Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCovariant chiral nucleon-nucleon contact Lagrangian up to order $mathcal{O}(q^4)$
117
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $mathcal{O}(q^0)$, $mathcal{O}(q^2)$, $mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.
rate research
Read More
The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $mathcal{O}(q^2)$, $mathcal{O}(q^3)$ and $mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.
We study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory (BChPT) up to the next-to-next-to-leading order. The inherent power counting breaking terms are removed within extended-on-mass-shell scheme. We perform the first combined study of the pion-nucleon and kaon-nucleon scattering data in covariant BChPT and show that it can provide a reasonable description of the experimental data. In addition, we find that it is possible to fit the experimental baryon masses and the pion-nucleon and kaon-nucleon scattering data simultaneously at this order, thus providing a consistent check on covariant BChPT. We compare the scattering lengths of all the pertinent channels with available experimental data and those of other approaches. In addition, we have studied the leading order contributions of the virtual decuplet and found that they can improve the description of the $pi N$ phase shifts near the $Delta(1232)$ peak, while they have negligible effects on the description of the $K N$ phase shifts.
Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2leq Lleq 6$ and mixing angles with $2leq Jleq6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic corrections play an important role in F-waves especially the $^3text{F}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the nonrelativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.
We calculate the lambda-nucleon scattering phase shifts and mixing angles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. Scattering amplitudes are obtained by solving the corresponding coupled-channel integral equations that have a milder ultraviolet behavior compared to their non-relativistic analogs. This allows us to consider the removed cutoff limit in our leading-order calculations also in the $^3P_0$ and $^3P_1$ partial waves. We find that, in the framework we are using, at least some part of the higher-order contributions to the baryon-baryon potential in these channels needs to be treated nonperturbatively and demonstrate how this can be achieved in a way consistent with quantum field theoretical renormalization for the leading contact interactions. We compare our results with the ones of the non-relativistic approach and lattice QCD phase shifts obtained for non-physical pion masses.
Motivated by the recent experimental measurements of differential cross sections of the $Sigma^{-}p$ elastic scattering in the momentum range of $470$ to $850$ MeV$/c$ by the J-PARC E$40$ experiment, we extend our previous studies of $S=-1$ hyperon-nucleon interactions to relatively higher energies up to $900$ MeV$/c$ for both the coupled-channel $Lambda prightarrow(Lambda p, Sigma^{+}n, Sigma^{0}p)$, $Sigma^{-}prightarrow(Lambda n, Sigma^{0}n, Sigma^{-}p)$ and single-channel $Sigma^{+}prightarrowSigma^{+}p$ reactions. We show that although the leading order covariant chiral effective field theory is only constrained by the low energy data, it can describe the high energy data very well, in particular, the J-PARC E40 differential cross sections. In particular, we predict a pronounced cusp structure close to the $Sigma N$ threshold in the $Lambda pto Lambda p$ reaction, which can be checked in the future using, e.g., the Femtoscopy technique. The predicted total and differential cross sections are of relevance for ongoing and planned experiments.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
