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Violation of Lepton Flavor Universality and New Physics
Hyun Min Lee
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DOI: 10.22661/AAPPSBL.2018.28.2.02

Violation of Lepton Flavor Universality and New Physics



We review the status of probing new physics beyond the Standard Model of particle physics through violation of lepton flavor universality. We focus on the measurements of semi-leptonic B-meson decays, recently reported by LHCb, BaBar and Belle experiments.

* hminlee@cau.ac.kr


The Standard Model (SM) of particle physics has been well established, reaching a culmination with the passing of sanity checks after the discovery of the Higgs boson at the Large Hadron Collider (LHC). We have confirmed that the Higgs mechanism works for the spontaneous breaking of electroweak symmetry and that it generates masses of elementary particles such as quarks and leptons through the couplings to the Higgs field as predicted in the SM. The larger the Higgs couplings, the heavier the particle masses. However, the hierarchy of fermion masses and the mixing patterns of quarks and leptons, the so-called flavor structure, cannot be understood within the SM, and baryon asymmetry, dark matter and dark energy in the Universe are not explained.

One of the successes of the SM consists in the precision tests of charged and neutral current interactions. Flavor violating charged currents in the SM are induced at the tree level by the charged current W+-interactions due to the Cabibbo-Kobayashi-Maskawa (CKM) matrix VCKM [1], given by




On the other hand, flavor-changing neutral currents (FCNCs) are suppressed by loop diagrams due to the Glashow-Iliopoulos-Maiani (GIM) mechanism. Thus, FCNC processes are sensitive probes to the violation of flavor universality due to the new physics beyond the SM.


Recently, there have been interesting hints for the violation of lepton flavor universality at LHCb, which is one of main detectors running at the LHC. The semi-leptonic decays of B-mesons, such as B+K+𝑙+𝑙- and B0K*0𝑙+𝑙- with 𝑙 being muon( μ) or electron(e), have been measured and the results are presented in terms of the ratios of decay branching ratios, RK*(B K*μ+μ-)/(B K*e+e-) [2, 3], in Fig. 1, as follows,




in the energy bins, 0.045 GeV2 < q2 < 1.1 GeV2, and 1.1 GeV2 < q2 < 6.0 GeV2, respectively. Thus, while RK* is predicted to be almost equal to 1 in the SM due to lepton flavor universality, the individual measurements at LHCb show more than 2σ deviations from the SM predictions, hinting at the violation of lepton flavor universality.

Fig. 1: Measured values for RK and RK* at LHCb, taken from Ref. [2, 3].

The deviations in RK* are supported by the reduction in the angular distribution of B K*μ+μ-, the so called P'5 variable [4]. As B- and K-mesons are bound states of quarks, both semi-leptonic decays of B-mesons are due to bottom to strange quark transitions as b +μ- at the quark level. Taking into account hadronic uncertainties in the B-meson decays [5], the combined significance from RK* becomes about 4σ.

There is another long-standing puzzle in different semi-leptonic decays of B-mesons from BaBar [6], Belle [7] and LHCb [8]. Taking into account the measured values for RD=(B Dτν)/(B D𝑙ν) and RD*=(B D*τν)/(B D*) with 𝑙=e, μ for BaBar and Belle and 𝑙=μ for LHCb, the Heavy Flavor Averaging Group [9] reported the experimental world averages in Fig. 2, as follows,



These measurements would tell us again the violation of lepton flavor universality between tau and the other leptons. The above semi-leptonic decays of B-mesons are due to bottom to charm quark transitions as b cττ at the quark level.

Fig. 2: World averaged values for RD and RD* at BaBar, Belle and LHCb, taken from Ref. [9].

Taking into account the lattice calculation of RD, which is RD = 0.299±0.011 [10], and the uncertainties in RD* in various groups [11, 12], we quote the SM predictions for these ratios as follows,



Therefore, the best fit values for RD and RD* including the new physics contributions [13] become


Then, the combined derivation between the measurements and the SM predictions for RD* is about 4.1σ, similar to the case with RK*.


The effective Hamiltonian for b +μ- in the SM is given by


where [14], and , and αem is the electromagnetic coupling. Both penguin and box diagrams contribute to the bottom to strange quark transition process in the SM, as shown in Fig. 3. New physics contributions can modify the Wilson coefficients by and , etc. As to the new physics contribution to RK*, for = 0, the best-fit value required for B-meson anomalies is given by

Fig. 3: Feynman diagrams for b+μ- decay.

Fig. 4: Feynman diagram for bcτv̄τ decay.

= -1.10 [15], (while taking [-1.27, -0.92] and [-1.43, -0.74] within 1σ and 2σ errors), to explain the RK* anomalies. On the other hand, for = - and others being zero, the best-fit value for new physics contribution is given by = -0.61 [15], (while taking [-0.73,-0.48] and [-0.87,-0.36] within 1σ and 2σ errors).

There have been many attempts to derive the modified Wilson coefficients for RK* beyond the SM, such as extra U(1) gauge bosons or leptoquark scalars with specific couplings to bottom quark and muon [16, 17]. However, there is the need to explain the origin of new flavor-dependent couplings specific to bottom quark and muon; in contrast, other meson decays and mixings lead to stringent constraints on the couplings to light quarks and electrons. Given that the corrections to the Wilson coefficients are just about 14 percent of the SM values, we also need to suppress bottom and/or lepton couplings to new particles with weak-scale masses or consider new charged particles to enter only in the loop processes [16].

The effective Hamiltonian for b cττ in the SM is given by


where Ccb=1 in the SM. The charged current W+-interactions contribute to the bottom to charge transition at the tree level as shown in Fig. 4. The new physics contribution involves modified charged currents, described by the dimension-6 four-fermion vector operators, and/or scalar operators, . Then, in order to explain the RD*

Fig. 5: Projected sensitivity for the measurements of RK* at Belle II, taken from Ref. [19].

Fig. 6: Projected sensitivity for the measurements of RD and RD* at Belle II and LHCb, taken from Ref. [20]. anomalies in eq. (9), the Wilson coefficient for the new physics contribution should be ΔCcb = 0.1 from eq. (11), while taking [0.072,0.127] and [0.044,0.153] within 1σ and 2σ errors.

Unlike the case of RK*, the RD* anomalies require sizable Wilson coefficients from new physics, so extra charged gauge bosons or leptoquark scalars/vectors with weak-scale masses have order one couplings to bottom quark and tau lepton [18].

It is anticipated, as in Figs. 5 and 6, that the on-going and future LHCb with Run 2 and HL-LHC data will measure the rates of semi-leptonic B-meson decays with better precision and that the forthcoming Belle II experiment can eventually test the lepton flavor universality in B-meson decays up to a few percent level at least with data of 5 ab-1 [19, 20].


We have provided a brief summary of recent measurements of semi-leptonic B-meson decays at LHCb, BaBar and Belle experiments and their implications for new physics. There are 2σ deviations from the SM values in individual channels, but combined significances for RK* or RD* are about 4σ, respectively. If those B-meson anomalies are confirmed by LHCb and Belle II experiments with more data, they would become a strong hint for new physics violating the lepton flavor universality and help unravel the origin of the flavor structure in the SM.

Acknowledgments: The work is supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016 R1A2B4008759).


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Hyun Min Lee is an associate professor at Department of Physics in Chung-Ang University in Korea. After receiving a PhD from Seoul National University he worked at Bonn University, Germany; DESY (Deutsches Elektronen-Synchrotron), Germany; Carnegie Mellon University, USA; McMaster University, Canada; CERN (European Organization for Nuclear Research), Switzerland; and KIAS (Korea Institute for Advanced Study), Korea; before joining Chung-Ang University in 2013. His research field is theoretical particle physics and cosmology beyond the Standard Model.

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