Abstract
We evaluate QCD effects in the neutrinoless double beta ($0\nu\beta\beta$) decay, originating from new physics short-range mechanism in the form of five dimension-9 operators. For this, we employ the one-loop and two-loop renormalization group equations (RGEs) for the corresponding Wilson coefficients, performing the RGE-evolution from the new physics scales (estimated as $\Lambda ~ \sim 10^2$ GeV) to the typical spacelike $0\nu\beta\beta$-scale $Q \sim 0.1$ GeV. Since the latter scale is clearly nonperturbative, we apply various infrared-safe (IR-safe) variants of QCD where the running coupling has no Landau singularities at low spacelike $Q$. We point out that the correct treatment of the IR-safe analogs of the (noninteger) powers of the couplings is important. It turns out that in most cases of the considered operators the resulting QCD effects can be significant in this process, i.e., can be stronger than the effects of the present uncertainties in the nuclear matrix elements.
Highlights
One of the basic questions of high-energy physics is whether the neutrinos, and/or their more exotic fermionic relatives if they exist, are Majorana or Dirac particles
These short-range QCD effects can be explored by considering solutions of the renormalization group equations (RGEs) for the Wilson coefficients and evolving them from the scales Λ2LNV of the new physics down to the Fermi motion scales Q2 ∼ 0.01 GeV2
For evaluation of QCD correction to the 0νββ decay, we need the physical observable, i.e., the half-life quantity based on operator product expansion (OPE)
Summary
One of the basic questions of high-energy physics is whether the neutrinos, and/or their more exotic fermionic relatives if they exist, are Majorana or Dirac particles. Wilson coefficients are multiplied with nuclear matrix elements (NMEs), which can have very different sizes These short-range QCD effects can be explored by considering solutions of the renormalization group equations (RGEs) for the Wilson coefficients and evolving them from the scales Λ2LNV of the new physics down to the Fermi motion scales Q2 ∼ 0.01 GeV2. One important practical problem in such a calculation is that the mentioned RGEs, being (one- or two-loop) perturbative, are considered to involve the usual perturbative QCD coupling aðQ2Þ [≡αsðQ2Þ=π], which, in turn, has the so-called Landau singularities at low positive Q2 ≲ 0.1GeV2.
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