Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

Details Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

2000-02-18

arxiv.org/abs/hep-lat/0002023v2

Phys.Rev. D62 (2000) 074508

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages, an appendix and minor changes added

Scientific paper

10.1103/PhysRevD.62.074508

In the domain-wall formulation of chiral fermion, the finite separation between domain-walls ($L_s$) induces an effective quark mass ($m_{\rm eff}$) which complicates the chiral limit. In this work, we study the size of the effective mass as the function of $L_s$ and the domain-wall height $m_0$ by calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator in the topologically-nontrivial background fields. We find that, just like in the free case, $m_{\rm eff}$ decreases exponentially in $L_s$ with a rate depending on $m_0$. However, quantum fluctuations amplify the wall effects significantly. Our numerical result is consistent with a previous study of the effective mass from the Gell-Mann-Oakes-Renner relation.

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