Enhancement of Hadronic $b$ Quark Decays

A class of previously unknown strong-interaction corrections is found to enhance the rate of nonleptonic decays of the $b$ quark by 5%–8%. This effect decreases the predicted fraction of semileptonic decays and brings it into fair agreement with experimental results. As well as solving a long-standing puzzle of measurements disagreeing with the standard model prediction, our work suggests a way for future precise studies of nonleptonic $b$ quark decays and their application to searching for “new physics.”

Figure 1

Main decay channels of the quark $b$: (a) semileptonic, (b) nonleptonic with light quarks, (c) nonleptonic with an extra charm quark. $d^{\prime }$ and $s^{\prime }$ denote the approximate flavor eigenstates: combinations of $d$ and $s$ quarks which couple to $u$ and $c$ in weak decays.

Figure 2

Examples of the three types of QCD corrections to the squares of the nonleptonic decay amplitudes: (a) corrections on the heavy quark line, (b) on the light quark line, (c) between the lines. The solid and wavy lines correspond to the same fields as in Fig. 1b, and the springs denote gluons.

Figure 3

Examples of factorized contributions to the four-loop diagram of Fig. 2c from various regions of virtuality of the two gluons: (a) hard-hard, (b) hard-soft, (c) soft-soft. In (a), (b) there is also, not shown, a second $W$ boson propagator, which reduces to an overall factor $1/m_W^2$. In (c), there are two such factors. The circles and crosses in the soft subgraphs indicate places from which hard subgraphs have been taken.