# Implications of lepton flavor universality violations in decays

###### Abstract

Present measurements of and transitions differ from the standard model predictions of lepton flavor universality by almost . We examine new physics interpretations of this anomaly. An effective field theory analysis shows that minimal flavor violating models are not preferred as an explanation, but are also not yet excluded. Allowing for general flavor violation, right-right vector and right-left scalar quark currents are identified as viable candidates. We discuss explicit examples of two Higgs doublet models, leptoquarks as well as quark and lepton compositeness. Finally, implications for LHC searches and future measurements at the (super)B-factories are presented.

Introduction. Universality of weak interactions is one of the key predictions of the standard model (SM). The BaBar collaboration recently performed a test of its consequences in semileptonic quark transitions via measurements of branching fractions normalized to the corresponding modes (with ) :2012xj ()

(1) | |||||

(2) |

where the statistical and systematic uncertainties have been combined in quadrature. Both values in Eqs. (1), (2) are consistent with previous measurements BDTold (), but are also significantly larger (at significance when combined) than the SM values and BDTSM (). If confirmed, this would signal a violation of lepton flavor universality (LFU) in semileptonic transitions at the level.

Intriguingly, there are also hints of LFU violations in semileptonic transitions. The most recent world average of the leptonic branching fraction measurements BT (), is somewhat larger than its SM prediction with CKM element taken from the global fit Charles:2011va (). In contrast, the measured exclusive semileptonic transition branching fraction BPT (); LFUPK () is consistent with the CKM unitarity predictions Laiho:2012ss (). One can get rid of dependence by considering the ratio

(3) |

The SM prediction is , where we have used the recent Lattice QCD estimates of the relevant form factor and the decay constant Laiho:2009eu (). The measured value in Eq. (3) is more than a factor of 2 bigger – a discrepancy with significance if gaussian errors are assumed (for previous discussion of this tension see Lunghi:2010gv ()). In order to avoid having to extrapolate lattice form factor results over the whole phase space, one may also consider only the region of high Khodjamirian:2011ub (), in which case the discrepancy between the SM expectations and experiment for is at the level of .

For later convenience we can summarize all the three experimental values as (), and , giving a combined excess of () above the SM expectations. These hints of LFU violations in semileptonic and transitions can be contrasted to the pion and kaon sectors where LFU for all three lepton generations has been tested at the percent level and found in excellent agreement with the SM expectations LFUPK () .

In this Letter we explore the possibility that the hints of LFU violations in semileptonic decays are due to new physics (NP). We first perform a model independent analysis using effective field theory (EFT), which then allows us to identify viable NP models. Implications for other flavor observables and LHC searches are also derived.

LFU Violations in decays and NP. We first study NP effects in and using EFT. The SM Lagrangian is supplemented with a set of higher dimensional operators, , that are generated at a NP scale above the electroweak symmetry breaking scale GeV

(4) |

where are the canonical dimensions of the operators , and are the dimensionless Wilson coefficients (below we will mostly use rescaled versions ). We also make two simplifying requirements that at the tree level (i) no dangerous down-type flavor changing neutral currents (FCNCs) and (ii) no LFU violations in the pion and kaon sectors are generated. The lowest dimensional operators that can modify and then have the following form,

(5) | ||||

(6) | ||||

(7) | ||||

(8) |

where , , and are generational indices. We work in the down quark mass basis, , and charged lepton mass basis, . Our requirement that there are no down-type tree-level FCNCs means that we impose flavor alignment in the down sector for operators and . In this way we get rid of all tree level FCNCs due to while and still generate effects in and transitions. The first process is typically obscured by SM tree level contributions (i.e. Kamenik:2009kc ()), while the second will induce an interesting monotop signature at the LHC Kamenik:2011nb ().

Other operators can either be reduced to the above using equations of motion, or have vanishing hadronic matrix elements and thus cannot affect (e.g., ). Note that are tau lepton flavor specific, while in the case of LFU violations are induced by the helicity suppression of the leptonic current, as can be easily seen by integrating by parts and using equations of motion.

In addition, new light invisible fermions could mimic the missing energy signature of SM neutrinos in the decays Kamenik:2011vy (). We thus also consider the lowest dimensional operators coupling to SM quarks and charged leptons and invariant under the SM gauge group

(9) |

In the following we consider a single NP operator contributing to and at a time and later compare this to some explicit NP model examples.

Minimal flavor violation. The flavor structure of and is completely determined by our requirement that there are no tree level FCNCs in the down sector. The charged currents are then proportional to the same CKM elements as in the SM realizing the Minimal Flavor Violation (MFV) structure MFV (). The effect of is to rescale the SM predictions for , by a universal factor , where . The best fit to the three LFU ratios is obtained for with a value of (for the SM, ). Both and are then well accommodated, while the tension remains at the level. The effective NP scale probed is TeV.

The contributions of can be readily computed using results of Kamenik:2008tj (); BDTSM (). In the case of we also need to take into account a significant experimental efficiency correction due to the different kinematics induced by the operator compared to and the SM :2012xj (). Effectively this amounts to multiplying the term quadratic in by a correction factor of . The same argument applies for the operators and (near ). Switching on only the operator the best fit point is , where with both and perfectly accommodated, while a tension with the observed value of remains (see Fig. 1 left). Irrespective of , the central measured values of and can never be simultaneously obtained using only BDTSM (). The preferred value of points to a very low effective NP scale of GeV.

The relative strength of semileptonic and transitions generated by the or operators is fixed only once we explicitly specify the flavor structure. For , and , MFV implies leading to extremely suppressed effects in . Consequently we do not consider these operators within MFV. On the other hand, in the case of the MFV hypothesis is satisfied by taking . The corrections to and now also depend on the mass of the new invisible fermion . Close to thresholds the contributions to are suppressed relative to the ones in . Varying both and the best fit of is reached for and (see Fig. 1 right). Significant tensions between the three observables remain.

Generic flavor structures. In the presence of more general flavor violation the NP contributions to are no longer related to those in . We thus parametrize the contributions of and operators to semileptonic transitions by () , and to semileptonic transitions by . The effect of is to rescale the SM expectations by and by . For we obtain On the other hand contributions of can be obtained from the corresponding expressions for in the previous section with obvious modifications for the different flavor and chiral structure.

We fit the data to pairs of using CKM inputs from the global fit Charles:2011va (). The results are presented in Fig. 2.

Considering the NP operator , all three LFU ratios can now be perfectly accommodated at and (analogously for at , and ). Interestingly, a good fit necessarily implies the presence of large CP violating contributions, suppressed by an effective NP scale TeV. Similarly, NP contributions from can now simultaneously explain both and discrepancies. The best fit of is obtained at and . The required size of NP contributions points to a low NP scale of GeV. On the other hand, generic flavor structures do not significantly improve the MFV fit of the operator, due to the tension between and (present also for , see Fig. 1). Nonetheless, both and can now be accommodated simultaneously provided the parameters are near , and (at which point ) .

Explicit models. Specific NP models in general contribute to more than one operator of the effective Lagrangian in Eq. (4). The agreement with data for operators suggests an obvious candidate – the two-Higgs doublet model (2HDM), where charged Higgs () exchanges generate both and . No tree level FCNCs arise in 2HDMs with natural flavor conservation where the two Higgs doublets couple exclusively to and/or . The four types of natural flavor conservation 2HDMs: Type I, Type II, “lepton specific” and “flipped” Branco:2011iw () give and , respectively. Here is the ratio of the two Higgs doublets’ vacuum expectation values. Imposing the GeV bound from direct searches at LEP Heister:2002ev () (even stronger constraints can been derived from one-loop charged Higgs contributions to FCNC processes Deschamps:2009rh ()) and so that the Yukawas are perturbative, we find that none of the natural flavor conservation 2HDMs can simultaneously account for the three LFU ratios.

In principle there is enough freedom in the Higgs couplings to quarks to explain the observed LFU ratios using 2HDMs with more general flavor structure. A simple limit is that only one of the Higgs doublets obtains a vacuum expectation value. The charged Higgs is then part of the remaining Higgs doublet (). The interaction terms generate and Wilson coefficients for the and operators, generalizations of Eqs. (8) and (7), respectively. The best fit regions have a fourfold amiguity with two solutions for , and two solutions for . These values are large enough to pose severe flavor building problems. The products are roughly three (four) orders of magnitude larger than the corresponding Yukawas giving fermion masses, . Furthermore, in order to satisfy FCNC bounds from , and mixing, there needs to be at least an order of magnitude cancellation between different contributions even for (to suppress transitions, a viable solution is also ). If such a charged Higgs is lighter than the top quark, it could be observed in decays. The null results of existing searches at ATLAS and CMS imply for the mass between GeV and GeV Aad:2012tj (). If the charged Higgs is heavier than the top, the dominant signal could come from production with, e.g., the cross section at the 8 TeV LHC of for GeV. Also for larger masses and resonance searches Aad:2012ej () become effective, since then decays predominantly to and depending on the relative sizes of and .

An alternative possibility is represented by leptoquarks. In particular, scalar leptoquarks forming the , and representations of the SM gauge group as well as vector leptoquarks in the , and representations can contribute to (semi)leptonic charged current meson decays at the tree level. In general they will also induce dangerous FCNC operators and are thus potentially severely constrained Dorsner:2009cu (). As an example we consider the scalar electroweak triplet leptoquark with renormalizable interactions to 3rd generation SM fermions (aligned with the mass basis of down-like quarks and charged leptons) Integrating out at the tree level induces a contribution to with . LFU violations in transitions (and partially ) can then be accommodated provided GeV. The most severe constraints on these parameters come from electroweak precision tests ewpt () requiring GeV, in tension with the value preferred by decays. Additional contributions to electroweak precision observables from the UV completion of the effective model could soften this tension. Most constraining direct bound on the mass of is from the CMS search for 3rd generation scalar leptoquarks decaying to CMS (). Taking into account the branching ratio we obtain a bound GeV. Future dedicated searches using also the decay channel Davidson:2011zn () or associated production with the monotop signature Kamenik:2011nb () could further constrain this model.

Modifications of semileptonic transitions involving the third generation quarks and leptons are also expected in models of strong electroweak symmetry breaking or composite Higgs models where the heavier SM fermions are expected to be partially or mostly composite Kaplan:1991dc (). The exchange of strong sector vector resonances will induce contributions to which can be parametrized as

(10) |

where and are the strong sector vector resonance coupling and mass, while is the mass of the strong sector fermion resonances () transforming as under the SM gauge group. Furthermore, are compositeness fractions of -th generation left handed quarks and leptons respectively, parametrizing the mixing of chiral fermions with strong sector fermion resonances (again assuming down type mass alignment), while are the couplings of right-handed chiral up- and down-type quarks to the composite Higgs and fermion resonance fields in . For concreteness we fix (third generation compositeness, the first two generations of left-handed fermions can be completely elementary), and fit , and to the three LFU ratios. A good fit to all three observables is obtained for TeV in two regions, around and but also and . Note that non-zero (signaling compositeness of right-handed quarks) are required to fit and simultaneously within . Similarly to the in 2HDMs, the strong sector charged vector resonances are susceptible to and resonance searches Aad:2012ej () at the LHC. Another interesting channel is the resonant or Higgs associated production of fermionic resonances through or fusion.

Prospects. It is important that the indications of LFU violation in and decays are verified using related decays. Measuring the branching ratio Khodjamirian:2011ub () could confirm LFU violation in transitions. In the SM one has

(11) |

using form factor estimates from the lattice Laiho:2009eu (), and where the uncertainty is dominated by the shape of the scalar form factor as extracted from the lattice simulation Dalgic:2006dt (). A measurement of this observable should be possible at the (super)B-factories. It would also help to disentangle the possible underlying NP, since different effective operators in Eqs. (5)–(8) give different contributions compared to . A similarly useful observable probing LFU in transitions would be the purely leptonic decay of the meson . The experimental prospects for such a measurement are more uncertain, however.

The NP interpretations of the LFU violation in decays have also interesting implications for the direct searches at the LHC. In addition to the model dependent searches for on-shell production of the relevant NP states, there are also some generic signatures that are more tightly related to the fact that LFU violation is seen in decays. All the models either predict contributions to channel where is the physical neutral Higgs boson (for the models that match onto , and EFT operators), the monotop signature (for and operators) or the channels. The latter are possible for all EFT operators, but the final state with a top quark is directly related to the strength of decay LFU anomalies only for and operators.

In conclusion, we have shown that the indications for the violation of LFU in decays can only partly be explained in presence MFV modifications of the left-left vector currents coupling to the third generation quarks and leptons. A better fit to current data is provided by non-MFV right-right vector or right-left scalar currents. We have also shown how such effects could arise from 2HDMs, from leptoquark models or from models with composite quarks and leptons.

###### Acknowledgements.

We thank D. Bečirević, A. Falkowski, and R. Harnik for useful discussions. This work was supported in part by the Slovenian Research Agency. JZ was supported in part by the U.S. National Science Foundation under CAREER Award PHY-1151392.## References

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