Inclusive and at the B factories
John Walsh
INFN, Sezione di Pisa
Largo B. Pontecorvo 3, 56127 Pisa, ITALY
I report here recent measurements of observables from the inclusive decays and . Included are measurements of the branching fractions and CP asymmetries for both channels, as well as the forwardbackward lepton asymmetry in inclusive decays, which is the first measurement of this quantity.
PRESENTED AT
FPCP 2014 – Flavor Physics & CP Violation
Marseille, France, May 26–30, 2014
1 Introduction
Radiative and electroweak penguin decays, in particular the decays and , have proven to be powerful probes of New Physics (NP) in the flavour sector. These flavourchanging neutral current decays are prohibited at tree level in the Standard Model (SM). This makes them sensitive to NP effects, which can contribute at the same level as the SM, namely at the oneloop level, as can be seen in Fig. 1.
A general review of radiative and electroweak penguin physics can be found in section 17.9 of reference [1]. One usually distinguishes between exclusive and inclusive measurements, where in the former case, the measurement is performed on a particular final state, for example . Recent results on exclusive measurements were presented at this conference by Patrick Owen and Akimasa Ishikawa [2]. Inclusive analyses attempt to include all final states for a given parton level process. This has theoretical advantages, since the calculation of inclusive radiative and electroweak penguin decays is much more precise than the corresponding calculations on exclusive decay modes. In the latter, hadronic effects tend to cause theoretical uncertainties to grow significantly.
From an experimental point of view, truly inclusive measurements are significantly more challenging: since the decay is not fully reconstructed, there are fewer kinematic constraints available in the event selection. Typically, a fullyinclusive measurement will try to tag one meson in the event and then look for an inclusive signature of the signal from the other . An example would be requiring a high lepton to tag a semileptonic decay and then require a highenergy photon in the same event, as a signal of the process. In such fully inclusive analyses the backgrounds generally tend to be higher than for exclusive measurements, leading to higher uncertainties.
This difficulty is somewhat alleviated with the sumofexclusives (SOE) technique, whereby a large number (typically tens) of exclusive final states are reconstructed to capture as much as the full rate as possible. Usually 50–70% of the total rate is selected and the missing part must be estimated using simulation. This generally leads to a larger systematic uncertainty than one obtains with the fully inclusive techniques.
In these proceedings, I will report on a measurement of the CP asymmetry in inclusive decays, using a fully inclusive method, as well as measurements of the branching fraction and CP asymmetry using the sumofexclusives technique. I will also report measurements of the branching fraction, CP asymmetry and forwardbackward (FB) lepton asymmetry in decays. The FB lepton asymmetry measurement is the first ever made of this quantity for the inclusive decay.
2 Measurements on inclusive
2.1 Branching fraction using sumofexclusives
Measurements of the branching fraction of the inclusive process have been very useful in putting significant constraints on parameters of models of NP [5]. A significant portion of the credit for this success must be attributed to the theorists who have made a precise calculation of the SM branching fraction at NNLO [6]. The result reads:
(1) 
Belle reports a preliminary measurement of the inclusive BF using the sumofexclusive technique based on their full (4S) dataset of 710 fb. They fully reconstruct 38 exclusive final states. The hadronic system (labeled ) consists of 1 or 3 kaons (at most one ), up to one and up to four pions (with a maximum of two ). These states comprise about 70% of the total rate. The large continuum background is reduced using a multivariate classifier using the neural network technique. The 12 inputs to this classifier are primarily eventshape variables, i.e., quantities that can separate the more jetty continuum events from the nearly isotropic events.
The signal is determined by fitting the beamconstrained mass, in bins of the hadronic system mass from 0.6 to 2.8 GeV. Note that is directly related to the photon energy in the rest from of the decaying meson:
so the quoted mass range corresponds to a photon energy range of 1.9–2.6 GeV. Figure 2 shows an example fit of , for the hadronic mass bin GeV. The resulting spectrum, obtained after performing all the fits, is shown in Figure 3. The narrow peak at around 0.9 GeV corresponds to the contribution. The obtained partial branching fraction is:
(2) 
For comparison to the theoretical calculation, this partial rate is extrapolated to GeV (equivalent to GeV), leading to the result:
(3) 
The largest contributions to the systematic error are the uncertainty in the fragmentation model and the description of the probability distribution function (PDF). The result is compatible with the current world average value as calculated by the Heavy Flavor Averaging Group [7]:
(4) 
2.2 CP asymmetry using sumofexclusives
Babar has performed a measurement of the CP asymmetry in inclusive , using their full dataset of 429 fb [8]. The CP asymmetry is defined as:
(5) 
This quantity is expected to be small in the SM, with a range of % [9]. The authors of this paper suggest measuring a new quantity, , which is the difference of measured on charged and neutral mesons:
(6) 
The authors point out that a measurement of this quantity would give information on the chromomagnetic dipole Wilson coefficient :
(7) 
where is a hadronic parameter, with a calcualted range of MeV. Since, is essentially known from the BF measurements, measuring would give the first experimental constraints on . In the SM, where the Wilson coefficients are all real, we have .
The Babar measurement starts with 38 fullyreconstructed exclusive channels, 16 of which are selftagging and hence used in the measurement. Photons with centerofmass energy greater than 1.6 GeV are combined with a hadronic system havng 1 or 3 kaons, up to 3 pions and 1 particle. Neutral pions and s are reconstructed in their decay modes. Charged particle identification is performed to distinguish charged pions and kaons. B candidates are required to have GeV and GeV, where as measured in the centerofmass. Two multivariate classifiers are employed: one to suppress continuum backgrounds and the other to select the best candidate in events where multiple candidates have been identified.
Fits to the B candidate mass are performed to extract the yields for , , and decays (see Fig. 4).
The resulting raw asymmetries are corrected for inherent detector asymmetry (%) and possible background asymmetry (%). Combining the charged and neutral modes together, the full is obtained:
(8) 
while the simultaneous fit to the charged and neutral samples gives:
(9) 
This allows us to put the following constraints on the Wilson coefficients:
Should the theoretical uncertainty on the hadronic parameter be reduced, the constraint provided by this measurement will improve substantially as shown in Fig. 5.
We now turn to a preliminary Belle measurement of the CP asymmetry in fully inclusive events. As noted above, the fully inclusive method makes no requirements on the accompanying hadronic system (). The basic strategy is to select a highenergy photon and reduce the substantial continuum background by requiring a high lepton in the event, along with some missing energy. This lepton comes from the other B in the event, which has decayed semileptonically. This lepton tagging method is very effective at reducing the continuum, although it does little to combat the background, where the highenergy photon comes from a B decay that is not . A large fraction of the background is removed by vetoing events where the highenergy photon is consistent with the decays and . The remaining background is then subtracted by using MC predictions that have been corrected by performing studies on real data.
One consequence of employing the fully inclusive method is that the event sample will contain the Cabbibosuppressed decays , as well as . For branching fraction measurements, the component is subtracted from the total rate. In the case of the CP asymmetry, we cannot do that and we end up measuring the asymmetry for the socalled “untagged” decay, i.e., . Because of Uspin symmetry, this quantity is almost identically zero to very high precision [9], so any significant nonzero measurement of would be an indication of New Physics.
The sign of the tagging lepton, which contains information on the flavour of the parent B meson, is used to construct the measured asymmetry:
(10) 
Figure 6 shows the photon energy spectrum for events with a positively or negatively charged lepton tag.
The resulting asymmetry must be corrected for mixing, background and detector effects:
(11) 
This mistag rate arises mostly from mixing, but it is also corrected for cascade decays (where the lepton comes from a decay) and for particle misidentification. The mistag rate is found to be: . The detector asymmetry is determined from data using a tagandprobe method with : %. The asymmetry of the background was determined on events with GeV and is found to be %.
The final result then, with a photon energy cut of 2.1 GeV, reads:
(12) 
This result is consistent with zero asymmetry and also with previous measurements of this quantity.
3 Measurements on inclusive
The process is closely related to , as can be observed in their Feynman diagrams (Fig. 1): the photon in the final state is replaced by a pair of leptons. The more complex final state allows for a wide variety of observables that are sensitive to NP effects, especially observables that involve an angular analysis of the final state leptons. Furthermore, for most observables, we have theoretical predictions as a function of the dilepton invariant mass, , which is a powerful tool for finding NP and possibly distinguishing among NP models. However, the decay rate for this channel is quite small: about 2 orders of magnitude smaller than the rate. This makes measurements quite challenging, especially inclusive measurements. For this reason, few inclusive measurements have been made on and those have all employed the experimentally easier sumofexclusives method (described above in Sec. 1).
3.1 Branching fraction and
Babar has used its full dataset (471 million pairs) to measure the branching fraction and CP asymmetry in inclusive decays [10]. Twenty exclusive final states are reconstructed: 10 different hadronic systems (combinations of charged or neutral kaons paired with zero, 1 or 2 charged or neutral pions) are combined with either a pair of muons or electrons. These modes account for about 70% of the total rate. Kaons, pions, muons and electrons are selected using particle identification. The kinematics of B decays are exploited, placing requirements on and a multivariate classifier (based on a likelihood ratio LHR) is used to reduce the background from continuum events.
The event yields are extracted by a 2dimensional fit to and the LHR. The fits are performed in bins of , which are shown in Table 1.
bin  GeV 

0  1.6–6.0 
1  0.2–2.0 
2  2.0–4.3 
3  4.3–6.8 
4  10.1–12.9 
5  14.2 
An important aspect of the selection is the veto of charmonium events, i.e., the decays followed by . These events have the same final state as the signal events and candidates with in the range (6.8,10.1) GeV and (12.9,14.2) GeV are explicitly vetoed. These vetoed events are a very valuable control sample – they are used for a wide variety of checks on the simulation of the signal.
An example fit for modes in bin 5 is shown in Fig. 7: on the left is shown the projection of the fit, while the right plot shows the projection of LHR. For each plot, the signal has been enhanced by making a loose cut on the other variable. One can see the low statistics which are available in a single bin. The full set of plots is provided in [10] and its supplementary material.
The derived branching ratios from the event yields have been determined for the and modes separately, as well as for the combination, in each of the 6 bins. These results are presented in [10], although here we show the results for which the best theoretical predictions are available [11], i.e., bins 0 and 5.
Channel  This measurement  SM theory 

GeV  
GeV  
In the experimental measurements, the first uncertainty listed is statistical, the second is experimental systematic and the third is modeldependent systematic related to the extrapolation to the full hadronic mass spectrum and inclusion of the missing modes. These results are compatible with expectations, although the BF in the high region is approximately above the SM value. We note that it also is from the most favoured value of the beyondSM contribution , which has been proposed to explain recent observations in the channel by the LHCb Collaboration [12].
The CP asymmetry is also determined from the event yields, using the 14 selftagging modes i.e., excluding the modes with . No modeldependent extrapolation of signal rates is attempted, so the result pertains only to the modes utilized. The result obtained
(13) 
is consistent with the SM prediction of very small CP asymmetry [13].
3.2 Forwardbackward lepton asymmetry in
Belle has made the first measurement of the forwardbackward lepton asymmetry in inclusive decays [14]. The asymmetry, defined as follows:
(14) 
is sensitive to NP effects. Here is the angle between the positive (negative) lepton and the B meson momentum in the centerof mass frame in or ( or ) decays.
The Belle analysis, based on their dataset of 772 million pairs, employs the sumofexclusives technique, using 10 selftagging modes, which account for roughly 50% of the total rate. The event selection is standard: PID for charged particles, multivariate classifier (neural net, in this case) to suppress continuum backgrounds and explicit charmonium vetoes. The quantity is measured in 4 bins. Events are divided into forward and backward subsamples and the signal yields are extraced by a fit to the B candidate mass (Fig. 8).
The raw yields are corrected for efficiency, which varies considerably over and . Simulated events are used to derive the correction factors. Figure 9 shows the results as a function of . The results are consistent with the SM expectation [15]. Table 3 reports the results in numerical form. This is the first measurement of for inclusive .
1st bin  2nd bin  3rd bin  4th bin  
range  ()  [0.2,4.3]  [4.3,7.3]  [10.5,11.8]  [14.3, 25.0] 
()  [4.3,8.1]  [10.2,12.5]  
(theory) 
4 Conclusions
Inclusive measurements of the decays and are important tools for constraining models of New Physics. The measurements presented herein use the full datasets from the Babar and Belle experiments and represent the state of the art regarding these channels at the Bfactories. While inclusive has been wellstudied at the B factories, measurements of the channel are still in their infancy. Because of the difficulties of making inclusive measurements at hadron colliders, further progress will have to await the advent of the Belle II experiment, which is expected to come online within a few years. The prospects at a very highluminosity machine are very exciting: the large statistics will lead to precision measurements in , while full reconstruction of tagside hadronic B decays will lead to new possibilities in and the Cabbibosuppressed decay .
ACKNOWLEDGEMENTS
I am grateful to the organizers of FPCP 2014 in Marseille. They did a wonderful job of organizing a stimulating and interesting conference.
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