The Extended Chiral Quark Model in a Tamm-Dancoff Inspired Approximation

A procedure inspired by the Tamm-Dancoff method is applied to the chiral quark model which has been extended to include additional degrees of freedom: a pseudoscalar isoscalar field as well as a triplet of scalar isovector fields. The simpler, generic $\sigma$ -- model has been used before as a test for the Tamm-Dancoff inspired approximation (TDIA). The extended chirial quark model is employed here to investigate possible novel effects of the additional degrees of freedom as well as to point out the necessesity to introduce a SU(3) flavour. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained in TDIA are compared with experimental values.Comment: 14 pages, LaTe

Vector mesonic phase and the chiral bag model

The mesonic sector of the standard chiral bag model was enlarged to include the vector and axial vector components. New model openly displays the current field identities. It's predictions are close to the older model. This seems to be the consequence of the chiral invariance and of the PCAC and CVC constraints. Particle masses, the axial-vector coupling constant, the proton magnetic moment and the charge radius have been calculated

A non-hedgehog solution for the chiral bag

The chiral sigma model, embedded in the chiral-bag environment, is solved by an ansatz which conserves isospin and spin separably. This chiral ansatz is treated in two ways: i) as a set of operator equations of motion solved between quark states and ii) the hamilton operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is completely analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e. hadron masses) can be found with chiral quarks as well as with hedgehog quarks. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained with chiral quarks are of the same quality, or better than those obtained using the usual hedgehog-based approximation

A non-hedgehog solution for the chiral bag

The chiral sigma model, embedded in the chiral-bag environment, is solved by an ansatz which conserves isospin and spin separably. This chiral ansatz is treated in two ways: i) as a set of operator equations of motion solved between quark states and ii) the hamilton operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is completely analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e. hadron masses) can be found with chiral quarks as well as with hedgehog quarks. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained with chiral quarks are of the same quality, or better than those obtained using the usual hedgehog-based approximation

Statička svojstva nukleona u pristupu potaknutom Tamm-Dancoffovom aproksimacijom

A version of the chiral bag model, which contains the linear σ-model dynamics and is quantized by using the constituent quark operators, has been solved using a Tamm-Dancoff inspired approximation. Model gives reasonable values for the axial coupling constant gA = Δu-Δd = 1.28, for the combination hAS = Δu+Δd = 0.38, and for the proton magnetic moment μp = 2.77. These values, which match the combinations Δu±Δd of the quark density functions, are consequences of the chiral character of the model.Primjenom postupka potaknutog Tamm-Dancoffovom aproksimacijom, riješena je inačica modela kiralne vreće koja sadrži dinamiku linearnog σ modela i kvantizirana je primjenom operatora konstitutivnih kvarkova. Model daje dobre vrijednosti za konstantu aksijalnog vezanja uz vrijednost kao i za magnetski moment protona. Te vrijednosti, koje su u suglasju s vrijednostima funkcija kvarkovske gustoće, posljedica su kiralnog značaja modela

Ne–ježevska rješenja za kiralnu vreću

The chiral sigma model, embedded in the chiral-bag environment, is solved by an ansatz which conserves isospin and spin separably. This chiral ansatz is treated in two ways: i) as a set of operator equations of motion solved between quark states and ii) the hamilton operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is completely analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e. hadron masses) can be found with chiral quarks as well as with hedgehog quarks. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained with chiral quarks are of the same quality, or better than those obtained using the usual hedgehog-based approximation.Kiralni sigma model, smješten u okolišu kiralne vreće je rješen pomoću uvrštenja (“ansatz”) koji čuva izospin i spin, svaki posebno. To kiralno uvrštenje je obradeno na dva načina: i) kao skup operatorskih jednadžbi, koje se riješe medu kvarkovskim stanjima i ii) Hamiltonijan se usrednji između odgovarajućih hadronskih stanja, pa se jednadžbe gibanja izvedu za ta prosječna polja. Drugi pristup je potpuno analogan uobičajenom koji upotrebljava ježevske kvarkove i koji je ovdje također reproduciran. Pokazalo se kako se energijski minimumi (tj. hadronske mase) mogu naći i na kiralnim i na ježevskim kvarkovima. Modelska predviđanja za aksijalno– vektorsku konstantu vezanja i za nukleonski magnetski moment su jednako dobra ili bolja nego ona koja su dobijena u uobičajenoj ježevskoj aproksimaciji

Ne–ježevska rješenja za kiralnu vreću

The chiral sigma model, embedded in the chiral-bag environment, is solved by an ansatz which conserves isospin and spin separably. This chiral ansatz is treated in two ways: i) as a set of operator equations of motion solved between quark states and ii) the hamilton operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is completely analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e. hadron masses) can be found with chiral quarks as well as with hedgehog quarks. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained with chiral quarks are of the same quality, or better than those obtained using the usual hedgehog-based approximation.Kiralni sigma model, smješten u okolišu kiralne vreće je rješen pomoću uvrštenja (“ansatz”) koji čuva izospin i spin, svaki posebno. To kiralno uvrštenje je obradeno na dva načina: i) kao skup operatorskih jednadžbi, koje se riješe medu kvarkovskim stanjima i ii) Hamiltonijan se usrednji između odgovarajućih hadronskih stanja, pa se jednadžbe gibanja izvedu za ta prosječna polja. Drugi pristup je potpuno analogan uobičajenom koji upotrebljava ježevske kvarkove i koji je ovdje također reproduciran. Pokazalo se kako se energijski minimumi (tj. hadronske mase) mogu naći i na kiralnim i na ježevskim kvarkovima. Modelska predviđanja za aksijalno– vektorsku konstantu vezanja i za nukleonski magnetski moment su jednako dobra ili bolja nego ona koja su dobijena u uobičajenoj ježevskoj aproksimaciji

Vektorska mezonska faza i kiralni vrećasti model

The mesonic sector of the standard chiral bag model was enlarged to include the vector and axial vector components. New model openly displays the current field identities. It\u27s predictions are close to the older model. This seems to be the consequence of the chiral invariance and of the PCAC and CVC constraints. Particle masses, the axial-vector coupling constant, the proton magnetic moment and the charge radius have been calculated.Mezonski sektor u standardnom kiralnom vrećastom modelu je povećan uključivanjem vektorskih i aksialno-vektorskih komponenata. Novi model otvoreno pokazuje poljestruje identiteta. Njegova pretkazivanja su bliža starijem modelu. To je, čini se, posljedica kiralne nepromjenljivosti te PCAC i CVC uvjeta. Proračunati su: čestične mase, aksialnovektorska vezna konstanta, protonski magnetski moment i nabojni polumjer

Vektorska mezonska faza i kiralni vrećasti model

The mesonic sector of the standard chiral bag model was enlarged to include the vector and axial vector components. New model openly displays the current field identities. It\u27s predictions are close to the older model. This seems to be the consequence of the chiral invariance and of the PCAC and CVC constraints. Particle masses, the axial-vector coupling constant, the proton magnetic moment and the charge radius have been calculated.Mezonski sektor u standardnom kiralnom vrećastom modelu je povećan uključivanjem vektorskih i aksialno-vektorskih komponenata. Novi model otvoreno pokazuje poljestruje identiteta. Njegova pretkazivanja su bliža starijem modelu. To je, čini se, posljedica kiralne nepromjenljivosti te PCAC i CVC uvjeta. Proračunati su: čestične mase, aksialnovektorska vezna konstanta, protonski magnetski moment i nabojni polumjer

Statička svojstva nukleona u pristupu potaknutom Tamm-Dancoffovom aproksimacijom

A version of the chiral bag model, which contains the linear σ-model dynamics and is quantized by using the constituent quark operators, has been solved using a Tamm-Dancoff inspired approximation. Model gives reasonable values for the axial coupling constant gA = Δu-Δd = 1.28, for the combination hAS = Δu+Δd = 0.38, and for the proton magnetic moment μp = 2.77. These values, which match the combinations Δu±Δd of the quark density functions, are consequences of the chiral character of the model.Primjenom postupka potaknutog Tamm-Dancoffovom aproksimacijom, riješena je inačica modela kiralne vreće koja sadrži dinamiku linearnog σ modela i kvantizirana je primjenom operatora konstitutivnih kvarkova. Model daje dobre vrijednosti za konstantu aksijalnog vezanja uz vrijednost kao i za magnetski moment protona. Te vrijednosti, koje su u suglasju s vrijednostima funkcija kvarkovske gustoće, posljedica su kiralnog značaja modela