Present and Future in Semileptonic B Decays

In this talk I review the status of our ability to extract the CKM matrix elements |Vub| and |Vcb| from semileptonic decays. I will review both exclusive and inclusive methods and put a strong emphasis on how to ensure keeping the extractions model independent.Comment: 10 pages, Invited plenary talk presented at 9th International Symposium on Heavy Flavor Physics, Caltech, Sep. 10-13, 200

Home Education: Globalization Otherwise?

Home Education seems to be a successful way to educate. Academic results and socialization processes in home education are promising. Already home education is global, home educators everywhere educate their children themselves without schools. They develop new forms of local and international co-operation. Is home education an impulse to a renewing of modern education? Is home education globalization otherwise?home education, globalization, educational politics, pedagogy

Periodicity of free subgroup numbers modulo prime powers

We completely characterise when the sequence of free subgroup numbers of a finitely generated virtually free group is ultimately periodic modulo a given prime power.Comment: AmS-LaTeX; 18 page

Heavy Quark Fragmenting Jet Functions

Heavy quark fragmenting jet functions describe the fragmentation of a parton into a jet containing a heavy quark, carrying a fraction of the jet momentum. They are two-scale objects, sensitive to the heavy quark mass, $m_Q$, and to a jet resolution variable, $\tau_N$. We discuss how cross sections for heavy flavor production at high transverse momentum can be expressed in terms of heavy quark fragmenting jet functions, and how the properties of these functions can be used to achieve a simultaneous resummation of logarithms of the jet resolution variable, and logarithms of the quark mass. We calculate the heavy quark fragmenting jet function $\mathcal G_Q^Q$ at $\mathcal O(\alpha_s)$, and the gluon and light quark fragmenting jet functions into a heavy quark, $\mathcal G_g^Q$ and $\mathcal G_l^Q$, at $\mathcal O(\alpha_s^2)$. We verify that, in the limit in which the jet invariant mass is much larger than $m_Q$, the logarithmic dependence of the fragmenting jet functions on the quark mass is reproduced by the heavy quark fragmentation functions. The fragmenting jet functions can thus be written as convolutions of the fragmentation functions with the matching coefficients $\mathcal J_{i j}$, which depend only on dynamics at the jet scale. We reproduce the known matching coefficients $\mathcal J_{i j}$ at $\mathcal O(\alpha_s)$, and we obtain the expressions of the coefficients $\mathcal J_{g Q}$ and $\mathcal J_{l Q}$ at $\mathcal O(\alpha_s^2)$. Our calculation provides all the perturbative ingredients for the simultaneous resummation of logarithms of $m_Q$ and $\tau_N$.Comment: 48 pages, 11 figure