Baryon Mass Splittings Research Articles

Mixing effects of Σ0−Λ0 in Λc+ decays

We analyze the mixing between $\Sigma^0$ and $\Lambda^0$ based on the baryon masses. We distinguish the contributions from QCD and QED in the baryon mass splittings. We find that the mixing angle between $\Sigma^0$ and $\Lambda^0$ is $(2.07\pm 0.03)\times 10^{-2} $, which leads to the decay branching fraction and up-down asymmetry of $\Lambda_c^+ \to \Sigma^0 e^+ \nu_e$ to be ${\cal B}(\Lambda_c^+ \to \Sigma^0 e^+ \nu_e)=(1.5\pm 0.2)\times 10^{-5}$ and $\alpha(\Lambda_c^+ \to \Sigma^0 e^+ \nu_e)=-0.86\pm 0.04$, respectively. Moreover, we obtain that $\Delta {\cal B}\equiv {\cal B}(\Lambda_c^+\to \Sigma^0 \pi^+) - {\cal B}(\Lambda_c^+\to \Sigma^+\pi^0)=(3.8\pm 0.5)\times 10^{-4}$ and $\Delta \alpha \equiv\alpha(\Lambda_c^+\to \Sigma^0 \pi^+) -\alpha(\Lambda_c^+\to \Sigma^+\pi^0)=(-1.6\pm 0.7)\times10^{-2}$, which should vanish without the mixing.

Decuplet to octet baryon transitions in chiral perturbation theory

We have systematically investigated the decuplet (T) to octet (B) baryon (Trightarrow Bgamma ) transition magnetic moments to the next-to-next-to-leading order and electric quadruple moments to the next-to-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. Throughout our calculation, we have adopted the small-scale scheme and have not considered the 1/M recoiling corrections directly. We count the octet and decuplet baryon mass splitting delta , the small momenta p, and the pion mass m_{phi } as the same order small-scale parameter, which was denoted as epsilon . Our results for the transition magnetic moments show reasonably good convergence of the chiral expansion. The analytical expressions may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.

The 't Hooft Coupling and Baryon Mass Splitting in the Large-Nc Quark Model**Supported by the National Natural Science Foundation of China under Grant No 11265014.

We study the 't Hooft coupling gt and the mass splitting of the ground-state baryons in terms of the large Nc-inspired quark model, by which the Hartree wavefunctions of light quarks are obtained. By fitting the spectra of decuplet and octet baryons, we obtain the 't Hooft coupling gt to be around 1.57. We generalize the scenario to the case of heavy baryons, such as ΛAc, gt values which does not deviate much from 1.57, as well as to the case of mesons with gt far from that for baryons. The consequence is discussed.

Dispersive estimate of the electromagnetic charge symmetry violation in the octet baryon masses

We explore the electromagnetic contribution to the charge symmetry breaking in the octet baryon masses using a subtracted dispersion relation based on the Cottingham formula. For the proton-neutron mass splitting we report a minor revision of the recent analysis of Walker-Loud, Carlson, and Miller [Phys. Rev. Lett. 108, 232301 (2012)]. For the electromagnetic structure of the hyperons we constrain our analysis, where possible, by a combination of lattice QCD and SU(3) symmetry-breaking estimates. The results for the baryon mass splittings are found to be compatible with recent lattice $\mathrm{QCD}+\mathrm{QED}$ determinations. The uncertainties in the dispersive analysis are dominated by the lack of knowledge of the hyperon inelastic structure.

Evidence for nonanalytic light quark mass dependence in the baryon spectrum

Using precise lattice QCD computations of the baryon spectrum, we present the first direct evidence for the presence of contributions to the baryon masses which are non-analytic in the light quark masses; contributions which are often denoted "chiral logarithms". We isolate the poor convergence of SU(3) baryon chiral perturbation theory to the flavor-singlet mass combination. The flavor-octet baryon mass splittings, which are corrected by chiral logarithms at next to leading order in SU(3) chiral perturbation theory, yield baryon-pion axial coupling constants D, F, C and H consistent with QCD values; the first evidence of chiral logarithms in the baryon spectrum. The Gell-Mann--Okubo relation, a flavor-27 baryon mass splitting, which is dominated by chiral corrections from light quark masses, provides further evidence for the presence of non-analytic light quark mass dependence in the baryon spectrum; we simultaneously find the GMO relation to be inconsistent with the first few terms in a taylor expansion in m_s - m_l, which must be valid for small values of this SU(3) breaking parameter. Additional, more definitive tests of SU(3) chiral perturbation theory will become possible with future, more precise, lattice calculations.

Excitations of single-beauty hadrons

In this work we study the predominantly orbital and radial excitations of hadrons containing a single heavy quark. We present meson and baryon mass splittings and ratios of meson decay constants (e.g., ${f}_{{B}_{s}}/{f}_{B}$ and ${f}_{{B}_{s}^{\ensuremath{'}}}/{f}_{{B}_{s}}$) resulting from quenched and dynamical two-flavor configurations. Light quarks are simulated using the chirally improved lattice Dirac operator at valence masses as light as ${M}_{\ensuremath{\pi}}\ensuremath{\approx}350\text{ }\text{ }\mathrm{MeV}$. The heavy quark is approximated by a static propagator, appropriate for the $b$ quark on our lattices ($1/a\ensuremath{\sim}1--2\text{ }\text{ }\mathrm{GeV}$). We also include some preliminary calculations of the $O(1/{m}_{Q})$ kinetic corrections to the states, showing, in the process, a viable way of applying the variational method to three-point functions involving excited states. We compare our results with recent experimental findings.

Isospin mass splittings of heavy baryons in heavy quark symmetry

In this paper, the electromagnetic mass differences of heavy hadrons are discussed, while the relevant hyperfine interactions are ignored. The effects of one-photon exchange interaction and up-down quark mass difference are parametrized. Two mass difference equations $2{\ensuremath{\Sigma}}_{c}^{+}\ensuremath{-}({\ensuremath{\Sigma}}_{c}^{++}+{\ensuremath{\Sigma}}_{c}^{0})=2{\ensuremath{\Sigma}}_{b}^{0}\ensuremath{-}({\ensuremath{\Sigma}}_{b}^{+}+{\ensuremath{\Sigma}}_{b}^{\ensuremath{-}})$ and $({\ensuremath{\Xi}}_{cc}^{+}\ensuremath{-}{\ensuremath{\Xi}}_{cc}^{++})+({\ensuremath{\Xi}}_{bb}^{\ensuremath{-}}\ensuremath{-}{\ensuremath{\Xi}}_{bb}^{0})=2({\ensuremath{\Xi}}_{bc}^{0}\ensuremath{-}{\ensuremath{\Xi}}_{bc}^{+})$ for the heavy baryons are obtained. In addition, the masses of ${\ensuremath{\Sigma}}_{b}^{0}$, ${\ensuremath{\Xi}}_{b}^{0}$, and ${\ensuremath{\Xi}}_{cc}^{++}$ are predicted based on the known experimental data.

Model-independent analysis for determining mass splittings of heavy baryons

We study the hyperfine mass differences of heavy hadrons in the heavy quark effect theory. The effects of one-gluon exchange interaction are considered for the heavy mesons and baryons. Based on the known experimental data, we predict the masses of some heavy baryons in a model-independent way.

Model-independent bottom baryon mass predictions in the1/Ncexpansion

Recent discoveries of the ${\ensuremath{\Xi}}_{b}$, ${\ensuremath{\Sigma}}_{b}$, and ${\ensuremath{\Sigma}}_{b}^{*}$ baryons at the Tevatron are in good agreement with model-independent mass predictions made a decade ago based on a combined expansion in $1/{N}_{c}$, $1/{m}_{Q}$, and $SU(3)$ flavor symmetry breaking. Using the new experimental data as input, mass predictions for the undiscovered bottom baryons ${\ensuremath{\Xi}}_{b}^{\ensuremath{'}}$, ${\ensuremath{\Xi}}_{b}^{*}$, ${\ensuremath{\Omega}}_{b}$, and ${\ensuremath{\Omega}}_{b}^{*}$ and for many unmeasured bottom baryon mass splittings are updated. The observed ground state charm baryons exhibit the mass hierarchy previously predicted by the $1/{N}_{c}$, $1/{m}_{Q}$, and $SU(3)$ flavor-breaking expansion.

Charmonium dissociation cross sections and p– A collisions

Charmonium dissociations by nucleons are first studied from a quark–quark potential in combination with quark exchange mechanism. Wave functions of nucleons and charmed baryons involved in dissociation reactions result from a fit to mass splittings of baryons with spins 1 2 and 3 2 . Transverse momentum and x F distributions of prompt J/ ψ produced in 800 GeV/ c p–Be collisions are calculated by using NRQCD dσ/d t ̂ for parton–parton scatterings and taking into account initial transverse-momentum distributions of partons inside nucleons. We emphasize that the new dissociation cross sections of J/ ψ, ψ′ and χ cJ give rise to remarkable differences of J/ ψ, ψ′ and χ c suppressions at large negative x F in p–W collisions at s NN =38.8 and 41.6 GeV and p–Au collisions at s NN =130 GeV .

Baryon-pion scattering in the1/Ncexpansion: Tree diagram cancellations

Tree amplitudes for baryon-pion scattering are studied in the ${1/N}_{c}$ expansion. Generalized large-${N}_{c}$ consistency conditions are obtained to all orders in baryon mass splittings. For baryons with spin $J\ensuremath{\sim}\mathcal{O}(1),$ the leading order in ${N}_{c}$ tree amplitudes can be evaluated keeping only terms up to a given finite order in baryon mass splittings.

Isospin mass splittings of baryons in potential models

We discuss the isospin-breaking mass differences among baryons, with particular attention in the charm sector to the $\Sigma_c^{+}-\Sigma_c^0$, $\Sigma_c^{++}-\Sigma_c^0$, and $\Xi_c^+-\Xi_c^0$ splittings. Simple potential models cannot accommodate the trend of the available data on charmed baryons. More precise measurements would offer the possibility of testing how well potential models describe the non-perturbative limit of QCD.

πNσterm,s¯sin the nucleon, and the scalar form factor: A lattice study

We report on a lattice QCD calculation of the $\ensuremath{\pi}N\ensuremath{\sigma}$ term, the scalar form factor, and $〈N|\overline{s}s|N〉$. The disconnected insertion part of ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}$ is found to be 1.8\ifmmode\pm\else\textpm\fi{}0.1 times larger than the connected insertion contribution. The ${q}^{2}$ dependence of ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}({q}^{2})$ is about the same as ${G}_{E}({q}^{2})$ of the proton so that ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}(2{m}_{\ensuremath{\pi}}^{2})\ensuremath{-}{\ensuremath{\sigma}}_{\ensuremath{\pi}N}(0)=6.6\ifmmode\pm\else\textpm\fi{}0.6$ MeV. The ratio $y=\frac{〈N|\overline{s}s|N〉}{〈N|\overline{u}u+\overline{d}d|N〉}=0.36\ifmmode\pm\else\textpm\fi{}0.03$. Both results favor a ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}\ensuremath{\sim}53$ MeV, slightly larger than our direct calculation of ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=49.7\ifmmode\pm\else\textpm\fi{}2.6$ MeV. We also compute ${F}_{s}$ and ${D}_{s}$ and find that the agreement with those from the octet baryon mass splittings crucially depends on the inclusion of the large disconnected insertion. Finally, we give our result for the $\mathrm{KN}\ensuremath{\sigma}$ term.

Heavy baryon masses in the 1/mQ and 1/Nc expansions.

The masses of baryons containing a single heavy quark are studied in a combined expansion in 1/{ital m}{sub {ital Q}}, 1/{ital N}{sub {ital c}}, and SU(3) flavor symmetry breaking. Heavy quark baryon mass splittings are related to mass splittings of the octet and decuplet baryons. The {Sigma}{sub {ital c}}{sup {asterisk}}, {Xi}{sub {ital c}}{sup {prime}}, and {Omega}{sub {ital c}}{sup {asterisk}} are predicted to the level of a few MeV. A number of bottom baryon mass splittings are predicted very accurately. {copyright} {ital 1996 The American Physical Society.}

Hadron spectrum with Wilson fermions.

We present results of a high statistics study of the quenched spectrum using Wilson fermions at $\ensuremath{\beta}=6.0$ on ${32}^{3}$\ifmmode\times\else\texttimes\fi{}64 lattices. We calculate the masses of mesons and baryons composed of both degenerate and nondegenerate quarks. Using nondegenerate quark combinations allows us to study baryon mass splittings in detail. We find significant deviations from the lowest order chiral expansion, deviations that are consistent with the expectations of quenched chiral perturbation theory. We find that there is a \ensuremath{\sim}20% systematic error in the extracted value of ${m}_{s}$, depending on the meson mass ratio used to set its value. Using the largest estimate of ${m}_{s}$ we find that the extrapolated octet mass splittings are in agreement with the experimental values, as is ${M}_{\ensuremath{\Delta}}\ensuremath{-}{M}_{N}$, while the decuplet splittings are 30% smaller than experiment. Combining our results with data from the GF11 collaboration we find considerable ambiguity in the extrapolation to the continuum limit. Our preferred values are $\frac{{M}_{N}}{{M}_{\ensuremath{\rho}}}=1.38(7)$ and $\frac{{M}_{\ensuremath{\Delta}}}{{m}_{\ensuremath{\rho}}}=1.73(10)$, suggesting that the quenched approximation is good to only \ensuremath{\sim}10-15%. We also analyze the $O(\mathrm{ma})$ discretization errors in heavy quark masses.

Chiral Lagrangian for baryons in the1Ncexpansion

A $\frac{1}{{N}_{c}}$ expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet $\ensuremath{\pi}$, $K$, $\ensuremath{\eta}$, and ${\ensuremath{\eta}}^{\ensuremath{'}}$ in a combined expansion in chiral symmetry breaking and $\frac{1}{{N}_{c}}$. Strong $\mathrm{CP}$ violation is included. The chiral Lagrangian correctly implements nonet symmetry and contracted spin-flavor symmetry for baryons in the large ${N}_{c}$ limit. The implications of nonet symmetry for low-energy baryon-pion interactions are described in detail. The procedure for calculating nonanalytic pion-loop corrections to baryon amplitudes in the $\frac{1}{{N}_{c}}$ expansion for finite ${N}_{c}$ is explained. Flavor-27 baryon mass splittings are calculated at leading order in chiral perturbation theory as an example.

Baryons in the SU(2) and SU(3) NJL model: A review of results

The semibosonized Nambu - Jona-Lasinio model in its SU(2) and SU(3) versions with scalar and pseudoscalar couplings is applied on the chiral circle to baryons (chiral quark soliton approach). The parameters of the model are fixed in the meson sector reproducing tf π , m π and m K . The constituent mass is chosen to be 420 MeV and no further parameter is adjusted. The baryons arise as a soliton of N c valence quarks coupled to the polarized Dirac sea. The calculations include 1 N c - rotational corrections and for the strange mass treated perturbatively the value m s = 180 MeV is used. The following agreement with the experimental data is obtained: With less than 15% deviation from experiment we obtain 〈 r 2 〉 c p , μ p , μ n , gA = g A (3), σ πN , g A (8), G p E ( q 2), G p M ( q 2), G n M ( q 2), E2 M1 , Δ- N-splitting, mass splittings of octet and decuplet baryons, magnetic moments of hyperons, isospin splittings of the octet and the Gottfried sum rule. With 30% deviation and at the borderline of exp. errors appear the electric neutron form factor and the other spin quantities g A (8) and Δu, Δd and Δs. Predictions are made for scalar form factor, strange form factors and tensor charges.

Baryon mass splittings in chiral perturbation theory.

Baryon masses are calculated in chiral perturbation theory at the one--loop-${\cal O}(p^3)$ level in the chiral expansion and to leading order in the heavy baryon expansion. Ultraviolet divergences occur requiring the introduction of counter--terms. Despite this neccessity, no knowledge of the counter terms is required to determine the violations to the Gell--Mann Okubo mass relation for the baryon octet or to the decuplet equal mass--spacing rule, as all divergences cancel {\it exactly} at this order. For the same reason all reference to an arbitrary scale $\mu$ is absent. Neither of these features continue to higher--powers in the chiral expansion. We also discuss critically the absolute neccessity of simultaneously going beyond the leading order heavy baryon expansion, if one goes beyond the one-loop-${\cal O}(p^3)$ level. We point out that these corrections in $1/M_B$ generate new divergences $\propto m^4/M_{10}$. These divergences together with the divergences occuring in one-loop-${\cal O}(p^4)$ graphs of chiral perturbation theory are taken care of by the same set of counter--terms. Because of these unknown counter--terms one cannot predict the baryon mass splittings at the one-loop-${\cal O}(p^4)$ level. We point out another serious problem of going to the one-loop-${\cal O}(p^4)$ level. When the decuplet is off its mass--shell there are additional $\pi N\Delta$ and $\pi\Delta\Delta$ interaction terms. These interactions contribute not only to the divergent terms $\propto (m^4/M_{10})$, but also to nonanalytic terms such as $\propto (m^4/M_{10}){\rm ln}(m/M_{10})$. Thus without a knowledge of the coupling constants appearing in these interactions one cannot carry out a consistent one-loop-${\cal O}(p^4)$ level calculation.

From effective Lagrangians, to chiral bags, to Skyrmions with the large-Nc renormalization group.

We explicitly relate effective meson-baryon Lagrangian models, chiral bags, and Skyrmions in the following way. First, effective Lagrangians are constructed in a manner consistent with an underlying large-${\mathit{N}}_{\mathit{c}}$ QCD. An infinite set of graphs dress the bare Yukawa couplings at leading order in 1/${\mathit{N}}_{\mathit{c}}$, and are summed using semiclassical techniques. What emerges is a picture of the large-${\mathit{N}}_{\mathit{c}}$ baryon reminiscent of the chiral bag: hedgehog pions for r\ensuremath{\ge}${\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{-}}1}$ patched onto bare nucleon degrees of freedom for r\ensuremath{\le}${\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{-}}1}$, where the ``bag radius'' ${\mathrm{\ensuremath{\Lambda}}}^{\mathrm{\ensuremath{-}}1}$ is the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived in which the bare Yukawa couplings, baryon masses, and hyperfine baryon mass splittings run with \ensuremath{\Lambda}. Finally, this RG flow is shown to act as a filter on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit \ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty} exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.

Baryons with many colors and flavors.

Using recently developed diagrammatic techniques, I derive some general results concerning baryons in the 1/N expansion, where N is the number of QCD colors. I show that the spin-flavor relations which hold for baryons in the large-N limit, as well as the form of the corrections to these relations at higher orders in 1/N, holed even if ${\mathit{N}}_{\mathit{F}}$/N\ensuremath{\sim}1, where ${\mathit{N}}_{\mathit{F}}$ is the number of light quark flavors. I also show that the amplitude for a baryon to emit n mesons is O(1/${\mathit{N}}^{\mathit{n}/2\mathrm{\ensuremath{-}}1}$), and that meson loops attached to baryon lines are unsupressed in the large-N limit, independent of ${\mathit{N}}_{\mathit{F}}$. For ${\mathit{N}}_{\mathit{F}}$>2, there are ambiguities in the extrapolation away from N=3 because the baryon flavor multiplets for a given spin grow with N. I argue that the 1/N expansion is valid for baryons with spin of order 1 and arbitrary flavor quantum numbers, including, e.g., baryons with isospin and/or strangeness O(N). This allows the formulation of a large-N expansion in which it is not necessary to identify the physical baryons with particular large-N states. SU(${\mathit{N}}_{\mathit{F}}$) symmetry can be made manifest to all orders in 1/N, yet group theory factors must be evaluated explicitly only for ${\mathit{N}}_{\mathit{F}}$=N=3. To illustrate this expansion, I consider the nonsinglet axial vector currents, baryon mass splittings, and matrix elements of s\ifmmode\bar\else\textasciimacron\fi{}s and s\ifmmode\bar\else\textasciimacron\fi{}${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\mu}}}$${\ensuremath{\gamma}}_{5}$s in the nucleon.