Nuclear $0 u2beta$ decays in $B-L$ symmetric SUSY model and TeV scale left-right symmetric model

In this paper we take B-L supersymmetric standard model (B-LSSM) and TeV scale left-right symmetric model (LRSM) as two types of typical ones beyond SM to study the nuclear neutrinoless double beta decays ($0 u2beta$) and to see the senses for the present data and the expected data in the near future of the decays. In the study we pay much attention onto the QCD corrections in the energy-scale region from $mu=M_W$ to $musimeq 1.0;$GeV, but we treat the nuclear effects in the decays as done in the relevant literatures. For these two models the decay half-life of the nuclei, $^{76}$Ge and $^{136}$Xe, $T^{0 u}_{1/2}$($^{76}$Ge, $^{136}$Xe), are precisely estimated with the model parameters allowed by experiments and the results are presented properly. Results show that the concerned QCD corrections to the half-life of the $0 u2beta$ decays for the two models are quite sizable. The interference effects between the different contributions happened only in the model LRSM are specially analyzed. According to the numerical results, an optimistic conclusion is obtained that the $0 u2beta$ decays for the models may be observed in the next generation of the underground observations.

Mass spectra and wave functions of $T_{QQbar Qbar Q}$ tetraquarks

The compact tetraquark states with fully heavy quark contents $QQbar Qbar Q$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$. Our results show that the three ground states of $ccbar cbar c$ locate in the mass range of $6.4sim6.5$GeV, and the $bbbar bbar b$ states in mass range of $19.2sim19.3$GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$,(or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCbs observation $X(6900)$ is less likely to be the ground states of compact $ccbar cbar c$ tetraquarks but might be the first or second excited states. In addition, a widely used propagator-like form factor is also investigated and discussed.

Inclusive production of heavy quarkonium $eta_Q$ via $Z$ boson decays within the framework of nonrelativistic QCD

In the paper, the inclusive production of heavy quarkonium $eta_Q$ ($Q=b$ or $c$) via $Z$ boson decays within the framework of nonrelativistic QCD (NRQCD) effective theory are studied. The contributions from the leading color-singlet and color-octet Fock states are considered. Total and differential decay widths for the inclusive decays $Z to eta_c+X$ and $Z to eta_b+X$ are presented. It is found that the decay $Zto eta_Q +X$ is dominated by the $^3S_1^{[8]}$ component, so the decays can be inversely adopted to determine the values of the long-distance matrix elements $langle {cal O}^{eta_{c}}(^{3}S_{1}^{[8]})rangle$ and $langle {cal O}^{eta_{b}}(^{3}S_{1}^{[8]})rangle$ respectively. The numerical results show that at an $e^+e^-$ collider running at the $Z$ pole with a high luminosity around $10^{35}{rm cm}^{-2}{rm s}^{-1}$ (a super $Z$ factory), there are about $4.5times 10^7$ $eta_c$ meson events and $6.2times 10^5$ $eta_b$ meson events to be produced per operation year, and the inclusive decays may be used for clarifying some problems on the heavy quarkonium $eta_Q$ and NRQCD.

The complete study on polarization of $Upsilon(nS)$ hadroproduction at QCD next-to-leading order

Applying the nonrelativistic quantum chromodynamics factorization formalism to the $Upsilon(1S,2S,3S)$ hadroproduction, a complete analysis on the polarization parameters $lambda_{theta}$, $lambda_{thetaphi}$, $lambda_{phi}$ for the production are presented at QCD next-to-leading order. With the long-distance matrix elements extracted from experimental data for the production rate and polarization parameter $lambda_{theta}$ of $Upsilon$ hadroproduction, our results provide a good description for the measured parameters $lambda_{thetaphi}$ and $lambda_{phi}$ in both the helicity and the Collins-Soper frames. In our calculations the frame invariant parameter $tilde{lambda}$ is consistent in the two frames. Finally, it is pointed out that there are discrepancies for $tilde{lambda}$ between available experimental data and corresponding theoretical predictions.

Recently observed $P_c$ as molecular states and possible mixture of $P_c(4457)$

Recently observed spectrum of $P_c$ states exhibits a strong link to $Sigma_c bar{D}^{(*)}$ thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer structures. Utilizing the effecitve lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the $Sigma_c bar{D}^{(*)}$ interactions and three $P_c$ states. We confirm that $P_c(4312)$ and $P_c(4440)$ are good candidates of $Sigma_c bar{D}$ and $Sigma_c bar{D}^{*}$ molecules with spin-$frac12$, respectively. Unlike other molecular calculations, our results indicate $P_c(4457)$ signal might be a mixture of spin-$frac32$ and spin-$frac12$ $Sigma_c bar{D}^{*}$ molecules, where the latter one appears to be an excitation of $P_c(4440)$. Therefore we conclude that, confronting three LHCb $P_c$ signals, there may exist not three, but four molecular states.

GKZ-hypergeometric systems for Feynman integrals

Basing on the systems of linear partial differential equations derived from Mellin-Barnes representations and Millers transformation, we obtain GKZ-hypergeometric systems of one-loop self energy, one-loop triangle, two-loop vacuum, and two-loop sunset diagrams, respectively. The codimension of derived GKZ-hypergeometric system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. Taking GKZ-hypergeometric systems of one-loop self energy, massless one-loop triangle, and two-loop vacuum diagrams as examples, we present in detail how to perform triangulation and how to construct canonical series solutions in the corresponding convergent regions. The series solutions constructed for these hypergeometric systems recover the well known results in literature.

Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^*$ through $W^+$-boson decays

In this paper, we calculate the total decay widths for the $W^+$-boson decays, $W^+ to B_c+b+bar{s}+X$ and $W^+ to B^*_c+b+bar{s}+X$, up to next-to-leading order (NLO) accuracy within the framework of the nonrelativistic QCD theory. Both the fixed-order and the fragmentation approaches are adopted to do the calculation. Differential decay widths $dGamma/dz$ and $dGamma/ds_1$ are also given. We find that the NLO corrections are significant in those two $W^+$ decay channels. Our numerical results show that at the LHC, there are about $7.03times 10^4$ $B_c$-meson events and $5.10times 10^4$ $B^*_c$-meson events to be produced via the $W^+$-boson decays per operation year.

The NLO fragmentation functions of heavy quarks into heavy quarkonia

In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium $J/Psi$ or $Upsilon$. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. $mu_{F}=3 m_c$ for $cto J/Psi$ and $mu_{F}=3m_b$ for $bto Upsilon$, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial application of those fragmentation functions, we study the $J/Psi$ ($Upsilon$) production at a high luminosity $e^+e^-$ collider which runs at the energy around the $Z$ pole and could be a suitable platform for testing the fragmentation function.

The mass spectra and wave functions for the doubly heavy baryons with $J^P=1^+$ heavy diquark core

The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $Xi_{cc}$, combine into a heavy `diquark core in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon. Namely both of the combinations, the two heavy quarks inside the baryon into a diquark core in color anti-triplet and the heavy diquark core with the light quark into the baryon, are depicted by relativistic Bethe-Salpeter equations (BSEs) with an accordingly QCD inspired kernel respectively, although in the paper only the heavy diquark cores with the quantum numbers $J^P=1^+$ are considered. Since the `second combination is of the heavy diquark core and the light quark, so the structure effect of the diquark core to the relevant kernel of the BSE is specially considered in terms of the diquark-core wave functions. The mass spectra and wave functions for the `low-laying doubly heavy baryons in the flavors $(ccq)$, $(bcq)$ and $(bbq)$ and in the quantum numbers $J^P=frac{1}{2}^+$, $J^P=frac{3}{2}^+$, achieved by solving the equations under the so-called instantaneous approximation, are presented properly and some comparisons with the others results under different approaches in the literature are made.

The $B_c (B_c^*)$ meson production via the proton-nucleus and the nucleus-nucleus collision modes at the colliders RHIC and LHC

In the paper, we make a comprehensive study on the hadroproduction of the $B_c (B_c^*)$ meson via the gluon-gluon fusion mechanism at the RHIC and LHC colliders. Total and differential cross sections via the proton-nucleus ($p$-N) and nucleus-nucleus (N-N) collision modes have been discussed under various collision energies. To compare with those via the proton-proton collision mode at the LHC, we observe that sizable number of $B_c (B_c^*)$-meson events can also be produced via the $p$-N and N-N collision modes at the RHIC and LHC. If assuming the spin-triplet $B^*_c$ meson directly decays to the spin-singlet $B_c$ meson with $100%$ probability, $1.2 times 10^5$ and $4.7 times 10^5$ $B_c$-meson events can be produced via the $p$-Au and Au-Au collision modes at the RHIC in one operation year; $5.8 times 10^6$ and $4.6 times 10^6$ $B_c$-meson events can be produced via the $p$-Pb and Pb-Pb collision modes at the LHC in one operation year.