arXiv subjects

Ruilin Zhu

Publications and source records attributed to Ruilin Zhu.

At least 55 records · Page 3Linked to original sources

arXiv2020

Open-charm tetraquark $X_c$ and open-bottom tetraquark $X_b$

Motivated by the LHCb observation of exotic states $X_{0,1}(2900)$ with four open quark flavors in the $D^- K^+$ invariant mass distribution in the decay channel $B^\pm \to D^+ D^- K^\pm$, we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with $J^P=0^+$ and an orbitally excited tetraquark with $J^P=1^-$, respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of $su \bar d \bar c$ and $ d s \bar u \bar c$, which are in the $\bar 6$ or $15$ representation of the flavor SU(3) group. We point that these two states can be found through the decays: $X^{(\prime)}_{d s \bar{u}\bar{c}}\to (D^- K^-, D_s^- π^-) $, and $X^{(\prime)}_{s u \bar{d}\bar{c}}\to D_s^-π^+ $. We also apply our analysis to open bottom tetraquark $X_b$ and predict their masses. The open-flavored $X_b$ can be discovered through the following decays: $X_{ud\bar s\bar{b}}\to B^0K^+$, $X^{(\prime)}_{d s \bar{u}\bar{b}}\to (B^0 K^-, B_s^0 π^-) $, and $X^{(\prime)}_{s u \bar{d}\bar{b}}\to B_s^0π^+ $.

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arXiv2020

Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions

We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.

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arXiv2020

Master Integrals for two-loop QCD corrections to Quasi PDFs

We compute the master integrals for two-loop QCD corrections to quasi parton distribution functions (PDFs) in large momentum effective theory. Analytical results of the master integrals are derived using the method of differential equations, along with a proper choice of canonical basis. The results of master integrals are expressed in terms of Goncharov polylogarithms. These integrals allow to extract the two-loop short-distance matching coefficients between quasi and light cone PDFs in large momentum effective theory, and are helpful to extract the nucleon PDFs from first principles.

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arXiv2019

Analyzing doubly heavy tetra- and penta-quark states by variational method

Motivated by the very recent observations of hidden charm pentaquarks $P_c(4312)^+$, $P_c(4440)^+$ and $P_c(4457)^+$ of the LHCb Collaboration, we systematically study the spectra of the doubly-heavy (with or without charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic constituent quark model. The model independent variational method is employed to solve the Schrödinger equation, where the test functions adopted are symmetric for the light quarks. In our study, the $P_c(4312)^+$ may be assigned as the ground state with spin-parity $\frac{1}{2}^-$ or $\frac{3}{2}^-$, while the $P_c(4440)^+$ and $P_c(4457)^+$ may be assigned as the excited states with $\frac{1}{2}^-$, which might all belong to the sextet with $s_{c\bar{c}}=1$ and $s_\ell=\frac{3}{2}$. It is notable that our working framework is quite similar to that of Hydrogen molecule, but with different potential structure. We also classify these pentaquarks and tetraquarks in light of the heavy quark symmetry and their decay properties are analyzed. Several promising channels for the observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in experiment are proposed.

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arXiv2019

Model independent investigation of the $R_{J/ψ,η_c}$ and ratios of decay widths of semileptonic $B_c$ decays into a P-wave charmonium

Experimental measurements of decay branching fractions of semitaunic and semimuonic $B_c$ into $J/ψ$ has challenged the lepton flavor universality in standard model with about two standard deviations. In this paper, we first investigate the unitary constraint on form factors of $B_c$ meson into $S$-wave and $P$-wave charmonium. Such constraint leads to the exploration of the $R_{J/ψ}$ and other ratios $R_{η_c}$, $R_{h_c}$, and $R_{χ_{cJ}}$ in a model-independent way. These results together with future experimental measurements can be used to explore the lepton flavor universality in a more systematic way. In addition, we point out that the helicity-dependent ratios $R^L_{J/ψ}$ and $R^\perp_{J/ψ}$ can also provide complementary information.

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arXiv2019

Weak Decays of Stable Open-bottom Tetraquark by SU(3) Symmetry Analysis

The exotic state $X(5568)$ which was observed by D0 Collaboration is very likely to be a tetraquark state with four different valence quark flavors, though the existence was not confirmed by other collaborations. The possibility of such state still generate lots of interests in theory. In the paper, we will study the properties of the state under the SU(3) flavor symmetry. This four quark state with a heavy bottom quark and three light quarks(anti-quark) can form a $6$ or $\overline {15}$ representation. The weak decays can be dominant and should be discussed carefully while such state is stable against the strong interaction. Therefor we will study the multi-body semileptonic and nonleptonic weak decays systematically. With the help of SU(3) flavor symmetry, we can give the Hamiltonian in the hadronic level, then obtain the parameterized irreducible amplitudes and the relations of different channels. At the end of the article, we collect some Cabibbo allowed two-body and three-body weak decay channels which can be used to reconstruct $X_{b6}$ states at the branching fraction up to be $10^{-5}$.

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arXiv2018

Form factors for semileptonic $B_{c}$ decays into $η^{(')}$ and Glueball

We calculated the form factors of $B_{c}$ transitions into $η^{(')}$ meson and pseudoscalar Glueball, where the $B_{c}$ meson is a bound state of two different heavy flavors and is treated as a nonrelativistic state, while the mesons $η^{(')}$ and Glueball are treated as light-cone objects since their masses are smaller enough compared to the transition momentum scale. The mechanism of two gluon scattering into $η^{(')}$ dominated the form factors of $B_{c}$ decays into $η^{(')}$. We considered the $η-η'-$Glueball mixing effect, and then obtained their influences on the form factors. The form factors of $B_{c}$ transitions into $η^{(')}$ and pseudoscalar Glueball in the maximum momentum recoil point were obtained as follows: $f^η_{0,+}(q^2=0)=1.38^{+0.00}_{-0.02}\times 10^{-3}$,$f^{η'}_{0,+}(q^2=0)=0.89^{+0.11}_{-0.10}\times 10^{-2}$ and $f^{G}_{0,+}(q^2=0)=0.44^{+0.13}_{-0.05}\times 10^{-2}$. Also phenomenological discussions for semileptonic $B_{c}\toη^{(')}+\ell+\barν_\ell$, $B_{c}\to G(0^{-+})+\ell+\barν_\ell$ and $D_{s}\to η+\ell+\barν_\ell$ decays are given.

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arXiv2018

Weak Decays of Stable Doubly Heavy Tetraquark States

In the light of the recent discovery of the $Ξ^{++}_{cc}$ by LHCb collaboration, we study the stable doubly heavy tetraquarks. These states are compact exotic hadrons which can be approximated as the diquark-anti-diquark correlations. In the flavor SU(3) symmetry, they form an SU(3) triplet or anti-sextet. The spectra of the stable doubly heavy tetraquark states are predicted by Sakharov-Zeldovich formula. We find that the $T^+_{cc\bar{u}\bar{d}}({\bf 3})$ is about 16MeV below the $DD^*$ threshold, while $T^{-}_{bb\bar{u}\bar{d}}({\bf 3})$ is about 73MeV below the $BB^*$ threshold. We then study the semileptonic and nonleptonic weak decays of the stable doubly heavy tetraquark states. The decay amplitudes are parametrized in terms of SU(3)-irreducible amplitudes. Ratios between decay widths of different channels are also derived. At the end, we collect the Cabibbo allowed two-body and three-body decay channels, which are most promising to search for the stable doubly heavy tetraquark states at LHCb and Belle II experiments.

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arXiv2018

Weak decays of $B_c$ into two hadrons under flavor SU(3) symmetry

A large number of $B_c$ meson events have been recorded at the LHCb detector, especially some two-body hadronic decay modes. We analyzed the weak decays of the $B_c$ meson into two hadron states under the flavor SU(3) symmetry. The relations among amplitudes of $B_c$ into $ D+P(V)$, $B+P(V)$, $P(V)+P(V)$, $T_8+\bar T_8$ and $T_{10}+\bar T_{10}$ were investigated systematically, where $P$ ( $V$) denotes a light pseudoscalar (vector) meson and $T_{8,10}$ denotes a light baryon. The $η-η'$ mixing and $ω-ϕ$ mixing effects are also considered for the phenomenological discussions. We obtained the relations among decay widths of different $B_c$ decay channels. These results are helpful to study the two-body decay properties of the $B_c$ meson and test the flavor SU(3) symmetry.

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arXiv2018

Inclusive $h_c$ production and energy spectrum from $e^+ e^-$ annihilation at Super $B$ factory

We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^+e^-$ annihilation at Super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO short-distance coefficient (SDC) accompanying the color-octet production operator $\mathcal{O}_8^{h_c}(^1S_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphysical endpoint singularity. With the aid of the soft-collinear effective theory, those large endpoint logarithms are resummed to the next-to-leading logarithmic (NLL) accuracy. Consequently, further supplemented with the non-perturbative shape function, we obtain the well-behaved predictions for the $h_c$ energy spectrum in the entire kinematic range, which awaits the examination by the forthcoming Belle II experiment.

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arXiv2018

Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmonium

We investigated the form factors of the $B_{c}$ meson into $P$-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were obtained, and the asymptotic expressions were studied in the infinite bottom quark mass limit. Employing the general form factors, we discussed the exclusive decays of the $B_{c}$ meson into $P$-wave orbitally excited charmonium and a light meson. We found that the relativistic corrections lead to a large correction for the form factors, which makes the branching ratios of the decay channels $\mathcal{B}(B_{c} ^{\pm }\to χ_{cJ}(h_c) +π^{\pm }(K^{\pm }))$ larger. These results are useful for the phenomenological analysis of the $B_{c}$ meson decays into $P$-wave charmonium, which shall be tested in the LHCb experiments.

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arXiv2018

Doubly charmed tetraquarks in a diquark-antidiquark model

We study the spectra of the doubly charmed tetraquark states in a diquark-antidiquark model. The doubly charmed tetraquark states form an antitriplet and a sextet configurations according to flavor SU(3) symmetry. For the tetraquark state $[qq'][\bar c\bar c]$, we show the mass for both bound and excited states. The two-body decays of tetraquark states $T^{cc}[0^+]$ and $T^{cc}[1^{--}]$ to charmed mesons have also been studied. In the end,the doubly charmed tetraquarks decays to a charmed baryon and a light baryon have been studied in the SU(3) flavor symmetry.

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arXiv2018

Gluon quasidistribution function at one loop

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the $P^z$ evolution equation for quasi parton distribution functions, and find that the $P^z$ evolution kernels are identical to the DGLAP evolution kernels.

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arXiv2017

Graviton-mediated dark matter model explanation the DAMPE electron excess and search at $e^+e^-$ colliders

The very recent result of the DAMPE cosmic ray spectrum of electrons shows a narrow bump above the background at around 1.4 TeV. We attempt to explain the DAMPE electron excess in a simplified Kaluza-Klein graviton-mediated dark matter model, in which the graviton only interacts with leptons and dark matter. The related phenomenological discussions are given and this simplified graviton-mediated dark matter model has the potential to be cross-tested in future lepton collider experiments.

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arXiv2017

Relativistic corrections to the form factors of $B_c$ into $S$-wave Charmonium

We investigate the form factors of $B_c$ meson into $S$-wave charmonium within the nonrelativistic QCD effective theory and obtain the next-to-leading order relativistic corrections to the form factors, where both the $B_c$ meson and the charmonium are treated as the nonrelativistic bound states. Treating the charm quark as a light quark in the limit \ $m_c/m_b\to 0$, some form factors are identical at the maximum recoil point, which are consistent with the predictions in the heavy-quark effective theory and the large-energy effective theory. Considering that the branching ratios of $B^+_c \to J/ψD_s^+$ and $B^+_c \to J/ψD_s^{*+}$ have been measured by the LHCb and ATLAS Collaborations recently, we employ the form factors of $B_c$ meson into $S$-wave charmonium at the next-to-leading order accuracy to these two decay channels and obtain more precise predictions of their decay rates. Numerical results indicate that the factorizable diagrams dominate the contribution in these two channels, while the colour-suppressed and the annihilation diagrams contribute less than 10 percent. Our results are consistent with the LHCb and ATLAS data.

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arXiv2016

Radiative $h_{c/b}$ decays to $η$ or $η^\prime$

Motivated by recent measurements of the radiative decay rates of the \emph{P}-wave spin singlet charmonium $h_c$ to the light meson $η$ or $η^\prime$ by the BESIII Collaboration, we investigate the decay rates of these channels at order $αα_s^4$. The photon is radiated mainly from charm quark pairs in the lowest order Feynman diagrams, since the diagrams where a photon radiated from light quarks are suppressed by $α_s$ or the relative charm quark velocity $v$, due to Charge parity conservation. The form factors of two gluons to $η$ or $η^\prime$ are employed, which are the major mechanism for $η$ and $η^\prime$ productions. $η(η^\prime)$ is treated as a light cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio ${\cal B}(h_c\to γη^\prime) = (1.94^{+0.70}_{-0.51})\times 10^{-3}$ in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of $h_c\to γη$ is also within the range of experimental error after including the larger uncertainty of the total decay width $Γ_{h_c}$. The applications of these formulae to the radiative decays to $η(η^\prime)$ of the \emph{P}-wave spin singlet bottomonium $h_b(nP)$ are presented. These studies will shed some light on the $η- η^\prime$ mixing effects, the flavor SU(3) symmetry breaking, as well as the nonperturbative dynamics of charmonium and bottomonium.

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arXiv2016

Hidden charm octet tetraquarks from a diquark-antidiquark model

Four exotic charmonium-like states, i.e. $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, have been observed very recently by LHCb Collaboration in the decay process $B^+\to J/ψϕK^+$ using the 3${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt s= 7$ and $8$ TeV. In this paper, we investigate systematically the properties of hidden charm tetraquark states. The hidden charm tetraquarks form an octet configuration and a singlet configuration according to flavor $SU(3)$ symmetry. Based on a diquark-antidiquark model, the hidden charm tetraquarks spectra are given. The previous XYZ exotic states altogether with the newly ones $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, can be well classified into certain representations. The spin-parities and masses of the XYZ are predicted, most of which are in agreement with the data. We particularly find that $Z_c(4430)$ may be treated as the first radial excitation of $Z_c(3900)$, while the $Y(1^{--})$ states can be obtained by the first orbital excitation of the $X/Z$ states. Besides, we calculate the decay widths of the hidden charm tetraquarks into two charmed mesons. This work gives a general tetraquark description for the XYZ states, which is helpful to uncover their inner structures.

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arXiv2016

Can $X(5568)$ be a tetraquark state?

Very recently, the D0 collaboration has reported the observation of a narrow structure, $X(5568)$, in the decay process $X(5568)\to B^0_sπ^\pm$ using the 10.4${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt s= 1.96$ TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, $b,s,u,d$. In this work, we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor $[su][\bar b\bar d ]$ and the spin-parity $J^P=0^+$, is about 150 MeV higher than the $X(5568)$. Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors in the future are severely needed towards a better understanding its nature and the classification of hadron exotic states.

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