K-M matrix elements and Decays of the B meson to J/Psi
Richard Wilson
Harvard University
Cambridge, MA 02138
Work of the CLEO collaboration
Abstract. This talk discusses some of the last work on B meson decays of the CLEO collaboration, which work is, in fact, improvements in precision of much earlier work of the same collaboration. New theoretical developments have enabled us to present much improved numbers on the matrix elements Vcb, and Vub. Also some recent work on the decay of B mesons to J/Psi plus other particles will be briefly presented.
INTRODUCTION
This talk was first prepared for a conference in Tashkent in September 2001. But the terrorist act on September 11th made me cancel the trip. My heart goes out to the 3000 victims of that attack as it does to the million or so starving Afghans.
I first became interested in the idea of colliding electron beams in 1956 when we informally proposed to study build an electron-electron ring at Harvard, (which proposal was delayed till our accelerator was completed when it became moot) and we proposed colliding electron-positron beams in 1959. Alas, our proposal was rejected in favor of another, and I was lucky somewhat later to be invited to participate in the Cornell Electron Storage Ring (CESR) starting in 1977 (figure1).
figure1. The CESR storage ring layout figure 2. The CLEO Mark II detector
Interestingly the linear accelerator injector was the one we had ordered for the Cambridge Electron Accelerator in 1961 and which had been declared government surplus in 1972. Romantically the name Caesar has often been accompanied by the name Cleopatra so the detector that I helped to build was called CLEO. (Figure 2) The important features for this experiment are: good particle momentum measurement, and absence of spurious high energy particles, good particle discrimination for electrons (by a CsI detector) and muons (by range), and gamma ray measurement (with the CsI crystals) with good resolution. All with high angular coverage and high efficiency. CLEO began operation in the fall of 1979 and in February 1980 we had our first new result - the production of the predicted upsilon resonance (4S). (Figure 3)
Figure 3. Mass spectrum of upsilon resources.
I had the honor and pleasure of being the first to describe this result, together with my other work (on muon scattering), on a visit to Beijing, China, in March of the same year (1980). The (4S) was just above the threshold for decay into particles and although the width of the upsilon (1S), (2S) and (3S) resonances was equal to the CESR resolution, the width of the (4S) is greater than the resolution indicating that it decays rapidly (into B particles). Historically it is interesting that the first extraction of the (4S) resonance used the Fox-Wolfram R2 shape variable to suppress continuum background. We still use this parameter for this purpose but combine it with several others, using a neutral net, to get a single parameter to reduce the continuum background. Since 1960 the study of these B particles has been the primary task of CESR and CLEO. This task was aided by the fact that over 20 years the skilled physicists at CESR produced the highest luminosity of any colliding beam facility in spite of the beams being injected from a synchrotron which (in the 1960s) many doubters had thought was too difficult. However, the colliding beams at Stanford and KEK have overtaken CESR, and have an asymmetric collision arrangement enabling identification of the B decay vertex. As a result the CLEO collaboration has officially stopped running electron-positron colliding beams at the energy of the (4S). I will present the latest, and almost the last, of these results in what is the latest, and perhaps my last, of my own talks on high energy physics.
Right from the start of CESR and CLEO operation a major focus has been the study of the elements of the Cabibbo-Kobayashi-Miskawa (C-K-M) matrix (figure 4) and its convenient approximation describing the couplings between the various quarks.
Figure 4. C-K-M matrix
Of these couplings Vud is known from decay of nucleons and nuclei, particularly of I = 0 to I = 0 nuclear transitions, and Vus is known from strange particle decays. Vcb , and Vub were, until recently when BABAR and BELLE got going, accessible only to CLEO and PETRA. I will also present some more recent results on the process b s which proceeds by a penguin diagram, and gave us some early information about the top quark. Finally I will conclude with a set of results over the last 2 years from my latest and perhaps the last, of my graduate students in this field. Alexei Ershov, from Serpukhov in Russia, and Daniel Kim, an American of Korean ancestry. Ours was truly a fine international collaboration.
The easiest way to measure Vcb is obviously to study the decays of B mesons into leptons. Indeed a study of the inclusive electron and muon spectra was first performed in 1980 (and presented in the High Energy Physics conference of that year at Madison, WI, USA by my former student Professor Edward Thorndike) by looking at the inclusive lepton spectrum assumed to derive mostly from decay into charmed particles (B Xc l ) where Xc represents any group of particles containing a charmed particle, either a meson or an electron. We first measured the branching ratio into leptons, and assuming that charged and neutral leptons were produced approximately equally found the decay width . The measurements were compared to a theory which assumed that the quarks in the decaying B meson were free (a spectator model). The decay with for this channel is given by: = (Gf2|Vcb|2MB5/1923)0.3689. This first result had an accuracy of about 25%. Although the theoretical derivation had an error of 25% or so, the experimental error at the time was also large. Now I present the latest result for Vcb which we believe to be accurate to 2 ½%. The improvements come from experimental improvements and form using the Heavy Quark Effective Theory (HQET). This leads to a double expansion of (1/MB) and s and terms in (1/MB), s , (1/MB)2 and s2 , and the first term in this expansion is the “simple” equation above. MB is known to be 5.313 Gev and s is also known. 2 and 1 to 4 are set to (0 0.05 Gev), 1 to [(0.5 Gev)3 (0.5 Gev)3] and 2 to 0.128 0.01 but we need to measure the coefficients 1 and .
The study of Vub came (and still comes) from examining the electrons beyond the kinematical end point of the spectrum from decay into charmed mesons. This was first seen reliably by CLEO about 1978. Again the improvement comes from looking at higher terms in the expansion in (1/Mb).
The measurement of b s + .
The improved measurement comes primarily from understanding the corrections and measurement of 1 and but also a larger sample of B decays. We start by a look at the kinematically simpler reaction b s + where similar HQET corrections appear and use these to measure 1 and (Chen et al. 2001). Since the B mesons are produced almost at rest we expect a “peak” in the ray spectrum at about half the
B mass, spread by the momentum distribution of the b quarks.
Figure 5. Photon energy spectra (weights per Figure 6. Fully subtracted.
100 MeV)The upper plot (a) shows the on measurement of rays
Y (4S)and scaled off- resonance spectra. in B production
The lower plot (b) show their difference and
the spectrum estimated for all other B decay
processes.
In the CLEO detector which shown in figure 2 the gamma rays are detected by a set of Cesium iodide (CsI) crystals in a barrel shaped arrangement. The resolution in energy is good. Most of the gamma rays came from the reaction e+ + e- to a continuum rather than the reaction e+ + e- to (4S) with subsequent decay of the B particles. Since, the continuum also produces rays, the experiment relies on the detail of excluding these rays. The continuum was reduced by using an array of “shape cuts”. decay of These cuts rely upon the fact the continuum is isotropic, whereas the B particles from the the (4S) are back to back. Several cuts were used and combined into a single variable using a neural net. The (reduced) background was determined and subtracted by runs at an energy just below the (4S) resonance. The full spectrum and the continuance background after application of all cuts are shown in figure 5. We also exclude rays that could come from other known decays of the B such as from 0 and 0 mesons. These are shown in figure 5. The fully subtracted spectrum of gamma rays is shown in figure 6.
The spectator model (Ali and Greub 1991) suggests that we should find a spectrum of gamma rays near 2.4 Gev and we examine carefully include all gamma rays between 2.0 and 2.8 Gev. We indeed find a peak just below 2.4 Gev. The detail of the spectrum, and the calibration of our detector, are sufficient that, after correction for the excellent resolution, we can measure (for the first time) the first and second moments of the gamma ray spectrum:
<E>= 2.346 0.034 GeV
<E2> - <E>2 = 0.0226 0.0069 GeV2
The Heavy Quark Equivalent Theory (HQET), assuming parton-hadron duality, (Bauer, 1998; Ligeti et al., 1999; Falk and Ligeti, 2001) gives the following results for the first moment.
The expression for the second moment converges sufficiently slowly in (1/MB)3 that we do not try to extract parameters from it. Since most of the numbers are known, this gives the OPE parameter:
bar = (0.35 0.08 0.10) GeV
An interesting result aside from the measurement of Vcb, is the measurement of Br (b s + ) also gives us a new value for the branching ratio:
Br (b s + )= (3.21 0.43 0.27+0.18-0.10) x 10-4
or (3.21 0.53) x 10-4
This may be compared to the theoretical result using the “standard model” for which we have
two alternates
Br (b s + )= (3.28 0.33) x 10-4 and (3.73 0.30) x 10-4
depending upon which quark mass is used.
This result confirms the previous result that we find no room for “new physics” beyond the standard model but, of course, unless we know exactly what “new physics” we are looking for we cannot place a precise limit.
The next step in the argument comes from a careful reexamination of the lepton spectrum in
B Xc l (Cronin-Hennesy et al. (2001). The use of the shape variables to reduce continuum background and the subtraction using data at an energy just below the (4S) resonance is similar to the use in the study for b s + . From this we can determine the moments of the hadronic mass (MX)2 of Xc. This is aided by our extensive knowledge of some specific components BD l and BD* l decays which are a large component thereof. The resultant spectrum of MX2 is shown in the figure 7.
Figure 7. BXℓv spectrum shows contributions from different
processes.
The moments become.
<MX2 - MD2 = 0.251 0.023 0.062 GeV2.
<(MX2 - MD*2 )2 = 0.639 0.056 0.178 GeV2
<(MX2 - <Mx2 >)2 = 0.576 0.048 0.163 GeV2
The errors on these moments are dominated by systematic errors and we cannot hope for rapid improvements using better statistics. Following advice from theorists we only use the first moment in what follows.
Using HQET, the first moment can then be expressed in terms of several parameters of which and 1 were the important unknowns:
Since we have already derived we can insert the derived value into the formula and derive
1 = - 0.236 0.071 0.078 Gev2
Then we use:
(a)the measured branching ratio
Br (B Xc l )* = 10.39 0.46%, from CLEO.
(b) the lifetimes for charged and neutral B mesons
1.58 0.032 ps and 1.653 0.028 ps respectively
(c)and the ratio of the charged and neutral production in (4S) decays:
f charged / f neutral = 1.04 0.08
to derive the semileptonic decay width:
sl = (0.427 0.020) x 10-10 Mev
Combining this with the theoretical value:
we find at last:
|Vcb| = (4.04 0.09 0.05 0.08) x 10-2
where the errors are (in order) from measuring sl ,from measurement of and 1, and from scale uncertainty in
The new measurement of Vub
(Bornheim et al. 2002)
The measurement of |Vub| has consisted in looking for leptons of momentum above the cutoff for leptons coming from charm decays - between 2.2 and 2.6 GeV. The number of leptons in this region is quite small and there are two major experimental problems. We have to be sure that the tails of the resolution function of the detector are adequately understood, and that these are not a spill over from the decays due to charm. And we have to be sure that they are not one of the many hadrons masquerading as leptons. It was not until 1988 that we were sure of this excess above 2.3 Gev. Since also we only measure a small fraction of the leptons coming from the charmless decays, (the rest having momenta below 2.2 Gev) we also very dependent on the theory of the semileptonic decay.
The lepton spectrum from B decay after the continuum has been subtracted using the same complex neural net procedure used for determination of |Vcb|. As before, the most important part of the measurement is the accurate subtraction of the b c events. Also important is the correction for the b u events missed by the cuts. Although ten years ago the measurement was limited by statistics, it is no longer and it is necessary to make the same careful examination as in measurement of |Vcb|. Again moments are calculated using the results of b s +
The result becomes:
|Vub| = (4.08 0.34 0.44 0.16 0.24) x 10-3
where the first two errors are experimental (statistical and systematic) and the last two are theoretical. Combining them we get:
|Vub| = (4.08 0.63) x 10-3.
These two measurements together show, as expected, that the components of the C-K-M matrix get smaller as one proceeds down the matrix. In addition, the ratio of the K-M matrix elements is an interesting quantity in discussing the unitarity triangle.
Figure 8. Lepton spectrum from B decays showing the subtraction of bc events calculated by Monte Carlo from the total spectrum.
Figure 9. Beam eyeview of CLEO dectector. One of the events, B →(J/ψ)K0, and (J/ψ)→µ+µ;K0→00 was reconstructed from data. The tracks of the two muons are evident in the muon chambers. The four showers at 6 o’clock come from the K0. The K0 direction of flight is almost perpendicular to the beam direction.
Beauty decays to charm.
At age 75 the decay of Beauty is especially evident. It is encouraging that the principal decay is to Charm. Over the last few years it has been realized, primarily by Alexei Ershov, that the decays of B mesons to the channel (J/) + X is a powerful channel for examining the decay of B to Charmonium states. This arises because of the narrowness of the (J/). This leads to a very easy identification by the decay into two leptons, and the consequent small background. Of course in this decay there are also rays produced from radiative correction effects and radiation of electrons in the beam pipe and other material. These are detected in the CsI crystals and if their directions are along the electron direction, their energy is added to that of the electrons. An event for [B (J/)Ks0] is shown in figure 9 I will merely summarize the results here because they have mostly been published already.
A) Firstly we measured the decays:
B c1 and B c2 by looking for the decay c1 and c2 into J/ + and the subsequent decay of J/ into two leptons. The results were:
Br [B c1 + X] = (3.83 0.31 0.4) x 10-3
Br [B c2 + X] < 1.7 x 10-3
Non relativistic QCD (NRQCD) suggests that the ratio of these two branching ratios should be 5 to 3 if a color octet model dominates, but 0 (as observed) if a color singlet model dominates.
B) We have found several exclusive decay modes.
Br [B (J/)Ks0] = (9.5 0.8 0.6) x 10-4
Br [B c1 Ks0] = (3.9 0.5 0.4) x 10-4
Br [B (J/) K0] = (2.5 1.0) x 10-4
These decay modes may be useful in measuring the parameter sin 2 in the K-M matrix but that must be left to our colleagues at BABAR and BELLE.
C. Dr Kim has just finished his study of the polarization and the spectrum of the (J/) in the decays B (J/) +X.
It is a long process, but the result for the average value of , which parametrizes the polarization is:
(J/) = - 0.32 0.07 0.05
((2S))= - 0.45 0.21 0.04
Although these are preliminary until the CLEO collaboration agrees, it has been publicly presented in Dr. Kim’s PhD thesis. Previous measurements were:
(J/) = - 0.92 0.16 0.09 (BELLE)
(J/) = - 0.424 0.023 (BABAR)
ACKNOWLEDGEMENTS
I am grateful for the good fellowship of the CLEO collaboration over nearly 25 years and acknowledge in particular the most recent Harvard collaborators, Hitoshi Yamamoto, George Brandenburg, Roy Briere, Yong-Sheng Gao, Alexei Ershov and Daniel Kim. Edward Thorndike and collaborators were responsible for the recent work on b s + and Professor Poling and collaborators on b u decays. The CESR designers and staff, were skillful, responsive and friendly. Of course it was critical that the excellent scientific administrators in DOE and NSF were responsive to our incessant requests for funds.
REFERENCES
Ali A. and Greub C. Phys Lett. B 259:182 (1991)
Chen S et al. (CLEO) (2001) “Branching Fraction and Photon Energy Spectrum for b s” Phys. Rev. Letts. 87(25); 251807
Ligeti Z., Luke, M., Manohar A.V. and Wise M.B. Phys Rev D 60:03409 (1999)\
Bauer C., Phys Rev D 57:5611 (1998)
Falk A. and Ligeti Z. Private Communication (2001)
Cronin-Hennesy et al. (CLEO) (2001) “Hadronic Mass Moments in Inclusive Semi-leptonic B Meson Decays” Phys.Rev. Letts. 87(25); 25108
Bornheim A. et al. (CLEO) “Improved measurement of |Vub| with Semi-leptonic B Decays” Phys. Rev. Letts. 88 in press (2002)
Ershov A.V. (2001) “Beauty Decays to Charmonium” Ph.D. thesis Harvard University.
Kim D. (2001) “Properties of Inclusive B production” Ph.D. thesis Harvard University.
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