Possible use of inclusive spectroscopy in B decays

Nuclear Physics B (Proc. Suppl.) 13 (1990) 491-493 North-Holland

491

POSSIBLE USE OF INCLUSIVE SPECTROSCOPY IN B DECAYS Harry J. LIPKIN Department of Nuclear Physics, Weizmann Institute of Science, Rehovot 76100, Israel, and School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel, and High Energy Physics/Physics Divisions, Argonne National Laboratory, Argonne, IL 60439 Inclusive K s spectroscopy is suggested for detecting and using quasi-two-body decay modes of the form B ° ~ X K s , where X denotes a narrow state like a charmonium or charmed meson state not easily detected directly because of low branching ratios to observable final states. The particular state of most interest in discussions of C P tests is B ° --* J / ¢ K s , but others like B ° ~ ¢ ' K s ~ ¢~r~rKs, B ° --* ¢ " K s --* D D K s , B ° --* ~ I f s and B ° --* D ° K s might be of interest. Decays to the U P eigenstates B ° -+ (c~.)Ks, where the charmonium state may be any radial excitation of the J/d2 or rk are of particular interest for tests of C P violation. However, the efflciencies for the detection of these states are small because of the small branching ratio of the charmonium states to completely observable final states. It is therefore suggested that better statistics might be obtained by examining the inclusive K s spectrum. Since the decay B ° ~ J / ¢ I f s is quasi-two-body, the momentum of the K s is uniquely defined in the rest frame of the decaying B and rough estimates indicate that if it is produced in the decay of a slowly moving B from T(4S) decay, the smearing of the momentum may not be excessive. Therefore the decay B ° ~ J / ¢ K s . might be observable as a signal in the inclusive I f s spectrum. The crucial point which determines the feasibility of this method is the signal to noise ratio. Using the inclusive spectrum clearly increases both signal and noise. The signal is improved because it includes all events with the desired final state recoiling against the kaon, with no loss due to branching ratio of the detectable signature, detection efficiencies, etc. The noise level is increased because of the presence of other decay modes which can produce a K s in this momentum range, and because of the smearing of the momentum due to the initial mo-

0920-5632/90/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

mentum of the decaying B °. The question is whether the increase in noise can be controlled sufficiently by judicious cuts to eliminate background so that the overall effect is an improvement in signal to noise. Consider an experiment which tests C P violation by measuring the asymmetry in the decay of a B ° -/}o pair where one decays into J / d / K s and the other into a mode with either a positive or a negative lepton. Let N 4denote the numbers of events in a particular experiment in which this decay occurs with a positive or a negative lepton respectively. We compare two possible ways to determine the asymmetry parameter ~ which measures the extent of C P violation. The conventional method uses only events with a fully determined J/C/decay. Let B R denote the branching ratio to the observed final state mid .7 the detection efficiency for this state. The difference denoted by D~c between the number of exclusive events observed with positive and negative leptons is then given by D ~ c = 2rl. B R . ~ + ¢ 2 7 " B R . N

(1.)

= 27i • B R . ~[1 4- ~ / N / ( 2 t I • B R . ~)]

The fractional statistical error is therefore 6D,,~ = %/N1(2~. B R . ~)]

(lb)

However one can also look at the inclusive K s spectrum in the momentum bin which contains all the

402

tLJ. Lipkin / lndusive spectroscopy in B decays

B ° ~ J / ~ 2 K s decays and determine the difference be-

tween the number of events observed with positive and negative leptons. Here the efficiency is !00% for detecting these decays, but there is also a background denoted by B so that the number of events observed in the inclusive spectrum bin with positive and negative leptons is now N + B 4- ~. For this case Dine -- 2~ 4- ¢ 2 ( N + B) -- 2~[1 4- ¢ ( N -I- B)/2~] (2a) and the fractional statistical error is ~D,,o = X/(N + S)/2~l

(2b)

Which method gives a better result depends upon the ratio ~Di,~c x/t1. B R ~D~ - ~/N/(N + B)

(3)

The question is therefore which is greater, the detection efficiency x branching ratio ~/. B R in the conventional exclusive method or the signal to background ratio ~ N

in the inclusive method. In the case where

Yl" B R ~. 1/10, a l ~ o n a b | e voiue for the detection of

the J'/@ via the ]eptonic decay mode, the inclusive technique will be competitive even if the background is ten times bigger than the signal. Combining the exclusive and inclusive data can give improved statistics as well as a consistency check. All possible cuts for reducing background should be investigated, with particular attention paid to the :~earch for better cuts possible in future experiments with improved technologies. One example is time information obtainable with vertex detectors having a high resolution. In experiments where the T(4S) is produced in flight by e+ - e- awnihilation with unequal energies, it is in principle possible to resolve the vertices for the decays of the two mesons and also the secondary vertices for the decays of any charmed particles produced in the primary B decay. Since charmonium decays are either strong or electromagnetic, all B decays of the form B ° ~ (c~)?(s m ghere (c~) denotes a bound charmonium state below ~he naked charm threshold are prompt and all observed hadrons are emitted from a single vertex. Decays

to a bound charmonium state above the naked charm threshold will have two additional vertices corresponding to the decays of the two secondary charmed particles. Thus in principle the B decays can be separated into three groups depending upon the number of charmed particles in the final state. Decays with no charmed particles in the final state include mainly decays into charmonhJm, and a small number of charmless B decays which probably will not produce kaons. Decays with a single diarmed particle in the final state are the main source of background for the detection of Ks-charmonium final states via the inclusive spectrum. If these can be separated out by the presence of the secondary vertex, the background will be reduced considerably. Decays with two charmed particles in the final state will include events where charmonium is produced above the DD threshold and will be interesting in their own right. The inclusive spectrum technique can also be applied to other decays with narrow states recoiling against the kann; e.g. B ° -* ~b'Ks, B ° ~ ~b"Ks, B ° ~ Tklfs and B ° ~ D ° K s . The B ° - , ~b'Ks signal might be sharpened by observing the two charged pions emitted in the decay ~b' - , J/¢Tr+Ir - which has a branching ratio of 33% and placing the appropriate constraints on the missing mass of the unobserved J / ¢ . For the case of the B ° - , ~l~Ks, where direct detection of the ~ is difficult, this method might be the best way to either detect this mode or to put a reliable upper limit on the branching ratio. All these final states with charmonium have the same eigenvalue of C P . Although the ~ has the opposite eigenvalue of CP from the ~b sta~es, the decay B ° ~ ~l~Ks is s wave, while the decays to ~b states are p-wave, and this opposite parity gives the same C P eigenvalue for all these final states. Thus the events for all these decays can be combined to improve statistics in an experiment which tests C P by observing asymmetries in the decays of a B ° - [~° pair where one decays into a C P eigenstate. The B ° ~ D ° K s may be more easily detected in this way than directly because of th:~ higher energy of the K s and the consequently lower background in the inclusive spectrum. If this decay mode turns out to be

H.J. Lipkin / Iadusive spectroscopy in B decays

493

appreciable, it may offer interesting possibilities since

The Particle Data Group tables give inclusive branching

it is also a mixed state. It could he used in exclusive spectroscopy w :i t1. , events selected for D ° decays into U P eigenstates. The decays

for D4- ~ K s X and Do ~ K s X and 47 4-9% and 66 48% respectively when charged kaons are included as well

B ~ g/"K ~ D D K

ratios for D -~ K X as 244-8% and 16+5% respectively

as K s but KL decays are not detected. This gives a good probability for observing a D D K s event as K K K s X . One can look at the k~on momentum spectrum in events

have not yet been observed but may have a significai, t

containing two or three kaons and see ff there is a signal

branching ratio, since the particle data book gives

at the appropriate momentum corresponding to ~b"Ks

B + ~ g/(2S)K + = .22 4- .17 x 10 -2 =~

decay. One can also examine inclusive J/g~ spectroscopy

B ° --~ ~b(2S)K ° = .11 4-.08 x 10 -2

where the J/4/is completely determined and look at the momentum range for the J/~b relevant to the J/~PKs

However, the branching ratios for detecting D's would

decay. Here one loses the product of detection efficiency

make the direct observation of this mode with fully reconstructed events extremely difficult. The question is

x branching ratio ~/. B R for the J/~b over the case of

whether the ~b"Ks --~ D D I f s decay mede can be de-

inclusive Ks spectroscopy, but gains both the efficiency of K s detection and a factor of four because these event~

tected without fully reconstructing the event because

include both the KL events and the K ± events from de-

of the unique momentum of the kaon emitted from the

cays of B + produced equally with B ° in T(4S) decays.

decay of a B at rest, which will hopefully not be too

This gives good statistics for the determination of the

smeared by the initial B momentum, and because of the large branching ratio for the D's into strange particles.

branching ratio but the determination of C P asymmetries becomes more complicated.