulas are generally applicable to the production of an S- or P-wave quarkonium state in association with any number of elementary particles. The main new ingredients derived in this paper are the local and integrated soft counterterms for the colour-singlet and colour-octet P-wave bound states. It, therefore, paves the way to the automation of the NLO calculations for heavy quarkonium inclusive and associated production processes.

Transverse momentum spectra of f0(980) from coalescence model

We use a coalescence model to generate f0(980) particles for four configurations: ss¯ meson, uu¯ss¯ tetraquark, KK¯ molecule, and uu¯ p-wave state. The phase-space information of the coalescing constituents is taken from a multi-phase transport (AMPT) simulation of proton-proton (pp) and proton-lead (pPb) collisions at the LHC. It is shown that the transverse momentum spectra and production yields of f0(980) differ significantly among the configurations. It is suggested that the pT spectra of the f0(980) compared to those of other hadrons (such as pion) and the ratio of the f0(980)pT spectra in pPb over pp collisions can be exploited to tell the configuration of the f0(980).

Further study on the production of P-wave doubly heavy baryons from Z-boson decays

In this paper, we carried out a systematic investigation for the excited doubly heavy baryons production in Z-boson decays within the NRQCD factorization approach. Our investigation accounts for all the P-wave intermediate diquark states, i.e.〈cc〉[P11]3¯, 〈cc〉[PJ3]6, 〈bc〉[P11]3¯/6, 〈bc〉[PJ3]3¯/6, 〈bb〉[P11]3¯, and 〈bb〉[PJ3]6 with J=(0,1,2). The results show that contributions from all diquark states in P-wave were 7%, 8%, and 3% in comparing with S-wave for the production of Ξcc, Ξbc and Ξbb via Z-boson decay, respectively. Based on these results, we predicted about 0.539×103(106) events for Ξcc, 1.827×103(106) events for Ξbc, and 0.036×103(106) events for Ξbb can be produced annually at the LHC (CEPC). Additionally, we plot the differential decay widths of Ξcc, Ξbc and Ξbb as a function of the invariant mass s23 and energy function z distributions, and analyze the theoretical uncertainties in decay width arising from the mass parameters of heavy quark.

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

The Λ-type P-wave bottom baryon states via the QCD sum rules* *Supported by the National Natural Science Foundation of China (12175068) and the Postgraduate Students Innovative Capacity Foundation of Education Department of Hebei Province, China (CXZZBS2023146)

Our study focuses on the Λ-type P-wave bottom baryon states with spin-parity , . We introduce an explicit P-wave between the two light quarks in the interpolating currents (these light quarks are antisymmetric in the flavor space, thus giving rise to the designation of Λ-type baryon) to investigate the and states within the framework of the full QCD sum rules. The predicted masses show that and could be the P-wave bottom-strange baryon states with spin-parity and , respectively; meanwhile, and could be the P-wave bottom baryon states with spin-parity and , respectively. Moreover, and may have two remarkable under-structures or Fock components at least.

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

We studied the effect of momentum space anisotropy on heavy quarkonium states using an extended magnetized effective fugacity quasiparticle model (EQPM). Both the real and imaginary part of the potential has been modified through the dielectric function by including the anisotropic parameter ξ. The real part of the medium-modified potential becomes more attractive in the presence of the anisotropy and constant magnetic field. The binding energy of the 1S, 2S, and 1P quarkonium states including anisotropy effects for both the oblate and the isotropic case were studied. We find that the binding energy of QQ¯ states becomes stronger in the presence of anisotropy. However, the magnetic field is found to reduce the binding energy. The thermal width of the charmonium and bottomonium 1S states has been studied at constant magnetic field eB=0.3 GeV2 for isotropic and prolate cases. The effect of magnetic field on the mass spectra of the 1P state for the oblate case was also examined. The dissociation temperature for the 1S, 2S, and 1P states of charmonium and bottomonium has been determined to be higher for the oblate case with respect to the isotropic case.

Some Applications of Renormalization Group to Few-Body Problems in EFT

General aspects of applying renormalization group in perturbative calculations are briefly discussed. Next, an application of the Wilsonian renormalization group with multitude of cutoff parameters to halo EFT for P-wave shallow states is considered.

Lagrange-mesh calculations of P-wave resonances in three-body atomic systems

The resonance energies and widths of the P-wave states of helium and of the positronium ion are studied under the hypothesis that their constituting particles interact trough pure or screened Coulomb forces. The resonances are investigated by combining the Lagrange-mesh method and the complex scaling method. This approach is proved to be efficient: rather simple to implement, fast, and accurate. The obtained results improve by several orders of magnitude the best literature results.

The study of P-wave Ds mesons in coupled channel framework

We developed a coupled channel framework connecting the quark model and lattice QCD to systematically investigate the inner structures of the four lowest P-wave Ds states. The cs¯ core and D(⁎)K channels were considered. The possible coupling of cs¯ with the D(⁎)K channel and the channel-channel potentials were described by the quark-pair creation model and the light meson exchanging model, respectively. The lattice QCD data was treated as input by using the hamiltonian effective field theory. Our results showed that the physical Ds0⁎(2317) and Ds1⁎(2460) contain important bare cs¯ core and D(⁎)K component, while the Ds1⁎(2536) and Ds2⁎(2573) are almost the cs¯ mesons.

Zcs (4000)+ and Zcs (4220)+ in a Multiquark Color Flux-Tube Model

We systematically investigate the mass spectrum, spatial configuration and magnetic moment of the ground and p-wave states with various color-spin configurations in a multiquark color flux-tube model. Numerical results indicate that the state Zcs (4000)+ can be described as the compact state with 13S1. Its main color-spin configuration is and its magnetic moment is 0.73μ N. The state can be depicted as the compact state with 11 P 1 (or 13 P 1). Its main color-spin configuration is (or ) and its magnetic moment is 0.12μ N (or 0.64μ N). The physical state should be the mixture of these two different color-spin configurations and deserves further investigation. In addition, we also predict the properties of the states with other quantum numbers in the model.

Production of double heavy quarkonia at super Z factory

Within the color singlet model, we calculate the exclusive production of double charmonia, double bottomonia, and double B_c mesons at future super Z factory. The two heavy quarkonia or B_c’s are either two S-wave Fock states (^1S_0, ~^3S_1), or one S-wave and one P-wave states (^1P_1,~^3P_J~(J=0,1,2)). The top three Z^0 propagated channels in cross sections for double charmonia are sigma {(J/psi +h_c)}_{Z^0}=(454.0^{+39.1}_{-59.2})times 10^{-5} fb, sigma {(eta _c+chi _{c2})}_{Z^0}=(284.2^{+22.2}_{-35.3})times 10^{-5} fb, and sigma {(eta _c+chi _{c0})}_{Z^0}=(137.0^{+9.9}_{-16.4})times 10^{-5} fb. For double bottomonia, they are sigma {(eta _b+Upsilon )}_{Z^0}=(428.6^{+67.9}_{-60.9})times 10^{-4} fb, sigma {(Upsilon +chi _{b2})}_{Z^0}=(230.6^{+23.6}_{-22.2})times 10^{-4} fb, and sigma {(Upsilon +Upsilon )}_{Z^0}=(119.9^{+18.4}_{-16.6})times 10^{-4} fb. For double B_c mesons, they are sigma {(B_c^{*+}+B_c^{*-})}_{Z^0}=(1150^{+87}_{-84})times 10^{-3} fb, sigma {(B_c^{*+}+chi _{bc2}^-)}_{Z^0}=(1133^{-16}_{+22})times 10^{-3} fb, and sigma {(eta _{bc}^++B_c^{*-})}_{Z^0}=(634.6^{+47.8}_{-45.8})times 10^{-3} fb. Here the uncertainties come from the varying masses of constituent heavy quarks, which bring up to 20% corrections. The cross sections of double B_c mesons are roughly one order of magnitude larger than those of the double bottomonia, and two orders of magnitude larger than those of the double charmonia. To make it helpful for experimental study, we present the total cross sections sigma as functions of CM energy sqrt{s}, sigma as functions of the renormalization scale mu , the angle distributions dsigma /dcostheta , and the p_T distributions dsigma /dp_{t}. We also find that the initial state radiation can bring about 30–40% suppresions when 1%m_Z energy is losing, and cross sections can increase by about 2–3 times or decrease by an order of magnitude when adopting different potential models which becomes the major source of uncertainty. The numerical results show that it might be not optimistic for the experimental observation, but it is still far from excluded at the FCC-ee and also the CEPC running in the Z factory mode.

The investigations of the P-wave Bs states combining quark model and lattice QCD in the coupled channel framework

Combining the quark model, the quark-pair-creation mechanism and B(*) overline{K} interaction, we have investigated the near-threshold P-wave Bs states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the Ds sector by fitting the lattice data. The masses of the bottom-strange partners of the {D}_{s0}^{ast }(2317) and {D}_{s1}^{ast }(2460) are predicted to be {M}_{B_{s0}^{ast }}={5730.2}_{-1.5}^{+2.4} MeV and {M}_{B_{s1}^{ast }}={5769.6}_{-1.6}^{+2.4} MeV, respectively, which are well consistent with the lattice QCD component. The two P-wave Bs states are the mixtures of the bare overline{b}s core and B(*) overline{K} component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the 0+ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the T-matrix of the Boverline{K} scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation.

Excited doubly heavy baryons production via top-quark decays

Within the framework of NRQCD, we calculate the production of the excited doubly heavy baryons ${\mathrm{\ensuremath{\Xi}}}_{bQ}$ through the semi-inclusive production process $t\ensuremath{\rightarrow}⟨bQ⟩[n]\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{bQ}+\overline{Q}+{W}^{+}$, where $Q=b$ or $c$ quark. The intermediate diquark state $⟨bQ⟩[n]$ is in the excited P-wave state, including ${[}^{1}{P}_{1}]$ and ${[}^{3}{P}_{J}]$ ($J=0,1,or\text{ }2$) in both color anitriplet state $\overline{\mathbf{3}}$ and color sixtuplet state $\mathbf{6}$; that is, $⟨bc⟩{[}^{1}{P}_{1}{]}_{\overline{\mathbf{3}}/\mathbf{6}}$, $⟨bc⟩{[}^{3}{P}_{J}{]}_{\overline{\mathbf{3}}/\mathbf{6}}$, $⟨bb⟩{[}^{1}{P}_{1}{]}_{\overline{\mathbf{3}}}$, and $⟨bb⟩{[}^{3}{P}_{J}{]}_{\mathbf{6}}$. We find that the contributions from the P-wave states are about one order lower than the S-wave contributions, and this conclusion is consistent with others. We also analyze the invariant mass and angle differential distributions, and the theoretical uncertainty from the mass parameters, the transition probability, and the renormalization scale. Finally, we can expect that about $1.14\ifmmode\times\else\texttimes\fi{}{10}^{3--5}$ events of excited ${\mathrm{\ensuremath{\Xi}}}_{bc}$ and $2.47\ifmmode\times\else\texttimes\fi{}{10}^{1--3}$ events of excited ${\mathrm{\ensuremath{\Xi}}}_{bb}$ can be produced per year at the LHC with $\mathcal{L}={10}^{34--36}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}{\mathrm{s}}^{\ensuremath{-}1}$.

Excited doubly heavy baryons production via Higgs decays

Through the interaction of Higgs with heavy quarks in standard model, we have systematically studied and predicted the production of excited doubly heavy baryons based on non-relativistic QCD theory. The decay widths, differential distributions, and major theoretical uncertainties of the excited doubly heavy baryons via the process H rightarrow langle QQ'rangle [n] rightarrow Xi _{QQ'}+ bar{Q'} + bar{Q} are discussed in detail. The spin and color quantum number of the intermediate P-wave diquark state langle QQ'rangle [n] can be langle ccrangle [^{1}P_{1}]_{varvec{bar{3}}}, langle ccrangle [^{3}P_{J}]_{varvec{6}}, langle bcrangle [^{1}P_{1}]_{varvec{bar{3}}/ textbf{6}}, langle bcrangle [^{3}P_{J}]_{varvec{bar{3}}/ textbf{6}}, langle bb rangle [^{1}P_{1}]_{varvec{bar{3}}} and langle bbrangle [^{3}P_{J}]_{textbf{6}}, with J=0, 1, 2. The contributions from all summed P-wave states can be about 3.05%, 3.23% and 2.19% of the S-wave states for the production of Xi _{cc}, Xi _{bc} and Xi _{bb}, accordingly. Therefore, there will be about 0.41times 10^4 events of Xi _{cc}, 6.35times 10^4 events of Xi _{bc} and 0.28times 10^4 events of Xi _{bb} produced per year at the HL-LHC, and a smaller number of events would be produced at the CEPC or ILC but with a cleaner background to be measured by the experiments.

Momentum dependent gap in holographic superconductors revisited

We reconsider the angular dependence in gap structure of holographic superconductors, which has not been treated carefully so far. For the vector field model, we show that the normalizable ground state is in the p-wave state because s-wave state is not normalizable. On the other hand, in the scalar order model, the ground state is in the s-wave. The angle dependent gap function is explicitly constructed in these models. We also suggest the modified ansatz of the vector order which enables to discuss the order px ± ipy gap. We have also analytically investigated the critical temperature and the behavior of the gap near there. Interestingly, for the fixed conformal dimension of the Cooper pair operator, the critical temperature in vector model is higher than that of the scalar model.

S- and p-superfluidity of Fermi atoms in Bose–Fermi mixtures

The p-wave superfluid is characterized by nontrivial topological characteristics essential for fault-tolerant quantum state manipulation. However, the practical realization of the p-wave state remains a challenging problem. We study the s- and p-wave superfluidity in mixtures of fermionic and spinor bosonic gases and derive a general set of the gap equations for these superfluid states. Numerically solving the gap equations for the s-wave state, we quantify the physical conditions for the realization of the pure p-wave state in a well-controlled environment of atomic physics in the absence of an admixture of the s-wave state.

Searching for velocity-dependent dark matter annihilation signals from extragalactic halos

We consider gamma-ray signals of dark matter annihilation in extragalactic halos in the case where dark matter annihilates from a p-wave or d-wave state. In these scenarios, signals from extragalactic halos are enhanced relative to other targets, such as the Galactic Center or dwarf spheroidal galaxies, because the typical relative speed of the dark matter is larger in extragalactic halos. We perform a mock data analysis of gamma rays produced by dark matter annihilation in halos detected by the Sloan Digital Sky Survey. We include a model for uncorrelated galactic and extragalactic gamma ray backgrounds, as well as a simple model for backgrounds due to astrophysical processes in the extragalactic halos detected by the survey. We find that, for models which are still allowed by other gamma ray searches, searches of extragalactic halos with the current Fermi exposure can produce evidence for dark matter annihilation, though it is difficult to distinguish the p-wave and d-wave scenarios. With a factor 10×larger exposure, though, discrimination of the velocity-dependence is possible.