In this work, we calculated the form factors of the weak decay process $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+$$ , where the final charm baryon represents an excited state with spin-parity $$\frac{1}{2}^-$$ . Utilizing the light-cone QCD sum rules approach, we incorporated the contributions of the lowest two charm baryon states: the ground state $$\varLambda _c$$ with $$J^P=\frac{1}{2}^+$$ and the excited state $$\varLambda _c(2595)^+$$ with $$J^P=\frac{1}{2}^-$$ in the hadronic representation of the $$\varLambda _b \rightarrow \varLambda _c(2595)^+$$ transition correlation function. This approach allows us to extract the form factors of the $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+$$ from $$\varLambda _b^0 \rightarrow \varLambda _c^+$$ transition. During the light-cone QCD sum rules procedure, we employed the light-cone distribution amplitudes (LCDAs) of the $$\varLambda _b$$ baryon. Furthermore, by combining these form factors with the helicity amplitudes of the bottom baryon transition matrix elements, we calculated the differential decay widths for the processes $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\ell ^-\bar{\nu }_\ell $$ and provided the optimal choice of the interpolating current for $$\varLambda _c$$ in this process. Additionally, within the lifetime of $$\varLambda _b^0$$ , we obtained the absolute branching fractions for the semileptonic decays $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+ \ell ^- \bar{\nu }_\ell $$ . With the branching fractions of $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+ \ell ^- \bar{\nu }_\ell $$ calculated in this work, we also determined the parameter $$\mathcal {R}(\varLambda _c(2595)^+)$$ which tests the lepton flavor universality. This parameter is defined as the ratio of branching fractions $$\mathcal {B}r(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\tau ^-\bar{\nu }_\tau )$$ and $$\mathcal {B}r(\varLambda _b^0 \rightarrow \varLambda _c(2595)^+\mu ^-\bar{\nu }_\mu )$$ . Our results provide a valuable theoretical test for these decay channels and offer insights into the LCDAs of bottom baryons, paving the way for further in-depth investigations.

China

Hui-Hui Duan

Yong-Lu Liu

Qin Chang

Ming-Qiu Huang

Form factors of $$\varLambda _b^0 \rightarrow \varLambda _c(2595)^+$$ within light-cone QCD sum rules

The GLR-MQ equation is a nonlinear evolution equation that takes into account the shadowing effect, which tames the growth of the gluon at small-x. In this study, we analytically solve for the first time the nonlinear GLR-MQ equation using the homogeneous balance method. The definite solution of the GLR-MQ equation is obtained by fitting the MSTW2008LO gluon distribution data. We find that the geometric scaling is an inherent property of our analytical solution. Furthermore, the gluon distribution functions derived from our solution are capable of accurately reproducing the MSTW2008LO data across most regions. These results indicate that our analytical solution from the homogeneous balance method is valid to describe the gluon behavior at small-x and moderate <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> regions. Moreover, the saturation scale <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>s</mi></mrow></msub></math> has been extracted from our analytical solution, we find that the energy-dependent saturation scale obeys the exponential law <math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mspace width="0.2em"></mspace><mo>∝</mo><mspace width="0.2em"></mspace><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mi>λ</mi><mi>Y</mi></mrow></msup></math>. We also perform a numerical simulation using the analytical results at <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>5</mn><mspace width="0.25em"></mspace><msup><mrow><mtext>GeV</mtext></mrow><mrow><mn>2</mn></mrow></msup></math> as the initial condition. We find that our analytical results are consistent with the numerical results in small-x.

Yanbing Cai

Xiaopeng Wang

Xurong Chen

New analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation

We numerically study for the first time the nonlinear GLR-MQ evolution equations for nuclear parton distribution function (nPDFs) to next-to-leading order accuracy and quantify the impact of gluon recombination at small <math><mi>x</mi></math>. Using the nCTEQ15 nPDFs as input, we confirm the importance of the nonlinear corrections for small <math><mi>x</mi><mo>≲</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, whose magnitude increases with a decrease of <math><mi>x</mi></math> and an increase of the atomic number <math><mi>A</mi></math>. We find that at <math><mi>x</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> and for heavy nuclei, after the upward evolution from <math><msub><mi>Q</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math><mi>Q</mi><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the quark singlet <math><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> and the gluon <math><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> distributions become reduced by 9%–15%, respectively. The relative effect is much stronger for the downward evolution from <math><msub><mi>Q</mi><mn>0</mn></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math><mi>Q</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, where we find that <math><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> is suppressed by 40%, while <math><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> is enhanced by 140%. These trends propagate into the <math><msubsup><mi>F</mi><mn>2</mn><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> nuclear structure function and the <math><msubsup><mi>F</mi><mi>L</mi><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> longitudinal structure function, which after the downward evolution become reduced by 45% and enhanced by 80%, respectively. Our analysis indicates that the nonlinear effects are most pronounced in <math><msubsup><mi>F</mi><mi>L</mi><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> and are already quite sizable at <math><mi>x</mi><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for heavy nuclei. We have checked that our conclusions very weakly depend on the choice of input nPDFs. In particular, using the EPPS21 nPDFs as input, we obtain quantitatively similar results.

Germany

J. Rausch

Finland

V. Guzey

Australia

M. Klasen

Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions

Semileptonic decay processes of <math><mrow><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>Ξ</mi><mo>ℓ</mo><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> are studied by light-cone QCD sum rules in this paper. The six form factors of <math><msub><mi>Ξ</mi><mi>c</mi></msub><mo>→</mo><mi>Ξ</mi></math> semileptonic transition matrix elements are calculated by this method with the light-cone distribution amplitudes of <math><mi>Ξ</mi></math> baryon up to twist six. With the six form factors, the absolute branching ratios of <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> and <math><mrow><msubsup><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>→</mo><msup><mrow><mi>Ξ</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> are calculated by the helicity amplitude formalism of semileptonic differential decay widths. The ratios of absolute branching ratios of electron and muon final-state processes give the proof of lepton flavor universality. Our results are in accordance with the recent experimental and theoretical reports.

Semileptonic decay of <math><mrow><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>→</mo><mi>Ξ</mi><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> from light-cone QCD sum rules

In this work, we analyze the semileptonic decay processes of  $$\varLambda _b \rightarrow \varLambda _c$$  <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mo>→</mo> <msub> <mi>Λ</mi> <mi>c</mi> </msub> </mrow> </math>   in the light-cone sum rule approach. In order to calculate the form factors of the  $$\varLambda _b$$  <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math>   baryon transition matrix element, we use the light-cone distribution amplitudes of  $$\varLambda _b$$  <math> <msub> <mi>Λ</mi> <mi>b</mi> </msub> </math>   obtained from the QCD sum rule in the heavy quark effective field theory framework. With the calculation of the six form factors of the  $$\varLambda _b \rightarrow \varLambda _c$$  <math> <mrow> <msub> <mi>Λ</mi> <mi>b</mi> </msub> <mo>→</mo> <msub> <mi>Λ</mi> <mi>c</mi> </msub> </mrow> </math>   transition matrix element, the differential decay widths of  $$\varLambda _b^0 \rightarrow \varLambda _c^+ \ell ^- {\overline{\nu }}_\ell (\ell = e, ~\mu , ~\tau )$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mi>b</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> <mrow> <mo>(</mo> <mi>ℓ</mi> <mo>=</mo> <mi>e</mi> <mo>,</mo> <mspace width="3.33333pt"></mspace> <mi>μ</mi> <mo>,</mo> <mspace width="3.33333pt"></mspace> <mi>τ</mi> <mo>)</mo> </mrow> </mrow> </math>   and their absolute branching fractions are obtained. Additionally, the ratio of  $$R(\varLambda _c^+) \equiv {\mathcal {B}}r(\varLambda _b^0 \rightarrow \varLambda _c^+ \tau ^- {\overline{\nu }}_\tau )/{\mathcal {B}}r(\varLambda _b^0 \rightarrow \varLambda _c^+ \mu ^- {\overline{\nu }}_\mu )$$  <math> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mo>≡</mo> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <msubsup> <mi>Λ</mi> <mi>b</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>τ</mi> <mo>-</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <msubsup> <mi>Λ</mi> <mi>b</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <mo>)</mo> </mrow> </mrow> </math>   is also obtained in this work. Our results are in accord with the newest experimental result and other theoretical calculations and predictions.

Light-cone sum rule analysis of semileptonic decays  $$\varLambda _b^0 \rightarrow \varLambda _c^+ \ell ^- {\overline{\nu }}_\ell $$  <math> <mrow> <msubsup> <mi>Λ</mi> <mi>b</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msubsup> <mi>Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <msup> <mi>ℓ</mi> <mo>-</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>ℓ</mi> </msub> </mrow> </math>

In this study, we consider all P-wave   $\Omega_{b}$   states represented by interpolating currents with a derivative and calculate the corresponding masses and pole residues using the QCD sum rule method. Because of the large uncertainties in our calculation compared with the small difference in the masses of the excited   $\Omega_{b}$   states observed by the LHCb collaboration, it is necessary to study other properties of the P-wave   $\Omega_{b}$   states represented by the interpolating currents investigated in the present work to gain a better understanding of the four excited   $\Omega_{b}$   states observed by the LHCb collaboration.

Yong-Jiang Xu

 -wave ω States: Masses and Pole Residues  

In this paper, we construct <math><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></math>-molecule-type interpolating currents <math><msub><mi>J</mi><mrow><mo>(</mo><mo>±</mo><mo>)</mo><mi>μ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>, calculate the corresponding mass and magnetic moment using the QCD sum rule method and its extension in the weak electromagnetic field, and study the processes of <math><msub><mi>Z</mi><mrow><mo>(</mo><mo>±</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></math> to <math><msub><mi>η</mi><mi>c</mi></msub><msup><mi>K</mi><mo>*</mo></msup></math>, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>K</mi></math>, <math><mover><mi>D</mi><mo>¯</mo></mover><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math>, and <math><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><msub><mi>D</mi><mi>s</mi></msub></math> via three-point sum rules. The numerical values are <math><msub><mi>m</mi><msub><mi>Z</mi><mrow><mo>(</mo><mo>±</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></msub><mo>=</mo><mn>3.9</mn><msubsup><mn>9</mn><mrow><mo>−</mo><mn>0.14</mn></mrow><mrow><mo>+</mo><mn>0.17</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, <math><msub><mi>λ</mi><msub><mi>Z</mi><mrow><mo>(</mo><mo>±</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></msub><mo>=</mo><mn>2.0</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>0.16</mn></mrow><mrow><mo>+</mo><mn>0.28</mn></mrow></msubsup><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mn>5</mn></msup></math>, and <math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mo>(</mo><mo>±</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></mrow></msub><mo>=</mo><mn>0.1</mn><msubsup><mrow><mn>8</mn></mrow><mrow><mo>−</mo><mn>0.09</mn></mrow><mrow><mo>+</mo><mn>0.16</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math> with <math><msub><mi>μ</mi><mi>N</mi></msub></math> the nucleon magneton, <math><msub><mi>Γ</mi><msub><mi>Z</mi><mrow><mo>(</mo><mo>+</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></msub><mo>=</mo><mn>17.4</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>8.08</mn></mrow><mrow><mo>+</mo><mn>12.70</mn></mrow></msubsup></math>, and <math><msub><mi>Γ</mi><msub><mi>Z</mi><mrow><mo>(</mo><mo>−</mo><mo>)</mo><mi>c</mi><mi>s</mi></mrow></msub></msub><mo>=</mo><mn>13.8</mn><msubsup><mn>6</mn><mrow><mo>−</mo><mn>6.51</mn></mrow><mrow><mo>+</mo><mn>10.37</mn></mrow></msubsup></math>. The masses are in agreement with the recently measured value of <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> by the BESIII Collaboration, <math><msubsup><mi>m</mi><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mrow><mi>exp</mi></mrow></msubsup><mo>=</mo><mo>(</mo><msubsup><mn>3982.5</mn><mrow><mo>−</mo><mn>2.6</mn></mrow><mrow><mo>+</mo><mn>1.8</mn></mrow></msubsup><mo>±</mo><mn>2.1</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The widths are compatible with the experimental value <math><msubsup><mi>Γ</mi><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mrow><mi>exp</mi></mrow></msubsup><mo>=</mo><mspace></mspace><mo>(</mo><msubsup><mn>12.8</mn><mrow><mo>−</mo><mn>4.4</mn></mrow><mrow><mo>+</mo><mn>5.3</mn></mrow></msubsup><mo>±</mo><mn>3.0</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The magnetic moment and the various decay modes can help us to determine the inner structure of <math><msub><mi>Z</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo>(</mo><mn>3985</mn><mo>)</mo></math> when being confronted with experimental data in the future.

Chun-Yu Cui

<math><msubsup><mover><mi>D</mi><mo>¯</mo></mover><mi>s</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></math> molecular state with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math>

In this paper, we tentatively assign the  $$P_{c}(4312)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4312</mn> <mo>)</mo> </mrow> </mrow> </math>   to be a  $$\bar{D}\Sigma _{c}$$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </mrow> </math>   molecular state with quantum number  $$J^{P}=\frac{1}{2}^{-}$$  <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> </mrow> </math>  , and calculate its magnetic moment using the QCD sum rule method in external weak electromagnetic field. Starting with the two-point correlation function in external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the magnetic moment from the linear response to the external electromagnetic field. The numerical value of the magnetic moment of  $$P_{c}(4312)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4312</mn> <mo>)</mo> </mrow> </mrow> </math>   is  $$\mu _{P_{c}}=1.75^{+0.15}_{-0.11}$$  <math> <mrow> <msub> <mi>μ</mi> <msub> <mi>P</mi> <mi>c</mi> </msub> </msub> <mo>=</mo> <mn>1</mn> <mo>.</mo> <msubsup> <mn>75</mn> <mrow> <mo>-</mo> <mn>0.11</mn> </mrow> <mrow> <mo>+</mo> <mn>0.15</mn> </mrow> </msubsup> </mrow> </math>  .

The magnetic moment of  $$P_{c}(4312)$$  <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4312</mn> <mo>)</mo> </mrow> </mrow> </math>   as a  $$\bar{D}\Sigma _{c}$$  <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </mrow> </math>   molecular state

The weak decay process of  $$\varOmega _c$$  <math> <msub> <mi>Ω</mi> <mi>c</mi> </msub> </math>   to  $$\varXi $$  <math> <mi>Ξ</mi> </math>   is calculated in the method of QCD light-cone sum rule. The decay width of  $$\varOmega _c^0 \rightarrow \varXi ^- l^+ \nu _l$$  <math> <mrow> <msubsup> <mi>Ω</mi> <mi>c</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msup> <mi>Ξ</mi> <mo>-</mo> </msup> <msup> <mi>l</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>l</mi> </msub> </mrow> </math>   and its decay branching ratio are also calculated with the form factors from this work’s calculation. To the twist-6 distribution amplitudes, the form factors  $$f_1=0.66\pm 0.02, f_2=-0.76\pm 0.03, g_1=0.06\pm 0.01$$  <math> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.66</mn> <mo>±</mo> <mn>0.02</mn> <mo>,</mo> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mn>0.76</mn> <mo>±</mo> <mn>0.03</mn> <mo>,</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.06</mn> <mo>±</mo> <mn>0.01</mn> </mrow> </math>   and  $$g_2=-0.44\pm 0.01$$  <math> <mrow> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mn>0.44</mn> <mo>±</mo> <mn>0.01</mn> </mrow> </math>   are given at zero recoil point. The result of the semileptonic decay width of  $$\varOmega _c^0 \rightarrow \varXi ^-l^+\nu _l$$  <math> <mrow> <msubsup> <mi>Ω</mi> <mi>c</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msup> <mi>Ξ</mi> <mo>-</mo> </msup> <msup> <mi>l</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>l</mi> </msub> </mrow> </math>   is  $$\varGamma =(7.51\pm 0.36)\times 10^{-15}~\mathrm{{GeV}}$$  <math> <mrow> <mi>Γ</mi> <mo>=</mo> <mrow> <mo>(</mo> <mn>7.51</mn> <mo>±</mo> <mn>0.36</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>15</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mi>GeV</mi> </mrow> </math>   , and the prediction of the decay branching ratio  $$Br(\varOmega _c^0\rightarrow \varXi ^-l^+\nu _l)=(3.06\pm 0.15)\times 10^{-3}$$  <math> <mrow> <mi>B</mi> <mi>r</mi> <mrow> <mo>(</mo> <msubsup> <mi>Ω</mi> <mi>c</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msup> <mi>Ξ</mi> <mo>-</mo> </msup> <msup> <mi>l</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>l</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>3.06</mn> <mo>±</mo> <mn>0.15</mn> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math>  . These results fit well with other works, and the decay width and branching ratio are improved. This not too small branching ratio gives a good direction to explore this decay channel in the future experiments.

Semileptonic decay of  $$\varOmega _c^0 \rightarrow \varXi ^- l^+ \nu _l$$  <math> <mrow> <msubsup> <mi>Ω</mi> <mi>c</mi> <mn>0</mn> </msubsup> <mo>→</mo> <msup> <mi>Ξ</mi> <mo>-</mo> </msup> <msup> <mi>l</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>l</mi> </msub> </mrow> </math>   from light-cone sum rules

In this article, we study the ground states and the first radial excited states of the flavor antitriplet heavy baryon states   $\Lambda_Q$   and   $\Lambda_Q$   with the spin-parity   $\Lambda_Q$   by carrying out operator product expansion up to vacuum condensates of dimension   $\Lambda_Q$   in a consistent way. We observe for the first time that the higher dimensional vacuum condensates play an important role, and obtain very stable QCD sum rules with variations of the Borel parameters for the heavy baryon states. The predicted masses   $\Lambda_Q$  ,   $\Lambda_Q$  , and   $\Lambda_Q$   for the first radial excited states   $\Lambda_Q$  ,   $\Lambda_Q$  , and   $\Lambda_Q$  , respectively, are in excellent agreement with the experimental data and support assigning   $\Lambda_Q$  ,   $\Lambda_Q$  , and   $\Lambda_Q$   to be the first radial excited states of   $\Lambda_Q$  ,   $\Lambda_Q$  , and   $\Lambda_Q$  , respectively. The predicted mass   $\Lambda_Q$   for   $\Lambda_Q$   can be confirmed using experimental data in the future.