The search for New Physics can be done directly and indirectly. New, massive particles can be created at high energy experiments like the LHC and future experiments at the energy frontier, and thus allow for a direct search of NP particles. An alternative are low energy, precision measurements of certain decay processes. Optimal processes are decays that are theoretically predictable and experimentally measureable with a small uncertainty. Discrepancies between the theoretical prediction and the experimental result may occur and provide indirect hints for NP. The field of flavor physics investigates, among others, the decays of Kaons and B mesons.
The purpose of this section is to present some of the recent discrepancies around the 3σ level between theory predictions and experimental results and thereby provide a motivation for the search for the decayB0→πτ ν.
The CKM matrix elements|Vcb|and|Vub|can be determined by measuring exclusive decays like B → π`ν`, or inclusively by measuring all B → Xu`ν` decays. The results of both methods differ by roughly 3σ though, shown in Table2.3. Preliminary results of exclusive measurement of |Vcb| by Belle via B(B →D`ν`), use improved models and lattice QCD results and are in better agreement with the value obtained from inclusive determination [32].
Recently, measurements ofb→s`+`−processes, have produced intriguing results. These decays are forbidden at tree level in the SM, but can proceed via box or penguin diagrams, shown in Figure 2.5. New, heavy particles may contribute in these diagrams and affect the decay process. The decay rates for the processes shown below are quite low, in the order ofO(10−7).
Furthermore, the theoretical computation is more difficult than tree-level decays. In order to better understand the deviations from the SM, both theory calculations have to be improved, and more data has to be taken.
In the SM, the gauge bosons couple to all leptons with the same coupling strength, a phenomenon called lepton universality. Recent measurements of the ratio RK of the branching fractions B B+→K+µ+µ− and B B+→K+e+e− by LHCb [33], show a deviation of 2.6σ. Earlier measurements by Belle [34] and BaBar [35] are in agreement with the SM prediction, but have a higher statistical uncertainty. The results of all experiments are shown in Figure 2.6a. The result of B B+→K+e+e− alone is compatible with the SM prediction, according to LHCb, though, so the discrepancy is likely to originate from the b→sµ+µ− transition.
The angular analysis of B0 → K∗0µ+µ− shows deviations from the SM predictions, too. The
|Vcb| |Vub|
Inclusive (42.2±0.7)×10−3 (4.41±0.15+0.15−0.17)×10−3 Exclusive (39.5±0.8)×10−3 (3.28±0.29)×10−3
Table 2.3.: World averages of |Vcb| and |Vub|, obtained from inclusive and exclusive determi-nations [10]. The new, preliminary result from Belle is not yet included in the exclusive value of |Vcb|.
theoretical calculation of the angular distribution of the observableP50 does not depend heavily on a good understanding of the involved hadronic form factors and is therefore a useful observable to test the SM. It is a composite variable constructed from observables of the angular analysis of the branching fraction and is defined in [36, 37]. The LHCb experiment measured P50 in bins of the mass squared of the muon pair, q2, and compared the results against recent theory calculations [38]. They obtain agreement with the SM calculation in the low q2 region, but observe a deviation at the 3.7σ level in the region 4.0 GeV2 < q2 <8.0 GeV2. The results are shown in Figure2.6b.
A third deviation in ab→s`+`−process has been observed in the differential branching fraction of the decay Bs0 → φµ+µ− by LHCb. The difference between theory predictions [39, 40] and experiment in the region 1.0 GeV2 < q2 < 6 GeV2, where precise theoretical calculations are available, is found to be at the 3.5σ level. The results are shown in Figure2.6c.
b W− s
u,c,t
γ,Z
`+
`−
(a)
b u,c,t s
W− W+
ν
`− `+
(b)
Figure 2.5.: (a) Penguin and (b) box Feynman diagram for theb→s`+`− process in the SM.
As mentioned above, theb→s`+`−transitions are higher order processes described by penguin or box diagrams, and therefore challenging both theoretically and experimentally. There are, however, also tree-level decays that are sensitive to NP scenarios. Models that include a charged Higgs boson can influence (semi-)leptonicB decays into a τ ντ pair, as for example B0 → πτ ν.
At the tree-level, these decays are theoretically clean. On the other hand, the decays are experimentally challenging. Due to the short lifetime of the τ lepton, it decays inside of the detector, and has to be reconstructed from its decay products. The final state therefore contains 2-3 neutrinos, which are not directly detectable, but result in missing momentum. Advanced reconstruction techniques have to be applied, as will be described in more detail in Chapters4 and 5. While the branching fraction of the decays is in the order of O(10−4) or higher, the reconstruction efficiency is usually quite low.
Two decays involving a τ lepton have been studied by Belle and BaBar, before, and will briefly be presented here. First measurements of the branching fraction B B+→τ+ντ showed a deviation from the SM prediction in the order of 2σ[43–45]. However, more recent measurements by Belle [46,47] using improved analysis methods are in good agreement with the SM.
The measurement of the ratio R(D(∗)) = BB →D(∗)τ ντ
/BB →D(∗)`ν` with ` being a light lepton, ` =eor µ, by BaBar [48] showed a deviation of 2.4σ from the theory prediction.
While new results from Belle [49] are in better agreement with the SM, LHCb [50] sees a similar disagreement in R(D∗), but did not measureR(D). Belle and BaBar reconstruct the τ lepton into τ+ → e+νeν¯τ and τ+ → µ+νµν¯τ, while LHCb uses τ+ → µ+νµν¯τ, only. The Heavy Flavor Averaging Group (HFAG) prepared a combination of the three results for the EPS-HEP conference 2015 [7]. R(D) andR(D∗) exceed the SM predictions by 1.7σ and 3.0σ, respectively.
Combining both measurements shows a deviation from the SM prediction at the 3.9σ level.
(a) (b)
(c)
Figure 2.6.: (a) Results of RK by BaBar, Belle, and LHCb. Plot taken from Ref. [41]. (b) Results on P50 by LHCb. The figure includes the results on the 2011 data (blue) and the results on the full LHC run 1 dataset (black). Plot taken from Ref. [42].
(c) Measurement of the differential branching fractiondB Bs0 →φµ+µ−/dq2 by LHCb. The grey areas indicate vetoes to exclude charmonium resonances.
The results on both observables, as well as the combination of both observables is shown in Figure 2.7.
The analysis presented in this thesis is the search forB0 →π−τ+ντ at the Belle experiment and will be described in more detail below.
R(D)
Figure 2.7.: Average ofR(D) andR(D∗) and of the combination for the EPS-HEP 2015 by the HFAG [7]. See the text for an explanation of how the combination is obtained.