OCHA-PP-75 Induced Light-Quark Yukawa Couplings as a probe of Low-Energy Dynamics in QCD

We examine the heavy-quark-induced Yukawa interaction between light quarks and a light Higgs eld, which is facilitated in the chiral limit by the dynamical mass of light quarks anticipated from the chiral-noninvariance of the QCD vacuum. A low-energy estimate of the strong coupling near unity can be obtained from a comparison of the explicit perturbative calculation of the induced Yukawa interaction at zero momentum to a Higgs-low-energy theorem prediction for the same interaction. Deceased 1 The e ective coupling of zero-momentum Higgs particles to nucleons is well-known [1, 2] to be approximately of magnitude 70MeV Nh=h i, where Nh is the number of heavy quark avours, and where h i is the vacuum expectation value of the Higgs eld. Although this result is physical only if the mass of the Higgs is light compared to Few, the electroweak scale, we can nevertheless use it at the quark level to probe the strong coupling at low energies. In this paper we consider the coupling of a zero momentum Higgs particle to light quarks to get insight into the magnitude of the low-energy QCD coupling. In other words, we augment QCD with a light (gedanken) Higgs boson in order to explore nonperturbative QCD dynamics. Speci cally, we compare Higgs-low-energy theorem predictions appropriate for light quarks to the explicit perturbative calculation of the Yukawa interaction induced via heavy-quarks. This comparison provides an estimate of the QCD coupling characterizing the latter calculation. In both cases, we work in the chiral limit in which the light quark is assumed to have no tree-level Yukawa interaction, but is assumed to obtain mass dynamically via the chiral noninvariance of the QCD vacuum [3, 4, 5]. For the low-energy theorem calculation of the light-quark Yukawa interaction, this assumption implies an e ective quark mass proportional to QCD, leading to a calculation identical in form to the low-energy-theorem prediction [2] for the Higgs-nucleon interaction. For the explicit perturbative calculation, we consider a mass function suggested by Holdom [6] that falls o with momentum with asymptotic =p behaviour. The comparison of the quark-level low-energy theorem to the explicit quark-level calculation suggests a low energy value for s near unity, as anticipated from chiral symmetry breaking [3, 5] and other low-energy considerations [7]. To begin the perturbative quark-level calculation, we rst consider the coupling of the zero 4-momentum Higgs eld to two gluons that is induced by a heavy quark triangle (Figure 1), with p corresponding to the external gluon momentum [8]. The triangle is given by the