The invariant differential cross sections for inclusive pi(0) and eta
mesons at midrapidity were measured in pp collisions at root s = 2.76
TeV for transverse momenta 0.4 < pT < 40 GeV/c and 0.6 < pT < 20 GeV/c,
respectively, using the ALICE detector. This large range in pT was
achieved by combining various analysis techniques and different triggers
involving the electromagnetic calorimeter (EMCal). In particular, a
newsingle-cluster, shower-shape based method was developed for the
identification of high-pT neutral pions, which exploits that the showers
originating from their decay photons overlap in the EMCal. Above 4
GeV/c, the measured cross sections are found to exhibit a similar
power-law behavior with an exponent of about 6.3. Next-to-leading-order
perturbative QCD calculations differ from the measured cross sections by
about 30% for the pi(0), and between 30-50% for the. meson, while
generator-level simulations with PYTHIA 8.2 describe the data to better
than 10-30%, except at pT < 1 GeV/c. The new data can therefore be used
to further improve the theoretical description of pi(0) and eta meson
production