arXiv subjects
Publications and source records attributed to I. I. Bigi.
A theoretical treatment for the weak decays of heavy-flavour hadrons has been developed that is genuinely based on QCD. Its methodology as it applies to total lifetimes and the underlying theoretical issues are sketched. Predictions are compared with present data. One discrepancy emerges: the beauty baryon lifetime appears to be significantly shorter than expected. The ramifications of those findings are analyzed in detail.
Both Cabibbo allowed and doubly forbidden transitions contribute coherently to $D\rightarrow K_{S,L}+π's$ decays. This leads to several intriguing and even quantitatively significant consequences, among them: (i) A difference between $Γ(D^+\rightarrow K_S π^+)$ and $Γ(D^+\rightarrow K_L π^+)$ and between $Γ(D^0\rightarrow K_S π^0)$ and $Γ(D^0\rightarrow K_L π^0)$ of roughly 10\% ; similarly $Γ(D^+\rightarrow [K_Sπ^0]_{K^*} π^+) \neq \frac{1}{4}Γ(D^+\rightarrow [K^-π^+]_{K^*} π^+)$, and more generally $Γ(D\rightarrow \bar K^0+π's) \neq 2Γ(D\rightarrow K_S+π's)$. (ii) A change in the relative phase between the isospin 3/2 and 1/2 amplitudes as extracted from the observed branching ratios for $D^+\rightarrow K_Sπ^+$, $D^0\rightarrow K_Sπ^0 ,\, K^-π^+$. (iii) If New Physics intervenes to provide the required {\em weak} phase, then CP asymmetries of up to a few per cent can arise in $D^+\rightarrow K_Sπ^+$ vs. $D^-\rightarrow K_Sπ^-$, $D^0\rightarrow K_Sπ^0$ vs. $\bar D^0\rightarrow K_Sπ^0$, $D^+\rightarrow [K_Sπ^0]_{K^*}π^+$ vs. $D^-\rightarrow [K_Sπ^0]_{K^*}π^-$, etc.; an asymmetry of the same size, but opposite in sign occurs when the $K_S$ is replaced by a $K_L$ in the final state.
We show how sum rules for the weak decays of heavy flavor hadrons can be derived as the moments of spectral distributions in the small velocity (SV) limit. This systematic approach allows us to determine corrections to these sum rules, to obtain new sum rules and it provides us with a transparent physical interpretation; it also opens a new perspective on the notion of the heavy quark mass. Applying these sum rules we derive a lower bound on the deviation of the exclusive form factor $F_{B->D^*}$ from unity at zero recoil; likewise we give a field-theoretical derivation of a previously formulated inequality between the expectation value for the kinetic energy operator of the heavy quark and for the chromomagnetic operator. We analyze how the known results on nonperturbative corrections must be understood when one takes into account the normalization point dependence of the low scale parameters. Relation between the field-theoretic derivation of the sum rules and the quantum-mechanical approach is elucidated.
the KM expectations of large CP asymmetries in $B$ decays are reviewed. I describe some observable signatures for the intervention of New Physics and list benchmarks defining the `ultimate' measurements in beauty physics. I also stress the need for dedicated searches for CP asymmetries in $D$ decays; attaining a sensitivity level of $10^{-3}$ could well reveal New Physics and thus lead to a new paradigm.
A list is given of those open questions concerning the dynamics of charm decays where there exists a strong need for an answer. Such a need is based on lessons to be learnt about QCD -- either in their own right or for a better understanding of $B$ physics -- or on searches for New Physics with a small background from the Standard Model. The major items on this list are: lifetimes of the $Ξ_c^{0,+}$ baryons; semileptonic branching ratios of $D_s$, $Λ_c$ and $Ξ_c$ hadrons and absolute branching ratios for those states; radiative decays $D\rightarrow γK^*,\, γρ/ω, \, D_s \rightarrow γϕ/ω,\, D\rightarrow l^+l^-K/K^*$; $D^0-\bar D^0$ oscillations down to a sensitivity below $10^{-4}$ and CP asymmetries in non-leptonic $D$ decays down to 0.1\%. Ongoing and already approved experiments will produce important new insights, which are unlikely to provide sufficient answers to all these questions yet. It is discussed how a third-generation fixed-target experiment like CHARM2000 or a $τ$-charm factory can fill the bill.
The Standard Model contains a natural source for CP asymmetries in weak decays, which is described by the KM mechanism. Beyond $ε_K$ it generates only elusive manifestations of CP violation in {\em light-}quark systems. On the other hand it naturally leads to large asymmetries in certain non-leptonic beauty decays. In particular when $B^0-\bar B^0$ oscillations are involved, theoretical uncertainties in the hadronic matrix elements either drop out or can be controlled, and one predicts asymmetries well in excess of 10\% with high parametric reliability. It is briefly described how the KM triangle can be determined experimentally and then subjected to sensitive consistency tests. Any failure would constitute indirect, but unequivocal evidence for the intervention of New Physics; some examples are sketched. Any outcome of a comprehensive program of CP studies in $B$ decays -- short of technical failure -- will provide us with fundamental and unique insights into nature's design.
After re-stating why beauty physics is so special and sketching its present status I attempt to map out an itinerary for the next fifteen years. The basic elements are listed for a research program that allows to define and probe the KM unitarity triangle in a manner where the numerical uncertainties are reduced to the few percent level. Dedicated experiments at the LHC will be essential in exploiting the discovery guarantee in beauty physics to the fullest. This paper is dedicated to Prof. H. Kastrup on the occasion of his 60th birthday. I have spent five years at his institute at the RWTH Aachen and I truly enjoyed the stimulating atmosphere he created by encouraging intellectual exchange unimpeded by hierarchical privileges.
The key quantity of the heavy quark theory is the quark mass $m_Q$. Since quarks are unobservable one can suggest different definitions of $m_Q$. One of the most popular choices is the pole quark mass routinely used in perturbative calculations and in some analyses based on heavy quark expansions. We show that no precise definition of the pole mass can be given in the full theory once non-perturbative effects are included. Any definition of this quantity suffers from an intrinsic uncertainty of order $\Lam /m_Q$. This fact is succinctly described by the existence of an infrared renormalon generating a factorial divergence in the high-order coefficients of the $α_s$ series; the corresponding singularity in the Borel plane is situated at $2π/b$. A peculiar feature is that this renormalon is not associated with the matrix element of a local operator. The difference $\La \equiv M_{H_Q}-m_Q^{pole}$ can still be defined in Heavy Quark Effective Theory, but only at the price of introducing an explicit dependence on a normalization point $μ$: $\La (μ)$. Fortunately the pole mass $m_Q(0)$ {\em per se} does not appear in calculable observable quantities.
In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.
We present some straightforward applications of the QCD heavy quark expansion, stated in previous papers [1-3], to the inclusive widths of heavy flavour hadrons. We address the question of the $D_s$ lifetime and argue that -- barring Weak Annihilation (WA) -- $τ(D_s)$ is expected to exceed $τ(D^0)$ by several percent; on the other hand WA could provide a difference of up to $10\div20\%$ of {\it any} sign. We extract $m_c$, $m_b$ and $|V_{cb}|$ from $Γ\ind{SL}(D^+)$ and $Γ\ind{SL}(B)$. The values of the quark masses are somewhat higher, but compatible with estimates from QCD sum rules; we obtain $|V_{cb}|\simeq 0.043$ for $τ(B)=1.4$ psec and $BR_{SL}(B)=10.5$\% . We discuss the associated uncertainties in the $1/m_Q$ expansion as well as some consequences for other electroweak decays.
There is a recent claim by Guralnik and Manohar \cite{GM} to have established a rigorous lower bound on $\bar Λ$, the asymptotic difference between the mass of a heavy flavour {\em hadron} and that of the heavy flavour {\em quark}. We point out the flaw in their reasoning and discuss the underlying physical problem. An explicit counterexample to the GM bound is given; one can therefore not count on a refined proof to re-establish this bound. *********** Uses LaTeX No figures No macros file used.
Theoretical descriptions for the nonleptonic decays of heavy flavour hadrons have emerged that incorporate non-perturbative corrections in a systematic way and are genuinely based on QCD. One can reproduce $τ(D^+)/τ(D^0)$, $BR_{SL}(D^+)$ and $BR_{SL}(D^0)$ as due mainly to destructive interference in $D^+$ decays; one predicts $τ(B^-)$ to exceed $τ(B_d)$ by a few per cent; $BR_{SL}(B)$ is reduced only slightly, raising the prospects of a serious and tantalizing conflict with ARGUS \& CLEO data. It is emphasized that the lifetimes for the two mass eigenstates in the $B_s$-$\bar B_s$ system could differ by 30\% or even more. The status of phenomenological treatments of non-leptonic two-body modes is briefly reviewed.
Second-generation theoretical technologies -- heavy quark expansions, QCD sum rules and QCD simulations on the lattice -- are arriving on the scene, allowing a treatment of charm decays that is genuinely based on QCD. The availability of those theoretical tools strengthens the case for the need for comprehensive precision measurements of charm decays. It is pointed out that the decays of charm mesons as well as of charm baryons have to be systematically analysed to gain control over theoretical uncertainties. A $τ$-charm factory with $E_{c.m.}\leq 5.5$ GeV is optimally suited for such a program. It would lead to a deeper understanding of QCD that would also prepare us better for exploiting the discovery potential anticipated in beauty decays. In addition it is quite conceivable (though certainly not guaranteed) that there arise fundamental surprises, such as non-canonical rare $D$ decays, $D^0$-$\bar D^0$ oscillations and CP violation in charm decays which would dramatically alter our perspective on Nature's fundamental forces.
A general relationship is formulated between the contributions of `Weak Annihilation' (WA) to inclusive semileptonic decays of heavy flavour hadrons and the matrix elements of four fermion operators. We argue that nonperturbative contributions from low energy hadronic final states provide the dominant impact of WA on the semileptonic $b\ra u$ width of $B^-$ mesons. In that case WA affects the lepton spectrum mainly in its endpoint region -- i.e. beyond the kinematical boundary for $b\ra c$ transitions -- and we expect thelater to look quite different in $B^-$ than in $B_d$ decays. At present we are unable to make a truly quantitative prediction; yet a detailled experimental comparison of the $B^-$ and the $B_d$ lepton spectra will enable one to determine the size of the relevant matrix elements and to check directly to what extent the factorization approximation works here. Using universal analyticity properties of the decay amplitude we analyze WA in the perturbative regime and rederive our earlier results about the absence of a power enhancement due to gluon emission in a more general way. We address also the problem of the invariant mass of hadrons in the final state in semileptonic $B$ decays and identify nontrivial cancellations in $\aver{M^2\ind{hadr}}$.
We derive the lepton spectrum in semileptonic beauty decays from a nonperturbative treatment of QCD; it is based on an expansion in $1/m_Q$ with $m_Q$ being the heavy flavour quark mass. The leading corrections arising on the $1/m_Q$ level are completely expressed in terms of the difference in the mass of the heavy hadron and the quark. Nontrivial effects appear in $1/m_Q^2$ terms affecting mainly the endpoint region; they are different for meson and baryon decays as well as for beauty and charm decays.
A selfconsistent treatment of nonperturbative effects in inclusive nonleptonic and semileptonic decays of beauty and charm hadrons is presented. It is illustrated by calculating semileptonic branching ratios, lifetime ratios, radiative decay rates and the lepton spectra in semileptonic decays.
We present a selfconsistent method for treating nonperturbative effects in inclusive nonleptonic and semileptonic decays of heavy flavour hadrons. These effects give rise to powerlike corrections $\propto 1/m_Q^n\,$, $n \ge 2$ with $m_Q$ denoting the heavy quark mass.The leading correction to the semileptonic branching ratio occurs for n=2. It is expressed in terms of the vector-pseudoscalar mass splitting: $δBR\ind{sl}/BR\ind{sl} \simeq BR\ind{nl}\, \cdot \,6\,(\,(M_V^2-M_P^2)/m_Q^2)\cdot (c_+^2 - c_-^2)/2N_c$ and yields a {\it reduction} of $BR\ind{sl}$. This nonperturbative correction contributes to the nonleptonic width with a sign opposite to that of the perturbative terms that are non-leading in $1/N_c$. In beauty decays the former reduces the latter by 20 \% whereas in charm decays they more or less cancel. This leads to a {\it reduction} of $BR\ind{sl}$ by no more than 10 \% in beauty decays and by a factor of roughly two in charm decays. We confront these results with those obtained from phenomenological models of heavy flavour decays and find that such models are unable to mimic these leading corrections by a specific choice of quark masses or by invoking Fermi motion.