Cvetic, Gorazd

We evaluate QCD effects in the neutrinoless double beta (0νββ) decay, originating from a 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 for the corresponding Wilson coefficients, performing the RGE evolution from the new physics scales (estimated as Λ ∼ 102 GeV) to the typical spacelike 0νββ scale Q ∼ 0.1 GeV. Since the latter scale is clearly nonperturbative, we apply various IR-safe variants of QCD in which 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.

We use the known renormalon structure of Bjorken polarised sum rule (BSR) to evaluate the leading-twist part of that quantity. In addition, we include and Operator Product Expansion (OPE) terms and fit this expression to available experimental data for inelastic BSR. Since we use perturbative QCD (pQCD) coupling, which fails at low squared spacelike momenta due to Landau singularities, the fit is performed for where . Due to large BSR experimental uncertainties, the extracted value of the pQCD coupling has very large uncertainties, especially when is varied. However, when we fix the pQCD coupling to the known world average values, the and residue parameters can be determined within large but reasonable uncertainties.

Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles. There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as π±,K± and B±, in scenarios where extra neutrinos are heavy and can be on their mass shell. We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model (νMSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.

Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) Γ\oline 1p‑n(Q2) leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of BSR. In our previous work [1], this evaluation (resummation) was performed using perturbative QCD (pQCD) coupling a(Q2)≡αs(Q2)/π in specific renormalisation schemes. In the present paper, we continue this work, by using instead holomorphic couplings [a(Q2)↦A(Q2)] that have no Landau singularities and thus require, in contrast to the pQCD case, no regularisation of the resummation formula. The D=2 and D=4 terms are included in the Operator Product Expansion (OPE) of inelastic BSR, and fits are performed to the available experimental data in a specific interval (Qmin2,Qmax2) where Qmax2=4.74GeV2. We needed relatively high Qmin2≈1.7GeV2 in the pQCD case since the pQCD coupling a(Q2) has Landau singularities at Q2≲1GeV2. Now, when holomorphic (AQCD) couplings A(Q2) are used, no such problems occur: for the 3δAQCD and 2δAQCD variants the preferred values are Qmin2≈0.6GeV2. The preferred values of αs in general cannot be unambiguously extracted, due to large uncertainties of the experimental BSR data. At a fixed value of αsMS\oline (MZ2), the values of the D=2 and D=4 residue parameters are determined in all cases, with the corresponding uncertainties.