Spacetime noncommutativity and ultrahigh energy cosmic ray experiments

If new physics were capable of pushing the neutrino-nucleon inelastic cross section 3 orders of magnitude beyond the standard model prediction, then ultrahigh energy (UHE) neutrinos would have already been observed at neutrino observatories. We use such a constraint to reveal information on the scale of noncommutativity (NC) ${\Lambda }_{\mathrm{NC}}$ in noncommutative gauge field theories where neutrinos possess a tree-level coupling to photons in a generation-independent manner. In the energy range of interest (${10}^{10}$ to ${10}^{11}\mathrm{GeV}$), the $\theta$ expansion ($|\theta |\sim 1/{\Lambda }_{\mathrm{NC}}^2$) and, therefore, the perturbative expansion, in terms of ${\Lambda }_{\mathrm{NC}}$, retains no longer its meaningful character, forcing us to resort to those NC field theoretical frameworks involving the full $\theta$ resummation. Our numerical analysis of the contribution to the process coming from the photon exchange impeccably pins down a lower bound on ${\Lambda }_{\mathrm{NC}}$ to be as high as 900 (450) TeV, depending on the estimates for the cosmogenic neutrino flux. If, on the other hand, one considers a surprising recent result that occurred in Pierre Auger Observatory data, that UHE cosmic rays are mainly composed of highly ionized Fe nuclei, then our bounds get weaker, due to the diminished cosmic neutrino flux. Nevertheless, we show that, even for the very high fraction of heavy nuclei in primary UHE cosmic rays, our method may still yield remarkable bounds on ${\Lambda }_{\mathrm{NC}}$, typically always above 200 TeV. Albeit, in this case, one encounters a maximal value for the Fe fraction, from which any useful information on ${\Lambda }_{\mathrm{NC}}$ can be drawn, delimiting thus the applicability of our method.

Figure 1

$\nu N\to \nu +\mathrm{\text{anything}}$ cross sections vs ${\Lambda }_{\mathrm{NC}}$ for $E_{\nu }={10}^{10}\mathrm{GeV}$ (thick lines) and $E_{\nu }={10}^{11}\mathrm{GeV}$ (thin lines). The FKRT and PJ lines are the upper bounds on the neutrino-nucleon inelastic cross section, denoting different estimates for the cosmogenic neutrino flux (see the text). Standard model (SM) denotes the SM total (charged current plus neutral current) neutrino-nucleon inelastic cross section. The vertical lines denote the intersections of our curves with the RICE Collaboration results.

Figure 2

The intersections of our curves with the RICE Collaboration results (cf. Figure 1) as a function of the fraction of Fe nuclei in the UHE cosmic rays. The terminal point on each curve represents the highest fraction of Fe nuclei, above which no useful information on ${\Lambda }_{\mathrm{NC}}$ can be inferred with our method.