4 good agreement with current experimental data, Fig.3, and the Luttinger sum rule is reconciled. We also ar- gue that the quantum critical point observed in magnetic quantum oscillations (divergence of the effective mass) is the same quantum critical point that is observed in neu- tron scattering, which signatures the onset of the static incommensurate magnetic order. We thank D. Haug, V. Hinkov and B. Keimer for im- portant discussions and for communicating unpublished data. We acknowledge useful comments by S. Borisenko and C. Zhang. energy ≈ 40 meV, and the number of filled Landau levels at B = 60Tesla is N = ϵ$_{F}$ / ℏ ω$_{c}$ ≈ 6, ω$_{c}$ being the syn- chrotron frequency. Amplitude of MQO is proportional to exp {− π Γ / ℏ ω$_{c}$ } , Ref. [32]. Assuming that the expo- nent is ∼ 1, and relating the impurity broadening to the mean free path and to the Fermi velocity, Γ = ℏ v$_{F}$ /l , we estimate the holon mean free path l ∼ 70 a ∼ 270 ˚ A. A divergence of the effective mass at approaching y = 0 . 49 from higher doping has been reported [11]. The effective mass has been extracted via temperature de- pendence of the MQO signal. The divergence was inter- preted [11] as a QCP due to a metal-insulator transition. Here we suggest an alternative explanation for this QCP, based on the current theory and on the evidences from neutron scattering. Besides the Lifshitz points x$_{0}$ and x$_{1}$ , the spiral theory also predicts a QCP at x$_{QCP}$ ≈ 0 . 1 which separates regions of static and dynamic spin spi- ral. The neutron scattering data [19–22] demonstrate this QCP in YBCO at doping level x$_{QCP}$ ≈ 0 . 09, see discussion in the introduction. As one should expect, the precise position of this QCP depends on the applied magnetic field. The quasistatic neutron scattering in YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{45}$ is enhanced in the field [22], which indi- cates that magnetic field shifts the QCP towards higher doping. Most likely in the field 60-80 Tesla used in MQO, the QCP is located between YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{47}$ and YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{49}$. The point is that the field is hardly suf- ficient to close the spin-wave pseudogap Δ$_{sw}$ ∼ 10 meV in YBa$_{2}$Cu$_{3}$O$_{6}$$_{.}$$_{5}$ [19]. The QCP is driven by the long- wave-length quantum fluctuations, while holon pockets are formed at a shorter semiclassical scale. Therefore MQO frequencies are not sensitive to the magnetic QCP. Effective mass in a quantum field theory always de- pends on the momentum transfer q , m ∗ → m ∗ $_{q}$. The effective mass extracted from fitting neutron scattering data is relevant to the semiclassical scale q ∼ p$_{F}$ ∝ √$_{x}$$_{.}$ This mass does not “see” the magnetic QCP. However, the amplitude of the MQO signal is formed at the length scale l ∼ 70 a ∼ 270 ˚ A, which corresponds to a very small q and the corresponding effective mass is sensitive to the magnetic QCP. It is known [33] that the quasiparticle residue Z vanishes at a magnetic QCP. Since m ∗ ∝ 1 /Z , this implies that the effective mass is diverging. Alter- natively one can say that the holon scattering rate from critical magnons is diverging. This gives a natural expla- nation of the divergence observed in Ref. [11], and also explains why position of the QCP observed in neutron scattering coincides with that observed in MQO: they are the same QCP. In summary, we explained the MQO frequencies based on the spin-spiral theory of lightly doped Mott insulator. Fit of the incommensurate neutron scattering data shown in Fig.2 determines free parameters of the theory, and al- lows us to calculate frequencies of MQO as functions of doping. In the doping region 0 . 06 < x < 0 . 13 the theory predicts three different frequencies, which yields a fairly [1] P. W. Anderson, Science 235 , 1196 (1987). [2] F. C. Zhang and T. M. Rice, Phys. Rev. B 37 , R3759 (1988). [3] M. R. 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