Recent Bottom Physics Results from Threshold Machines

Dave Z. Besson

University of Kansas Lawrence, KS 66045 (January 4, 1994)

Recent (within the last year) contributions to our understanding of B-decays from the threshold machines (CESR and DORIS) are reviewed. This includes increasingly precise measurements of the structure of hadronic and semileptonic decays of B-mesons, and the first observation of radiative B-meson decays. Particular attention is paid to those results which give direct information on fundamental parameters such as the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. Prospects for improvement are summarized at the end of this article.

INTRODUCTION

The Standard Model of weak interactions provides a framework for understanding heavy quark decay. Knowledge of the CKM matrix which rotates the quark mass eigenstates to the quark weak force eigenstates gives a quantitative basis for calculating heavy quark decay rates, provided less-calculable strong force effects can be understood. If, as stipulated, all the CKM elements are non-zero, the inclusion of a phase into this matrix provides an explanation for how CP- is violated.

In the simplest picture based on the CKM model, the dominant decay of a b- or c- quark occurs via emission of a W-boson. The W-boson then hadronizes without (“external” W-emission) or with (“internal” W-emission) the participation of the light “spectator” quark, as sketched in Figure 1. The raw relative probabilities of internal or external W-emission should be roughly the same. However, for internal W-emission, the system into which the W hadronizes must match in color the spectator quark, introducing a suppression of the amplitude by a factor of \frac{1}{N_{colors}}. The dominant decay therefore is expected to result from external W-emission. In this simplified picture, the semileptonic branching ratio b should then be given by the frequency with which the W materializes as an lν_{l} pair relative to the total number of channels available:

b = \frac{W → (eν_{e})}{W → (eν_{e} + μν_{μ} + τν_{τ} (p.s.) + Rdū + Rsc̄(p.s.))}  (1)

In the above equation, p.s. indicates that the τν and sc̄ rates are phase space

\begin{matrix}c \\ ◯ \end{matrix} 1993 American Institute of Physics 1

FIG. 1. External (left) and internal (right) W-emission spectator diagrams. These lead to final states such as Dπ.

TABLE 1. Comparison of decay widths expected for bottom vs. charm

Expected for B-decay  Charm analogue, data (20)
\frac{Γ(B^{0}→\overline{D}^{0}π^{0})}{Γ(B^{0}→D^{−}π^{+})} ∼ 1/18 (N_{colors}=3)  \frac{Γ(D^{0}→\overline{K}^{0}π^{0})}{Γ(D^{0}→K^{−}π^{+})} =0.5
τ_{B^{0}} = τ_{B^{+}}  τ_{D^{0}} = 0.4 × τ_{D^{+}}
B(b → Xℓν_{ℓ})=17%  B(D^{+} → Xℓν_{ℓ})=17%
B(D^{0} → Xℓν_{ℓ})=7%
\frac{Γ(B^{0}→D^{−}π^{+})}{Γ(B^{+}→\overline{D}^{0}π^{+})} =1  \frac{Γ(D^{0}→K^{−}π^{+})}{Γ(D^{+}→\overline{K}^{0}π^{+})} = 3.3±1.0

suppressed relative to the other states; R is the additional color multiplicity factor, and is given by the ratio of e^{+}e^{−} → hadrons relative to e^{+}e^{−} → μ^{+}μ^{−} at momentum scales equal to M_{W} in b → cW. We therefore expect that the rates for, e.g. B^{−} → D^{0}π^{−} and B^{0} → D^{−}π^{+} should be equal, as both correspond to simple external W-emission graphs. Predictions for decays of bottom hadrons based on this simple picture in which internal W-emission is considered negligible are presented in Table 1. Also presented is a comparison with data from the charm system.

As outlined in the Table, and detailed in another presentation to this conference (1), the charm sector shows marked departures from this simple model. Of particular note is the factor of 2.5 discrepancy between the D^{+} and D^{0} lifetimes. This has been explained as the result of at least three contributing effects: 1) destructive interference between the external W-emission process (∝ a parameter designated as ‘a_{1}’) and the internal W-emission process (∝ a_{2}) for common D^{+} final states (K̄^{0}π^{+}, e.g.) reduces the total D^{+} decay width;

2) “annihiliation” or “exchange” diagrams which are otherwise helicity suppressed for the D^{0} (K̄^{0}η, e.g.) are enhanced due to soft gluon emission. These can open up more decay channels to the D^{0} as well as constructively interfering with spectator graphs giving the same final state; and 3) final-state interactions can deplete external W-emission final states such as K^{−}π^{+} and can feed final states such as K̄^{0}π^{0}. Simple interpretation of the charm meson data on hadronic decays can therefore be difficult.

Measurements of weak decays of bottom hadrons offer more promise for reliably testing predictions for flavor-changing heavy quark decays. The heaviness of the bottom system compared to charm makes the b-sector less susceptible than the charm sector to such effects as final state interactions. Another attractive feature of the bottom-sector is as a probe of new physics: the magnitude of the CKM matrix element which determines the strength of the dominant b-quark decay process (V_{cb}) is sufficiently small so as to inhibit the overall B-decay rate. This allows rare processes to compete with the dominant decay modes.

SEMILEPTONIC DECAYS

Phenomenology

The semileptonic decays of heavy quarks are traditionally used as a starting point for testing theories of weak decays, as they are immune to final state interactions between the W- decay products and the quarks at the lower vertex. These are therefore exclusively external W-emission processes. In the free-quark b →XW picture, there is a simple relation between CKM elements, b-quark mass, and the decay rate of the b into c or u quarks:

\frac{1}{τ_{b}} ∼ Γ_{b→qℓν_{ℓ}} ∼ \frac{G_{F} m_{b}^{5}}{192π^{3}} (γ_{cb}|V_{cb}|^{2} + γ_{ub}|V_{ub}|^{2}).  (2)

Here, γ_{xb} incorporates phase space, and possible strong corrections. The usual approach at threshold has been to fit the inclusive lepton momentum spectrum to the sum of a “primary” (b → cℓν) and a “cascade” (b → c + X; c → sℓν) spectrum. However, because these two momentum spectra overlap over much of the available phase space, one must rely on models to specify the lepton spectra. “Form factor” models, as discussed in the charm review talk at this conference (1), give not only the lepton momentum spectrum, but the charm hadron momentum spectrum, as well as the population of possible polarization states. These models specify the rate and polarization for a given charmed hadron as a function of the (off-shell) mass of the W squared (q^{2}).

Many of the predictions for the Dalitz plot distributions by such models are common. They may often be inferred by treating the decay as a quasi-two body decay: B → D + W and considering the various spin-parity configurations favored by simple energy and angular momentum considerations. For example, the decay B → Dℓν_{ℓ} can be considered a 0^{−} → 0^{−}1^{−} process. Angular momentum conservation demands that the spin-1 W be longitudinally polarized and that the decay be P-wave. Because of the P-wave nature of this process, the D meson must have high momentum in order to overcome the p^{(2ℓ+1)} angular momentum barrier. Furthermore, the polarization of the W, coupled with the fact that the decay is V-A, produces a lepton momentum spectrum which is moderately hard. Similar arguments can be used to infer the characteristics expected for the decay into D^{∗}ℓν - in this case, the decay can be S-, P- or D-wave, and the suppression of low momentum charmed mesons is no longer necessarily present.

The form factor evolution with q^{2} in such models is generally determined by calculating q^{2} at some preferred value and then extrapolating across the kinematically allowed q^{2} range with some smooth dependence. Since the form factors are related to the likelihood of the final state c-quark binding with the spectator quark to form a stable hadron, they tend to be largest when the c-quark is emitted at rest (i.e., q_{max}^{2}). At this point, the rate for the b → c transition is also most reliably calculated. In fact, in Heavy Quark Effective Theory (HQET (2)), the rate in this kinematic limit of q^{2} → q_{max}^{2} is well determined and can therefore be used to extract a value for the CKM matrix element |V_{cb}|. HQET also prescribes relationships between the various possible form factors in B-decay (one for B → Dℓν, three for B → D^{∗}ℓν). This allows for a full description of the kinematics for this process in terms of just one particular form-factor ξ(y), the so-called Isgur-Wise function. The variable y is defined as: y= \frac{E_{D^{∗}}}{m_{D^{∗}}} = \frac{m_{B}^{2}+m_{D^{∗}}^{2} −q^{2}}{2m_{B}m_{D^{∗}}}; the kinematic limit q_{max}^{2} therefore maps to E_{D^{∗}} = m_{D^{∗}}, or y=1.

Note that, in measuring the inclusive production of leptions, what we actually measure are the semileptonic fractions of B^{+} and B^{0} (‘b_{+}’ and ‘b_{0}’, respectively) weighted by their respective production fractions at the Υ(4S), f_{+} and f_{0} (f_{+} +f_{0} =1, by the assumption that BB̄ decays saturate the Υ(4S) width).^{1} In comparing with the inclusive b → leptons values from LEP (3), one must therefore also know the production fractions of B^{+}, B^{0}, B_{s}, Λ_{b}, Ξ_{b}, etc., at ECM = M_{Z^{0}}, and the lifetimes of each of these b-flavored hadrons.

Recent experimental results

CLEO have presented in 1993 (4) a new measurement of the inclusive semileptonic spectrum produced in B-meson decays (denoted ‘CLEO93’ to indicate that this is a 1993 measurement). They fit their inclusive muon and

1It is not guaranteed that f_{+} and f_{0} are identical at CESR and DORIS, given the different beam spreads of the two machines and the possibility that the ratio \frac{f_{+}}{f_{0}} is a function of the energy above threshold.

FIG. 2. CLEO93 fit to inclusive semileptonic spectrum, separately for electrons and muons. Contributions from the various components of the overall momentum spectrum are as indicated.

electron spectra to a sum of: b → cℓν_{ℓ}, b → uℓν_{ℓ}, and b → cX, c → sℓν_{ℓ}, using both the “free-quark” model of Altarelli et al.(‘ACCMM’) (5) as well as the exclusive final state model of Isgur et al. (‘ISGW*’) (6). In the former approach, the b → c transition is likened to the familiar μ → e transition; the rate has a form similar to Equation 2. In this model, the properties of the final state charmed hadron depend on the spectator quark momentum distribution, which translates into a range of mass and momenta for the D-states.

In the Isgur et al. approach, the rate is explicitly calculated knowing the possible final state charmed hadrons. In the original model, the fraction of B → Dℓν_{ℓ} for which the emerging “D”-meson is a D^{∗∗} was calculated to be 11%.^{2} In fitting the spectrum, however, this fraction can be left as a free parameter and determined from the fit itself. It is important to understand that, in the fit to the ISGW* model, there is no explicit allowance made for semileptonic decays where the charm quark emerges in a non-resonant Dπ system, a D_{s}K system, or a Λ_{c}p̄ system. If these are considerable, they will most likely be absorbed into the D^{∗∗} component or the cascade component of the total rate.

The results of the CLEO93 fit to the ISGW* model with floating D^{∗∗} fraction are shown in Figure 2 and given in Table 2. The fraction of b → charmed meson semileptonic decays which are B → D^{∗∗}ℓν_{ℓ} is determined

2Experimentally, the distinction between true D^{∗∗}’s and non-resonant Dπ or D^{∗}π is very weak in this measurement.

TABLE 2. Summary of 1993 CLEO fits to inclusive semileptonic momentum spectrum, using the Altarelli et al.(ACCMM) and Isgur et al. (ISGW*) models.

Model  γ_{c}(ps^{−1})  B(b → cℓν)%  |V_{cb}|
ACCMM  40 ± 8  10.48 ± 0.07 ± 0.33  0.042 ± 0.001 ± 0.004
ISGW*  42 ± 8  10.87 ± 0.10 ± 0.33  0.042 ± 0.001 ± 0.004

from the fit to be 21±8%. This compares with the 3σ CLEO 1.5 result of 32% (7). The product cascade branching fraction: b → c → sℓν in the ISGW model fit is determined to be 9.53±0.30%, consistent with the tabulated values of B → D^{+}X and B → D^{0}X and the known D^{+} and D^{0} semileptonic branching fractions. Inspection of the Figure shows that the b → c component almost entirely saturates the spectrum, leaving very little room for b → u. We shall return to this shortly. Overall, the branching ratios are in good agreement with the older CLEO 1.5 measurement for this quantity of 11.2±0.3±0.4% (7). Note that allowing the D^{∗∗} component in the ISGW* model to vary between 10% and 30% has about a 10% relative effect on the calculated branching ratio.

Also included in the Table is an estimate of the CKM matrix element |V_{cb}|, based on Equation 2. One is cautioned that, if we were to include the full range of suggested masses for the bare b-quark mass, the systematic error on |V_{cb}| would be larger by at least a factor of two. The raw value of |V_{cb}| is in remarkable agreement with the expectation that this CKM matrix element be of order tan^{4}θ_{c}(∼ λ^{2}, where λ=tan^{2}θ_{c}).

Fit to semileptonic spectrum with reduced model dependence

ARGUS93 (8) have measured the b → c spectrum with substantially reduced model dependence using BB̄ events containing two detected leptons. They do this by taking advantage of correlations in angle and sign between the two leptons, after requiring that one of the leptons be well-identified as a “primary” lepton. The second lepton will then be either a cascade from the same B, or a primary or a cascade from the opposite B̄. Due to the fact that at threshold the B’s are produced very nearly at rest, leptons from the opposite B̄ have no angular correlation with the primary lepton. In the case of a cascade from the same B, the two leptons have a strong angular correlation and tend to be in opposite hemispheres. In addition, there is a sign correlation for the leptons from the opposite B̄ - the primary(/cascade) lepton will have the opposite(/same) sign as the primary tag lepton. Therefore, measuring leptons in the same hemisphere as the primary tag will give a measure of the primary or secondary spectrum, depending on the sign correlation, with very little dependence on model. This is possible down to the momentum limits of the ARGUS lepton identification system (600 MeV/c). The results of their fit to the primary spectrum are shown in Figure 3.

FIG. 3. Normalized ARGUS93 primary lepton momentum spectrum ( \frac{1}{N_{B}} \frac{dN}{dp_{e^{−}}}) with fits to ISGW (dashed) and ACCMM (solid) models overlaid. The calculated inclusive semileptonic branching ratios are 9.9±0.5±0.4% and 9.6±0.5±0.4%, respectively.

ARGUS93 thereby determine the rate for the cascade process (Figure 4): b → c → sℓν = 7.98 ± 0.8 ± 1.0%, somewhat lower than CLEO, although consistent with the naive expectation. By conducting a similar charge/angle analysis of kaons relative to leptons, ARGUS are able to determine that the fraction of semileptonic decays proceeding through b → cℓν; c → s = 0.99 ± 0.02±0.04, consistent with near saturation of the inclusive semileptonic rate by b → c. This measurement also carries very little dependence on the inclusive D → K + X branching ratios (9).

Measurement of b → u decays

As is evident from Figure 2, the b → cℓν component of the lepton momentum spectrum dominates over the b → uℓν component up to about 2.3 GeV/c. Beyond this point, the higher mass of the c-quark relative to the u-quark phase space strongly suppresses the production of high momentum leptons in the b → c process. Evidence for b → u can then be obtained by counting leptons (after subtracting the contribution from the continuum) in the momentum interval 2.3 GeV/c - 2.6 GeV/c. However, the smallness of the momentum byte being considered makes quantitative statements on the total b → u rate extremely model-dependent. Different models will prescribe different fractions of total leptons which would populate this momentum in-

FIG. 4. ARGUS93 secondary lepton momentum spectrum ( \frac{1}{N_{B}} \frac{dN}{dp_{e^{−}}}). The curve represents the expectation for B → D + X, followed by D semileptonic decays.

TABLE 3. Partial branching fraction (ΔB_{ub}(p)) for b → uℓν over the indicated momentum interval.

ΔB_{ub}(p)×10^{−6}
(2.3< p_{lepton} <2.6 GeV/c)
Model  Events: tight/loose cuts  |V_{ub}/V_{cb}|
ISGW  121 ± 17 ± 15 / 139±25  0.101±0.010
KS  115 ± 16 ± 15 / 136±24  0.056±0.006
BSW  122 ± 17 ± 16 / 141±25  0.073±0.007
ACCMM  153 ± 21 ± 20 / 151±26  0.075±0.008

terval. Unfortunately, HQET cannot yet offer firm predictions here, since the transition of interest is a heavy-to-light, and not a heavy-to-heavy transition. It is hoped that new measurements on semileptonic charm decay may be able to offer some insight in that regard.

A summary of a new CLEO measurement (10) of the partial branching ratio for b → uℓν using leptons in the momentum interval 2.3-2.6 GeV/c is shown in Table 3. Here, “tight” and “loose” refer to the stringency with which background leptons from the continuum are suppressed. “Loose” criteria are essentially the same as those used in the original CLEO observation of b → u transitions with this technique. (In the Table, KS and BSW refer to the models of Körner-Schuler (11) and Bauer, Stech and Wirbel (12), respectively.)

The lepton momentum spectrum near the endpoint is shown in Figure 5. For completeness, a listing of previous determinations of |V_{ub}| from this tech-

FIG. 5. CLEO93 inclusive lepton momentum spectrum. In the top plot (a), the unshaded histogram is dN/dp_{lepton} from Υ(4S) data; shaded (with fit) is dN/dp_{lepton} for continuum. The data points in the lower plot (b) are 4S minus continuum; the b → cℓν component is the histogram. The excess is interpretted as b → uℓν.

nique is shown in Table 4.

Of interest is the fact that the new CLEO measurement for |V_{ub}| is smaller than the first estimates derived from this technique. Also of interest is the fact that the sum of (b → c + b → u) is considerably smaller than the naive expectation for this value (17%), as well as the QCD corrected value of 12% (15). Driving up the primary lepton branching ratio with more non-resonant Dnπ states will have the unwanted consequence of driving down the cascade branching ratio, which is constrained by the B → D^{0} and B → D^{+} inclusive branching fractions. The fact that the ALEPH measurement (3) for B → cτν_{τ} agrees exactly with expectation also makes it difficult to better match the 12% expectation by absorbing fewer leptons into W → τν_{τ}.

Measurement of b_{+} and b_{0} separately

Unfortunately, the inclusive measurements are insensitive to possible lifetime differences between the charged and neutral B-mesons. Having performed a charge-weighted average of semileptonic fractions as above, we would like to measure b_{+} and b_{0} separately, with no dependence on \frac{f_{+}}{f_{0}} . This can be done by tagging an event as a B^{0}B̄^{0} or B^{+}B^{−} event by reconstructing a B in the event. We then determine the fraction of times a tag has an additional

TABLE 4. Recent V_{ub} determinations based on inclusive high momentum leptons from B-decay.

Expt.  Model  | \frac{V_{ub}}{V_{cb}} |
ARGUS (13)  ACCMM  0.11±0.01
ISGW  0.20±0.02
KS  0.11±0.01
WSB  0.13±0.02
CLEO 1.5 (14) ACCMM 0.12±0.02
ISGW  0.19±0.03
KS  0.10±0.01
WSB  0.08±0.02

lepton from the B̄ in the same event.^{3} CLEO93 (16) uses four classes of tags to make this measurement:

• Fully reconstructed hadronic B^{0} (492 ± 31) and B^{+} (919±42) tags

• B^{+}→\overline{D}^{∗0}ℓ^{+}ν_{ℓ} (231 ± 30) and B^{0}→D^{∗−}ℓ^{+}ν_{ℓ} (378 ± 30) tags for which the D^{∗} is fully reconstructed

• ‘Partially’ reconstructed B^{0}→D^{∗+}π^{−} (754±51) tags, for which the D^{∗+} four-vector is inferred from observation of the slow π^{+} emitted in the decay D^{∗+} → π^{+}D^{0}. Here, the constraint that the sum of the D^{∗+} energy plus the π^{−} energy must equal the Beam energy can produce a rather narrow (σ ∼ 5 MeV) B-mass peak.

• Partially reconstructed B^{0}→D^{∗+}ℓν_{ℓ} (7100 ± 182) tags, for which the D^{∗+} four-vector is inferred from observation of the slow π^{+} emitted in the decay D^{∗+} → π^{+}D^{0}. Here, the B-signal peak is much broader than for the previous case, due to the undetected neutrino. The signal observed by the CLEO collaboration with this technique is illustrated in Figure 6.

Putting together the results from all their tags, CLEO obtain: b_{+} = (12.0 ± 1.7±1.8) and b_{0} = (11.4±0.7±1.3), where the principal systematic error arises from the model dependence in extraction of the total rate. Taking the ratio of these gives a value for \frac{b_{+}}{b_{0}} = \frac{τ_{B^{+}}}{τ_{B^{0}}} of 1.05±0.16±0.15, in good agreement with a value of 1.07±0.12 obtained by averaging the Fermilab and LEP results (3).

The ratio of lifetimes is therefore entirely consistent with 1.0. By contrast, the corresponding ratio for charm is 2.5. Evidence for the equality of the charged and neutral lifetimes provides perhaps the strongest evidence that the B-meson is a simpler weak decay system than the D-meson.

3This technique is very powerful in that it can be sensitive to non BB̄ decays of the Υ(4S).

FIG. 6. CLEO93 signal for partially reconstructed B → D^{∗+}ℓν, showing signal and background (top) and background subtracted signal (bottom).

Interestingly, the threshold, as well as the above threshold measurements for this ratio both give values greater than 1.0. This is consistent with the lifetime ordering expected by having the exchange mode available to the B^{0}, but not the B^{+}. (15)^{4}

Measurement of exclusive semileptonic decays

The ratio of B(B^{+} → D^{∗0}ℓ^{+}ν)/B(B^{0} → D^{∗−}ℓ^{+}ν)

Reconstruction of exclusive decays of B-mesons offer a more direct probe of semileptonic B-decays than inclusive decays, as they can directly probe the D/D^{∗}/D^{∗∗} fractions, as well as the various allowed polarizations as a function of q^{2}. At threshold, we detect B → D^{∗}ℓν decays by calculating the square of the neutrino mass (‘MM^{2}’), i.e., the mass squared recoiling against D^{∗}ℓ: MM^{2} = (E_{beam} − E_{D^{∗}} − E_{ℓ})^{2} − (p_{B} − p_{D^{∗}} − p_{ℓ})^{2}. Although the magnitude of p_{B} is known and is small (< p_{B} >∼340 MeV), its direction is unknown without tagging the B̄; the approximation p_{B} = 0 is adequate for seeing a signal, but is the dominant contributor to the large signal width.^{5}

4As we shall see, such ordering cannot be explained by the (external W-emission ± internal W-emission) model invoked to explain the lifetime difference observed for D^{+} decays relative to D^{0} decays.

5As the size of the tagged B̄ sample increases, it may be possible to more frequently use an estimator for the B-direction by using the four-vector of the tag; this would

TABLE 5. CLEO93 results for |V_{cb}| and the Isgur-Wise slope parameter ρ̂ extracted from the \frac{dΓ}{dy} distribution measured for B → D^{∗}ℓν.

Isgur-Wise ξ(y) form  |V_{cb}| × 10^{3}  ρ̂^{2}
1 − ρ̂^{2}(y − 1)  38 ± 6 ± 4  1.2 ± 0.5 ± 0.3
\frac{2}{y+1} exp(−(2ρ̂^{2} − 1) \frac{y−1}{y+1} ) BSW  38 ± 6 ± 4  1.2 ± 0.6 ± 0.3
( \frac{2}{y+1} )^{2ρ̂^{2}} POLE  38 ± 5 ± 4  1.1 ± 0.5 ± 0.2
exp(−ρ̂^{2}(y − 1)) ISGW  37 ± 5 ± 4  1.0 ± 0.4 ± 0.2
1 − ρ̂^{2}(y − 1) + ϵ^{2}(y − 1)^{2}  38 ± 10 ± 4  1.2 ± 0.5 ± 0.3

CLEO93 (17) measure both B^{−} → D^{∗0}ℓν as well as B^{0} → D^{∗−}ℓν with the D^{∗} observed in the D^{∗} → Dπ^{0} mode.^{6} If the charged:neutral B-meson production fraction \frac{f_{+}}{f_{0}} were equal to one, then the ratio: \frac{B^{−}→D^{∗0}ℓν}{B^{0}→D^{∗−}ℓν} would be

equal to the ratio of lifetimes. More precisely, this ratio equals \frac{f_{+}τ_{+}}{f_{0}τ_{0}} . CLEO93 obtains a value of 1.20±0.20±0.19 for this ratio, compared with the value from ARGUS92 (18) of 1.22±0.40. These numbers can be compared directly with the lifetime ratio obtained from tagging to determine f_{+}/f_{0}=1.14±0.20, consistent with 1.0. Naively, one might suspect that the direction of corrections to f_{+}/f_{0} could be to enhance f_{+} through Coulomb interactions.

B→D^{∗}ℓν_{ℓ}, exclusive, and V_{cb}

There are new measurements from CLEO93 (19) (‘FR’=Full Reconstruction of the D^{∗+}) and ARGUS93 (18) (‘PR’=Partial Reconstruction of the D^{∗+}) giving the branching ratio for this decay: ARGUS93(PR): B(B̄^{0} → D^{∗+}ℓ^{−}ν̄) = (4.50 ± 0.30 ± 0.40) % CLEO93(FR): B(B̄^{0} → D^{∗+}ℓ^{−}ν̄) = (4.50 ± 0.44 ± 0.44) % ARGUS90(FR): B(B̄^{0} → D^{∗+}ℓ^{−}ν̄) = (5.20 ± 0.50 ± 0.60) %

From HQET, we can use the magnitude of the rate at q_{max}^{2}(y = 1) to determine V_{cb}. Experimentally, we must extrapolate a distribution of rate as a function of y (\frac{dΓ}{dy}) to y=1 using some parameterization for the Isgur-Wise function ξ(y). The CLEO93 data for \frac{dΓ}{dy} are shown in Fig. 7, with various fits corresponding to various parameterizations for the Isgur-Wise function ξ(y) overlaid. The corresponding values for |V_{cb}| (using a value of B-meson lifetime τ_{B}=1.49 ps (3)) are given in Table 5. The lower values of |V_{cb}| obtained here compared with previous extractions using this technique result more from the new B-lifetime measurements than anything else.

narrow the missing mass spectrum by an order of magnitude.

6This allows a convenient cancellation of uncertainties associated with reconstruction of the slow transition π^{0}.

FIG. 7. CLEO93 dΓ/dy distribution.

Comment on inclusive vs. exclusive semileptonic rates

From the above discussion, the average inclusive semileptonic branching ratio at threshold is seen to be 9.5-11%, depending on the experiment and the model used. By contrast, the new measurements of the exclusive process B(B → D^{∗}ℓν) give values of 4-5.5%, consistent with the older measurements of this quantity. The 1992 Particle Data Group (20) value of B(B → Dℓν) is 1.7±0.4%, consistent with the expectation that the ratio for semileptonic \frac{B→D^{∗}ℓν}{B→Dℓν} should be 2-3. There appears to be a clear undersaturation of the inclusive rate by the exclusive channels. The present statistics are almost certainly sufficient to begin ruling out specific possibilities for making up this difference. For instance, consider the case where the deficit is made up by D^{∗∗}(J^{P} = 1^{+}) production in semileptonic decay. Since the (relatively narrow) 1^{+} must decay to D^{∗}π and is prohibited from decaying to Dπ, there should be fair experimental sensitivity to direct searches for B → D_{1}ℓν (see (21), e.g.). This would be corroborated by the observation of a very noticeable shoulder at MM^{2} >0 in the MM^{2} distribution when calculated from only p_{D^{∗}} and p_{ℓ}.

Searches for exclusive b → u final states

Here again, the motivation is that the q^{2} reach for exclusive searches is potentially larger than for the inclusive measurement. CLEO93 has used a refinement of an old technique to perform a search for B → πℓν. Previously, searches for exclusive decays of the type B → ρℓν and B → ωℓν by the ARGUS and CLEO collaborations exploited the near-hermiticity of the detectors and required that the “missing” momentum and energy be consistent with that expected for a single, undetected neutrino. CLEO93 actually use the “missing” momentum and energy to determine the neutrino four-vector, which allows them to calculate a B mass using (p_{B} = p_{ν} + p_{ℓ} + p_{π}). Their results (22), compared with their other published results for the ρℓν case (23), and the implied limits on |V_{ub}/V_{cb}| are given below:^{7}

CLEO93  CLEO92
Model BR(B→πℓν_{ℓ})/|V_{ub}/V_{cb}| BR(B→ρℓν_{ℓ})/|V_{ub}/V_{cb}|
(ISGW) < 3.3 × 10^{−4}/ < 0.30 < 1.6 × 10^{−4}/ < 0.13
(KS) < 4.7 × 10^{−4}/ < 0.19 < 2.3 × 10^{−4}/ < 0.08
(BSW) < 4.5 × 10^{−4}/ < 0.18 < 2.7 × 10^{−4}/ < 0.10

EXCLUSIVE HADRONIC B-DECAYS

With its very large data sample, CLEO93 now have a total of almost 1.5K fully reconstructed hadronic B decays, which it has used to perform increasingly sensitive tests of models of B-decays (24), as well as make fundamental measurements of the B-sector. Their B-signals for charged and neutral B’s are shown in Figure 8. Based on this large sample, for instance, CLEO have determined the \overline{B}^{0}-B^{−} mass difference to be 0.26±0.29±0.17 MeV. Averaged in with previous measurements (20) gives a value of 0.2±0.3 MeV for this mass difference, consistent with zero.

Factorization

In the simplest picture of heavy quark decay, all decays of the variety b → cW are put on equal footing, independent of whether the W decays into a lepton-neutrino pair or a quark-antiquark pair. Then, just as we can express B→Dℓν_{ℓ} as a product of two separate currents: hadronic×leptonic: < D|J_{μ}|B > × < 0|A_{μ}|ℓν_{ℓ} > (×V_{cb}); we can express B→Dπ as a product of two separate currents: hadronic×hadronic: < D|J_{μ}|B > × < π|A_{μ}|0 > (×V_{cb})

If this is the case, as one might expect, one can relate rates (and polarizations) for semileptonic decays (B → D^{∗−}ℓν, e.g.) to hadronic decays (B → D^{∗−}D_{s}, e.g.), provided they are evaluated at the same value of (q^{2}) (25):

R = \frac{Γ(B^{0} → D^{∗−}D_{s})}{\frac{dΓ}{dq^{2}} (B^{0} → D^{∗−}ℓ^{−}\overline{ν}_{ℓ})|_{q^{2}=m_{Ds}^{2}}} = 6π^{2}f_{D_{s}}^{2}|V_{cs}|^{2}

7The previous ARGUS result on this topic has not been published and has been purposely excluded from this compilation after consultation with the authors

FIG. 8. CLEO93 reconstructed B signal observed in many hadronic modes. “ΔE” is the difference between a B-candidate’s energy and the beam energy, and should be zero for true B-mesons.

This is a deceptively powerful statement. It is not a priori obvious that one could so easily derive information on, e.g., B → D^{∗}D_{s} from semileptonic decays; in the case of B → D^{∗}D_{s}, e.g., the D^{∗} must be longitudinally polarized, whereas for the semileptonic case, there is no such restriction. Fortunately, the spin multiplicity corrections are understood and calculable. Therefore, in principle, given a measured dΓ/dq^{2} spectrum from semileptonic decays, as shown in Figure 9, one can use that spectrum to make predictions for the hadronic sector.

Factorization tests - polarization measurements

If factorization holds, the polarization of the vector W at M_{W} = M_{ρ} is the same whether the W materializes as a ℓν or a ρ^{+}. Therefore, the polarization of the final state in the decay B^{0} → D^{∗−}ρ^{+} should be the same as the polarization of the final state in the decay B^{0} → D^{∗−}ℓν, provided we evaluate the polarization of the ℓν system at q^{2} = m_{ρ}^{2}. We expect that, owing to the V-A nature of the weak decay, as q^{2} → 0, the D^{∗−} in the semileptonic decay will tend towards total longitudinal polarization. In this kinematic limit, the ℓ and ν are colinear and back to back with the D^{∗−}. The ℓ and ν helicities tend to anti-align; consequently, the D^{∗−} tends to the helicity zero state, i.e., the fraction of times that the D^{∗−} is longitudinally polarized (\frac{Γ_{L}}{Γ} ) tends to 1.0. At the other kinematic limit, as q^{2} → q_{max}^{2}, the D^{∗−} momentum goes

FIG. 9. \frac{dΓ}{dq^{2}} spectrum for lepton-neutrino system; combining results for B→D^{∗}ℓν_{ℓ} from the ARGUS and CLEO experiments.

TABLE 6. CLEO93 Summary of B^{−}→D^{0}+nπ branching ratios B.

B^{−} Mode/D mode  # of evts  B(%)  B average (%)
D^{0}π^{−}/K^{−}π^{+}  63 ± 8  0.39±0.05
D^{0}π^{−}/K^{−}π^{+}π^{0}  142 ± 16  0.53±0.06  0.470±0.034±0.047 ± 0.020
D^{0}π^{−}/K^{−}π^{+}π^{+}π^{−}  97± 12  0.45±0.06
D^{0}ρ^{−}/K^{−}π^{+}  77 ± 10  1.27 ±0.16
D^{0}ρ^{−}/K^{−}π^{+}π^{0}  79 ± 15  0.86±0.18  1.069±0.097±0.164 ± 0.038
D^{0}ρ^{−}/K^{−}π^{+}π^{+}π^{−}  92 ± 13  1.1±0.16

to zero, and the D^{∗−} helicity becomes less well-defined. In this limit, simple spin counting gives: Γ_{L}/Γ = 1/3.

For the final state D^{∗−}ρ^{+}, the measured value of Γ_{L}/Γ = 0.90±0.07±0.05, in excellent agreement with the factorization prediction of 0.88 (24).

Factorization tests - partial widths

The B-decay branching ratios compiled in Tables 6-8 can be used to test the factorization hypothesis. ^{8} In general, the results are in good agreement with previous results on these hadronic branching ratios (20).

8These use the CLEO93 determinations of the D^{0}→K^{−}π^{+} and B→D^{+}K^{−}π^{+}π^{+} branching ratios submitted to this conference. The last error shown in the Tables reflects the uncertainty in these BR’s.

TABLE 7. Summary of \overline{B}^{0}→D^{+}(D^{+}→K^{−}π^{+}π^{+})+nπ modes
B̄^{0} Mode  # of  B(%)  B average (%)
D^{+}π^{−}  76±10  0.22±0.03  0.221±0.029±0.019 ± 0.031
D^{+}ρ^{−}  86±11  0.62±0.08  0.617±0.079±0.084 ± 0.086

TABLE 8. Branching Ratios (%) for B^{−} → D^{∗}(nπ); D^{∗} → D^{0}π
B^{−} Mode/D^{0} mode  # of  B(%)  B average (%)
D^{∗0}π^{−}/K^{−}π^{+}  19±5 0.38±0.10
D^{∗0}π^{−}/K^{−}π^{+}π^{0}  48±9 0.57±0.11 0.501±0.0635±0.0673 ± 0.0388
D^{∗0}π^{−} /K^{−}π^{+}π^{+}π^{−}  26±6 0.51±0.13
D^{∗0}ρ^{−} /K^{−}π^{+}  32±6 1.95±0.28
D^{∗0}ρ^{−}/K^{−}π^{+}π^{0}  43±9 1.44±0.30 1.411±0.186±0.287 ± 0.110
D^{∗0}ρ^{−}/K^{−}π^{+}π^{+}π^{−}  17±5 0.94±0.30
D^{∗0}π^{−}π^{−}π^{+} /K^{−}π^{+}π^{0} 34.7±11.2 0.87±0.30  0.75±0.17±0.15±0.09
D^{∗0}π^{−}π^{−}π^{+} /K^{−}π^{+}π^{+}π^{−} 14.1±9.1 0.67±0.44
B̄^{0} Mode/D^{0} mode # of B(%) B average (%)
D^{∗+}π^{−}/K^{−}π^{+}  19±5 0.22±0.06
D^{∗+}π^{−}/K^{−}π^{+}π^{0}  37±7 0.32±0.06 0.265±0.036±0.035 ± 0.013
D^{∗+}π^{−}/K^{−}π^{+}π^{+}π^{−}  17±4 0.22±0.06
D^{∗+}ρ^{−}/K^{−}π^{+}  15.3±4.0 0.50±0.16
D^{∗+}ρ^{−}/K^{−}π^{+}π^{0}  25.0±5.3 1.00±0.20 0.735±0.106±0.131 ± 0.034
D^{∗+}ρ^{−}/K^{−}π^{+}π^{+}π^{−}  11.6±3.8 0.73±0.20
D^{∗+}π^{−}π^{−}π^{+} /K^{−}π^{+}  6.1±2.7 0.35±0.17
D^{∗+}π^{−}π^{−}π^{+} /K^{−}π^{+}π^{0} 19.1±6.2 0.60±0.22  0.66±0.15±0.09 ± 0.05
D^{∗+}π^{−}π^{−}π^{+}/K^{−}π^{+}π^{+}π^{−} 18.4±5.4 1.36±0.48

TABLE 9. Comparison of experimental ratios of branching ratios

R_{Exp.} (GeV^{2})  R_{T heo.} (26) (GeV^{2})
B̄^{0} → D^{∗+}π^{−}/B̄^{0} → D^{∗+}ℓ^{−}ν̄  1.18 ± 0.16 ± 0.15  1.22 ± 0.17
B̄^{0} → D^{∗+}ρ^{−}/B̄^{0} → D^{∗+}ℓ^{−}ν̄  2.98 ± 0.43 ± 0.18  3.26 ± 0.46
B̄^{0} → D^{∗+}a_{1}^{−}/B̄^{0} → D^{∗+}ℓ^{−}ν̄  4.3 ± 0.23 ± 0.60  3.0 ± 0.50

Using the measured values for the π^{+}, ρ^{+} and a_{1} decay constants, we can make predictions for their partial widths relative to semileptonic widths (R_{Exp.}), as shown in Table 9.

Again, the agreement with the factorization hypothesis is quite good.

Factorization and HQET: Spin Symmetry

If the factorization hypothesis is valid, as it seems to be, then HQET predicts that the rates for B→XW will be the same for the case where X is a pseudoscalar (D) as the case where X is a vector state (D*). In terms of spins:

Γ(<↑↓ + ↑↓ |) = Γ(<↑↓ − ↑↓ |)

Figure 10 shows that this works well for the bottom system, but again works rather poorly for charm. One may wonder here why the ratio of branching ratios for exclusive semileptonics \frac{B→D^{∗}ℓν_{ℓ}}{B→Dℓν_{ℓ}} should be 2-3, while spin symmetry tells us that the ratio for \frac{D^{∗}W}{DW} should be 1.0. In fact, this latter statement is true in the low q^{2} limit where the D^{∗} polarization in the semileptonic decay is constrained by factorization. At high q^{2} values, spin multiplicity factors must be included.

The combination of factorization and spin symmetry has other applications. Since M_{D_{s}} ≈ M_{D_{s}^{∗}}, the \frac{dΓ}{dq^{2}} partial widths are very similar at q^{2} = M_{D_{s}}^{2} and q^{2} = M_{D_{s}^{∗}}^{2}. The D_{s}^{∗} decay constant can then be extracted from a measurement

of the ratio of \frac{B(B→D_{s}^{∗}X)}{B(B→D_{s}X)} once the D_{s} decay constant is known, provided D_{s} production results primarily from direct coupling to the W-boson.

Hadronic decay rates for comparable B^{0} and B^{+} modes

Recall that two-body hadronic final states produced in charged B decays such as Dπ, Dρ, Da_{1}, etc., are accessible through both the internal as well as the external W-emission diagram which can therefore interfere; for neutral B decays, they are accessible through either diagram, but not both.^{9} Figure 11

9For the purposes of this discussion, we will not consider the exchange diagram, which is expected to be heavily suppressed on helicity grounds in B-decay.

FIG. 10. Comparison of ratios of partial widths of two-body B and D modes, testing the spin symmetry hypothesis of HQET.

shows the ratio of B^{+}/B^{0} decay widths compared to D^{+}/D^{0}. Surprisingly, whereas the D^{+} partial widths are smaller than the comparable D^{0} partial widths,^{10} the B^{+} partial widths are generally larger than the corresponding B^{0} partial widths. In terms of the parameters a_{1} and a_{2}, (\frac{a_{2}}{a_{1}} )_{charm} ∼ −0.4, for bottom: (\frac{a_{2}}{a_{1}} )_{bottom} ∼ +0.24.^{11} This estimate is obtained from both the partial widths observed for the charged B modes which can decay to D^{0}W through both internal and external W-emission diagrams, as well as the partial widths for the exclusive a_{2} modes (ψ(′)K(^{∗}), e.g.).

In principle, this constructive interference could have an impact on the relative charged and neutral B lifetimes, however the much larger phase space available in B-decay should mitigate this effect compared to charm. Nevertheless, it is interesting to note that the ratio of charged to neutral lifetimes measured so far is opposite in sign to what one would expect based on this simple interference argument.

10This, of course, follows directly from the dilated lifetime of the charged D relative to the neutral D.

11This conclusion about the relative sign of a_{2} and a_{1} persists even when the production ratio \frac{f_{+}}{f_{0}} is changed from the assumed value of 1.0 to an extreme value of 1.2.

FIG. 11. Comparison of charged vs neutral B and D two-body rates. If a_{2}/a_{1} = 1, we expect all ratios to be equal to one.

Searches for two-body B → D^{∗∗} hadronic modes

If indications from the semileptonic sector that there is a considerable amount of B-decay which proceeds through something other than B → DW or B → D^{∗}W are correct, then B decays to D^{∗∗}’s may be large. Experimentally, we are most sensitive to the narrower (j=3/2) D^{∗∗} states - the 1+ D^{∗∗}(2420) and 2+ D^{∗∗}(2460), for which the total width is inhibited by the p-wave angular momentum barrier. The lower mass (j=1/2) 0+ and 1+ states are expected to be broad, and consequently will be less distinct on top of a large background. However, if B decays to these final states are clean enough, then two-body decays of bottom may provide the best handle on their masses and widths to date. Compiled in Table 10 is a listing of two-body decays involving D^{∗∗}’s which have been searched for recently. So far, we have not observed large signals in any modes.

B Decay Modes with ψ’s

B-decays to ψ’s are important for at least three reasons:

• They allow us to evaluate a_{2}, and therefore the degree of “colorsuppression” present in B-decay,

• Modes such as ψK_{s}^{0} are CP-eigenstate modes, and therefore can be used to measure one angle of the unitarity triangle,

TABLE 10. Branching Ratio’s (%) for B^{−} → D^{∗∗0}(nπ)
Modes  CLEO93 (24)  ARGUS (27)
D^{∗∗0}(2420)π^{−}  (12 ± 5 ± 4 ± 3) × 10^{−4}  (30 ± 8 ± 6) × 10^{−4}
D^{∗∗0}(2460)π^{−}  < 2.7 × 10^{−3}  < 4 × 10^{−3}

(D^{∗∗0} → D^{∗+}π^{−})

D^{∗∗0}(2460)π^{−}  < 1.5 × 10^{−3}

(D^{∗∗0} → D^{+}π^{−})

D^{∗∗0}(2460)π^{−}  < 1.75 × 10^{−3}

(D^{∗∗0} → D^{0}π^{−})

D^{∗∗0}(2420)ρ^{−}  < 1.7 × 10^{−3}
D^{∗∗0}(2460)ρ^{−}  < 5 × 10^{−3}

• A measurement of the inclusive production rates for B → ψ allows the higher energy machines to derive a value for σ_{bb̄} based on the inclusive production rates of ψ and ψ′.

CLEO93 have new results (28) on the inclusive and exclusive rates for ψ and ψ′ production, as shown in Table 11, and presented in Figure 12.

In general, the results are in agreement with previous results (20), but with substantially improved precision. It is interesting to note that, despite the phase space suppression of \frac{W →cs̄}{W →ud̄}, no color suppressed decays involving D mesons (D^{0}π^{0}, e.g.) have yet been observed, with upper limits roughly an order of magnitude lower than the levels at which signals involving ψ’s have been observed. This is at least partly explainable by two things: a) the deeper potential well of the heavy-heavy cc̄ system enhances the probability of forming a bound ψ than a light-heavy D-meson, and b) the large mass of the ψ makes it likely that the inclusive rate will be saturated by a few simple two-body modes in which the s-quark binds with the spectator quark to form a stable hadron.

B-DECAYS OTHER THAN SIMPLE B → D TRANSITIONS

From the preceding discussion, we see that the B-system seems to behave, at least grossly, in accordance with our general expectations based on simple concepts such as factorization. We now consider rarer processes, such as those shown in Figure 13 and their interpretation.

Hadronic b → u transitions

Both CLEO (29) and ARGUS (30), within the last year, have searched for b → uW decays where the W materializes as a D_{s} meson. So far, no definite signals have been observed, probing |V_{ub}/V_{cb}|∼0.10-0.15. In analogy to the observation of a b → u signal in semileptonic decays using leptons past the

FIG. 12. CLEO93 inclusive momentum spectrum of ψ’s produced in B → ψ + X

TABLE 11. Inclusive and exclusive cc̄ production in B-decay

B(B→ψ+X(%))  B(B→ψ′+X(%))
CLEO-II BR  1.09±0.04±0.07  0.30±0.05±0.03
PDG92  1.12±0.16  0.46±0.20

Exclusive B-decay modes involving cc̄

B Mode  # of events  B(%)
B^{−} → ψK^{−}  43.4 ± 6.7  0.114 ± 0.018 ± 0.010
B^{0} → ψK^{0}  8 ± 2.8  0.084 ± 0.030 ± 0.009
B^{0} → ψK^{∗0}  22.9 ± 4.8  0.156 ± 0.034 ± 0.017
B^{−} → ψK^{∗−}(K^{−}π^{0})  5.9 ± 2.4  0.215 ± 0.104 ± 0.025
B^{−} → ψK^{∗−}(K^{∗−} → K_{s}π^{−})  5.0 ± 2.2  0.135 ± 0.060 ± 0.019
B^{−} → ψK^{∗−} (all)  10.9 ± 3.3  0.169 ± 0.056 ± 0.022
B^{−} → ψ′K^{−}  6.1 ± 2.4  0.061 ± 0.027 ± 0.016
B^{0} → ψ′K^{0}  0  < 0.09
B^{0} → ψ′K^{∗0}  4.6 ± 2.1  0.120 ± 0.060 ± 0.031
B^{−} → ψ′K^{∗−}(K^{−}π^{0})  1 ± 1  < 0.783
B^{−} → ψ′K^{∗−}(K_{s}π^{−})  1 ± 1  < 0.437
B^{−} → ψ′K^{∗−} (all)  2 ± 1.4  0.144 ± 0.102 ± 0.039 < 0.38

FIG. 13. B-decay diagrams producing Kπ and ππ final states. The left diagram is the standard spectator diagram, the right diagram is the hadronic penguin diagram.

FIG. 14. Box diagram for B-decay.

kinematic endpoint for b → c, searches are also ongoing for production of noncharmed mesons (ρ^{0}, ω, e.g.) beyond the charm kinematic endpoint. Such searches, however, require a very good knowledge of the production of these mesons in D decays.

BB̄ Mixing

The smallness of |V_{cb}| indicates that higher order processes may be competitive with tree-level processes. BB̄ mixing proceeds through the so-called box-diagram, which can also produce rare final states such as ℓ^{+}ℓ^{−} (Figure 14). Through this diagram, a B^{0} can oscillate to a B̄^{0}. At threshold, we produce only non-strange B-mesons, and therefore measure only B_{d}B̄_{d} mixing. The amount of B_{d}B̄_{d} mixing is generally specified by the so-called “mixing parameter” χ_{d}, given as: χ = \frac{Γ(B^{0}→\overline{B}^{0})}{Γ(B^{0}→B^{0})+Γ(B^{0}→\overline{B}^{0})} (≤0.5). The parameter χ is related to the mass difference δm between the weak B_{d} eigenstates (B_{1} − B_{2}) and their mean width Γ by: χ = (0.5)\frac{\frac{δm}{Γ}}{1+ \frac{δm}{Γ}} .

The mass difference δm can also be related to the parameters of the CKM matrix, the top quark mass m_{t}, (calculable) corrections F and η, the B decay constant f_{B}(∼ 150 MeV), and the ‘Bag’ parameter B (of order unity, and defined as: < B^{0}|b̄γ_{μ}(1 − γ_{5})d|\overline{B}^{0} >) by:

δm = \frac{G_{F}^{2}}{6π^{2}} f_{B}^{2}B_{B}m_{b}m_{t}^{2}F (\frac{m_{t}^{2}}{m_{W}^{2}} )η_{QCD}|V_{tb}^{∗}V_{td}|^{2}.

With some value for f_{B}^{2}B_{B}, precision measurements of mixing can therefore be translated into a contour in the |V_{td}| − m_{t} plane.

FIG. 15. ARGUS93 partially reconstructed B → D^{∗+}ℓν signal for events containing two leptons, with (left) and without (right) a requirement on the lepton sign correlation (see text).

At higher energy machines, where the decay vertices of b-flavored hadrons can be measured, δm can be determined directly by measuring the time dependence of oscillations:

P (B^{0}→\overline{B}^{0}) ∼ e^{−t/τ} (1 − cos[(δm)t])

At threshold, where the B’s are produced at rest, we cannot see the decay vertices, and can only infer δm through a measurement of χ_{d}. This is done by determining the number of events with same-sign primary lepton pairs, presumably due to direct semileptonic B-decays and B̄ oscillations into B’s, which also decay semileptonically, compared with the number of events with opposite-sign primary lepton pairs. ARGUS (18) and CLEO (31) measure mixing in both the ‘untagged’ mode, i.e., simply counting lepton pairs, and the ‘tagged’ mode, where one of the leptons must be consistent with being produced in the decay: B → D^{∗}lℓν_{l}. Tagging (as before) has the advantage of substantially reducing the errors due to uncertainties in \frac{f_{+}}{f_{0}} . The results are given in Table 12. Figure 15 shows the ARGUS partially reconstructed B → D^{∗+}ℓν signal for events containing two leptons. The top plot requires no lepton sign correlation, the bottom plot requires that the two leptons be of the same sign, and is used to derive the “tagged” value of χ_{d}. The weighted average for χ_{d} from the CLEO and ARGUS tagged samples is 0.152 ± 0.022 ± 0.020.

CLEO93 have also used their dilepton sample to look for CP-violation, as evidenced by an asymmetry in positive compared to negative same-sign

TABLE 12. Recent measurements of BB̄ mixing, in both the tagged and untagged modes, from ARGUS and CLEO

Group  technique  χ_{d}
ARGUS (18)  notag  0.165±0.036±0.047
CLEO (31)  notag  0.157±0.016±0.033
ARGUS (18)  tag  0.188±0.078±0.022
CLEO (31)  tag  0.149±0.023±0.021

dilepton pairs. They obtain a limit: ϵ_{B^{0}} <0.045 (90% c.l.), which is still an order of magnitude above the Standard Model expectation.

Hadronic penguins and Cabibbo suppressed two-body B-decays

CLEO93 have conducted a search (32) for the two-body decays: B^{0} → π^{+}π^{−} and B^{0} → K^{+}π^{−}. These have the distinctive topological feature of two back-to-back tracks embedded in an otherwise spherical hadronic event. Both of these processes can arise from either (or both of) spectator diagrams or hadronic penguin diagrams. The possibility of interference between these two diagrams opens the opportunity for observation of CP-violation (15), albeit without the same possibility for measuring the CKM-phase which is afforded by a measurement of ψK_{S}^{0}.

Owing to the experimental difficulties in separating Kπ from ππ, CLEO are unable to claim evidence of a positive signal in either channel individually. However if their events are interpretted as either Kπ or ππ, there is a signal at the 4.1σ level. Figure 16 shows the contour plots of π^{+}π^{−} event count vs. K^{+}π^{−} event count; the separation between the present event sample (the cross in the Figure) from the origin is evident. CLEO93 presently quote values of (1.3_{−0.6}^{+0.8}±0.2)×10^{−5} and (1.1_{−0.6}^{+0.7}±0.2)×10^{−5} as the most probable branching ratios for B→π^{+}π^{−} and B→K^{+}π^{−}, respectively. These correspond to 90% confidence level upper limits of < 2.9 × 10^{−5} and < 2.6 × 10^{−5}, respectively, on these branching ratios. In addition, they set a 90% confidence level upper limit of 0.7 × 10^{−5} on the branching ratio for B→K^{−}K^{+}.

The ARGUS collaboration (18) have performed a “semi-inclusive” search for hadronic penguin candidates, by considering final states: B → K(nπ^{±}). Such final states can include contributions from hadronic penguins, as well as cases where the B has decayed via an ordinary b → c transition to a D meson, which subsequently decays to a kaon plus charged pions. They observe a peak at the B-mass, and find one event in their sample which they claim is inconsistent with arising from either an ordinary B → D transition or continuum processes.

FIG. 16. B→π^{+}π^{−} vs. B→K^{+}π^{−} event count, as determined by the CLEO collaboration, and submitted to this conference.

TABLE 13. CLEO93 upper limits for two-body B decays to ϕ+X

Mode  1993 CLEO 90% CL U.L. on BR (Chau/Deshpande/BSW)
B(B^{+} → K^{+}ϕ)  2.1 × 10^{−5}  1.4 − 1.5 × 10^{−5}
B(B^{+} → K^{∗+}(K^{+}π^{0})ϕ)  1.2 × 10^{−4}  0.8 − 3.1 × 10^{−5}
B(B^{+} → K^{∗+}(K_{s}^{0}π^{+})ϕ)  2.5 × 10^{−4}  0.8 − 3.1 × 10^{−5}
B(B^{0} → K^{0}ϕ)  1.2 × 10^{−4}  0.9 − 1.2 × 10^{−5}
B(B^{0} → K^{∗0}(K^{+}π^{−})ϕ)  6.0 × 10^{−5}  0.9 − 3.1 × 10^{−5}
B(B^{0} → K^{∗0}(K_{s}^{0}π^{0})ϕ)  4.9 × 10^{−4}  0.9 − 3.1 × 10^{−5}
B(B^{0} → ϕϕ)  4.1 × 10^{−5}

Exclusive Hadronic Penguin B-Decay Modes

Modes such as ϕK contain three strange quarks in the final state, and are inaccessible through simple W-emission B-decay diagrams. Observation of such decays therefore allows a more definitive statement about the presence of hadronic penguin diagrams in B-decay than Kπ or ππ. CLEO93 have searched for such decays (33), and have calculated upper limits which represent a factor of 5 improvement over previous searches for these processes; their results are given in Table 13. These new limits are compared with the predictions of Chau et al. (34), Desphande et al. (35), and Bauer, Stech and Wirbel (36).

The upper limit for the ϕK^{+} mode, in particular, is beginning to approach the levels expected by theory.

FIG. 17. Penguin diagram for B → K^{∗}γ.

FIG. 18. CLEO93 signal for B → K^{∗}γ. The solid black are K^{∗0}γ(K^{∗0} → K^{−}π^{+}) events, white represents K^{∗−}γ(K^{∗−} → K^{−}π^{0}), and gray represents K^{∗−}γ(K^{∗−} → K_{s}^{0}π^{−}).

Radiative penguins, B → K^{∗}γ

Perhaps the most spectacular B-physics result to emerge this year has been the observation of the candidate radiative penguin decay mode: B → K^{∗}γ. CLEO93 observes this decay (37) in three final states: B → K^{∗0}γ; K^{∗0} → K^{−}π^{+}, B → K^{∗+}γ; K^{∗0} → K^{+}π^{0}, and B → K^{∗+}γ; K^{∗+} → K_{s}^{0}π^{+}. The diagram is shown in Figure 17. Inspection of the diagram and consideration of the quarks in the virtual loop leads one believe that the B-system is a more likely place to find radiative penguins than the charm system. The mass peak showing the three channels individually is displayed in Figure 18.

As further evidence that what is being observed is neither a continuum effect nor the result of some background from BB̄ decays, extensive Monte Carlo work was done, including a multidimensional likelihood analysis which used information other than m_{B}, such as event shape and energy flow. From this likelihood analysis, it was demonstrated that the observed events were inconsistent with arising from the continuum at the 99% confidence level. The observed events correspond to a branching ratio: B(B → K^{∗}γ) = (4.5 ± 1.5 ± 0.9) × 10^{−5}.

A search for inclusive penguin decays was also conducted which involved counting photons (after continuum subtraction) in the momentum interval (2.2 - 2.7 GeV/c). These are candidates for the quark level process b → sγ. From this search, and using an Altarelli-type model to give the expected spectrum of final state strange meson masses, an upper limit on the inclusive branching ratio B(b → sγ) < 5.4 × 10^{−4} was obtained. This is the most stringent limit to date (20).

Implications of the radiative penguin search

The upper limit on the inclusive radiative penguin rate can be used to probe physics beyond the Standard Model within the context of the Minimal Supersymmetric Standard Model (38). In particular, we can replace the Standard Model W in the radiative penguin diagram with a charged Higgs or a SUSY particle which could enhance the total rate for this process. Given the CLEO93 limit on b → sγ, inclusive, a restriction can then be placed on a charged Higgs mass for a specified value of tanβ (defined as the ratio of VeV’s of the up-Higgs to the down-Higgs fields). Of particular import is that, in this picture, the charged Higgs is probably too heavy for the process t → bH^{+} to occur, which means that the pp̄ collider searches for t → bW^{+} will not have to worry about possible cases where an H^{+} might replace the W^{+}. However, the inclusion of SUSY propagators can introduce destructive interference with other diagrams. This would reduce the sensitivity to m_{H^{+}}, and therefore make the limits on Higgs mass considerably weaker.

THRESHOLD MEASUREMENTS AND THE CKM MATRIX

The CKM matrix element V_{cb}

The magnitude of the coupling between charm and bottom quarks can be extracted in a number of ways with the present CLEO and ARGUS data. It can be extracted: a) exclusively, using the B→D^{∗}ℓν_{ℓ} spectrum at q_{max}^{2},

b) exclusively, using the B→D^{∗}ℓν_{ℓ} total width, integrated over all q^{2}, or c) inclusively (using the inclusive b → cℓν spectrum). Typically, a partial width is calculated, which is related to the B-lifetime and |V_{cb}|. For our purposes, we take the present B-lifetime to be the new average (1.49 psec (3)); the three methods above give values of |V_{cb}| in the range 0.035 - 0.047. All three of these techniques have their own particular systematics - the first technique requires some estimate of what constitutes a “reasonable” range of parameterizations for the Isgur - Wise function; the second and third rely on what fraction of the total semileptonic rate proceeds through D^{∗}ℓν, and the third has a very strong dependence on what value of the bare b-quark mass is assumed. What dominates the errors at this point are mostly modeling uncertainties, and not statistics.

Experimentally, it is hoped that some of these uncertainties will be reduced by an a more complete analysis of the B → D^{∗}ℓν Dalitz plot presently underway at CLEO (39,40). This analysis will be essential in providing a more complete description of the corresponding semileptonic decay as well, much as the analyses of the D→K^{∗}ℓν_{ℓ} Dalitz plot provided a more detailed description of charm semileptonic decay. However, determining the exact composition of the bottom semileptonic width which may be something other than Dℓν and D^{∗}ℓν may take some time, especially if these decays are some mixture of non-resonant D(^{∗})π, Λ_{c}p̄, Dτν, etc.

The CKM matrix element V_{ub}

The only confirmed measurement of |V_{ub}| comes from leptons at the maximum allowed momentum for b → u transitions, which gives a modeldependent estimate of |V_{ub}/V_{cb}| in the range 0.06-0.14, depending on which models are included. More work is needed to understand the q^{2} extrapolation from the restricted momentum interval in which we observe the signal across the entire q^{2} range.

In the near term, it is hoped that CLEO will soon be presenting results for exclusive decays based on a lepton momentum byte larger than that probed in the momentum endpoint analysis. The first results based on determination of the neutrino four-vector from hermiticity indicate that we may have more to gain here. It is also possible that we might infer information about this decay by using data on the heavy quark -to- light quark transitions D→Klν and D→πlν, and then imposing heavy quark symmetries.

Top couplings

Processes beyond tree level (box- and penguin- diagrams) are sensitive to the CKM matrix elements |V_{ts}| and |V_{td}|. The experimental constraints from these processes are, however, not yet better than the limits which can be derived from the CKM-matrix unitarity condition (V_{ud}V_{ub}^{∗}+V_{cd}V_{cb}^{∗}+V_{td}V_{tb}^{∗}=0, e.g.). From our measurements of mixing, and taking: m_{t} = 155±45 GeV, and \sqrt{f_{B}^{2}B}=215±40 MeV, we can derive an estimate of |V_{td}| ∼0.005-0.011, straddling the value we might have expected based on the Cabibbo angle (λ^{3} ∼0.008).

Having observed B → K^{∗}γ (dependent on |V_{ts}|), and determined its fraction of the total b → sγ width to be ≥5%, the most obvious task is determination of the remainder of the radiative b-decay width, and to (hopefully) turn the upper limit on the inclusive rate into a measurement. The rate for B → ργ (dependent on |V_{td}|), although expected to be only one order of magnitude smaller than B → K^{∗}γ, is made difficult by the large ρ width and the inherent particle identification systematics.

With an increased data set, and improved momentum resolution and particle identification, it is quite possible that the hadronic penguin candidates B → Kπ will be separated from B → ππ within the year, and reported in the next proceedings of this conference as signals rather than upper limits. Experimentally, the decay B → π^{0}π^{0} has no ambiguity with kaon modes. The decay B → K^{0}K^{0} has no ambiguity with pion modes. We look forward to new results on these decays in the near future as well.

Status of the CKM phase

The combination of the threshold BB̄ mixing measurements, the measurement of \frac{|V_{ub}|}{|V_{cb}|}, and measurements of CP-violation in the strange system, can constrain the allowed values of the CKM-phase. Since this is included in other write-ups for this conference (15,41,42), I will refer the interested reader to those contributions to these proceedings.

FUTURE IMPROVEMENTS IN THE SYSTEMATICS OF THRESHOLD MEASUREMENTS

The two assumptions that f_{+}/f_{0} = 1, and that f_{+} +f_{0}=1 will soon become the limiting systematics in many B-measurements at threshold. We have seen that, using a combination of tagged and untagged measurements, we can begin to narrow the allowed range for f_{+}/f_{0}. With enough double-tags, CLEO should be able to directly measure f_{+}/f_{0}. A tagged sample will also allow direct separation of B→Dℓν_{ℓ} from B→D^{∗}ℓν_{ℓ} by calculation of the initial B̄- meson four-vector using the values measured for the B. Such an event set will also allow us to probe two-body decays by the presence of a monochromatic line in the momentum spectrum of D^{0}’s, or inclusive tracks, after boosting back into the rest frame opposite the tag.

CONCLUSIONS

The program of B-physics at threshold has proved to be extremely successful in its ability to probe the fundamental parameters of the CKM matrix. The heaviness of the b-quark compared to the c-quark helps make interpretation of our data for the dominant decays in the bottom sector much less uncertain due to effects such as final state interactions, pole effects, etc. It also encourages us that interpretation of the rare decays which we are beginning to observe will also be straightforward and give us reliable estimates of top couplings, or perhaps beyond-the-standard-model couplings.

ACKNOWLEDGMENTS

I would like to give a heartfelt thanks to all of my colleagues at ARGUS and CLEO (particularly the graduate students) who did the real work that went into this talk and keep the experiments running. CPO will hopefully understand that the Z-95 Krokus hat, the envy of headbangers everywhere, in retrospect, would probably have been inappropriate for my presentation. Robert, from TRIUMF, by way of NYC, whose last name I can’t remember, I also thank for reminding me what the difference between a TeV and a VeV is.

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