Stefan Scherer
We provide an introduction to the power-counting issue in baryon chiral perturbation theory and discuss some recent developments in the manifestly Lorentz-invariant formulation of the one-nucleon sector. As explicit applications we consider the chiral expansion of the nucleon mass, its convergence properties, and calculations of the electromagnetic and axial form factors of the nucleon.
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The mass spectrum of the lowest lying octet baryons is calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. We work in the isospin limit and treat the decuplet baryons as dynamical fields. These results are necessary for extrapolating QCD and partially quenched QCD lattice simulations of the octet baryon masses.
The masses of the spin-3/2 baryons are calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. The calculation is performed for three light flavors in the isospin limit. These results are necessary for extrapolating QCD and partially quenched QCD lattice calculations of the decuplet baryon masses.
We have analyzed the chiral expansion of the baryon masses to second order in the quark masses, including strong isospin violation. The calculations are performed in Lorentz-invariant baryon chiral perturbation theory. Chiral extrapolation functions for three-flavor unquenched lattice simulations are derived. The matching to the two-flavor case and the sigma terms are also considered.
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $πN σ$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
It is argued that an appearance of the near parity doublets in the upper part of the light baryon spectrum is an evidence for the chiral symmetry restoration in the regime where a typical momentum of quarks is around the chiral symmetry restoration scale. At high enough baryon excitation energy the nontrivial gap solution, which signals the chiral symmetry breaking regime, disappears and the chiral symmetry should be restored. Thus one observes a phase transition in the upper part of the light baryon spectrum. The average kinetic energy of the constituent quarks in this region is just around t…
Relations for low-energy constants in baryon chiral perturbation theory with explicit $Δ(1232)$ derived from the chiral quark model
本文通过手征夸克模型建立显含Δ(1232)的重子手征微扰理论中直到第三阶的低能常数关系，涉及十个结构对应，为后续Δ(1232)重子研究提供基础。
We calculate the baryon octet masses to fourth order in chiral perturbation theory employing dimensional and cut-off regularization. We analyze the pion and kaon mass dependences of the baryon masses based on the MILC data. We show that chiral perturbation theory gives stable chiral extrapolation functions for pion (kaon) masses below 550 (600) MeV. The pion-nucleon sigma term in SU(3) is also investigated, we find σ_{πN} (0) = 50.7 - 53.7 MeV.
We calculate baryon decuplet to octet electromagnetic transition form factors in quenched and partially quenched chiral perturbation theory. We work in the isospin limit of SU(3) flavor, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. Our results are necessary for proper extrapolation of lattice calculations of these transitions. We also derive expressions for the case of SU(2) flavor away from the isospin limit.
We compute the magnetic moments of the octet baryons up to two orders in quenched chiral perturbation theory. In addition to the $\sim\sqrt{m_q}$ contributions that arise in QCD, there are lower-order contributions of the form $M_0^2\log m_q$ from loop diagrams involving hairpin interactions.
It has recently been suggested that the observed structure of parity doublets, seen in the spectrum of highly excited baryons, may be due to the effective restoration of chiral symmetry for these states. This chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. Moreover, if QCD dynamics implies the linear Regge trajectories for highly excited baryons, then the MacDowell symmetry requires the parity doubling to appear, which shows that linear Regge trajectories and chiral symmetry restoration are well compatible. On the contrary, in the low-en…
We report an analysis of the octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order with and without the virtual decuplet contributions. Particular attention is paid to the finite-volume corrections and the finite lattice spacing effects on the baryon masses. A reasonable description of all the publicly available $n_f=2+1$ lattice QCD data is achieved.Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as $σ_{πN}=55(1)(4)$ MeV and $σ_{sN}=27(27)(4)$ MeV.
This paper has been withdrawn by the author since it is too simple and naive.
We report on a recent study of the ground-state octet baryon masses using the covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-next-to-leading order. By adjusting the available 19 low-energy constants, a good fit of the $n_f=2+1$ lattice quantum chromodynamics results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved.
The quark model symmetry can be adopted to establish relations between the low-energy constants (LECs) in the baryon chiral perturbation theory ($χPT$) if one assumes that a baryon-baryon-meson coupling is described equivalently by a quark-quark-meson coupling at the quark level. Through the correspondence between the $SU(2)$ description and the $SU(3)$ description for the same coupling vertex at the quark level, we find some relations between the LECs in $SU(2)_{χPT}$ and $SU(3)_{χPT}$ up to the third chiral order. The $SU(3)_{χPT}$ LEC relations at the same order are also obtained. The numer…
The masses of baryons containing a heavy quark are calculated to next-to-leading order in partially quenched heavy hadron chiral perturbation theory. Calculations are performed for three light flavors in the isospin limit and additionally for two light non-degenerate flavors. The results presented are necessary for extrapolating lattice QCD and partially quenched lattice QCD calculations of the heavy hadron masses.
We calculate the electric charge radii of the SU(3) pseudoscalar mesons and the SU(3) octet baryons in quenched and partially quenched chiral perturbation theory. We work in the isospin limit, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. The results are necessary for the extrapolation of future lattice calculations of meson and baryon charge radii. We also derive expressions for the nucleon and pion charge radii in SU(2) flavor away from the isospin limit.
We present an analysis of the lowest-lying decuplet baryon masses in the covariant baryon chiral perturbation theory with the extended-on-mass-shell scheme up to next-to-next-to-next-to-leading order. In order to determine the $14$ low-energy constants, we perform a simultaneous fit of the $n_f=2+1$ lattice QCD data from the PACS-CS, QCDSF-UKQCD, and HSC Collaborations, taking finite-volume corrections into account self-consistently. We show that up to next-to-next-to-next-to-leading order one can achieve a good description of the lattice QCD and experimental data. Surprisingly, we note that t…
We study the chiral expansion of the baryon octet and decuplet masses in the isospin limit. It is illustrated that a chiral expansion of the one-loop contributions is rapidly converging up to quark masses that generously encompasses the mass of the physical strange quark. We express the successive orders in terms of physical meson and baryon masses. In addition, owing to specific correlations amongst the chiral moments, we suggest a reordering of terms that make the convergence properties more manifest. Explicit expressions up to chiral order five are derived for all baryon masses at the one-l…
We analyze meson-baryon scattering lengths in the framework of covariant baryon chiral perturbation theory at leading one-loop order. We compute the complete set of matching relations between the dimension-two low-energy constants in the two- and three-flavor formulations of the theory. We derive new two-flavor low-energy theorems for pion-hyperon and pion-cascade scattering that can be tested in lattice simulations.
We include the lowest-lying octet- and decuplet-baryons into partially quenched chiral perturbation theory. Perturbing about the chiral limit of the graded SU(6|3)_L x SU(6|3)_R flavor group of partially quenched QCD, we compute the leading one-loop contributions to the octet-baryon masses, magnetic moments and matrix elements of isovector twist-2 operators. We work in the isospin limit and keep two of the three sea quarks degenerate. The usefulness of the non-unique extension of the electric charge matrix and the isovector twist-2 operators from QCD to partially quenched QCD is discussed.
We calculate electromagnetic properties of the decuplet baryons in quenched and partially quenched chiral perturbation theory. We work at next-to-leading order in the chiral expansion, leading order in the heavy baryon expansion, and obtain expressions for the magnetic moments, charge radii, and electric quadrupole moments. The quenched calculation is shown to be pathological since only quenched chiral singularities are present at this order. We present the partially quenched results for both the SU(2) and SU(3) flavor groups and use the isospin limit in the latter. These results are necessary…
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 …
In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related…
Interactions of two baryons are considered in large $N_C$ chiral perturbation theory and compared to the interactions derived from the Skyrme model. Special attention is given to a torus-like configuration known to be present in the Skyrme model.
It is shown that in the large $N_c$ limit the light baryon spectrum exhibits the chiral restoration phase transition at high enough excitation energy. Such a phase transition is evidenced by the systematical parity doublets observed in the upper part of $N$ and $Δ$ spectra.
We compute the octet baryon charge radii to O(1/Heavy^3) in heavy baryon chiral perturbation theory. We examine the effect of including the decuplet of spin-3/2 baryons explicitly. We find that it does no t improve the level of agreement between the HBchiPT and experimental values for the Sigma^- charge radius.
We present a calculation of generalized baryon form factors in the framework of three-flavor covariant baryon chiral perturbation theory at leading one-loop order. This is needed for lattice calculations of the first moments of generalized parton distribution functions. The formulae we derive can be used to guide the chiral extrapolation of such lattice results.
It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin dependent hyperfine interaction, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor $(μ/Λ_χ$)^2 and higher.
I review the present status of three flavor baryon chiral perturbation theory in the heavy fermion formalism. It is argued that precise calculations have to include all terms quadratic in the quark masses. As examples, I consider the chiral expansion of the octet baryon masses, the baryon magnetic moments and kaon photoproduction off nucleons.
We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral representations [(3,3*)+(3*,3)] and [(8,1)+(1,8)] and the decuplet baryon fields belonging to the chiral representations [(3,6)+(6,3)] lead to the baryon masses which are consistent with the experimental data of ground baryon masses. We also calculate their decay constants, check our normalizations for baryon fields in PRD81:054002(2010) and find that they are well-…
Heavy baryon chiral perturbation theory is extended to include the effects of quenching. In this framework the leading nonanalytic dependence of the heavy baryon masses on the light quark masses is studied. The size of quenching effects is estimated by comparing the results of quenched and ordinary chiral perturbation theories. It is found that in general they can be large. This estimate is relevant to lattice simulations of the heavy baryon masses.
We discuss the question in the title employing manifestly covariant Baryon Chiral Perturbation Theory and recent high-statistics lattice results published in [1].
Interplay of baryonic chiral partners in fluctuations of net-baryon number density
本文采用宇称双重态模型分析正、负宇称核子及其关联子对净重子数密度涨落的影响，指出手征相变处正宇称核子涨落不能代表总净重子数涨落。
The thermal properties of cold dense nuclear matter are investigated with chiral perturbation theory. The evolution curves for the baryon number density, baryon number susceptibility, pressure and the equation of state are obtained. The chiral condensate is calculated and our result shows that when the baryon chemical potential goes beyond $1150 \mathrm{MeV}$, the absolute value of the quark condensate decreases rapidly, which indicates a tendency of chiral restoration.
We report on some recent developments in our understanding of the light-quark mass dependence and the SU(3) flavor symmetry breaking corrections to the magnetic moments of the ground-state baryons in a covariant formulation of baryon chiral perturbation theory, the so-called EOMS formulation. We show that this covariant ChPT exhibits some promising features compared to its heavy-baryon and infrared counterparts.
It is demonstrated that using a suitable renormalization condition one obtains a consistent power counting in manifestly Lorentz-invariant baryon chiral perturbation theory including vector mesons as explicit degrees of freedom.
We extend the chiral Lagrangian with heavy quark-diquark symmetry to quenched and partially quenched theories. These theories are used to derive formulae for the chiral extrapolation of masses and hyperfine splittings of doubly heavy baryons in lattice QCD simulations. A quark-diquark symmetry prediction for the hyperfine splittings of heavy mesons and doubly heavy baryons is rather insensitive to chiral corrections in both quenched and partially quenched QCD. Extrapolation formulae for the doubly heavy baryon electromagnetic transition moments are also determined for the partially quenched th…
The QCD sum-rule method has been widely used in studying various baryon properties. For a given problem, there are usually more than one sum rules and they do not work equally well. In this paper, we point out that chirality plays an important role in determining the reliability of a baryon sum rule. The contributions of positive- and negative-parity excited baryon states partially cancel each other in the chiral-odd sum rules, but add up in the chiral-even sum rules. As such, the chiral-odd sum rules are generally more reliable than the chiral-even sum rules. This allows one to identify the m…
We consider a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. As an application we discuss the chiral expansion of the nucleon mass.
I review recent results in baryon chiral perturbation theory, in particular related to pion-nucleon scattering and first systematic attempts to go beyond next-to-leading order in the case of three flavors. New insight into the chiral expansion of the baryon masses and magnetic moments is presented.
The issue of consistent power counting in baryon chiral perturbation theory is revisited.
We analyze lattice data for octet baryon masses from the QCDSF collaboration employing manifestly covariant Baryon Chiral Perturbation Theory. It is shown that certain combinations of low-energy constants can be fixed more accurately than before from this data. We also examine the impact of this analysis on the pion-nucleon sigma term, and on the convergence properties of baryon mass expansions in the SU(3) symmetry limit.
We include in a systematic way the eta' in baryon chiral perturbation theory. The most general relativistic effective Lagrangian describing the interaction of the lowest lying baryon octet with the Goldstone boson octet and the eta' is presented up to linear order in the derivative expansion and its heavy baryon limit is obtained. As explicit examples, we calculate the baryon masses and the pi N sigma-term up to one-loop order in the heavy baryon formulation. A systematic expansion in the meson masses is possible, and appearing divergences are renormalized.
We have studied the chiral soliton model in a thermal vacuum. The soliton equations are solved at finite temperature and density. The temperature or density dependent soliton solutions are presented. The physical properties of baryons are derived from the soliton solutions at finite temperature and density. The temperature or density dependent variation of the baryon properties are discussed.
We study the reaction $π^\pm p \to π^\pm π^+ n$ and $π^- p \to π^0 π^0 n$ in heavy-baryon chiral perturbation theory of chiral order three from threshold up to pion laboratory kinetic energies of 400 MeV. We find that the contributions from amplitudes of chiral order three are large and play an essential role in reproducing the experimental data.
Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as sums of two-particle irreducible contributions of time-ordered diagrams and the scattering amplitudes are obtained as solutions of integral equations. Ultraviolet renormalizability is achieved by solving integral equations for the leading order amplitude and including higher order corrections perturbatively. As an application of the developed formalism, pion-n…
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
We construct the complete and minimal O(q^2) and O(q^3) three-flavour Lorentz invariant chiral meson-baryon Lagrangians for the first time in the literature. We compare with previous three-flavour studies reducing the number of independent monomials and adding new ones that were missing.
Chiral symmetry aspects for baryon properties are studied. After a brief discussion on general framework, we introduce two distinctive chiral group representations for baryons: the naive and mirror assignments. Using linear sigma models, nucleon properties are studied in both representations. Finally, we propose an experiment to distinguish the two assignments in the reactions of pion and eta productions.
Studies of the baryon-baryon interaction involving hyperons within chiral effective field theory, so far performed up to next-to-leading order (NLO) in the chiral expansion, have shown that for the strangeness $S=-1$ ($ΛN$, $ΣN$) and $S=-2$ ($ΛΛ$, $ΞN$) sectors a consistent and satisfactory description of the available scattering data and experimental constraints can be achieved based on the assumption of broken SU(3) flavor symmetry. We explore the possible extension of this approach at the NLO level to strangeness $S=-3$ and $S=-4$ baryon-baryon systems where empirical information is rather …
The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance.
Using the unified scheme for describing both quark spin and orbital angular momenta in the chiral quark model developed in the previous work, the magnetic moments of octet and decuplet baryons are calculated. The numerical result shows that the overall agreement with data is improved by including the orbital contributions.
We investigate the production of baryons and antibaryons in the central rapidity region of high energy nuclear collisions within the framework of the Skyrme model taking into account the effects of explicit chiral symmetry breaking. We argue that the formation of disordered chiral condensates may lead to enhanced baryon-antibaryon production at low transverse momentum.
Mass differences of the flavor octet and decuplet ground-state baryons are studied in the perturbative chiral quark model. We present a way to understand the nontrivial spin- and flavor dependent mass differences, where both pseudoscalar mesons and gluons play a significant role.
We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the Σ^- charge radius and the Λ-Σ^0 transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory.
Reordering of the chiral perturbation series, proposed recently by Becher and Leutwyler in the framework of SU(2) baryonic ChPT, is applied to the SU(3) case. This results in improved convergence of the chiral expansion of static properties of the lowest lying baryon octet, which in most cases is quite impressive. Finite renormalization of coupling constants and the role it plays in the interpretation of effective field theories is discussed. Some future tests of the viability of the scheme are proposed too.
The complete renormalization of the weak Lagrangian to chiral order q^2 in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay Lambda -> p pi^- and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.
We cautiously review the treatment of pentaquark exotic baryons in chiral soliton models. We consider two examples and argue that any consistent and self-contained description must go beyond the mean field approximation that only considers the classical soliton and the canonical quantization of its (would-be) zero modes via collective coordinates.
We have systematically investigated the magnetic moments and magnetic form factors of the decuplet baryons to the next-to-next-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. We also calculate the charge and magnetic dipole form factors of the decuplet baryons. Our results may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.
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