DDO-TH 18/07
LEPTON NONUNIVERSALITY ANOMALIES & IMPLICATIONS
G.HILLER
Fakult¨at Physik, TU Dortmund, Otto-Hahn-Str.4, D-44221 Dortmund, Germany
We discuss avenues for diagnosing new physics hinted from lepton nonuniversality in rare b -decays, and physics implications. We are presently seeing ∼ . σ hints of new physics (NP) in rare semileptonic b → sll transitions,indicating lepton nonuniversality (LNU) between electrons and muons in each observable R K and R K ∗ , , R H = (cid:82) q q dq d B /dq ( ¯ B → ¯ Hµµ ) (cid:82) q q dq d B /dq ( ¯ B → ¯ Hee ) , H = K, K ∗ , X s , ... (1) R LHCb K = 0 . +0 . − . ± . , R LHCb K ∗ = 0 . +0 . − . ± .
05 (2)for the dilepton mass cuts q = 1 . for R K ∗ and 1 GeV for R K , and q = 6 GeV .In lepton-universal models including the SM holds R H = 1 up to tiny corrections of O ( m µ /m b )despite of the sizable hadronic uncertainties in the individual rates . Electromagnetic corrections are found to not exceed percent level . R H − R K,K ∗ by Belle and BaBar are consistent with one. We discussin section 2 which operators can be responsible for the deviation (2) from universality . Insection 3 lepton-specific measurements are emphazised as a means to understand whether thepresent LNU anomalies are due to physics beyond the standard model (BSM) in electrons, inmuons, or in both , , and CP violation is commented on. We discuss side effects from flavor in section 4, which addresses correlations with other sectors, such as charm, or Kaon physics , , as well as lepton flavor violation (LFV), and decays with τ ’s, or ν ’s. Collider implicationsand leptoquark signatures related to the b -decay anomalies are discussed in section 5 , , . Wecomment on the status of R D,D ∗ in section 6. One employs an effective low energy theory H eff = − G F √ V tb V ∗ ts (cid:80) i C i ( µ ) O i ( µ ) at dimension sixV,A operators O = [¯ sγ µ P L b ] [¯ (cid:96)γ µ (cid:96) ] , O (cid:48) = [¯ sγ µ P R b ] [¯ (cid:96)γ µ (cid:96) ] , (3) O = [¯ sγ µ P L b ] [¯ (cid:96)γ µ γ (cid:96) ] , O (cid:48) = [¯ sγ µ P R b ] [¯ (cid:96)γ µ γ (cid:96) ] , (4)S,P operators O S = [¯ sP R b ] [¯ (cid:96)(cid:96) ] , O (cid:48) S = [¯ sP L b ] [¯ (cid:96)(cid:96) ] , (5) a r X i v : . [ h e p - ph ] M a y P = [¯ sP R b ] [¯ (cid:96)γ (cid:96) ] , O (cid:48) P = [¯ sP L b ] [¯ (cid:96)γ (cid:96) ] , (6)tensors O T = [¯ sσ µν b ] [¯ (cid:96)σ µν (cid:96) ] , O T = [¯ sσ µν b ] [¯ (cid:96)σ µν γ (cid:96) ] . (7)This set of semileptonic operators is complete. To discuss LNU one needs to add lepton specificindices C i O i → C (cid:96)i O (cid:96)i , (cid:96) = e, µ, τ . In the SM, only O , O receive non-negligible and universalcontributions, C SM9 (cid:39) − C SM10 (cid:39) .
1, all other operators are BSM-induced.To interpret LNU data (2) it is useful to employ the approximation where BSM physicsenters the branching ratios linearly, schematically, with amplitude A = A SM + A NP , B = | A | = | A SM | + 2 Re( A SM A NP ∗ ) + | A NP | , (8)that is, assuming | C NP | (cid:28) | C SM | . The complementarity between R K and R K ∗ becomes manifest . In fact, it suffices to measure two different (by spin parity of the final hadron) R H ratios.Then, all others serve as consistency checks, because the Wilson coefficients C and C (cid:48) enterdecay amplitudes in specific combinations dictated by parity and Lorentz invariance C + C (cid:48) : K, K ∗⊥ , . . .C − C (cid:48) : K (1430) , K ∗ , (cid:107) , . . . (9)In addition, the K ∗⊥ amplitude is subleading at both high and low q windows. Here, C and C (cid:48) refer to V-A and V+A quark currents, respectively, and 0 , (cid:107) , ⊥ refers to longitudinal andtransverse parallel and perpendicular transversity, respectively. It follows that R K (cid:39) R η (cid:39) R K (1270 , , R K ∗ (cid:39) R Φ (cid:39) R K (1430) , (10)and all R H are equal if all C (cid:48) vanish.Which operators are responsible for the deviation (2) from universality in R K , R K ∗ ? Re[ C NP µ − C NP µ − ( µ → e )] ∼ − . ± . , Re[ C (cid:48) µ − C (cid:48) µ − ( µ → e )] ∼ . ± . . (11)The constraint from the B s → µµ branching ratio 0 < ∼ Re[ C NP µ − C (cid:48) µ ] < ∼ . R K and R K ∗ identifies the V-A-type operators as thedominant source behind the anomalies. Within leptoquark explanations, this singles out threekinds that can account for (2) at tree level: the scalar triplet leptoquark S , the vector triplet V and the vector singlet V , whereas the scalar doublet ˜ S is disfavored as it induces V+A Wilsoncoefficients. Furthermore, LHCb data allows one to predict R X s (cid:39) . ± .
07, the LNU ratiofor inclusive B → X s (cid:96)(cid:96) decays, which can be probed at Belle II. The observation of R H < b -decays to muons than on decays to electrons. Global b → s fits to Wilsoncoefficients from B → ( K, K ∗ ) µµ, B s → µµ precision studies are presently hinting at NP, too,and can point into the same direction as R K,K ∗ . Therefore, BSM effects in electrons are presentlynot necessary to account for the data. Analogous studies in B → Hee are, however, are requiredfor consolidation of this possibility. Early data are already available from Belle .Two main types of explicit BSM models can naturally address LNU at the required levelof ∼
15% on the SM amplitude: U (1) extensions with gauged lepton flavor ( Z (cid:48) -models) andleptoquarks , that can be charged under a flavor symmetry and couple non-universally .Inspection of (8) shows that close to maximal BSM-CP violation switches off SM-NP inter-ference. Together with R H < R H . Such large CP phases in the b → see transition can be searched for with theangular distribution in B → K ∗ ee , e.g. J , , . An explanation of R K is also possible at 2 σ with (pseudo)-scalar operators, a scenario that can be cross checked with the B → Kee angulardistribution . Side effects from flavor
From a flavor perspective, LNU generically implies LFV . This is obvious for leptoquarks (LQs),which couple with matrix structure λ q(cid:96) to quarks q and leptons (cid:96) of three generations each λ q(cid:96) = λ q e λ q µ λ q τ λ q e λ q µ λ q τ λ q e λ q µ λ q τ , (12)and rows=quarks, columns=leptons. Mixing of quark and lepton flavor in one coupling is verydifferent from the SM-Yukawas. The upper left sub-matrix in red indicates the couplings relevantfor Kaon and charm physics. Explaining R K,K ∗ requires λ bµ λ ∗ sµ − λ be λ ∗ se M (cid:39) . , (13)where M denotes the LQ mass. In matrix form, where entries with an (cid:48) ∗ (cid:48) do not matter, ∗ ∗ ∗ λ q e λ q µ ∗ λ q e λ q µ ∗ + Occam’s razor ( b → s fit) : ∗ ∗ ∗∗ λ q µ ∗∗ λ q µ ∗ . (14)The latter pattern assumes muon couplings only which is consistent with the global b → s fit.Viable patterns from flavor models simultaneously explain quark and lepton masses, and CKMand PMNS mixing
13 22 . For instance, models based on U (1) F N × A , with (cid:15), δ, c (cid:96) , c ν < ∼ .
2, give ρ d κ e ρ d ρ d κ τ ρκ e ρ ρκ τ κ e κ τ , c (cid:96) (cid:15) c (cid:96) (cid:15) c (cid:96) , c ν κ(cid:15) c (cid:96) (cid:15) + c ν κ(cid:15) c ν κ(cid:15) c ν κ c (cid:96) (cid:15) + c ν κ c ν κc (cid:96) δ + c ν κ(cid:15) c (cid:96) c (cid:96) δ + c ν κ(cid:15) . (15)LFV and off-diagonal couplings appear generically, as well as electron couplings, or taus. Phe-nomenological constraints apply
13 22 . LQs which are SU (2) L triplets couple doublets to doublets,implying BSM effects in b → sνν and b → c(cid:96)ν , see section 6. Predictions for charm decaysare given in Table 1 . They depend on the flavor pattern. Here, i): hierarchy, ii) muons onlyiii) skewed, 1) no kaon bounds 2) kaon bounds apply for SU (2) L -doublet quarks q = ( c, s ). Table 1:
Branching fractions for the full q -region (high q -region) for different classes of leptoquark couplings. Summationof neutrino flavors is understood. ”SM-like” denotes a branching ratio which is dominated by resonances or is of similarsize as the resonance-induced one. All c → ue + e − branching ratios are ”SM-like” in the models considered. See text. pattern B ( D + → π + µµ ) B ( D → µµ ) B ( D + → π + eµ ) B ( D → µe ) B ( D + → π + ν ¯ ν )i) SM-like SM-like < ∼ · − < ∼ · − < ∼ · − ii.1) < ∼ · − (2 · − ) < ∼ · − < ∼ · − ii.2) SM-like < ∼ · − < ∼ · − iii.1) SM-like SM-like < ∼ · − < ∼ · − < ∼ · − iii.2) SM-like SM-like < ∼ · − < ∼ · − < ∼ · − Producing LQs at the LHC happens through pair production with cross section σ ( pp → φ + φ − ) ∝ α s , recently, e.g.
24 25 26 . Single LQ production in association with a lepton σ ( pp → φ(cid:96) ) ∝ | λ q(cid:96) | α s depends on flavor, and is lesser phase space limited than pair production. Links with b -anomaliesand flavor are manifest via (13)-(15). While b -studies are in principle able to determine thecolumns, the lepton flavor structure of λ q(cid:96) , theory input is presently required to go on and break M S [TeV]0 . . . . λ . . . . . . . M S [TeV]10 − − − − − − − − σ [ pb ] √ s = 13 TeV 1 2 3 4 5 6 7 8 M S [TeV]10 − − − − − − − σ [ pb ] √ s = 33 TeV Figure 1 – Red bands: R K,K ∗ with flavor (16). Plot to the left shows λ b(cid:96) vs M . Green vertical band gives flavormodel prediciton λ b(cid:96) ∼ c (cid:96) which points to M < ∼ − √ s = 13 TeV and 33 TeV. Magenta, yellow, blue line corresponds to λ dµ = 1 , λ sµ = 1 , λ bµ = 1, respectively.Black dashed line: no-loss reach with 3 ab − . Green curve: pair production (LO Madgraph). Figures from . the ambiguity in the product λ b(cid:96) λ ∗ s(cid:96) . Quark hierarchies m b (cid:29) m s (cid:29) m d , when addressed with aflavor symmetry, imply hierarchies for LQs λ s(cid:96) ∼ ( m s /m b ) λ b(cid:96) . It follows that third generationquark couplings dominate. Together with (13) one obtains the range from R K,K ∗ data for λ b(cid:96) , M/ . < ∼ λ b (cid:96) < ∼ M / . . (16)In figure 1 the single and pair production cross section for the scalar triplet S is shown for √ s = 13 TeV and 33 TeV. One finds that beauty production wins – bg -fusion over dg - and sg -fusion– also at hadronic level despite its PDF suppression if λ q(cid:96) follow quark mass hierarchies.Inverted hierarchies λ s(cid:96) > λ b(cid:96) would be surprising from a symmetry-based flavor perspectiveand suggest means beyond. Looking for pp → (cid:96)(cid:96) ( (cid:48) ) q is therefore very important, yet the vanillatheory channel is b(cid:96)(cid:96) ( (cid:48) ) , or in pair production, bb(cid:96)(cid:96) ( (cid:48) ) , (cid:96), (cid:96) (cid:48) = e, µ , also LFV (cid:96) (cid:54) = (cid:96) (cid:48) , and t(cid:96)ν (cid:96) ( (cid:48) ) . We briefly comment on the status of LNU in b → c(cid:96)ν decays. Input is compiled in table 2 . R D ( ∗ ) = B ( B → D ( ∗ ) τ ν τ ) B ( B → D ( ∗ ) (cid:96)ν (cid:96) ) , ˆ R D ( ∗ ) ≡ R D ( ∗ ) /R SM D ( ∗ ) , (17)where in the denominator of R D ( ∗ ) (cid:96) = µ at LHCb and (cid:96) = e, µ at Belle and BaBar.ˆ R exp D = 1 . ± . , ˆ R exp D ∗ = 1 . ± . , (2016) (18)ˆ R exp D = (1 . ± . / (1 + x ) , ˆ R exp D ∗ = 1 . ± . , (NEW) (19)and x = 3 .
6% ( D ) and x = 5 .
5% ( D + ) from QED corrections , hence ˆ R exp D = 1 . ± .
16 and1 . ± .
16, respectively a . See, e.g. ,
37 38 for other recent SM predictions of R D ∗ .In some scenarios, such as LQs S , V and V BSM effects in R K,K ∗ imply BSM effects in R D,D ∗ , however, due to the large SM contribution in the tree level decays, at a reduced level.Flavor models predict effects up to few percent and around 10 percent in R D ∗ and R D ,respectively, below the present 1 σ ranges, (18)-(19). Current data on R K , R K ∗ , R D , R D ∗ in semileptonic B -meson decays hint at violation of lepton-universality, and therefore the breakdown of the SM. The April 2017 release of R K ∗ by LHCb has a There are two caveats on the QED effects: The dependence on experimental cuts and that the radiativecorrections are not for electrons.able 2: Experimental results and SM predictions for R ( ∗ ) D , ’NEW’ labels updates since 2016. See text. † Errorweighted average; we added statistical and systematical uncertainties in quadrature. R D R D ∗ BaBar . ± . ± .
042 0 . ± . ± . . ± . ± .
026 0 . ± . ± . - 0 . ± . ± . - 0 . ± . +0 . − . LHCb - 0 . ± . ± . - 0 . ± . ± . ± . † . ± .
050 0 . ± . . ± . . ± . SM NEW (0 . ± . . ± . strengthened the previous hints and allowed to pin down the Dirac structure of the underlyingphysics to be predominantly of V-A-type. Future data – LNU updates and other observables R Φ , R Xs ..., B → K ( ∗ ) ee – from LHCb and in the nearer future from Belle II are eagerly awaited.What makes these LNU-anomalies – iff true – so important? They are theoretically cleanand intimately linked to flavor: they can give new insights towards the origin of flavor andstructure by probing models of flavor. Correspondingly, one should look for imprints in othersectors: D , K physics, LFV, including µ − e conversion and lepton decays.In addition, new BSM model buildung has been triggered that deserves attention in directsearches at ATLAS and CMS and future colliders. Leptoquarks are flavorful and can be in reachof the LHC, where they can provide complementary information to rare decays, on the couplings λ s(cid:96) , λ b(cid:96) and masses M separately vs their product (13). Model-independent upper limits on M are at the few O (10) TeV level, 40 ,
45 and 20 TeV for S , V and V , respectively . The bulkof the parameter space lies outside of the LHC
25 26 . Acknowledgments
GH is happy to thank the organizers for the opportunity to speak at this wonderful conference,and her collaborators for great collaboration. This work is supported in part by the
Bundesmin-isterium f¨ur Bildung und Forschung (BMBF).
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