University of Groningen
Axial-Vector Currents and Chiral Symmetry
Sauerwein, Ubbi
DOI:
10.33612/diss.157530914
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Publication date: 2021
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Sauerwein, U. (2021). Axial-Vector Currents and Chiral Symmetry. University of Groningen. https://doi.org/10.33612/diss.157530914
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Chapter
5
Summary and Outlook
5.1
Summary
This thesis deals with the axial-vector currents of the baryon octet in relativis-tic Chiral Perturbation Theory. We establish analyrelativis-tical results for the axial-vector form factors at N2LO that include one-loop contributions. Therein, the
∆-isobar/decuplet particles are considered as an explicit degree of freedom. Since we are using on-shell masses in the one-loop contributions, particular attention is paid to a power counting scheme that leads to good convergence properties. It was demonstrated that the use of on-shell masses fulfills this condition. Furthermore, the use of on-shell masses with their finite volume dependence implies an implicit finite volume effect of the axial-vector form factors. While our analytical results are prepared to be confronted with QCD lattice data, a rich basis of QCD lattice data is so far only available in flavor-SU(2). However, we expect additional flavor-SU(3) QCD lattice data to be published within the next few years.
We fit our results for the axial-vector form factor of the nucleon to recent flavor-SU(2) QCD lattice data and find a very good description of the data with reasonable values for the fitted low-energy constants. Extrapolating our results for the axial-vector form factor to the infinite volume, we observe a first-order phase transition, which can be traced back to the use of on-shell masses in the one-loop contributions. We suggest further investigations on QCD lattices with two quark flavors. Specific QCD lattice ensembles are
74 CHAPTER 5. SUMMARY AND OUTLOOK cussed, for which we predict sizable implications of the non-analytic behavior in the axial-vector form factor of the nucleon.
5.2
Outlook
Unfortunately, for most of the flavor-SU(3) QCD lattice ensembles, which were used to fit the baryon octet and decuplet masses to high accuracy [29], axial-vector form factors are not available yet. Once the data basis is significantly enlarged further investigations are planned. The octet and decuplet masses can be used as on-shell masses in the one-loop contributions to the axial-vector form factors following the strategy of Chapter 4. On the other hand, a global flavor-SU(3) fit of octet and decuplet masses and the axial-vector form factors, as presented in Ref. [69] in flavor-SU(2), is our ultimate goal. The large amount of low-energy constants can be reduced by appropriate large-Nc relations, to be established in future works.
But also an extension of our analysis to other hadronic form factors might reveal additional interesting aspects and consolidate our framework. Many of our results from this work can directly be used for the derivation of the pseudoscalar form factor, for which a large set of flavor-SU(2) lattice data is already available.
5.3
Deutsche Zusammenfassung
Diese Thesis behandelt die Axialvektorstr ¨ome des Baryon Oktetts in rela-tivistischer Chiraler St ¨orungstheorie. Wir leiten analytische Resultate f ¨ur die Axialvektor-Formfaktoren zur n ¨achst-n ¨achstf ¨uhrenden Ordnung, die auch Ein-Schleifenbetr ¨age beinhaltet, ab. Das ∆-Isobar/Die Teilchen des Baryon Deku-pletts werden darin als explizite Freiheitsgrade behandelt. Aufgrund der Ver-wendung von On-Shell-Massen in den Ein-Schleifenbeitr ¨agen wird ein beson-derer Augenmerk auf ein Z ¨ahlschema, das gute Konvergenzeigenschaften verspricht, gelegt. Wir zeigten hier explizit, dass die Verwendung von On-Shell-Massen dies erf ¨ullt. Außerdem f ¨uhrt der endliche-Volumen-Effekt der On-Shell-Massen zu einem impliziten endlichen-Volumen-Effekt der Axialvek-tor-Formfaktoren. W ¨ahrend unsere analytischen Resultate f ¨ur einen Ver-gleich mit QCD-Gitterdaten vorbereitet sind, sind solche Daten derzeit nur f ¨ur den Flavor-SU(2) Fall verf ¨ugbar. Jedoch erwarten wir, dass in den n ¨achsten
Jahren auch Flavor-SU(3) QCD-Gitterdaten verf ¨ugbar sein werden.
Wir passen unsere Resultate f ¨ur den Axialvektor-Formfaktor des Nukleon an k ¨urzlich erschienene Flavor-SU(2) QCD-Gitterdaten an und erreichen eine sehr gute Beschreibung der Daten mit realistischen Werten f ¨ur die Niederen-ergiekonstanten. Bei der Extrapolation unserer Resultate f ¨ur den Axialvektor-Formfaktor ins unendliche Volumen beobachten wir einen Phasen ¨ubergang erster Ordnung, der auf die Verwendung von On-Shell-Massen in den Ein-Schleifenbeitr ¨agen zur ¨uckgef ¨uhrt werden kann. Wir regen weitere Berech-nungen auf Gittern mit zwei Quarks an und diskutieren spezifische QCD-Gitterensembles, f ¨ur die wir betr ¨achtliche Auswirkungen des nicht-analy-tischen Verhaltens des Axialvektor-Formfaktors des Nukleons vorhersagen.
5.4
Nederlandse Samenvatting
Deze thesis behandelt de axialevectorstromen van het baryon octet in rela-tivistische chirale storingstheorie. We stellen analytische resultaten vast voor de axiale-vector-vormfactoren in eerste orde in de perturbatie-serie, waarbij we eenluscontributies meenemen. Hierin nemen we de vrijheidsgraden van de ∆-isobaar en het baryon decuplet expliciet mee. Omdat we on-shellmas-sa’s gebruiken in de eenluscontributies, besteden we extra aandacht aan een powercounting-schema dat leidt tot goede convergentie-eigenschappen. We laten zien dat het gebruik van on-shellmassa’s inderdaad leidt tot goede con-vergentie-eigenschappen. Daarnaast zien we dat het gebruik van on-shell-massa’s met hun eindige volumeafhankelijkheid een impliciet eindig-volume-effect impliceert voor de axiale-vector-vormfactor. Onze analytische resul-taten zijn voorbereid om te worden vergeleken met rooster-QCD-data, maar tot nu toe is er alleen voor flavor-SU(2) de zulke data beschikbaar. Het is echter de verwachting dat de benodigde flavor-SU(3) data in de aankomende jaren zal worden gepubliceerd.
We fitten onze resultaten voor de axiale-vector-vormfactor van de nu-cleon aan recente flavor-SU(2) rooster-QCD data en vinden een zeer goede beschrijving van de data met aannemelijke waarden voor de gefitte lage-energieconstanten. Wanneer we onze resultaten voor de axiale-vector-vorm-factor extrapoleren naar het oneindige volume, zien we een eerste-orde-fase-overgang, die we kunnen terugvoeren naar het gebruik van on-shellmassa’s in de eenluscontributies. Wij stellen verder onderzoek voor, waarbij wordt gekeken naar rooster-QCD voor twee quarksmaken. Specifieke
rooster-QCD-76 CHAPTER 5. SUMMARY AND OUTLOOK ensembles worden behandeld, waarvoor we aanzienlijke implicaties voor-spellen voor het niet-analytische gedrag in de axiale-vector-vormfactor van de nucleon.
