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B meson phenomenology and lattice Chromodynamics

Phénoménologie des mésons B et Chromodynamique sur réseau

Abstract : We have studied some phenomenological aspects of the B meson physics by using
lattice QCD, which is a non perturbative method (based on the first
principles of Quantum Field Theory) of computing Green functions of the
theory. Pionic couplings $\hat{g}$ and $\tilde{g}$, parameterizing the effective chiral Lagrangian which
describes interactions between heavy-light mesons and soft pions, have been computed
beyond the quenched approximation (at ${\rm N_f}=2$). We have renormalised the
operator $\bar{q}\gamma_\mu \gamma^5 q$ non perturbatively by using
chiral Ward identities. We obtain $\hat{g}=0.4\div0.6$ and
$\tilde{g}=-0.1 \div -0.3$. We have estimated from an unquenched simulation
(at ${\rm N_f}=2$) the strange quark mass: the non perturbative renormalisation
scheme RI-MOM has been applied. After the matching in the $\msb$ scheme the
result is $m_s^{\msb}(2\,\gev)=101\pm 8^{+25}_{-0}~\mev$. We have proposed a
method to calculate on the lattice the Heavy Quark Effective Theory form
factors of the semileptonic transitions $B\to D^{**}$ at zero recoil. The
renormalisation constant of the operator $\bar{h}\gamma_i \gamma^5 D_j h$ has
been computed at one-loop order of the perturbation theory. We obtain
$\taud (1)=0.3\div 0.5$ and $\taut(1)=0.5\div 0.7$. Eventually the bag
parameter $B_{B_s}$ associated the $B_s-\bsb$ mixing amplitude in the Standard
Model has been estimated in the quenched approximation by
using for the strange quark an action which verifies the chiral symmetry at
finite lattice spacing $a$. Thus systematic errors are significantly reduced
in the renormalisation procedure because the spurious mixing of
the four-fermion operator $\bar{h}\gamma_{\mu L} q \bar{h} \gamma_{\mu L} q$
with four-fermion operators of different chirality is absent. The result
is $B_{B_s}=0.92(3)$.