arXiv subjects

Adam F. Falk

Publications and source records attributed to Adam F. Falk.

54 records · Page 3Linked to original sources

arXiv1994

Possible Puzzles in Nonleptonic B Decays

I discuss the recent controversy over the semileptonic branching ratio of the $B$ meson, pointing out that it is only the combination of this quantity with the reported charm multiplicity in $B$ decays which is in serious conflict with theoretical calculations. I consider possible solutions to the problem. (Invited talk presented at the Eighteenth Johns Hopkins Workshop on Current Problems in Particle Theory, Florence, Italy, August 31--September 2, 1994.)

hep-ph↗

arXiv1994

Inconclusive Inclusive Nonleptonic $B$ Decays

We reconsider the conflict between recent calculations of the semileptonic branching ratio of the $B$ meson and the experimentally measured rate. Such calculations depend crucially on the application of ``local duality'' in nonleptonic decays, and we discuss the relation of this assumption to the weaker assumptions required to compute the semileptonic decay rate. We suggest that the discrepancy between theory and experiment might be due to the channel with two charm quarks in the final state, either because of a small value for $m_c$ or because of a failure of local duality. We examine the experimental consequences of such solutions for the charm multiplicity in $B$ decays.

hep-ph↗

arXiv1994

Another Source of Baryons in $B$ Meson Decays

It is usually assumed that the production of baryons in $B$ meson decays is induced primarily by the quark level process $b\to c\bar ud$, where the charm quark hadronizes into a charmed baryon. With this assumption, the $Λ_c$ momentum spectrum would indicate that the transition $B\toΛ_c X$ is dominated by multi-body $B$ decays. However, a closer examination of the momentum spectrum reveals that the mass $m_X$ against which the $Λ_c$ is recoiling almost always satisfies $m_X\agt m_{Ξ_c}$. This fact leads us to examine the hypothesis that the production of charmed baryons in $B$ decays is in fact dominated by the underlying transition $b\to c\bar cs$, and is seen primarily in modes with two charmed baryons in the final state. We propose a number of tests of this hypothesis. If this mechanism is indeed important in baryon production, then there are interesting consequences and applications, including potentially important implications for the ``charm deficit'' in $B$ decays.

hep-ph↗

arXiv1994

QCD Corrections and the Endpoint of the Lepton Spectrum in Semileptonic B Decays

Recently, Neubert has suggested that a certain class of nonperturbative corrections dominates the shape of the electron spectrum in the endpoint region of semileptonic $B$ decay. Perturbative QCD corrections are important in the endpoint region. We study the effects of these corrections on Neubert's proposal. The connection between the endpoint of the electron spectrum in semileptonic $B$ decay and the photon spectrum in $b\rightarrow sγ$ is outlined.

hep-ph↗

arXiv1994

Heavy Quark Expansion for the Inclusive Decay $\bar B\toτ\,\barν\,X$

We calculate the differential decay rate for inclusive $\bar B\toτ\,\barν\,X$ transitions to order $1/m_b^2$ in the heavy quark expansion, for both polarized and unpolarized tau leptons. We show that using a systematic $1/m_b$ expansion significantly reduces the theoretical uncertainties in the calculation. We obtain for the total branching ratio ${\rm BR}(\bar B\toτ\,\barν\,X)=2.30\pm 0.25\%$, and for the tau polarization $A_{\rm pol}=-0.706\pm0.006$. {}From the experimental measurement of the branching ratio at LEP, we derive the upper bound $\lo\leq 0.8\gev^2$ for one of the parameters of the heavy quark effective theory.

hep-ph↗

arXiv1993

Recent Developments in the Theory of Heavy Quarks

Recent developments in the theory of heavy quarks are reviewed. In the area of heavy quark fragmentation, there has been progress in the study of both pertubative and nonperturbative processes, including the identification of new observable nonperturbative fragmentation parameters. There has also been considerable theoretical activity in the study of inclusive rare and semileptonic decays of bottom hadrons.

hep-ph↗

arXiv1993

Nonperturbative Contributions to the Inclusive Rare Decays $B\to X_sγ$ and $B\to X_s\ell^+\ell^-$

We discuss nonperturbative contributions to the inclusive rare $B$ decays $B\to X_sγ$ and $B\to X_s\ell^+\ell^-$. We employ an operator product expansion and the heavy quark effective theory to compute the leading corrections to the decay rate found in the free quark decay model, which is exact in the limit $m_b\to\infty$. These corrections are of relative order $1/m_b^2$, and may be parameterised in terms of two low-energy parameters. We also discuss the corrections to other observables, such as the average photon energy in $B\to X_sγ$ and the lepton invariant mass spectrum in $B\to X_s\ell^+\ell^-$.

hep-ph↗

arXiv1993

Production, Decay, and Polarization of Excited Heavy Hadrons

We discuss the production via fragmentation of excited heavy mesons and baryons, and their subsequent decay. In particular, we consider the question of whether a net polarization of the initial heavy quark may be detected, either in a polarization of the final ground state or in anisotropies in the decay products of the excited hadron. The result hinges in part on a nonperturbative parameter which measures the net transverse alignment of the light degrees of freedom in the fragmentation process. We use existing data on charmed mesons to extract this quantity for certain excited mesons. Using this result, we estimate the polarization retention of charm and bottom baryons.

hep-ph↗

arXiv1993

$\bar B\to\bar K\e^+\e^-$ in Chiral Perturbation Theory

The combined use of chiral $SU(3)$ and heavy quark symmetries allows one to relate the hadronic form factors for the decay $\bar B\to \bar K\e^+\e^-$ to those for $\bar B\toπ\e^-\barν$. We investigate departures from the symmetry limit which arise from chiral symmetry breaking. The analysis uses chiral perturbation theory and the heavy quark limit to compute the relevant hadronic matrix elements. We estimate the size of $SU(3)$ corrections by computing, at one loop order, the leading nonanalytic dependence on the light quark masses. The calculation is trustworthy only in the portion of the Dalitz plot in which the momentum of the kaon or pion is small. We find the corrections to be~$\sim40\%$.

hep-ph↗

arXiv1993

Heavy Quark Fragmentation to Baryons Containing Two Heavy Quarks

We discuss the fragmentation of a heavy quark to a baryon containing two heavy quarks of mass $m_Q\ggΛ_{\rm QCD}$. In this limit the heavy quarks first combine perturbatively into a compact diquark with a radius small compared to $1/Λ_{\rm QCD}$, which interacts with the light hadronic degrees of freedom exactly as does a heavy antiquark. The subsequent evolution of this $QQ$ diquark to a $QQq$ baryon is identical to the fragmentation of a heavy antiquark to a meson. We apply this analysis to the production of baryons of the form $ccq$, $bbq$, and $bcq$.

hep-ph↗

arXiv1993

Heavy Quark Fragmentation to Polarised Quarkonium

We calculate the polarisation of $ψ$'s and $Υ$'s produced by the fragmentation of heavy quarks. We find that fragmentation to transversely aligned quarkonium is slightly enhanced relative to longitudinally polarised. This net alignment corresponds to a $\sim 5\%$ asymmetry in the angular distribution of leptons produced in the subsequent decay of the quarkonium. We point out that the leading gluon contribution to $ψ$ and $Υ$ production arises from the evolution of the charm quark fragmentation function, rather than from direct gluon fragmentation.

hep-ph↗

arXiv1993

Excited Heavy Mesons and Kaon Loops in Chiral Perturbation Theory

We consider the effects of excited states on the $SU(3)$ breaking chiral loop corrections to heavy meson properties. In particular, we compare the size of kaon loops in which an excited heavy meson appears to the size of previously calculated loops with heavy mesons in the ground state. We find that the new effects may indeed be of the same magnitude as the old ones, but that there is a strong dependence on the unknown masses and coupling constants of the new states. As a result, we argue that the ground state loops alone may not be a trustworthy guide to $SU(3)$ corrections, and that the appropriate cutoff for a heavy-light chiral lagrangian which omits excited heavy mesons may be considerably smaller than the na\"ıve expectation of $Λ_χ\approx 1\gev$.

hep-ph↗

arXiv1992

Analyticity and the Isgur-Wise Function

We reconsider the recent derivation by de Rafael and Taron of bounds on the slope of the Isgur-Wise function. We argue that one must be careful to include cuts starting below the heavy meson pair production threshold, arising from heavy quark-antiquark bound states, and that if such cuts are properly accounted for then no constraints may be derived.

hep-ph↗

arXiv1992

Novel Spin and Statistical Properties of Nonabelian Vortices

We study the statistics of vortices which appear in (2+1)--dimensional spontaneously broken gauge theories, where a compact group G breaks to a finite nonabelian subgroup H. Two simple models are presented. In the first, a quantum state which is symmetric under the interchange of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of a third vortex with an appropriate $H$-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics. These results generalize to loops of nonabelian cosmic string in 3+1 dimensions. In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may possess fractional ``Cheshire spin'' which can be changed by passing an additional vortex through the system.

hep-th↗

arXiv1992

Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors

In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$. A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,ν$ and $B\to D^*\ell\,ν$ receive only small second order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.

hep-ph↗

arXiv1992

Second Order Power Corrections in the Heavy Quark Effective Theory II. Baryon Form Factors

The analysis of $1/m_Q^2$ corrections of the previous paper is extended to the semileptonic decays of heavy baryons. We focus on the simplest case, the ground state $Λ_Q$ baryons, in which the light degrees of freedom are in a state of zero total angular momentum. The formalism, while identical in spirit, is considerably less cumbersome than for heavy mesons. The general results are applied to the semileptonic decay $Λ_b\toΛ_c\,\ell\,ν$. An estimate of the leading power corrections to the decay rate at zero recoil, which are of order $1/m_Q^2$, is presented. It is pointed out that a measurement of certain asymmetry parameters would provide a direct measurement of $1/m_Q^2$ corrections. Finally, it is shown how the analysis could be extended to include excited heavy baryons such as the $Σ_Q$ and the $Σ_Q^*$.

hep-ph↗

arXiv1992

Strong Decays of Excited Heavy Mesons In Chiral Perturbation Theory

We construct an effective Lagrangian describing the interaction of soft pions and kaons with mesons containing a heavy quark and light degrees of freedom in an orbital $p$ wave. The formalism is easily extended to heavy mesons and baryons in arbitrary excited states. We calculate the leading contributions to the strong decays $\dtwo\to\dπ$, $\dtwo\to\dstarπ$ and $\done\to\dstarπ$. We confirm the relations between the rates previously obtained by Isgur and Wise using heavy quark symmetry, and find that the absolute widths are consistent with na\"ıve power counting. We also estimate the branching ratios for the two pion decays $\dtwo\to\dstarππ$, $\done\to\dstarππ$ and $\done\to\dππ$, which are dominated by pole graphs. Our predictions depend on the masses and widths of the as yet unseen scalar-pseudovector $p$-wave doublet. Heavy quark spin symmetry predicts $Γ(\dtwo\to\dstarππ): Γ(\done\to\dstarππ):Γ(\done\to\dππ)=3:1:2$, but this relation is badly violated in practice because $1/M$ effects arising purely from kinematics are large.

hep-ph↗

arXiv1992

The Residual Mass Term in the Heavy Quark Effective Theory

We reformulate the heavy quark effective theory in the presence of a residual mass term, which has been taken to vanish in previous analyses. While such a convention is permitted, the inclusion of a residual mass allows us to resolve a potential ambiguity in the choice of the expansion parameter which defines the effective theory. We show to subleading order in the mass expansion that physical quantities computed in the effective theory do not depend on the expansion parameter.

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