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Scalar and vector self-energies of heavy baryons in nuclear medium

View Article: PubMed Central - PubMed

ABSTRACT

The in-medium sum rules are employed to calculate the shifts in the mass and residue as well as the scalar and vector self-energies of the heavy ΛQ,ΣQ and ΞQ baryons, with Q being b or c quark. The maximum shift in mass due to nuclear matter belongs to the Σc baryon and it is found to be ΔmΣc=−936 MeV. In the case of residue, it is obtained that the residue of Σb baryon is maximally affected by the nuclear medium with the shift ΔλΣb=−0.014 GeV3. The scalar and vector self-energies are found to be ΣΛbS=653 MeV, ΣΣbS=−614 MeV, ΣΞbS=−17 MeV, ΣΛcS=272 MeV, ΣΣcS=−936 MeV, ΣΞcS=−5 MeV and ΣΛbν=436±148 MeV, ΣΣbν=382±129 MeV, ΣΞbν=15±5 MeV, ΣΛcν=151±45 MeV, ΣΣcν=486±144 MeV and ΣΞcν=1.391±0.529 MeV.

No MeSH data available.


The residue of the Λb baryon (left panel) and the Λc baryon (right panel) versus M2 in vacuum and nuclear medium at average values of s0 and x.
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fg0030: The residue of the Λb baryon (left panel) and the Λc baryon (right panel) versus M2 in vacuum and nuclear medium at average values of s0 and x.

Mentions: Now, we proceed to numerically analyze the sum rules obtained for the physical observables using these working windows and the values of other input parameters. To this end, first of all, in order to show how the OPE converges in our calculations we compare the variations of perturbative part, two-quark condensate, two-gluon condensate, mixed condensate and four-quark condensate with approximations in Eqs. (14) and (15) for instance in channel and p̸ structure with respect to at average values of other auxiliary parameters in Fig. 1. From this figure, we see that the OPE nicely converges, i.e., the perturbative part exceeds the nonperturbative contributions and the contributions reduce with increasing the dimension. Note that as is also clear from Eq. (13) the contribution of mixed condensate is exactly zero since the terms containing the mixed condensate have no imaginary parts and do not contribute to the spectral density. We also see that the four-quark condensate has least contribution to the sum rules and the approximations (14) and (15) seem reasonable. Similar results are obtained for other channels and structures. We plot the quantities under consideration, i.e. masses, residues, the vector self-energies with respect to at average values of the threshold and mixing parameters in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10 for both the nuclear medium and vacuum. Only in the case of vector self-energies we depict their variations with respect to the Borel parameter for different particles in medium since they do not exist in the vacuum. We shall also remark that we calculate the scalar self-energies via the shifts in masses compared to their vacuum values, hence we do not plot their variations with respect to , separately. First of all, we see that these figures depict considerable shifts on the values of observables due to nuclear matter when we compare them with their vacuum values. The next issue that should be emphasized is: the physical observables under consideration overall show weak dependence on the Borel parameter both in vacuum and nuclear medium in the selected windows. Extracted from the numerical calculations, we present the average numerical results for different quantities for both the nuclear matter and vacuum and also both the b and c-baryons in Table 3, Table 4, Table 5. The quoted errors in the values are due to the uncertainties coming from the calculations of the working regions of auxiliary parameters, errors of different input parameters as well as those related to different approximations used in the analyses. We present the existing predictions for parameters in and channels obtained via Ioffe current [22], [23] in Table 3, Table 4 as well.


Scalar and vector self-energies of heavy baryons in nuclear medium
The residue of the Λb baryon (left panel) and the Λc baryon (right panel) versus M2 in vacuum and nuclear medium at average values of s0 and x.
© Copyright Policy - CC BY
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5384447&req=5

fg0030: The residue of the Λb baryon (left panel) and the Λc baryon (right panel) versus M2 in vacuum and nuclear medium at average values of s0 and x.
Mentions: Now, we proceed to numerically analyze the sum rules obtained for the physical observables using these working windows and the values of other input parameters. To this end, first of all, in order to show how the OPE converges in our calculations we compare the variations of perturbative part, two-quark condensate, two-gluon condensate, mixed condensate and four-quark condensate with approximations in Eqs. (14) and (15) for instance in channel and p̸ structure with respect to at average values of other auxiliary parameters in Fig. 1. From this figure, we see that the OPE nicely converges, i.e., the perturbative part exceeds the nonperturbative contributions and the contributions reduce with increasing the dimension. Note that as is also clear from Eq. (13) the contribution of mixed condensate is exactly zero since the terms containing the mixed condensate have no imaginary parts and do not contribute to the spectral density. We also see that the four-quark condensate has least contribution to the sum rules and the approximations (14) and (15) seem reasonable. Similar results are obtained for other channels and structures. We plot the quantities under consideration, i.e. masses, residues, the vector self-energies with respect to at average values of the threshold and mixing parameters in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10 for both the nuclear medium and vacuum. Only in the case of vector self-energies we depict their variations with respect to the Borel parameter for different particles in medium since they do not exist in the vacuum. We shall also remark that we calculate the scalar self-energies via the shifts in masses compared to their vacuum values, hence we do not plot their variations with respect to , separately. First of all, we see that these figures depict considerable shifts on the values of observables due to nuclear matter when we compare them with their vacuum values. The next issue that should be emphasized is: the physical observables under consideration overall show weak dependence on the Borel parameter both in vacuum and nuclear medium in the selected windows. Extracted from the numerical calculations, we present the average numerical results for different quantities for both the nuclear matter and vacuum and also both the b and c-baryons in Table 3, Table 4, Table 5. The quoted errors in the values are due to the uncertainties coming from the calculations of the working regions of auxiliary parameters, errors of different input parameters as well as those related to different approximations used in the analyses. We present the existing predictions for parameters in and channels obtained via Ioffe current [22], [23] in Table 3, Table 4 as well.

View Article: PubMed Central - PubMed

ABSTRACT

The in-medium sum rules are employed to calculate the shifts in the mass and residue as well as the scalar and vector self-energies of the heavy ΛQ,ΣQ and ΞQ baryons, with Q being b or c quark. The maximum shift in mass due to nuclear matter belongs to the Σc baryon and it is found to be ΔmΣc=−936 MeV. In the case of residue, it is obtained that the residue of Σb baryon is maximally affected by the nuclear medium with the shift ΔλΣb=−0.014 GeV3. The scalar and vector self-energies are found to be ΣΛbS=653 MeV, ΣΣbS=−614 MeV, ΣΞbS=−17 MeV, ΣΛcS=272 MeV, ΣΣcS=−936 MeV, ΣΞcS=−5 MeV and ΣΛbν=436±148 MeV, ΣΣbν=382±129 MeV, ΣΞbν=15±5 MeV, ΣΛcν=151±45 MeV, ΣΣcν=486±144 MeV and ΣΞcν=1.391±0.529 MeV.

No MeSH data available.