Chiral Partners Research Articles

Light quark masses in multi-quark interactions

We suggest and discuss in detail a multi-quark three flavor Lagrangian of the Nambu -- Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses. It is shown that within the dynamical chiral symmetry breaking regime, the masses of the pseudo Goldstone bosons and their chiral partners, members of the low lying scalar nonet, are in perfect agreement with current phenomenological expectations. The role of the new interactions is analyzed.

Effects of entanglement and instanton suppression at finite temperature in a SU(2) entangled Polyakov–Nambu–Jona-Lasinio model with anomaly

We investigate the phase transitions characterized by deconfinement and restoration of chiral and axial symmetries, at finite temperature, in the framework of QCD inspired models. We compare the results obtained in the SU(2) Polyakov--Nambu--Jona-Lasinio model with anomaly and in its extended version, the entangled Polyakov--Nambu--Jona-Lasinio model. In the last version, four-quark vertices with entanglement between the chiral condensate and the Polyakov loop are considered. The thermodynamics of the phase transitions, the meson spectrum, and in particular the convergence of axial and chiral partners, will be analyzed, as well as the topological susceptibility. We find that an explicit temperature dependence of the coupling vertices is necessary in both models in order to have effective restoration of the ${\mathrm{U}}_{A}(1)$ symmetry.

Tilted axis rotation, candidates for chiral bands, and wobbling motion in138Nd

High-spin states in ${}^{138}$Nd were investigated using the reaction ${}^{94}$Zr(${}^{48}\mathrm{Ca},4n$), detecting coincident $\ensuremath{\gamma}$ rays with the gasp spectrometer. A rich level scheme was constructed including four bands of negative parity at low spins, eight bands of dipole transitions, and eight bands of quadrupole transitions at medium spins. The cranked shell model and the tilted-axis cranking model are used to assign configurations to the observed bands, where zero pairing is assumed. For selected configurations the case of finite pairing is also considered. A consistent notation for configuration assignment that applies for both zero and finite pairing is introduced. The observed bands are interpreted as rotation around the short and long principal axes (quadrupole bands), as well as around a tilted axis (dipole bands). The dipole bands have an intermediate character, between magnetic and collective electric rotation. A pair of dipole bands is identified as candidates for chiral partners. The possible existence of the wobbling mode at low deformation and medium spins is discussed. The consistent interpretation of the multitude of observed bands strongly supports the existence of stable triaxial deformation at medium spins in ${}^{138}$Nd.

DSA lifetime measurements in 132La in the context of spontaneous chiral symmetry breaking accompanied by the new S-symmetry

The lifetimes of the excited states belonging to three rotational bands of 132La have been measured with help of the DSA technique. The obtained results are interpreted in frame of the chiral symmetry breaking and recently postulated S-symmetry. Explanation of the absence of the characteristic B(M1) staggering in the chiral partner bands of 132La is suggested.

Confining but chirally symmetric dense and cold matter

The possibility for existence of cold, dense chirally symmetric matter with confinement is reviewed. The answer to this question crucially depends on the mechanism of mass generation in QCD and interconnection of confinement and chiral symmetry breaking. This question can be clarified from spectroscopy of hadrons and their axial properties. Almost systematical parity doubling of highly excited hadrons suggests that their mass is not related to chiral symmetry breaking in the vacuum and is approximately chirally symmetric. Then there is a possibility for existence of confining but chirally symmetric matter. We clarify a possible mechanism underlying such a phase at low temperatures and large density. Namely, at large density the Pauli blocking prevents the gap equation to generate a solution with broken chiral symmetry. However, the chirally symmetric part of the quark Green function as well as all color non-singlet quantities are still infrared divergent, meaning that the system is with confinement. A possible phase transition to such a matter is most probably of the first order. This is because there are no chiral partners to the lowest lying hadrons.

Initial Insights into Structure-Activity Relationships of Avian Defensins

Numerous β-defensins have been identified in birds, and the potential use of these peptides as alternatives to antibiotics has been proposed, in particular to fight antibiotic-resistant and zoonotic bacterial species. Little is known about the mechanism of antibacterial activity of avian β-defensins, and this study was carried out to obtain initial insights into the involvement of structural features or specific residues in the antimicrobial activity of chicken AvBD2. Chicken AvBD2 and its enantiomeric counterpart were chemically synthesized. Peptide elongation and oxidative folding were both optimized. The similar antimicrobial activity measured for both L- and D-proteins clearly indicates that there is no chiral partner. Therefore, the bacterial membrane is in all likelihood the primary target. Moreover, this work indicates that the three-dimensional fold is required for an optimal antimicrobial activity, in particular for gram-positive bacterial strains. The three-dimensional NMR structure of chicken AvBD2 defensin displays the structural three-stranded antiparallel β-sheet characteristic of β-defensins. The surface of the molecule does not display any amphipathic character. In light of this new structure and of the king penguin AvBD103b defensin structure, the consensus sequence of the avian β-defensin family was analyzed. Well conserved residues were highlighted, and the potential strategic role of the lysine 31 residue of AvBD2 was emphasized. The synthetic AvBD2-K31A variant displayed substantial N-terminal structural modifications and a dramatic decrease in activity. Taken together, these results demonstrate the structural as well as the functional role of the critical lysine 31 residue in antimicrobial activity.

Catalytic enantioselective nucleophilic addition of organolithium derivatives: pitfalls and opportunities

Organolithium reagents in solution are known to adopt oligomeric structures that are highly sensitive to the presence and nature of additives. In particular, the addition of lithium halides, chalcogenides or pnictogenides leads, in many cases, to well-defined complexes having the effect of decreasing the degree of aggregation of the original oligomer and often increasing the reactivity of the lithiated species itself. Incorporating a stereogenic element through the additive may allow the resulting complexes to be employed in stereochemically controlled reactions. In this context, two strategies can be applied that are the usual picture of a single metal in interaction with σ-donor (non-metalated) ligand(s) e.g. spartein, or, the possibility for the main group organolithium to be associated with another chiral lithiated partner forming organo(-bi-)metallic entities in which nucleophilicity and asymmetry are coupled. To date, engaging lithio reactants in the very classical enantioselective nucleophilic addition process with aldehydes remains a challenge due to the high intrinsic reactivity of the two partners. Nevertheless, taking advantage of a thorough understanding of the aggregation phenomena between the lithiated dipolar entities all along the catalytic cycle allows the fine-tuning of a substoichiometric enantioselective hydroxyalkylation of an aldehyde by an alkyllithium. We show the application of such a strategy to an example described recently.

Evaluating chiral symmetry restoration through the use of sum rules

We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector and axial-vector channels. We first present an update on constructing quantitative results for pertinent vacuum spectral functions. These spectral functions serve as a basis upon which the in-medium spectral functions can be constructed. A striking feature of our analysis of the vacuum spectral functions is the need to include excited resonances, dictated by satisfying the Weinberg-type sum rules. This includes excited states in both the vector and axial-vector channels. Preliminary results for the finite temperature vector spectral function are presented. Based on a rho spectral function tested in dilepton data which develops a shoulder at low energies, we find that the rho' peak flattens off. The flattening may be a sign of chiral restoration, though a study of the finite temperature axial-vector spectral function remains to be carried out.

Four-quark condensates in open-charm chiral QCD sum rules

Recently, in Hilger et al. (2011) [1] QCD sum rules for chiral partners in the open-charm meson sector have been presented at nonzero baryon net density or temperature up to and including mass dimension 5. Referring to this, details concerning the cancelation of infrared divergences are presented and important technical and conceptional ingredients for an incorporation of four-quark condensates beyond factorization and of other mass dimension 6 condensates are collected.

Hadronic SU(3) parity doublet model for dense matter and its extension to quarks and the strange equation of state

A chiral model is introduced that is based on the parity doublet formulation of chiral symmetry including hyperonic degrees of freedom. The phase structure of the model is determined. Depending on the masses of the chiral partners the transition to the chirally restored phase shows a first-order line with critical endpoints as function of chemical potential and temperature in additional to the standard liquid-gas phase transition of self-bound nuclear matter. We extend the parity doublet model to describe the deconfinement phase transition which is in quantitative agreement with lattice data at $\mu_B=0$. The phase diagram of the model is presented which shows a decoupling of chiral symmetry restoration and deconfinement. Loosening the constraint of strangeness conservation we also investigate the phase diagram at net strangeness density. We calculate the strangeness per baryon fraction and the baryon strangeness correlation factor, two quantities that are sensitive on deconfinement and that can be used to interpret lattice calculations.

Chiral QCD sum rules for open-charm mesons

QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. This allows for the identification of such QCD condensates which drive the non-degeneracy of chiral partners in lowest order of the strong coupling alpha_s and which therefore may serve as "order parameters" for chiral restoration (or elements thereof).

GENERALIZED ATMOSPHERIC SAMPLING OF KNOTTED POLYGONS

Self-avoiding polygons in the cubic lattice are models of ring polymers in dilute solution. The conformational entropy of a ring polymer is a dominant factor in its physical and chemical properties, and this is modeled by the large number of conformations of lattice polygons. Cubic lattice polygons are embeddings of the circle in three space and may be used as a model of knotting in ring polymers. In this paper we study the effects of knotting on the conformational entropy of lattice polygons and so determine the relative fraction of polygons of different knot types at large lengths. More precisely, we consider the number of cubic lattice polygons of n edges with knot type K, pn(K). Numerical evidence strongly suggests that [Formula: see text] as n → ∞, where μ0 is the growth constant of unknotted lattice polygons, α is the entropic exponent of lattice polygons, and NK is the number of prime knot components in the knot type K (see the paper [Asymptotics of knotted lattice polygons, J. Phys. A: Math. Gen.31 (1998) 5953–5967]). Determining the exact value of pn(K) is far beyond current techniques for all but very small values of n. Instead we use the GAS algorithm (see the paper [Generalised atmospheric sampling of self-avoiding walks, J. Phys. A: Math. Theor.42 (2009) 335001–335030]) to enumerate pn (K) approximately. We then extrapolate ratios [pn(K)/pn(L)] to larger values of n for a number of given knot types. We give evidence that for the unknot 01 and the trefoil knot 31, there exists a number M01, 31 ≈170000 such that pn (01) > pn (31) if n < M01, 31 and pn (01) ≤pn (31) if n ≥M01, 31. In addition, the asymptotic relative frequencies for a variety of knot types are determined. For example, we find that [pn(31)/pn(41)] → 27.0 ± 2.2, implying that there are approximately 27 polygons of the trefoil knot type for every polygon of knot of type 41 (the figure eight knot), in the asymptotic limit. Finally, we examine the dominant knot types at moderate values of n and conjecture that the most frequent knot types in polygons of any given length n are of the form [Formula: see text] (or its chiral partner), where [Formula: see text] are right- and left-handed trefoils, and N increases with n.

Partner bands of 126Cs – first observation of chiral electromagnetic selection rules

The lifetimes of the excited states belonging to the chiral partner bands built on the πh11/2⊗νh11/2−1 configuration in 126Cs have been measured using the DSA technique. For the first time the large set of the experimental transition probabilities is in qualitative agreement with all selection rules predicted for the strong chiral symmetry breaking limit.The selection rules originate from two general features of a chiral nucleus, namely, from the existence of well separated left- and right-handed systems built of three angular momentum vectors and extra symmetries appearing in addition to the chiral symmetry breaking.The B(M1) staggering resulting from these additional symmetries is sensitive to triaxiality of odd–odd nuclei as well as configuration of valence particles.

An Aldol-Based Build/Couple/Pair Strategy for the Synthesis of Medium- and Large-Sized Rings: Discovery of Macrocyclic Histone Deacetylase Inhibitors

An aldol-based build/couple/pair (B/C/P) strategy was applied to generate a collection of stereochemically and skeletally diverse small molecules. In the build phase, a series of asymmetric syn- and anti-aldol reactions were performed to produce four stereoisomers of a Boc-protected γ-amino acid. In addition, both stereoisomers of O-PMB-protected alaninol were generated to provide a chiral amine coupling partner. In the couple step, eight stereoisomeric amides were synthesized by coupling the chiral acid and amine building blocks. The amides were subsequently reduced to generate the corresponding secondary amines. In the pair phase, three different reactions were employed to enable intramolecular ring-forming processes: nucleophilic aromatic substitution (S(N)Ar), Huisgen [3+2] cycloaddition, and ring-closing metathesis (RCM). Despite some stereochemical dependencies, the ring-forming reactions were optimized to proceed with good to excellent yields, providing a variety of skeletons ranging in size from 8- to 14-membered rings. Scaffolds resulting from the RCM pairing reaction were diversified on the solid phase to yield a 14 400-membered library of macrolactams. Screening of this library led to the discovery of a novel class of histone deacetylase inhibitors, which display mixed enzyme inhibition, and led to increased levels of acetylation in a primary mouse neuron culture. The development of stereo-structure/activity relationships was made possible by screening all 16 stereoisomers of the macrolactams produced through the aldol-based B/C/P strategy.

Effective chiral restoration in theρ′meson in lattice QCD

In simulations with dynamical quarks it has been established that the ground state rho in the infrared is a strong mixture of the two chiral representations (0,1)+(1,0) and (1/2,1/2)_b. Its angular momentum content is approximately the 3S1 partial wave which is consistent with the quark model. Effective chiral restoration in an excited rho-meson would require that in the infrared this meson couples predominantly to one of the two representations. The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively determined excited state at different resolution scales. We present results for the first excited state of the rho-meson using simulations with n_f=2 dynamical quarks. We point out, that in the infrared a leading contribution to rho'= rho(1450) comes from (1/2,1/2)_b, in contrast to the rho. Its approximate chiral partner would be a h_1(1380) state. The rho' wave function contains a significant contribution of the 3D1 wave which is not consistent with the quark model prediction.

Band Interaction between Chiral Doublet Bands

Band interaction between the chiral doublet bands based on πh11/2 ⊗ vh−111/2 configuration is investigated in the particle rotor model with different triaxial deformation γ. The variation of chiral partner states with γ values is understood qualitatively based on the basic picture of two interaction levels, which is confirmed further by the calculated overlap integral of wave functions at different γ values. It is found that the interaction strengths of chiral partner states are obviously different for odd spins and even ones.

Experimental Projects for Spectroscopy of Pionic Atoms and N*(1535) in Nuclei

Chiral symmetry and its spontaneous breakdown play an important role as a link between QCD and nuclear physics in the lowest energy region of strong interaction where the quark and gluon degrees of freedom are hidden and pseudo-scalar mesons of massless Nambu-Goldstone bosons appear.1) Chiral condensate 〈qq〉 is known to parametrize the symmetry breaking, and is theoretically calculated on the plane of temperature and density. The theory tells that beyond certain energy density, the chiral condensate is expected to vanish and the symmetry restores.2) There are several experimental approaches to understand the chiral dynamics especially on its relation to the mechanism of hadron mass generation. One approach utilizes head-on collisions of heavy ions with relativistically high energies in order to reach and explore extremely high temperature region.3) The other takes examination of hadrons in nuclear matter which is regarded as extremely high density material.4)–8) The above theory predicts 30% reduction of the chiral condensate at the normal nuclear density to that in vacuum.9)–11) This article briefly describes two experimental projects to study the chiral dynamics both in the meson and in the baryon sectors,12) namely, “Precision spectroscopy of pionic atoms”13) and “N∗(1535) production and its in-medium spectroscopy”.14) The former pursues high precision systematic spectroscopy of deeply bound pionic atoms∗) in the RI beam factory in RIKEN. The systematic spectroscopy will serve unique and high quality information on the in-medium strong interaction strength between the pion and nuclei, which improves the precision of the quantitative estimation of the chiral condensate at the normal nuclear density.5) The latter, “N∗(1535) production and its in-medium spectroscopy”, has its own particular interest.14),15) According to the theories, N∗(1535) is a candidate of chiral partner of nucleons,12),16),17) and thus, the mass difference of the N∗(1535) and nucleon is reduced as the chiral symmetry restores. In-medium N∗(1535) spectroscopy will provide strong evidence of the hadron mass generation through direct measurement of the mass difference through possible level crossing between N∗(1535)-hole and η modes in the nuclear medium.18),19)

Nature of the σ meson as revealed by its softening process

The ππ scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the σ meson which is observed as the lowest scalar–isoscalar resonance. We compare several models with different origins of the σ meson, such as the chiral partner of the pion and the dynamically generated ππ molecule. We find that the dynamically generated σ meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. This behavior around the threshold energy region is universal as far as the bare σ pole stays away from the threshold throughout the symmetry restoration process. On the other hand, for m π = 0 , the dynamically generated σ behaves similarly to the chiral partner in the symmetry restoration limit, implying the possibility of the dynamically generated chiral partner.

Exploiting Lattice Potentials for Sorting Chiral Particles

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.

QCD sum rules for D mesons in dense and hot nuclear matter

Open charm mesons (pseudo-scalar and scalar as well as axial-vector and vector) propagating or resting in nuclear matter display an enhanced sensitivity to the chiral condensate. This offers new prospects for seeking signals of chiral restoration, in particular in pA and reactions as envisaged in first-round experiments by the CBM and PANDA collaborations at FAIR. Weinberg-type sum rules for charming chiral partners are presented, and the distinct in-medium modifications of open-charm mesons are discussed. We also address the gluon condensates near Tc and their impact on QCD sum rules.