Enhancement of Compton Scattering by an Effective Coupling Constant Bernardo Barbiellini Northeastern University Boston, Massachusetts Bernardo Barbiellini and Piero Nicolini, Phys. Rev. A 84, 022509 Content • Compton scattering & condensed matter physics in a nutshell. • Piston argument & renormalization group argument. • Engineering QED in graphite. • Simple experiments to test quantum gravity. Compton scattering The Compton scattering has been used to study the quantum nature of the hydrogen bond in ice. E.D. Isaacs et al., PRL 82, 600 (1999). Phase Diagram of Ice Ch. Bellin, B. Barbiellini, S. Klotz, T. Buslaps, G. Rousse, and A. Shukla, PRB 83, 094117 (X,eX) Cross section G. Kaplan, B. Barbiellini and A. Bansil, Phys. Rev. B 68, 235104 (2003). Imaging orbital character of doped holes in LSCO Y. Sakurai, M. Itou, B. Barbiellini, P. E. Mijnarends, R. S.Markiewicz,, S. Kaprzyk, J. -M. Gillet, S. Wakimoto, M. Fujita, S. Basak, Yung Jui Wang, W. Al-Sawai, H. Lin, A. Bansil, K. Yamada, Science 332, 698 (2011) Molecular orbitals Bands and Bloch states Evolution of the holes with doping At MIT p Character changes the most Classical radius of the electron According to Max Born r0 represents a fundamental scale. This radius depends on the EM interaction coupling. The three electronic lengths • The Bohr radius (i.e. atomic unit) is the the characteristic length scale of electron wave functions. • The Compton wavelength is clearly the characteristic length scale of QED (virtual electron-positron pairs are formed at that scale). • The Classical electron radius is the length at which renormalization effects become important. • These three scale are connected by α. The Piston argument: a pedestrian renormalization group approach dE = T dS − P dV + mc2dα Cross section enhancement Engineering the coupling α Connecting to the Planck scale Testing quantum gravity with (X,eX) setups • The coincidence measurement between the Compton scattered photon and the recoiled electron (X, eX) provides a filter for nearly free electrons (state selectivity). • The energy spectrum of the recoiled electron can be measured by the means of time of flight method. • A graphite foil is chosen as target and the incidence of the photons is varied near the K edge of C. Conclusion • The Compton scattering cross section grows exponentially if the effective coupling constant decreases. • The present enhancement effect is beyond QED perturbation theory since it cannot be described by a diagrammatic expansion. • The small factor exp(-1/3 α) connects the Thomson scattering length to the Planck radius. .