Model with Lepton-Flavour Non-Universality

Phenomenology of an SU(2) × SU(2) × U(1) model with lepton-flavour non-universality

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

Citation Boucenna, Sofiane M., Alejandro Celis, Javier Fuentes-Marti#n, Avelino Vicente and Javier Virto. "Phenomenology of an SU(2) × SU(2) × U(1) model with lepton-flavour non-universality." Journal of High Energy Physics, December 2016, 2016:59.

As Published http://dx.doi.org/10.1007/JHEP12(2016)059

Publisher Springer Berlin Heidelberg

Version Final published version

Citable link http://hdl.handle.net/1721.1/117195

Detailed Terms http://creativecommons.org/licenses/by/4.0/ JHEP12(2016)059 Y c U(1) × , Springer 2 model December 6, 2016 SU(2) December 14, 2016 November 15, 2016 : September 12, 2016 decays at BaBar, × : : : 1 − ` Avelino Vicente U(1) + c s` [email protected] 10.1007/JHEP12(2016)059 Revised × , Accepted Received Published → doi: b bosons. This model can ease , are found to be reduced with 0 , φ and Z ∗ K SU(2) c`ν Published for SISSA by and = 1. 0 → × ' M b W M R Javier Fuentes-Mart´ın, b ), with − e SU(2) + [email protected] , [email protected] Me , → B Alejandro Celis, Γ( / a . ) 3 − µ + 1608.01349 d The Authors. Mµ -physics data while satisfying stringent bounds from ﬂavour physics, and c Beyond Standard Model, Gauge Symmetry

We investigate a gauge extension of the Standard Model in light of the ob- B , → [email protected] B = Γ( M Albert Einstein Center forInstitute Fundamental Physics, for Theoretical Physics, UniversityCH-3012 of Bern, Bern, Switzerland E-mail: [email protected] Arnold Sommerfeld Center forLudwig-Maximilians-UniversitätMünchen, Theoretical Physics, FakultätfürPhysik, Theresienstrasse 37, 80333 München,Germany Instituto de Corpuscular, F´ısica Universitat deE-46071 València— València,Spain CSIC, Laboratori Nazionali di Frascati, INFN, Via Enrico Fermi 40, 100044 Frascati, Italy b c d a Open Access Article funded by SCOAP respect to the Standard Model expectation Keywords: ArXiv ePrint: tributions in flavour transitionstensions mediated in by electroweak precision data. Possibleupcoming ways experimental to measurements test are theR discussed. proposed Among new other physics predictions, scenario the with ratios Abstract: served hints of leptonBelle universality and violation LHCb. in The modelwhich breaks consists spontaneously of around an the extended TeVmixing gauge scale group to effects SU(2) the electroweak with gauge group. vector-like Fermion fermions give rise to potentially large new physics con- Sofiane M. Boucenna, and Javier Virto Phenomenology of an with lepton-flavour non-universality JHEP12(2016)059 25 31 7 24 26 decays 9 τν ) ∗ ( 10 – 1 – -pole observables D W → M R B 25 20 - and 4 Z 30 13 29 29 20 15 16 16 17 13 19 21 7 2 28 24 transitions transitions transitions transitions transitions 20 u u s s c → → → → → c b b d s A.1 Tadpole equations A.2 Scalar mass matrices 6.1 Differential distributions6.2 in Lepton universality6.3 tests in Lepton flavour6.4 violation Direct searches for new states at the LHC 5.1 Fitting procedure 5.2 Results of the fit 4.4 4.5 4.6 4.7 Lepton flavour violation 4.1 Leptonic tau4.2 decays 4.3 3.1 Fermion masses 3.2 Vector boson3.3 masses and gauge Gauge mixing boson couplings to fermions B Pseudo-observables for 7 Conclusions A Details of the model 5 Global fit 6 Predictions 4 Flavour constraints 3 Gauge boson and fermion masses and interactions Contents 1 Introduction 2 Description of the model JHEP12(2016)059 Y × 2 U(1) bosons. × SU(2) ] and Un- Z L 1 × 1 . and em SU(2) W × U(1) C EW −→ Y GUTs. Depending on how spontaneously breaks at the 6 decays, we will carry out here Y ]. While the construction of the U(1) B 4 × ]). The extra SU(2) factor implies U(1) 3 L × 2 SU(2) SU(2) TeV × −→ 1 – 2 – Y U(1) × 2 SU(2) × 1 SU(2) ] schemes (for a general classification, cf. ref. [ 2 . We remain agnostic as to the origin of such a gauge group but assume it is broken charged similarly to the lepton and quark doubletsFermion mixing but under effects the (facilitated other bygroup) SU(2) the group. between same the scalar exotic field andvector which breaks SM currents the fermions by original act modulatingbosons. as the a couplings source of of the flavour non-universal SM fermions to the new gauge TeV scale to the SM electroweak group following the pattern The SM fields are allnumbers charged they under one have of in the SU(2)’s the only, SM, with the whereas same newly quantum introduced vector-like fermions are The extended gauge symmetry SU(2) Y The salient features of our model are summarised as follows: The model we will analyse was first presented in ref. [ In this article we present a detailed phenomenological analysis focused on flavour ob- A large class of particularly attractive NP theories consider extensions of the SM • • • a generic analysis of thea model secondary and step. impose the constraints arising from these hints only as unified [ the existence of new force carriersIn in general, the form their of couplings heavySM partners to fields of and the matter the SM are exotic new dictated fields by (if the any). choice Inmodel any of case, has representations a been rich of motivated phenomenology the mainly is predicted. by recent anomalies in U(1) around the TeV scale.a Models long based on time an andby extra constitute various SU(2) well-motivated some factor frameworks, have ofthe been such the SU(2) considered as and most since SO(10) U(1) studied or factors NP are E theories identified, we as can they have for are instance predicted Left-Right [ extended gauge group occurs aroundpredicted. the TeV scale, In a particular, plethorathese flavour of models observables physics due are observables to generally constitute the impressive a precision powerful and probe reachservables of to of a current test experiments. minimal extension of the SM electroweak gauge group to SU(2) where its gauge groupvia is various embedded steps) into at amodel or larger valid above one at the which low TeV breaks energies.composite scale. to models the These In and constructions SM this string-inspired include (directly view, models. Grand or the Interestingly, Unified SM when Theories the is (GUT), last seen breaking as of an the effective The Standard Model (SM)gauge of group, particle is physics,energy an experiments based extremely at on successful both thethat the theory SU(3) is intensity that and widely accounts energy consideredexpected frontiers. for to to It a be show is up wide incomplete, nevertheless around range and a the theory manifestations TeV of scale. of high new physics (NP) are 1 Introduction JHEP12(2016)059 – – – − − 7 ` ` c`ν 43 10 + + ` decay ) s` → ∗ ( − b → level [ K µ b + σ → ]. In contrast sµ B 69 ] systematically – → from the tree-level 70 deviation from the b 67 σ τν ) 6 ) anomalies have been ∗ . ( ) ∗ ( D D 019, implying a combined ( . → 0 R B , ) ) , and ) ) 316 . The `ν τν . ) − ) − − − ∗ ∗ ` µ e ( ( µ region shows a 2 anomalies. Measurements of + + + + D D ` 2 ]. Models addressing the µ boson from an extended gauge group [ ) q ) B ∗ 0 ) = 0 ∗ Ke ( Kµ → → ( ∗ Z 42 , K K D B → B ]. Effects due to the presence of light sterile → ( 41 – 3 – → Γ( R Γ( 40 B → B ]. Additionally, a measurement of the ratio B Γ( Γ( 5 B ], leptoquarks (or, equivalently, R-parity violating ) = ) = 31 ∗ ( ) or – boson [ ) K ∗ observables the issue of hadronic uncertainties still raises D level [ 0 ( 24 049 and ( R . ]. This observable constitutes a clean probe of lepton non- σ D 0 R 6 W ( sµµ R → 036 [ . b 0 397 . ], or a ], or a massive resonance from a strong dynamics [ 39 66 – – ], it is clear that a common explanation to all anomalies is only possible 090 074 . . 32 0 ) = 0 56 23 +0 − . The latest average of BaBar, Belle and LHCb measurements for these – D µ ( 18 745 R . or e . New physics contributions to = 0 -decay anomalies, though mainly focused on models that can accommodate only = K B ` R A considerable amount of efforts and model building activities have been devoted to Let us now briefly summarise the current ], leptoquarks [ ]. While in the case of ]. Intriguingly, departures from the SM have also been reported in supersymmetry) [ neutrinos have also beenanomalies explored on in the other refs. hand [ involved55 mostly a to these references, which rely on tree-level universality violation, ref. [ some debate [ in the presence of NP. these one of the anomalies:explained either with charged scalars [ 9 observables such as branching fractions anddata angular performed distributions. by Global different fits groups to NP show explanation a of good these departures overall from agreement17 the and SM obtain with a significances consistent around the 4 performed by the LHCb collaborationSM, in the low- universal new physics (NP) effects as many sources of uncertainty cancel in the ratio [ with processes is deviation from the SM at the 4 transitions for different finalto state a leptons can great beoccurring precision used in given ratios to the such test as cancellation lepton flavour of universality many sources of theoretical uncertainties Figure 1 exchange of massive vector bosons. JHEP12(2016)059 is × 2 L (2.3) (2.1) (2.2) ]. 4 SU(2) anomalies. × 1 , providing a sµµ 1 → b can be decomposed in ). Nevertheless, among -meson decays [ ) , respectively, while the ∗ L ( 2 B ` , ], an extended perturbative , D ( 1 2 we provide our conclusions. 1 78 R . − − – and 7 ) ) L 2 1 72 L , , q ! 1 1 , , e ν , , 1 2 and SU(2) i i we present the model in detail. We

1 1 1 2 = ]. An eﬀective ﬁeld theory approach has at the 1-loop level. The MSSM with R- = ( = ( L 79 ,W ,W L ,B, R K 0 1 2 g g g R , SU(2) , – 4 – , ` , e : : : C and tree-level for , ` 1 3 1 2 1 6 2 3 − Y L K ) ) ) ! 2 1 1 R , , , d u 1 1 1 U(1)

SU(2) SU(2) , , , ]. 3 3 3 = . Our global fit main results and predictions are presented ] and some observations about the relevance of quantum 83 4 L 82 = ( = ( = ( q ], finding that it is difficult to address the – L R R 71 q corresponds to the usual hypercharge while the SM SU(2) d u , respectively. Finally, in section 80 , Y 6 72 3 is the SU(2) index. All of the SM left-handed fermions transform exclu- ], or strongly-interacting models [ , 4 2 , and section . A detailed description of the flavour and electroweak observables included in 5 3 = 1 components in the usual way, i . The factor U(1) 2 Y The plan of the paper is as follows: in section In our model, the massive gauge vector bosons arising from the breaking of the extended Unified explanations of both sets of anomalies are much more scarce. This is due to subscript denotes the hypercharge.SU(2) The SM doublets where the representations refer to SU(3) where sively under the second SU(2) factor, i.e. U(1) contained in the SU(2)electroweak product. group will The be gauge denoted bosons as: and gauge couplings of the extended Details of the model are provided in the appendices. 2 Description of theWe model consider a theory with the electroweak gauge group promoted to SU(2) derive the gauge bosonin and section fermion masses andthe mixings, global fit as is well given as inin the section section required textures gauge group [ been adopted in refs.effects [ have been given in ref. [ gauge group mediatepossible flavour explanation transitions to at the deviations tree-level from as the shown SM observed in in figure parity was analysed in ref. [ the difficulty of accounting forSM deviations at of different similar orders: sizethe in loop proposed processes level models that for we take find place those in based the on leptoquarks [ explored renormalizable models that explain JHEP12(2016)059 (2.8) (2.5) (2.6) (2.7) (2.4) , ! . 0 + 0 1 2 0 doublet with the ϕ ϕ − , Y φ 3 2 2 ) 2 2 6 3 6 / / 1 /

1 2 1 / 0 / / / / 1 1 1 ) , ., − 1 1 1 2 1 = 1 c 2 − − − . U(1) 0 , , 2 1 , ., + h 2 1 c . the usual Pauli matrix) and = ( R ¯ 2 1 1 1 2 = ( σ 3 matrices in family space. The φ e 0 + h L,R SU(2) e × R ! y , φ L L E N as a free parameter to be constrained 1 ` L !

, with , φ VL 0 + 2 + M 2 2 2 2 n ≡ ¯ σ 0 Φ Φ L R ) ∗ SU(2) L ¯ 2 Φ − , ˜ 0 φ u L,R 2 + Φ 2 Φ σ u L , C − R y 1 – 5 – ;

L Q 1 1 2 1 1 333 11 11 1 2 1 1 1 1 2 1 3 1 q 2 1 6 Q 1 ) + √ M 1 Φ = ( R , L . We summarise the particle content of the model in 2 ∗ , Q . Particle content of the model. φ d ) Φ = 3 d + = , y generations of vector-like fermions transforming as 1 2 VL VL = ( 1 1 1 3 3 3 3 3 L M ) q n n VL 2 Yukawa couplings represent 3 = (Φ , Table 1 n The SM fermions couple to the SM Higgs-like = L,R − L 1 − generations SU(3) φ , ! , 1 u,d,e , U D 0 y ! − L

φ 0 = ( R R L 0 L R + L,R φ L,R Φ φ ` q e and Φ d u ≡ ϕ ϕ φ L Q ∗ and

) . The 0 ∗ L,R φ = φ Q 2 φ iσ = (Φ ≡ 0 . ¯ ˜ Φ φ 1 with vector-like fermions, on the other hand, have gauge-invariant Dirac mass terms, with table Yukawa interactions. usual Yukawa terms, which we decompose as: by phenomenological requirements. Symmetryof scalars: breaking is a self-dual achievedtwo bidoublet via doublets Φ the (i.e., following Φ set = For the moment we take the number of generations In addition, we introduce JHEP12(2016)059 2 2 = /g and β 1 (2.9) g (2.12) (2.13) (2.11) (2.14) (2.15) (2.10) φ SU(2) . = for more × β . 1 c . 3.2 . , + h 2 ! φ 0 u em ., Φ) Φ c † 0 u . 0†

U(1) 2 1 + h µ φ Tr(Φ v R ., = e −→ c 3 0 . i 2 λ φ Y bosons. In the CP-conserving Φ h e Φ) + ) 0 + h e † y Y, ( L L Z U(1) + ` Φ) + L † L , 3 Φ × + )Tr(Φ T † ` 0 L ! and λ 0 R 246 GeV. With this breaking chain, the φ = β , φ Tr(Φ . Under the diagonal sub-group, β , 0 u R 0† v The scalar potential can be cast as follows: ) L 0 0 2 Φ ' φ L Y ( ˜ φ

( sin cos m v SU(2) 6 u + + 2 W v v λ e y 1 + 3 Yukawa matrices, respectively. After sponta- L √ u – 6 – 2 L q 3 4 . In the ﬁrst step, the original SU(2) = = | −→ × a 0 T 0 Q = Φ φ φ φ Y v Φ) + † q i | VL + v 0 + † TeV λ 2 n 1 φ 2 3 R λ h R T ∼ d U(1) 0 Q + u and φ )Tr(Φ × 2 = group is deﬁned as | = contain 12 real degrees of freedom, six of these become the d 0 φ 2 , e y VL † φ } Φ Q | 0 n φ em L 0 ! ( 2 φ φ 5 Q , φ 0 × v − L λ m Φ SU(2) =

0 + × φ, 2 φ ) + , the symmetry breaking proceeds via the following pattern: . Since the two doublets transformed originally in a ‘mirror’ way 4 1 { 0 are 3 1 0 0 | √ 2 φ φ φ φ | v 0† − L = , v 1 φ 2 φ u,d,e i + λ v e y )( SU(2) φ 2 φ h φ + v † 2 φ | and ( u = φ 4 | the diagonal generator of SU(2) λ 2 φ 2 q,` a v 3 λ , controls the size of the gauge mixing effects. In particular, the limit tan m + 0 T φ The scalar fields = transform as doublets and, as usual with two-Higgs doublet models (2HDM), we /v V 0 φ v corresponds to the purely diagonaldetails. limit with no gauge mixing, see subsection longitudinal polarization components of the parametrize their vevs as where under the two original SU(2) factors, it is clear that the ratio between their vevs, tan with group gets broken downφ to the diagonal SU(2) with the assumed vevcharge hierarchy of the unbroken U(1) develop vevs in the following directions: Assuming We will assume that the parameters in the scalar potential are such that the scalar fields neous symmetry breaking, these couplingsSM will chiral induce fermions. mixings between Thisits the is vector-like flavour and sector, crucial as for will the be phenomenology clearScalar of in potential the the and symmetry model, next breaking. sections. in particular in and where and our choice of representations allows us to Yukawa-couple them to the SM fermions via JHEP12(2016)059 (3.2) (3.3) (3.1) . u ∼ . µ A . c . , , is odd and all the + h   0 R , k L,R φ u Q q N 0. This can be justified λ ,D k . N R M 1 2 ' 0 ! M i L,R ,N φ φ d 0 L u v v L ` d d u,d,e N λ y e y e y M 1 2 2 ≡ ≡ 2 + 1 1 √ . With this notation the fermion √ I 0 0 R R E VL I L,R N   E n D = = M D L N 3 + heavy neutral Dirac fermions. It is never- E M M + VL symmetry under which ,..., n R , , – 7 – 2 D TeV. can be neglected,   Z D   = 1 0 ∼ u u Q φ I q L ` M u λ , , λ L M M 1 2 1 2 D 0 0 and , φ φ φ φ + v v v k v k L,R L,R u e u e VL R k y y L e e y y U ,U ,E 2 2 2 2 1 1 U 1 1 √ √ √ √ ,N i L,R i L i L,R M u ν e     , . . . , n L is of the same order of the largest scale in the scalar potential, i.e. U = = µ Further details of the scalar sector are given in appendix ≡ ≡ ≡ = 1 E U = I 1 L k f m M I I M L,R L,R N E 3, U , TeV. − L 2 , ∼ u = 1 i leads to three massless neutrinos and In order to have a manageable parameter space and simplify the analysis we will We will assume that N 1 assume that the Yukawa couplingsby of introducing a softly-brokenother fields discrete are even. Wearound take the the Dirac symmetry masses breaking of scale the vector-like fermions to be generically Note that we did not includeM any mechanism to generate neutrino masses,theless and straightforward consequently to account forconclusions neutrino by masses including without one impacting of our analysis the and usual mechanisms, such as the standard seesaw. The mass matrices areand given vevs in as terms of the Yukawa couplings, vector-like Dirac masses where mass Lagrangian after symmetry breaking is given by 3.1 Fermion masses We can combine the SM and the vector-like fermions as 3 Gauge boson andWe fermion now masses proceed and to interactions will the derive analysis the of masses the andas model the mixing presented neutral of in and the the charged gauge vectorial previous bosons currents. section. and fermions Here of we the model, as well and one charged scalar,system. The forming scalar an sector willat effective present the (constrained) a weak decoupling 2HDM scale behaviour, (to plusthe with be scale a CP-even associated SM-like singlet with Higgs the boson 125 GeV boson) and the rest of the scalars at limit the scalar spectrum is composed of three CP-even Higgs bosons, one CP-odd Higgs JHEP12(2016)059 (3.9) (3.8) (3.7) (3.4) (3.5) (3.6) (3.10) , , ...     VL + , n 1 2 ,L − Q,L , f W VL † Q,L M H n     2 Q q,` M 2 ) 2 λ 1 − f F i M ( − Q,L f 11 M Q,L † , f , M + , V , 1 u 21 R 2 u ,..., R F R f , W 3 unitary transformations , 1 . V 0 U D E     − = † f R ,L † † † R R u d e 1 × 1 y u d e = iH − F f Q † † † W W W u d e 22 y Q,L f + f M U U U M V 12 11 † → → → Q,L F 1 0 V 21 V → → → F R R R V = E U D R R R 11 † f † q,` F diag y λ is removed by choosing it to be hermitian. f V , † , f ' 2 , f W , d , e y , u L – 8 – y − L Q,L L † q,` f , 11 L L L Q,L U D q,` E 21 y λ f F d e M L u V . † † † λ u d e 0 1 4 † † † V † 21 u d e d F N 0 q,` 1 V V V − † q,` Q,L S S S S V † † † † λ − Q Q L L F u λ 2 1 4 f ; M V V V V S − → → → F f 1 2 M + − L L L f = − M → → → → ... e = d u 1 are given by . After the block-diagonalization, a further diagonalization − L L L L     + Q,L E q U f D N W 2 21     f Q,L V 2 M CKM i = H i V u √ 2 V H u, d, e 2 † Q,L = = 11 i Q,L = is the physical vector-like mass at leading order in M and f V V f W + f f V H s H 1     Q,L H = = = f and M f u V Q,L Q,L 1 by means of the following field transformations V f M Q, L = F The fermion mass matrices can be block-diagonalized perturbatively in the small ratio v/u = As in the SM,plings: only the one CKM combination matrix, of these transformations appears in the gauge cou- with of the SM fermion block can be done by means of the 3 and the matrices Here the freedom inFurthermore, the definition of defined in terms of the unitary matrices JHEP12(2016)059 . ) 2 = the ,A 0 l ) are 3 g/n V (3.17) (3.13) (3.16) (3.12) (3.14) (3.15) (3.11) W . In the ,Z = ,Z 1 0 h Z Z W . /n c 2 gets a mass 2 block and g     1 h × , ), with 0 0 g Z 3 and ˆ , . l . 2 2 = 3 2 β Z , c ,W g      W /n 2 2 1 2 Z h 0 2 β g g 1 ξ g c 2 0 Z g 2 φ v 2 2 0 1 2 − 2 φ g B v 2 = φ g g + v v 2 β 2 0 remains unbroken in that to ( 0 1 + 0 + 3 s = 0, only g W − g + cos g 3 2 s 2 φ 1 Y 2 β 2 W h 3 g v v g 2 s + W 2 Z v − 0 − g 2 2 2 1 g Z 0 g ,W 0 U(1) g g ξ 2 1 g Z 2 3 1 Z 2 1 2 × n 1 bosons. Before fully diagonalizing taking the value M W n M ) is just like in the SM and we obtain: 2 L g n 0 2 2 1 L = 2 φ u . = sin g g − = u v Z ,A 3 0 2 β 2 l 2 + c g g g Z , group remains unbroken in the first step). n 2 2 2 2 1 2 1 φ 2 β g g g g v c L and mixing. The mass eigenvectors ( 4 4 = 1 2 − − g g v/u − 2 h 2 = 0, diagonalize the top-left 2 ) to ( Z g 2 β 2 β – 9 – Z ≡ + 2 β v s c c ,Z ,A 2 β 2 2 ,W 1 2 ,B − l 2 2 1 2 2 g g s 3 = 0 g g l 2 u Z 2 φ 2 ζ 3 u B Z W − v 2 Z 0 2 0 − + (the SU(2) ξ v 2 β g W g g 0 2 β 2 2 s 1 1 3 2 φ 2 2 g 1 s g g 0 0 0 − v g 2 g sin 6= 0 and W g 2 3 − − − 2 v − 2 u 1 + 1 g The neutral gauge bosons mass matrix in the basis 2 1 3 h gauge boson. In order to do this we have to study the first g g 2 1 2 g W Z g g 2 W      u L ), by: 2 Z 1 2 l 2 1 1 4 1 ξ g 2 2 g n n n and the weak angle is defined as usual: ˆ g g n − ,Z = 1 , which is expected since SU(2) 2 = h 1 + and the gauge coupling of SU(2) 0 2 0 n ' l g Z 2 u 1 2 2 2 V = cos Z g g Z = 0 + ξ 2 2 M h + 2 g Z     g Z 2 1 is given by: + g 4 1 p 2 1 ) basis, the rotation from ( p g = = ,B 0 ,B = 2 2 1 4 3 3 2 V n 1 n = ,W M ,W 0 1 3 h Z W Z We define the parameter controlling the mixing as case. Moreover, wegiven, can in extract terms the of ( with the mixing suppressed by the ratio We see from thisM mass matrix that in the particular limit where We are now in conditionbasis to where write it the takes neutral the gauge form: boson mass matrix in the ( with ( electrically neutral SU(2) symmetry breaking step, i.e. identify the massless state with As a result we get: This matrix has oneeigenstates vanishing which eigenvalue, corresponding are tothis identified the mass with matrix photon the we and consider two first massive the rotation from Neutral gauge bosons. 3.2 Vector boson masses and gauge mixing JHEP12(2016)059 0 ), r 2 → iW (3.21) (3.22) (3.23) (3.19) (3.20) (3.25) (3.24) (3.18) ζ − , r 1 2 ψ, W gauge boson . , ( l 2 . L 2 1 3   = 0, diagonalize √ W T 2 v 2 1 2 β W = c g g ξ . W . 2 2 1 2 g g 2 1 r 2 12 − g v v 1 2 3 W − . remains unbroken in the + g 2 T 2 + cos 2 β 0 1 4 v 1 1 2 s L   g h 2 g g g W ' W + 2 2 2 2 µ h v 2 , with u g 2 , W W u 2 1 g g g ξ 2 0 + gZ ) where the SU(2) 2 (SU(2) 12 g 2 1 l 2 W 2 W 1 1 4 2 1 φ l g n g v M ] + − ,W M W ' ,W − = ψ = sin 2 1 1 h 2 12 2 2 l Z g g g Q 2 β W W c ζ ψ ,M 4 4 2 W 1 2 2 2 g g s = 2 2 u u = 3 2 u − + T 2 β 2 + 2 2 + ) µ 2 β c g 0 2 1 g 2 2 – 10 – 3 3 V s 1 2 2 1 2 2 φ g g ,W ,W g g ,M g T v + l 2 1 W 2 2 2 − . 2 2 g 1 n + − 2 u v W 2 g 2 1 g 1 2 2 ζ 2 β 3 g 2 g 1 W 2 /g 2 s W + T 2 g 1 4 1 ξ g 2 ' g   1 [( sub-group corresponds to the diagonal subgroup of the 3 g g 2 µ l T + ' 1 4 v W + L sin µ − Z 2 0 → ξ 1 2 1 1 2 3 g g 2 g 1 Z = In the basis − u β W 2 g W c h g + M W 1 1 4 2 2 2 V g 1 − W g + ' g ' 0 + µ M + W 0 The neutral currents of the fermions are given by 1 ξ 2 2 A W Z 2 1 1 Y ) the mass matrix reads: n l g µ ψ M M 0, the SU(2) B = 0   ,W e Q g h = cos h → 1 4 0 mixing presents the same structure as in the neutral gauge boson sector and W W µ µ ζ = h W ψγ ψγ + W 2 V = = − l M NC W Finally, the masses of the neutral massive vector bosons are given by L Neutral currents. with masses 3.3 Gauge boson couplings to fermions such that the physical eigenstates are given by: The reads: In the basis ( As before, it isappears convenient explicitly. to To obtain work this basis inthe in the terms mass of basis matrix the and ( original one, associatefirst we the set stage null of eigenvalue symmetry to breaking). We get: Charged gauge bosons. the charged gauge boson mass matrix is given by original SU(2) product andcorresponds to gauge the mixing limit vanishes. tan As anticipated in section In the limit JHEP12(2016)059 ) L 3.10 N R (3.30) (3.26) (3.31) (3.28) (3.29) (3.27) L E L O νe R i , i µ o R O γ R µ R ) and ( N ! E γ ., L 1 µ N c R . γ . − 3.4 νe µ N R F c γ N . R O f − M R + † + h µ N L γ R N E − 21 ] + h R , D F ψ L L − e R E V N ud R O E ! L R µ † † E Q 1 E µ 1 O P + ) ) ee R − γ µ R µ 2 W ee R R Nγ γ O s L P 22 22 Q,L Q,L O R D 11 µ E µ νγ )), we have F + V V − γ U µ ( ( V ud R + + γ L R D , and we introduced the following Nγ O f L d µ E 2 2 P 2 1 R 3.10 12 22 u Q,L Q,L ) g g U E µ + m L 2 V V + 3 γ † Uγ P − − T + † † D R R V u, d, e ) ) µ L 0 R 1 2 U R U + Q E L f u g g = U ) and ( P uγ L 12 12 L 1 m 3 Q,L Q,L [ + uu R µ 1 f T O V V − 2 uu µ VO R L ( O 3.4 ( ( µ − ) E µ Uγ O γ µ denoting the electric coupling and the electric e W γ µ µ γ L 12 22 µ L 2 11 Q,L Q,L 2 ψ + F γ L γ – 11 – P R g V V N √ V ψγ Q U E L µ R 0 U

+ n L U N + − µ L 21 2 l νγ 2 − P . F g 1 µ L Z and − + D V R + 2 2 γ 1 E Q 2 L D . + L R /g g W g D µ d − F 2 c N 2 1 Q L D D L /n ! g dd R 0 f M P VO gg O V + 2 f + Nγ 2 dd R µ µ O − µ µ − gg u . γ ≡ m ψ D O µ + γ γ

1 uγ L L ψ γ µ g =

( L ! L U D γ P R = e = 2 f U 2 1 2 D µ µ O eQ µ R h g g h h D u γ , m ! µ Similarly, the charged currents take the following form ! µ h µ D + l f U W Uγ

. 1 µ Z ! 2 2 h 1 2 ˆ 2 Σ ψγ c W , and ˆ Q,L 0 2 Σ g g g . ˆ 1 µ g 1 2 µ l O 2 µ W † √ Ω g N 2 A W W 0 √ − + − + , g − + h f 0 2 2 † 0 1 √ 1 E q,` g = CKM ˆ , and ﬁnally ˆ Σ g , Σ = √ √ ∆ V − D

, NC = = CC Q, L U = ≡ ≡ denotes the mass of a SM fermion with 0 = CC = f → L V →L L ff R F m Q,L L ψ O CC NC O L L and, in the fermion mass eigenbasis (see eqs. ( Charged currents. with Here definitions: charge of the fermions, respectively.we Applying can the easily transformations translate in the eqs. above ( interactions to the fermion mass eigenbasis with JHEP12(2016)059 (3.35) (3.34) (3.33) (3.32) can be = 2 since q,` , are mass . We have λ 0 VL 1 which then q,` ff R n O b,τ . ∆ = 1, NP contributions ,     2 decays without being in ) s,µ VL Yukawa couplings. On the n b,τ b,τ b,τ B , ∆ ∆ q,` , (∆     λ d,e s,µ † q,` − . ∆ b,τ ∆ s,µ 1 and ∆ λ 1 2 ∆ ∆     2 ' − 2 In order to accommodate the hints 2 ) 0 ,L ,L d,e b,τ s,µ f b,τ M s,µ 2 2 d,e = 1, the Yukawa couplings s,µ ∆ ∆ ∆ Q Q ∆ ∆ q,`     f (∆ λ f VL M M , that parametrize NP contributions to the d,e s,µ 2 2 n 1 − g ∆ ∆ q,` 2 2 Q,L ,L 1 g 1 + 0 0 f 4 M 2 – 12 – Q 2 1 ) 2 1 g g f M b,τ s,µ n d,e 2 − ∆     ∆ ) it is then clear that, for : 1 = (∆ 2 1 d,e d,e g q,` n − = 2 ∆ ∆ q,` 3.32 λ 1 λ = q,`     ), the matrix ∆ ∆ q,` = λ 3.5 are free real parameters, and without loss of generality we have =1 VL µ,τ q,` n ) and ( ∆ and ∆ 3.27 s,b , ∆ d,e In the rest of this article we will take the minimal setup consisting of If we consider the minimal scenario with Using eqs. ( texture for the Yukawa matrices implies approximate universal couplingsneed for at the second least and twoaccommodate the generations the third of observed families. vector-like hints fermions of Hence, in lepton we universality order violation. tothere have enough is freedom no to compellingorder reason to to reduce assume the additional vector-like number generations. of free Moreover, in parameters in the analysis we choose the following As we can see, inof the SM limit fermions of can no only gauge be boson suppressed mixing, if NP we contributions to fix the ∆ first family also ignored possible complexviolating phases observables. in From eq. theto ( couplings the since left-handed we gauge couplings are to not SM interested fermions in are CP given by Here ∆ chosen an appropriate normalization factor to simplify the expression of ∆ between the SM and vector-likeother fermions hand, generated right-handed by couplings the suppressed involving and SM they fermions, can be controlled neglected by for the interactionswritten we generically are as considering. left-handed gauge interactions withform SM fermions, can be readily written in the following where the second term is the source of lepton non-universality induced by the mixings of lepton universality violationtension from with the other recent bounds,the anomalies first we in family require of SM-likeWe negligible leptons now couplings and derive of a large theaccommodate the universality such conditions new violation constraints. among on gauge the bosons the other to number two. of generations of the exotic fermions to Flavour textures for the gauge interactions. JHEP12(2016)059 - ). )) i Z and 1 for Zd L,R ]. We (3.37) (3.38) (3.36) 3.27 ≤ W δg ) 85 , i 2 b,τ Zu L,R and describe + ∆ δg 2 (see eq. ( 2 s,µ Q,L L )(∆ 2 2 ), anomalous O /g 2 δm g pole, we use the fit to − , , W        , mass (     pole which are affected in our 2 b,τ 2 b,τ 2   ) and 2 2 1 2 W ∆ ∆ g g W b,τ b,τ couplings to quarks ( Z − − ∆ − Z (∆ s,µ and 2 s,µ 2 s,µ 2 b,τ − ∆ ∆ ∆ 0 Z 0 1 − − 2 + ∆ ) 2 1 ]. The fit includes the observables listed in 2 1 2 2 2 2 g g n n b,τ 2 s,µ ), normalized to the muon decay rate to cancel s,µ 84 ¯ ν ∆ r r – 13 – ν (∆ } s,µ 2 2 1 2 b,τ s,µ g g − 0 ∆ e, µ − 1 2 ) and anomalous 0 ∆ 0 ∆ g g i 00 1 00 ∆ 0 1              Z` L,R → { τ δg = = , i Σ = are free real parameters and the normalization factor is chosen q,` Q,L W ` L ∆ Ω µ,τ δg . We take the individual experimental branching ratios and lifetimes ). F ], and provides mean values, standard deviations and the correlation . G and ∆ 84 3.7 The left-handed currents, parametrized in terms of B 2 s,b ]. The relevant expressions for these pseudo-observables within our model are 84 -pole observables performed in ref. [ W We collect the list of flavour observables included in our analysis in table Regarding electroweak precision observables at the Note however that the free parameters have to satisfy the condition (1 2 couplings to leptons ( consistency with eq. ( 4.1 Leptonic tauLeptonic decays tau decays pose veryconsider stringent the constraints two on decay lepton rates flavour Γ( the universality dependence [ on of ref. [ given in appendix them in more detail in the following subsections. and tables 1 and 2matrix of for [ the following parameters:Z the correction to the The results for these “pseudo-observables” can be found in eqs. (4.5-4.8) and appendix B We consider in our analysis flavourlevel observables from receiving new the physics exchange contributionsfrom at of electroweak tree- the precision massive measurements vectormodel at due bosons. the to gauge Additionally, mixing we effects. consider bounds which, by construction, providemodate the the desired data. patterns for the NP contributions to accom- 4 Flavour constraints for convenience. now read where, again, ∆ JHEP12(2016)059 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 4.9 4.4 4.1 4.5 4.2 4.19 4.20 4.22 4.20 4.13 4.21 4.11 4.14 4.21 4.15 4.19 4.19 4.19 4.10 Eq. ( Eq. ( Eq. ( Eq. ( Eq. ( Eq. ( 6 6 4 3 7 7 10 10 10 10 10 · 10 · 8) Eq. ( · · · . · 0. Eq. ( 6(1) Eq. ( 2(1 . . 995(1) Eq. ( 223(5) Eq. ( 996(1) Eq. ( 921(1) Eq. ( 252(3) Eq. ( 663(2) Eq. ( 297(17) Eq. ( ...... 0 91(1) 0 037(2) 096(1) 939(4) . 3456(5) 3087(5) . . . . 7 . 4 8 1 1 1    ·      · 3) 0 . 00 ·· . 51 21 87 ·· . . . 0 49 45 = 1 . . +0 − 0 0 27 01 0 ··· S . . 10 0 0 . 02 0 ··· . 0    – 14 – − 08 6 6 . 4 3 7 7 10 02 0 ···· . . 0 10 10 0 0 10 10 10 10 − · · · · · ·      0(6) 9 . 13(15) 31 95(5) ( 95(09) 97(08) 0 660(3) 0 . . 397(49) 222(22) 0 316(19) 0 . . . . List of flavour observables used in the fit. . . 0 . 10 0 0 0 02(2) 13(3) 89(3) 90(5) 35 0 350(4) 320(4) ...... 4 8 1 7 1 1 ] Correlation SM Theory 2) 2) 0. Eq. ( 7) 0. Eq. ( 6) 0. Eq. ( . . . . 16 Table 2 1(0 3(0 3(1 6(1 . . . . ¯ ν 1 0 ¯ e ν eν ∗ ¯ πeν c ν ¯ ν − +0 − +0 µν eν eν Keν De D X → eν eν eν eν d → → + → decays → → → → s → → → → M ) 0 B B K D π K B K π µ D µ ) 0 τ ∗ e µ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ Γ ∆ µ e D / / / / / / / / / / D / / / NP NP NP NP 9 9 10 10 ( transitions ¯ ¯ ¯ ( ν ν s ν transitions ¯ ν transitions transitions C C C transitions C τν µ µν µν πν τν R Kν R c eν ∗ µν πµν M u u c s s Dµ Kµν → → → → X → D Coefficient Fit [ → s → τ π → Observable Experiment Correlation SM Theory Observable Experiment SM Theory Observable Experiment Correlation SM Theory Observable Experiment SM Theory Observable Experiment Correlation SM Theory Observable Experiment Correlation SM Theory ∆ → τ K → τ τ → + D → Γ Γ → B → Γ → → → Γ D Γ Γ B Γ B K Γ Γ b b s c d Leptonic Γ Γ Γ JHEP12(2016)059 → π (4.8) (4.4) (4.5) (4.6) (4.7) (4.1) (4.2) (4.3) ( B . lifetime, ) in order ) )+ τ . ` ib eν eν ∆ → aj → ]. ab δ δ π . π 90 ij ( ) – ) , + 2 B q ) 87 ib τ/π ∆ δ , , e/µ V ` aj δR , , → . The Wilson coefficients π ) ) SM ) SM + ( ) x eµ µτ eτ eµ ) ` ab ) ln ) (1 + ) δR + 2∆ x x x x ¯ ν ¯ ¯ ν ν 2 2 . Leading radiative corrections ( ( ( ( ∆ e e µ ij πν x # f f f f 2 ij δ 2 τ 2 P 5 µ 5 τ 5 τ V 5 µ (1 + 12 → → ` ab → → . These ratios constitute important 2 m ), normalized to Γ( m m m π ζ π − π /m π τ /m f (∆ 2 π | 2 µ 4 2 π 2 π . × − πν × ζ Γ( Γ( Γ( Γ( transitions. x m ud m 2 2 2 2 2 | ` ab | + | | V /m → /m − | − − 2 e 2 µ ∆ × × eµ eτ eµ µτ ` ij ij ij ij ij τ F u`ν 3 1 1 ij m 2 2 2 2 m x |C |C ∆ |C |C ) | | | | G " q → j j j j ` ab − − ]. We have: i,j ud ud ud ud i,j i,j i,j 2 1 3 1 2 µ ∆ – 15 – d + 8 1 1 ∆ |C |C |C |C 85 m 3 τ P P P P V ], and imposing the constraint x j j j j π ( − 8 m ) and Γ( 2 e 2 µ 86 = = m ` ib 0 P P P P m − 2 m µν 2 ) ) are given by ) ) ∆ W 2 ¯ ¯ ¯ = = ¯ ν ν ν ν ˆ g j ` aj = = M d → ) ) i ) ) 2 eν eν eν µν u ¯ ¯ ab ν ¯ ν ν π 2∆ ) = 1 SM SM e C e µ πν + → x → → → 0 ( ) ) ) ) ab τ µ → → µ τ → → f 2 ¯ W ν ¯ ν δ 2 e ˆ π g µ µν π τ πν π Γ( Γ( Γ( ij Γ( M V 4 Γ( Γ( Γ( Γ( . → and → → → F 2 0 + 2 π τ π π 2 ` G √ 4 ib Γ( ]. For the branching ratios we take the result of the constrained fit, which Γ( Γ( Γ( δ /m = 2 ` aj 86 δ j transitions m d F i 2 u ab u G = √ C 4 0 → `` = -boson propagator effects are included in the SM predictions [ x d b are given by ` W The model predictions for these ratios are: We calculate the experimental values for these ratios taking the averages for branching In our model, we have: a b ` ij ` ) = 1. We find a correlation of 49% between both ratios. The corresponding results are a C ` ij where the Wilson coefficients For the SM contributions we follow ref. [ constraints on flavour non-universality in fractions and lifetimes from the PDGµν [ summarized in table and 4.2 We consider the decay ratesto Γ( cancel the dependence on the combination C The resulting predictions in the SM can be found in table where gives a correlation of 14%the between decay both rates measurements. have Once ahas normalized correlation to a of the 45%, minor while impactThe the on experimental normalization the to results the are correlation muon summarized of decay in the rate table ratios because its uncertainty is negligible. from the PDG [ JHEP12(2016)059 ) ) ) ]. ], ν 3 ν ν → → ` + 91 86 + + ` 0 K + (4.9) 0 e e 0 (4.10) (4.11) (4.12) D )[ ¯ ), con- K K modes, 2 π → p ) in order 2 µν K + → → e ( ]. The SM eν K + + → O D s K → 92 , ) and Γ( D ν K 91 + Γ( ), Γ( , / µ )[ ν ) + . , , , SM → 4.8 τν µ 2 ) + ) SM SM → → ), ( ¯ ν ¯ ]. The SM predictions for ν K s ) ) + ) ) Kπ 92 SU(2) Kπ SU(2) πe ¯ 4.7 πµ ν ¯ ¯ ν ν D δ δ K e e µ Kν → → + + → → → , as well as the semileptonic ( + + → decay data done by the PDG [ K ), normalized to Γ( Kµ EM Ke EM K K K τ K K f δ δ mode is uncorrelated to the | + ) and Γ( Γ( Γ( Γ( Γ( Γ( Γ( Kν τ ). The SM contributions for the first us K V 1 + 1 + | → 4.6 × × × F Keν ]. The numerical results for the SM contri- ) ) τ i i 2 2 2 2 2 2 G | | | | | | 95 λ λ → j j j j j j ( ( – us us us us us us 2 1 3 1 2 1 – 16 – 93 (0) |C |C |C |C |C |C D (0) Ke Kµ ] I I j j j j j j ). These ratios pose also important constraints on can be found in ref. [ encoding phase-space factors, electromagnetic and Γ( non-universality. ) and Γ( ν 94 / P P P P P P = , ) + µ e µν ) ) τ/π 93 0 . = = = ¯ − ν ¯ ν given in eq. ( Kπ π SU(2) → 2 ) ) ) τ ) ) ) δR δ Kµν πe ¯ ¯ πµ ¯ ν ν ¯ ¯ ν ν ν us . ij , → e e K µ C Kν relies on Chiral Perturbation Theory to order 2 → πe → πµ → + and K` EM → → → δ + + → e D K → → e/µ K K K τ K K ), − Γ( + + → i / π Γ( Γ( Γ( µ Γ( λ Γ( Γ( ) K K are given by [ ( ) from the constrained fit to ν ν δR 3 Γ( Γ( 5 correlation matrix and calculate the three ratios of interest, including + (0) ` K` , we consider charged and neutral modes separately. For + I µ µ K × 0 0 π π K`ν transitions transitions → u → s → + 3 correlation matrix. These results are collected in table + D → → K × K c s For The model predictions for these ratios are: We take the experimental values for the decay rates Γ( ) is calculated comparing the averages for the individual rates with the ratio given by ν + 4.4 We consider the ratiosstraining Γ( respectively we take the separate branching ratios from the PDG assuming no correlation. For where quantities isospin corrections can bebutions found are in collected refs. in [ table two ratios are givencontributions by to the analogous expressions to eqs. ( with the Wilson coefficients including the correlation matrix.e The correlation betweenthe PDG, Γ( resulting in a correlationand of the 60%. semileptonic Assuming modes, no and correlation assumingwe between that Γ( construct the a 5 their 3 to cancel the dependence onratio the Γ( combination flavour non-universality. and Γ( The radiative correction factor both ratios are collected in table 4.3 We consider the decay rates Γ( The calculation of JHEP12(2016)059 ]. = → 5 . and 2 2 ξ + (4.15) (4.16) (4.13) (4.14) F D tension . G Γ( σ 2 . We note / d 1 ) ν M ∼ + ∆ µ / 0 s . ¯ K 2 M ) 3 , q i , → ,

(∆ ]. The parameter SM + 93(4). These two ratios, 0 . constitutes a strong con- SM 97 NP ) SM D sb ) db 2 W 2 s 3. ¯ ) ν ¯ ) C C ν . ˆ g ¯ ¯ ν ν M M 8 τ µ + ) = 0 Ke Kµ = 1 ν 2 2 ts td = → → + S → V V → e b s s with anomalous couplings). To the

i − NP d D D D D 2 Z C ξ K ]. The result is given in table Γ( Γ( Γ( Γ( s d 5 . B B → ). are given by and 2 × × 0 , M M 0 b i ) 4.6 2 2 2 2 D Z t NP | | | | d = j j j j x C cs cs cs cs 2 1 3 2

Γ( ( The observable ∆ – 17 – 0 / + |C |C |C |C sb db ) S j j j j C C b ν 2 i

) SM + d P P P P ? tb 2 C µ does not receive NP contributions at tree-level. ξ V − d = = = ti s d K V b B B ) ) ) M ) given in eq. ( ratios separately, obtaining Γ( i ( system. ¯ ¯ ¯ ν ν ¯ ν d ν M M 0 τ 2 C µ cs → ij W s 2 C D 0 Ke Kµ = M B π → → transitions that are loop-mediated in the SM but receive NP 4 D 2 F 018 is the loop function in the SM [ s d s s . → → s G 0 M M D D and D D ∆ ∆ = Γ( Γ( → + Γ( Γ( b coupling, independent of the coupling to leptons. In order to minimize D i b SM we take the individual branching fractions from the PDG, assuming no d 322 is a ratio of decay constants and matrix elements determined from lattice . C sb 0 d `ν Z (1) B transitions 05(9) and Γ( ]. For the SM prediction of the semileptonic modes we use the BESIII deter- . B → s d ) = 2 s 96 t 2 B x D we take the results from the PDG constrained fit, including the 5% correlation. ( → /f 0 ) = 1 s , which are known to subpercent precision [ ν b ν S (1) B + The theory prediction is given by: The experimental value for the ratio is obtained from the individual measurements for Our SM prediction for the leptonic decay modes includes electromagnetic corrections For The model predictions for these ratios are: + d,s ` B e s 0 − M 2 B ¯ Here f where the Wilson coefficients Mass difference instraint the on the the uncertainty from hadronic matrix elements,that we within consider our the model ratio ∆ set-up, ∆ ∆ contributions at tree-level in ourlevel model of precision (via we areCKM working, elements) the can normalization be factorsnecessary taken in in from the this tree-level SM case determinations amplitude to within ( consider the only SM, ratios and where it these is cancel not out. mination of the form factorThe parameters resulting in SM the predictions are simple given pole in scheme4.5 table as quoted in HFAG [ We consider here with the Wilson coefficients following [ correlation. The resulting experimental numbers for both ratios are collected in table We construct the K corresponding to the same theoretical quantityare (isospin-breaking effects combined are according neglected to here), thebetween PDG both averaging results, prescription. we rescale Since the there error is a by the factor K JHEP12(2016)059 ] − µ ]: 115 + (4.19) (4.17) (4.18) 16 φµ (both at → − s µ as a function form factors, + B function leads 2 , 2 χ V , − χ Kµ µ i . . + → → 3 1 ) µ , ` ∗ B 5 − B ) , from the FNAL/MILC ` γ K ]. i α α 2 W ` ξ 0 i s → ¯ ¯ `γ `γ 4 103 Q ] for ) and . – )( )( 0 i` B 2 ζ b b , see section 19 C i 99 2 R R [ ζ + + P P /u − − α α ` i 2 f aa µ ) and ) Q m 6] GeV sγ sγ ` aa 2 + , i` ) q µ ` C (∆ h = (¯ = (¯ 8). observables used in the fit of ref. [ h . (∆ → ` 0 9 ` 10 measurements at hadronic machines [ h 0 10 , bs s ) 2(1 s s`` bs q X . B =9 ) i B q ,Q → (∆ tb 0 ) are found to be negligible since the right-handed flavour – 18 – V b (∆ and ,Q ` = 31 ]. ∗ 2 0 W 5 ts 2 ) (in the bin [1 10 (at very low . The NP contributions to the Wilson coefficients , − ` γ ˆ V g 2 W 0 9 ] decays. 2 M SM α α µ − 2 114 − π ˆ g 8 Q ) α e – M e + 4 d ¯ ¯ `γ `γ ∗ 8 + 117 ts µ + [ F s 2 )( )( e M ∗ V observables. These observables are not included in our fit. ts 1 108 b b ∗ G X tb Ke √ ∆ V L L 1 4 V K / )[ sγ tb P P ]. s 2 φµµ → → V π α α α q → → 206(18)(6). The SM prediction is given by the first term in M π 2 α . F ⊃ − b B B → sγ sγ We consider all 104 2 B √ , F s G eff 6 √ B = (¯ = (¯ G ]. We follow the approach of ref. [ = 1 − H ), and provide the best fit points, standard deviations and correlation ` 9 )[ e ξ ` 10 2 = = ] for Q q 10 Q a 107 ] includes a C ]: , ) are ] and NP NP 9 10 , 107 Second, in order to provide simplified expressions to allow the reader to 16 e C C 98 16 – 9 NP i` 3 116 C C [ , ]. 105 couplings to down-type quarks are suppressed by µ + ) 16 0 10 µµ These are collected in table ( observables. C ) and results in (∆ Z SM i` , 4 → C µ (both at low and high Branching ratios for low and high Branching ratios, longitudinal polarizationables fractions [ and optimized angular observ- Branching ratios for 9 s`` s 4.15 C We implement the fit in two different ways. First, we construct the full = B The fit in ref.Contributions [ to the primed operators • • • 3 4 i` → C Using these four coefficients as “pseudoto observables” a and constructing linearised the approximation toreasonable the agreement fit. with We the have full checked fit. that the result of such a fitchanging is in We consider those coefficients receivingi.e. non-negligible ( NP contributions within ourmatrix. model, ( with of the model parameters,as including in all ref. theoretical [ repeat and the experimental fit correlations, without exactly of too the much effective work, weak we Hamiltonian perform a global fit to the relevant coefficients Definitions, theoretical expressionsfound and in discussions refs. onand [ take theoretical into uncertainties account thefor can lifetime be effect for collaborations [ eq. ( b QCD. We consider the latest determination of the parameter JHEP12(2016)059 ] ) ) ) ¯ ¯ ν ν ) = D e e ∗ ( The ) ) 118 ∗ ∗ D R ( ( (4.20) (4.22) (4.21) 5 ( ]. D D R ) we con- ], and the ∗ → 122 → D ) we use the 121 ( B − c ), and the in- R ¯ ν B ) using a hadronic X )[ Γ( ) measurements ` ) remains basically ( τ ∗ / ) ∗ ∗ , P ) Γ( ∗ R D ( ]. ¯ / D ν D ( ( ) ( µ ]. The resulting SM , D 25 SM ¯ ν R ) and R ) 5 R ∗ # µ ( D ) ) ) SM → ( ∗ ¯ ν ¯ decays ( ) ν D 017 [ ( ]. For . ) e R µ 0 ∗ B ) ) D ( τν ∗ ∗ → ( ∗ ) and ( Γ( D 127 ( D / , → D B D D ) 005 006 ( . . R , ¯ ν ], adding the covariance for the 0 → − R → → τ 126 +0 − × ) is obtained from the PDG aver- ) B B ). We use the SM predictions of SM c ∗ ) reported in table IV of ref. [ − − ) ) ( 118 ¯ ν 502 2 c ). The correlation between the two X . B B | ` 4.6 ]. The reported measurements are D ( ¯ ν 0 ]. Experimental results are however ) j X ) cb e ∗ 2 ( Γ( R − Γ( 2 ( ) | 81 ) as measures of flavour non-universality 123 ∗ → |C " R j ( = D ¯ ν cb 3 ` τ + D × × B c |C P 2 → 2 2 2 2 ]. Note that recent determinations of j | X Γ( | | | | j → j j j j ]. These measurements are not included in our analysis cb 1 B cb cb cb cb 2 1 3 1 P ). The allowed size of lepton flavour universality ≡ → – 19 – |C is still very large. Note that the measured tau polarization B |C |C |C |C ν 125 123 ( ) using a semileptonic tagging method [ ) 2 ( , [ ], the LHCb measurement of τ j j j j j ) B + ∗ Γ( ∗ P ( 17 20 / ) transitions is not trivial to account for given that . . D P P P P P Γ( samples in an analysis performed by the BaBar col- ) 124 0 ( Xe / D 120 ]. For the ratios Γ( ¯ ν +0 − , ) ( are given in eq. ( R µ = µ e, µ ¯ ν ] . The latter includes 47 . ) R → . ) = ) = τ ∗ 5 128 ) cb ) ij 0 ) 119 ( c c b ¯ 2 = ¯ ν ¯ . ∗ ν C ( and e X D X µ ` 2 ) ( ) ( D ∗ e ∗ 44 ( ( . ( R → → 0 R D D − c`ν B B = → → ) and Br( Γ( ) and the tau polarization asymmetry in → τ ν ∗ − − P ≡ + b non-universality. D B B ( ) c ], with the relevant parameters taken from HFAG [ µ R ) obtained in refs. [ and Γ( Xτ Γ( ∗ X ]. We use the values of Br( and the light leptons, as well as the ratios Γ( − ( D 129 026 029 transitions → e . . ( τ R 0 118 b ¯ c R +0 − 034 → . 0 b ) and The model expressions for these ratios are: The experimental value for the inclusive ratio New results for D 5 ( 276 . tag have been presented0 by the Belle collaborationbut in would ref. have [ athe negligible same impact and if the experimental addedasymmetry uncertainty given in is that well the compatible weighted with average the for SM prediction in Lattice QCD areSM compatible prediction with reported the one inwe used ref. derive here the [ [ SMform predictions factors using [ the Caprini-Lellouch-Neubertpredictions are parametrization given of in the table where the Wilson coefficients R performed by BaBar and Belleindependent [ Belle measurement of results are summarized in table laboration [ to extract the ratiosratios Γ( is estimated fromsystematic the and information statistical provided errors. insider For the [ the experimental latest values of HFAG average [ ages for Br( violating effects in experimental analyses tend tosamples. present combined This resultsreported aspect for separately was the for also electron the and stressed muon in data ref. [ We consider the exclusiveclusive ratios ratio between the constraining 4.6 JHEP12(2016)059 . . 2 } 2 ≡ χ Z g τµ (5.1) poles τµ . The (4.23) (4.25) (4.24) → 4 . , α, M W → Z ) F , Z G ) { and 3.36 and Z 3.17 µ 3 , 2 → ) ˆ x τ 2 exchange, the decay rate − σ . , ) . We construct a global , x 0 2 i ( } ( 5 τ ¯ η ¯ Z η , 1 2 m ¯ 0 ρ, ¯ ρ, Z − with the values of τ 2 ) v X λ,A, M ∆ 2 W = µ s λ, A, τµ 3 LR x ' 2 { ∆ C π 0 ]. , 4 1 4 is then determined as a function of 2 5 ζ W [ g n ) + 1 + ( . 8 + g 2 M 2 1536 − exp ) ]. 2 W ` bb ζ n O s 10 τµ LL ∆ 86 [ are given by h C ` ab − × 5 – 20 – π Z ∆ ` ab 2 ( 2 O − . τµ LR ( ζ M 48 ∆ 1 1 C 0 0 10 denoting the observables included in the analysis and − < 2 2 W W gauge coupling 2 2 × Σ ) = O ) = ) ˆ ˆ g g 2 T µ 2 and M M µ . ) 3 4 2 gauge coupling τµ 3 1 mass, note that τµ 1 LL and the electroweak vev exp 0 = = → < C → → 0 O b b Z ) τ ` ` τ Z a a − ` ` LL LR τµ g, g Γ( C C are included as pseudo-observables in the fit taking into account Γ( O ( receives tree-level contributions from → } : The : The SU(2) : Controls the size of gauge: mixing Determine effects, the see gauge eq. couplings ( to fermions, see eq. ( ¯ η 0 µ ≡ 2 τ occurs due to gauge mixing effects. The decay rate for ζ Z Z 3 g ¯ ρ, 2 ∆ . The SU(2) , χ M τµ → µ 3 τ ∆ ) is λ, A, → , + { b µ Z ∆ − , τ s ∆ + the corresponding experimental mean values. These are described in section − Σ being the covariance matrix, The decay µ + exp τ with O CKM inputs The observables will also dependfunction on the that CKM includes inputs informationtogether from with electroweak precision flavour data. data at It the reads 5.1 Fitting procedure We first fix thereported values in of table The observables considered will depend on seven model parameters: We use the HFAG limit Br( 5 Global fit where the Wilson coefficients We use the limit Br( is given by We consider current limitsThe on decay the lepton( flavour violating decays 4.7 Lepton flavour violation JHEP12(2016)059 ], 3 130 (5.3) (5.2) , the | ≤ 3 for . 2 a , − in two- ∆ } | 10 as no ob- = 2 , 14 data. The π . 2 min 2 ] ∼ 4 0 . we introduce χ µ,τ ] χ − , ] 86 ` √ 2 Q − + χ 130 < 075 2 130 M TeV . s` 2 χ 0 , × . To sample the . The allowed values → } τ ≡ 39 ). )[ ¯ . η     . It is enlightening to b ˆ x g < g 0 2 )[ ¯ , ρ, . In the 338 3 χ 03 8 22 . + − +66 − by . σ σ 0 +22 − x < and ∆ 016 + − . − µ µ λ, A, 0 x NP 1876(21) GeV [ 9 . , { 2 0 C . 383( 8212( (for . . 1 00 1 14 transitions from the global fit are . group with only tree-level processes [ − − 3000 GeV, 1 = 91 − σ . = 0 = 0 ` −     ≤ Z ¯ 2 , η + = A on the other hand holds in our model 0 range in table ' M s` Z 04 µ . q is bounded to be very small σ 1 σ NP M 10 minimum with the sign of ∆ 8, to be compared with the corresponding , → ] b . 2 b ≤ −C 86 CKMfitter χ [ ] ] ] 1436 18 for 95% CL. Allowed regions for the model ) and – 21 – = , λ = 54 . 2 { ˆ x 86 is found to be at − 130 L 130 µ = 2 NP 9 2 min = 6 M χ 1. The negative sign obtained for the combination C } TeV x > χ 2 GeV − within the 1 7. We derive contours of ∆ , ζ 1. While ∆ × χ . | . Electroweak and CKM inputs. 5 τ } − (for . ¯ η     ∆ | | 10 )[ + ¯ ρ, , 3 and four CKM quantities ]. = 93 | 06 . σ . )[ 21 µ,τ µ × 0 0 +30 − } 21 = Table 3 ∆ ∆ − 131 | − | 036 [ [ 2 SM +21 − . λ, A, , ζ , χ The latter are reported in the form ˆ { b 2 0 are around τ σ . . The relation 0 0 1 ∆ ∆ 6 s 137 . 132( , , 22541( / . e − s . µ NP 9 3 16638(1) emcee . C ∆ . Note that with the assumed flavour structure we have the correlation     ∆ , = 1 = 0 , = 0 1) 2 3 b ]. ' ¯ ρ = 1 α λ , g ` ∆ − 98 1. The minimum of the , F λ s 2 W G ≤ s ∆ ζ , lie in the region [GeV] 2 is related to the preference for negative values of ≤ 0 , g Z = (4 b 0 µ,τ There is a four-fold degeneracy of the At the best-fit point we obtain The global fit takes into account then seven model parameters These CKM inputs are obtained from a fit by the Z e ∆ M 6 s { NP 10 M allowed regions for the Wilsonshown coefficients in of figure C as used in ref. [ servable in the fit isof sensitive ∆ to the relativeallowed sign values between ∆ for ∆ ∆ value in thedimensional SM-limit planes after68% profiling confidence over level all (CL)parameters the and obtained other in ∆ parameters, this way taking are ∆ shown in figure find that the corresponding Yukawas are, up to a global sign, 11-dimensional parameter spaceensemble we sampler use the affine invariant Markov5.2 chain Monte Results Carlo ofWe the restrict fit the parameter spaceand to 0 500 GeV with the CKM values characterise the best-fit point in terms of the couplings appearing in the Lagrangian. We the values in table the asymmetric error: { JHEP12(2016)059 2900 0.2 3.15 95% CL 68% CL 95% CL 68% CL 95% CL 68% CL 2600 0.4 2300 2.65 2000 µ NP 0.6 9 2 C 2.15 g [GeV] ′ 1700 Z 0.8 M 1.65 1400 1.0 1100 1.15 800 1.2 (left). 0.02 0.01 0.02 0.01 0.05 0.03 0.00 0.04 500

0.65

3 e 1.0 9 1.0 0.2 0.2 0.1 0.1 0.5 0.5 0.7 0.7 0.3 0.3 0.9 0.9 0.8 0.8 0.0 0.0

0.6 0.6 0.4 0.4

ζ ζ NP – 22 – 0.01 1.5 95% CL 68% CL 95% CL 68% CL 0.4 . µ 0.21 95% CL 68% CL 1.0 NP 10 −C 0.8 0.41 0.5 = s µ µ NP 9 ∆ 0.0 µ ∆ NP C 9 0.61 C 1.2 0.5 0.81 1.0 1.6 1.01 1.5 transitions. The best fit point is illustrated with a star. The red line on the left plot . Allowed regions at 68% and 95% CL from the global fit for the Wilson coefficients of . Allowed regions for the model parameters at 68% and 95% CL from the global fit. The − 2.0 ` 2.0 + 1.21

0.5 0.01 1.0 0.03 0.5 0.01 0.05 0.07 0.0 0.03

1.2

1.0 0.2 0.8 0.0 0.6 0.4

µ 10

τ b C

∆ ∆ NP → b illustrates the correlation only in the absenceas of gauge gauge mixing mixing effects effects. can Departures be from sizeable, this see correlation figure are possible Figure 3 Figure 2 best fit point is illustrated with a star. JHEP12(2016)059 ) ) ) ∗ eν ∗ 1.1 ( D 4.07 ( D → ) gets ( . The R ) ∗ R 4 ( 4 1.0 95% CL 68% CL − 95% CL 68% CL D 4.05 ( 10 µν/K . Having an R × ζ ) → 0.9 ) show a strong ) eν ∗ ( 4.03 K → D K K ( 0.8 R Γ( R / in the direction of the ) 4.01 µν K 0.7 R → ) accommodates the current ) and ) c K ∗ ) are shown in figure ( ∗ X 3.99 Γ( ( ) with experiment. The flavour D D ) are found to be SM-like with c 0.6 ( ( R X R eν R ( ) ∗ ( R 3.97 0.5 D couplings are mostly left-handed, with

and

1.32 1.31 1.33

1.30 1.34 . A signiﬁcant enhancement of

0.2 0.1 0.3 0.0

0.4

(light-band). The best ﬁt point is illustrated 0 10 × ) ν eν → µ Γ( / ) ν µν → τ Γ( ¯ ¯ .

6 − K σ → 4 W /u -decays are found to be in good agreement R 2 f τ ) are SM-like. Note that the NP scaling of B ∗ m – 23 – Γ( D / ( is above its best-fit value whenever ) 0.35 0.35 R we also show the results of the global fit for K µν ) 95% CL 68% CL 95% CL 68% CL R ∗ 4 ( 1% level. As expected, 0.33 0.33 D ) because the ∼ ∗ (dark-band) and 2 → D σ ( 0.31 0.31 ) ) B R ∗ ∗ ) so that ) D D as an example in figure ∗ ( ( ( ], gauge mixing effects play a crucial role in the possible enhancement R ¯ R 0.29 0.29 ν D 4 ( eν R → 0.27 0.27 and ¯ ν/µ K 0.25 0.25 ) in this model. In figure µν R ) . Allowed regions at 68% and 95% CL from the global fit. Experimental values for these ∗ ( → D 0.23 0.23 ) is the same as for τ ( As noted in ref. [ Allowed values at 68% and 95% CL for

1.1 1.0 0.5 0.7 0.9 0.8 0.6 0.2 0.1 0.3 0.0 0.4

K R D ζ R ( with the SM andand experiment, we show the resulting allowed values for of as a function of the parameter controlling the size of gauge mixing effects between enhanced. Thepossible ratios deviations Γ( only at the correlation, in the region ofexperimental the values parameter space one where obtainsobservables a with slight light-mesons tension and in leptonic best fit pointLHCb presents measurement a while sizeableR the deviation from ratios thethe SM right-handed in couplings suppressedis by possible within the allowed parameter region. The model presents a positive correlation Figure 4 observables are also shown atwith 1 a star. JHEP12(2016)059 0 , 1 , `ν Z 25 29. ) . ∼ ∗ ( (6.1) 0 (5.4) 2 g D 007] playing . ≤ 0 ζ ) , ]. → c X B ( 003 144 . 65]. Similarly, R . [0 ) at face value, 0 ) , interactions with ≤ ∗ ∈ ) can provide an ( 2 1700 GeV. A limit 0 c . b decays see refs. [ D 24 X [0 ∼ . ( W ∆ ( 0 R ∈ R Z , cτν 78 and the combination β . and M 0 0 97] and → . Z ≤ 0 b for , with the parameter K . 1 − ). We are interested in possible , the massive gauge bosons, π K , g R 4 σ ). In the parameter space region lie within a very restricted region: R 02] 5.4 16 , . ≤ √ . σ 0 1 , 3.36 decays ≤ SM − 66 ), we get tan [ [0 . 2 g ) ∈ ∈ ) τ ν ∗ ) transitions at the Belle-II experiment will 3.17 s D ∗ D are positively correlated, going from polarization fractions are expected to be as ( . We find that the allowed points from the ( ( ∆ ) within 2 2 ∗ R ) 4 R D g cτν 4. Note that the ∗ , see eq. ( , D . ( , ζ ]. The inclusive ratio 2 a 3 – 24 – 5 5] D → → ∆ . = ( ≤ b 3 11] and . ) R , − ) B ∗ ˆ g 0 2 τ , . D D ( ≤ ( [1 [0 20% as suggested by the experimental measurements is and R R ∈ K ∼ | ∈ 2 τ R gauge coupling ∆ spectra and by measuring additional observables that exploit | ) are accommodated within 2 2 ) 2 gauge coupling satisfies 0 ∗ ) ( , g ) 1 ∗ ( D ( D ) of order 1. The situation is very different for p ∗ R , D − ( 99] B ζ and R . p 0 ( 1710] GeV , K , is affected in the model with a global rescaling factor, implying that forward- ]. Future measurements of ≡ R 94 is found to be within 1 . 500 GeV up to the perturbativity limit 2 1 τν q 143 [0 [500 ) can be derived in this region using eq. ( ∼ – ) within the parameter space region considered, we obtain 0 ∗ /g mass and the SU(2) , couple predominantly to the third fermion generation. ( c 0 0 β 2 ∈ 0 Z X D | ∈ 0 Z ( W gg µ 132 Z M , R → ∆ = M | ˆ B backward asymmetries as well asin the the SM. For125 recent studies of differentialbe distributions crucial in to disentangle possible new physics contributions in these decays [ which is compatibleadditional with handle current to data testin the [ proposed scenario. TheThe Dirac model structure gives of the rise new tofrom physics contributions the an can also enhancement be tested bythe using information rich kinematics and spin of the final state particles. The differential decay rate for imation. This gives rise to a clean prediction the LHC and flavour factories. 6.1 Differential distributions in Due to the gaugedecay structure amplitudes have of the the same Dirac model, structure new as the physics SM contributions contribution to to the a good approx- 6 Predictions In the following wefocusing take on the the parameter current spacesignatures region measured that described values can in be of eq. ( used to test or falsify this scenario with upcoming measurements at g the SM fermions are proportionalwhere to both 1 and The for on tan in this region the SU(2) only possible for no major role inglobal this fit accommodating case both as shown in figure enhancement of JHEP12(2016)059 . . 8 ≤ 9 re- − | ' lies − ) τ 0 (6.2) (6.3) exp ( 10 10 , very ∆ ) τµ | 8 × × µη − 2 µη . ]. On the 2 → , , , , , . 10 so that the → 1 → Z 2 τ τ 144 × τ ≤ 2 is proportional . ) 4 µ 3 µτ ≤ ) → → observables would be -meson anomalies in and Br( τ s , B 7 µη Z 2 − 95] at 95% CL 95] at 95% CL 94] at 95% CL 94] at 95% CL 94] at 95% CL 2 1) the decay . . . . . → → 0 0 0 0 0 , 10 b , , , , , /dq /dq τ K ) × ) 57 62 56 60 56 ζ R − 3 . . . . . − . is near its upper bound, µ e 1 [0 [0 [0 [0 [0 | + + τ ∈ ∈ ∈ ∈ ∈ ≤ ∆ | and Br( Me 6] 6] 6] Mµ , , , 19] 19] exp 8 , 1 , 1 ) − 0 [1 . . → → 1. In our model the decays . within each bin are strongly correlated, q K [1 [1 q 0 10 [15 [15 µη ∗ φ ∗ B φ φ B K × K R → testing lepton-flavour non-universality. Γ( | ' 0. When Γ( 9 d τ . d τ `` 3 – 25 – 2 ∆ ∗ 2 ,R,R ,R ,R,R | | ' and M K ≤ τ dq dq R ∗ ) 2 2 2 ∆ 2 2 1 0 2 → 1 q | q q K q R R B R µη ], defined analogously to ) that saturate the current experimental limit 1 µ , exchange, these will also be proportional to ∆ 3 → K ] = ) 0 146 2 2 ( , τ R → ], as explored in connection to the Z 7 , q . 2 τ 1 145 q 91] at 68% CL 90] at 68% CL 91] at 68% CL 90] at 68% CL 91] at 68% CL consequences of the violation of lepton flavour universality is [ 148 [ . . . . . , φ ]. In our model, the branching fraction for ∗ 0 0 0 0 0 M , , , , , , φ K R ∗ 156 62 66 61 64 61 – . . . . . = K [0 [0 [0 [0 [0 generic = M 149 ∈ ∈ ∈ ∈ ∈ ]. The observation of lepton flavour violating tau decays decays might , ] we obtain Br( M 6] 6] 6] ] for other observables in for , , , 19] 19] 158 1 , 1 , [ 140 . . [1 , 157 147 8 K [1 [1 d, s [15 [15 ∗ − φ 82 ∗ φ R , , with = K R K and is therefore suppressed for R 10 M 55 q R R 2 τ The expected values for R × See ref. [ 7 5 1, we obtain values for Br( . . therefore lie within the reachthe of current future experimental machines such bounds as byother Belle-II, an hand, where order due an of to improvement of magnitude thewell-below can the suppression be current of expected experimental gauge [ limit, mixing for effects which ( we obtain Br( largest rates possible will beceive obtained important for new physics contributionsFollowing through [ the axial-vector strange-quark current. close to the current experimental6 limits Br( refs. [ to ∆ 0 Semileptonic decays of the tautree-level contributions lepton from into a muon and a pseudo-scalar meson also receive lower values of one observable corresponding to lower values of6.3 another and viceversa. Lepton flavour violation One of thelepton first flavour violation [ where it is understood that a strong (positive) correlation exists among all the predictions, except for the factthe that results hadronic of uncertainties the are fit, mostly we independent find (but the small). following From expected ranges for the different ratios: with Confirming the violation of leptondefinite flavour evidence universality in in favour other of neware physics at work. Examples of such additional observables 6.2 Lepton universality tests in JHEP12(2016)059 , 0 ). . Z 0 res- 36% Z (6.4) (6.5) M 0 3.38 , ]. The 0 ∼ Z . 81 W one of the j Q,L ii ) and ( f Ω i , -leptons. In the x 3.37 2 τ ) 2 2 is between 2% and 1 2 ]. It was found that ij g g 0 ]. Searches for pair , Z 6 (Σ 159 −   can only decay into the 159 2 /M 2 boson would reduce the 0 ) 0 ) 2 ` 0 j Z 4 4 width, making the 1 2 -quarks. Z g g x 0 Z ∆ flavours are around 450 GeV ) is found to grow with Z 0 + − boson into a heavy vector-like s/c − 2 Z i 0 ) x e, µ Z (1 ( ]. = 3(1) for (un)coloured fermions /M 0 Q,L ii = µ,τ − Z C ` = X j 165 (Ω ` N boson would be produced at the LHC – x 0 + ) ), − 12% of its coupling to i Z 2 160 i ) x -quarks and xz x 2 q ∼ b mass (Γ have been defined in eqs. ( − ∆ − 0 + a generic heavy fermion and by (1 2 Z i − – 26 – Q,L yz F 1 TeV [ 0 0 (1 Z couple predominantly to the third fermion genera- Z + ∼ 1 TeV. 0 s,b M M = Z X xy & C q C , 0 0 3 2( N N Z 2 2   W ), heavy fermions and the massive vector bosons g − g M π π ) ˆ 2 ) ˆ π 2 2 j i ˆ g z 48 96 192 , x , x i i + ' 2 , x , x 0 -leptons the limits are around 270 GeV [ 0 700 GeV up to y Z τ 10% for Z (1 (1 ∼ 2 2 + Γ M coupling to the second quark generation is found to be at most / / & 2 1 1 0 0 x . We have denoted by λ λ width normalized by the Z Z 0 are positively correlated. Assuming that the 2 0 Z 0 ' ' Z Z /M ) ) 0 ) = i j /M ¯ Z M ¯ 2 i f F i i m F F x, y, z and = → ( → 0 0 i g λ x Z Z If kinematically open, additional decay channels of the The total The massive vector bosons The heavy vector-like leptons will be pair-produced at the LHC via Drell-Yan processes coupling to muons is found to be at most Γ( Γ( 0 Here and SM-like fermions. The matrices Σ and Ω fermions are light enough, openingfermion decay and channels a of SM-like the fermionprocesses or is into given a by: vector-like fermion pair. The decay rate for these where we have neglected fermion31%, mass effects. with Γ We obtain that Γ branching fractions to SMonance particles broader. by enhancing The the latter total scenario will generically be the case provided the vector-like SM fermions we have quark sector, the of the coupling tovia third Drell-Yan generation processes quarks. due The to its coupling to since ˆ production of heavy vector-like quarksthird at generation the fermion LHC and focusmasses bosonic primarily ranging states, into from setting final upper states limits with a on the vector-liketion. quark The LHC phenomenologyZ of this type of states has been discussed in ref. [ gauge bosons and charged leptonslike or leptons neutrinos. have Though beenproduction no cross-section performed dedicated by at searches recasting for existing thecurrent multilepton vector- LHC, searches limits [ for one a can heavywhile lepton obtain for doublet limits decaying decays on to into their mass and In this model we expectthe CP-conserving a limit plethora we of would newone have states charged two lying scalar, CP-even Higgs at cf. bosons, the section one TeV scale: CP-odd Higgs scalar and bosonsdue (in to their coupling to the massive electroweak gauge bosons. These will decay into 6.4 Direct searches for new states at the LHC JHEP12(2016)059 . 8 2 2) h , (6.6) (6.7) (6.8) M width 1 TeV) = 1 0 channel channel = i Z ( & − µ . − i τ , . τ ¯ 2 N 2 +

+ i h τ i ! ii τ i ) Q ) 2 τ ,N L Q i i f production cross- M y ¯ 0 ¯ E L u ( i Z + ∆ ii E ) 2 =1 2 µ 0 i L X mass region (

y → 0 . The mass of this scalar ( (∆ 0 2 2 2 3 h 3 Z Z h L − π M 2 f M 2 s h 18 α i 1 ]. We ﬁnd that it is possible to TeV. The dominant interactions L Q 0 i ' f ∼ M ¯ 170 ) ] evaluated at the scale Q [

u ii gg ) 2 1 2 2 171 g n Q → y ( boson a very wide resonance in this case: = 2 0 h 2.4.2) from the decays − L 10%) and the interpretation of the current Z 0 2 Γ( u Z h & aMC ) resonance remains reasonably narrow and there 2) and – 27 – 0 µ 0 , /M 0 Z 0 , y Z , Z Z 0 µ ) = 1 /M ! 0 Z ) i 0 Z 2 b gg 2 Z )( the production cross-section reads s i → M 2 s + ∆ 7 TeV would then be needed in order to test this scenario. h 1 2 2 . ,E √ 2 s h i 1 0 M + N Γ( − (∆ 2 TeV, making the µ . MadGraph (MG5 2 1 gg 1 0− Q = ( c ]. Among these, the strongest limits are those coming from ATLAS ∼ at the LHC is dominated by gluon fusion mediated by the heavy ∼ f W M T i ' 0 2 + L 1 169 0 ) µ Z h – Q 2 50%. 0 ), W M h i 0 f M − 166 2 W

→ ,D i 2 1 2 2 M U g n 30% pp 2( ( represents a dimensionless partonic integral which we estimate using the set σ ∼ = = ( 0 singlet originating from Φ. We will denote this state by decays into a heavy fermion and a SM-like fermion are accidentally suppressed due resonance becomes wide (Γ Q T i gg Z 0 = 8 TeV [ y L 0 ] while analysing a similar new physics case. c L ⊃ are with the heavy fermions and the heavy gauge vector bosons, these are described by Q Z s The proposed scenario also gives some predictions in the scalar sector relevant for The ATLAS and CMS collaborations have searched for a resonance in the Z 81 2 We find our main conclusions in this regard to agree with those posed previously by the authors of /M , the scalar spectrum will contain a heavy CP-even neutral scalar transforming as an 0 √ 8 ) h 0 Z ( Here of parton distribution functions MSTW2008NLO [ ref. [ The production of quarks and is determinedAt the by centre-of the mass same energy parameters entering in the low-energy global fit. with φ SU(2) is expected to be aroundof the symmetry breaking scale experimental results basedanymore. on the Dedicated search searcheswithin of the at mass a the range relatively LHC narrow for resonance a iscollider broad searches. not resonance Neglecting valid mixing in between the the scalar bidoublet Φ and the Higgs doublets exclude the low-mass region whereis the not much roomwidth. for The additional latterwith decay direct would channels searches require giving for having largethe these very contributions states light to at exotic colliders. the fermions, total In entering the in heavy conflict of about 20% for Γ at and they place important bounds onsection the at model. the We have LHC evaluated the using to the small entries oftherefore the give Σ small matrix contributions within toheavy the fermions, the parameter on total region the width other of inwhen hand, interest. general. can kinematically These give The allowed. decays a significant decays450 contribution For into GeV to instance, a we the pair if obtain total of a the contribution masses to of Γ the heavy leptons lie around The JHEP12(2016)059 . , , − 2 2, ` / − sγ and 2 + ZZ h 10 , s` − → ` M − b + ∼ → 1 TeV) is W 1%. Note s` b ) + ∼ ∼ → W 2 ) b h WW M WW → 2 → h = 13 TeV centre-of-mass 2 s h √ Br( / ) . Such accidental tuning would be γγ boson will manifest in this case as β ) will induce loop-mediated decays 2 290 fb at h → 6.6 − 2 h ] regarding the importance of suppressing 110 4 semileptonic decays, finding that the flavour ' − 7] TeV we have: Br( in eq. ( ` 1 TeV) the production cross-section converges . ) 1 2 – 28 – + 2 we have taken the local approximation for the , h ∼ h s` 25%, Br( [1 2 gg → h → ∼ ∈ b M pp → ) ( 0 Z σ 2 ]. The decays into electroweak gauge bosons are found h and M WW 1 TeV, and restricting the rest of the parameters to the region 173 c`ν , → ∼ → 2 2 172 h h 7 TeV (and b . into these fermions becomes kinematically open and will generically 1 M 2 ), we obtain fb [ Br( h / ∼ 3 ) 5.4 0 pole. More specifically, we have analysed the model in light of the current Z W M are confirmed in the future. 110 fb. The interactions of ZZ, Zγ and c`ν ∼ anomalies. We have taken a phenomenologically oriented approach in this work, . Assuming negligible tree-level decays, the → Z → c`ν 2 b From the model building point of view, there are many open questions which we have As derived from the phenomenological analysis, strong hierarchies in the flavour struc- Zγ h , → and not addressed in thisthe implementation work of and a wouldand mechanism lepton deserve mixing for further angles. the investigation, Our generation one model of of also the them lacks observed a being neutrino dark masses matter candidate, motivating the last points also bring usnew physics to effects, the once quantum question corrections ofthe are the considered. flavour validity structure These of corrections of our mightlevel the alter analysis, as theory, based remove well on accidental tree-level asThough tunings introduce such which analysis new hold lies at constraintsestablish beyond the from the the classical loop-induced viability scope processes of of the our such proposed work, as it framework would if be the relevant present in deviations order in to not invoking any flavour symmetrybe behind such the structure. exploration Onestructure. interesting of question We possible would confirm flavour thegauge symmetries conclusions bosons of mixing. accommodating ref. This the translates [ more in observed satisfactory a if tuning flavour of there tan was a dynamical or symmetry-based explanation behind. These hints of new physics in anomalies can be accommodated within the allowed regions ofture the of parameter the space. Yukawa couplingsb are required in order to accommodate both We have performed a phenomenological analysis ofextension a of renormalizable the and Standard perturbative Model. gauge Welevel took new into physics account contributions flavour observables as sensitive well toat tree- as the bounds from electroweak precision measurements however that in the casetree-level where some decay of of the heavydominate fermions over are the below loop-induced the threshold decays commented above. 7 Conclusions γγ a very narrow resonancesensitivity decaying for mainly dijet-resonances intoat at a the pair the level of LHCto of jets. around 10 be this The subdominant current massBr( experimental range and ( for fermionic loops. For described in eq. ( energy. For towards into gluons (which will hadronize into jets) and electroweak gauge bosons In writing the decay rate for JHEP12(2016)059 . 2 Φ (A.1) (A.2) m and 0 ]. 2 φ m 177 , 2 φ , m 0 , 3 φ . ] to cross-check some 3 φ v 3 v 2 1 u λ 3 λ 176 1 2 , λ 1 2 2 1 + + 175 [ + u µ µ u µ 0 φ 0 φ v φ v v 1 2 φ 1 2 v SPheno + 2 1 + , 2 + 2 u 6 u 0 = 0 ] and 5 2 φ λ i v λ V leads to three minimization conditions or tad- 6 + 174 ∂ ∂v [ λ + 2 2 φ – 29 – 0 v 2 φ + = 4 v i 2 φ λ 4 t v λ 5 0 SARAH φ λ v φ v 1 2 u 1 2 to produce most of the plots in the paper [ 1 2 + + 0 + φ φ v u v 0 2 φ 2 φ 2 Φ m m m = = = 0 u φ matplotlib φ t t t These three conditions can be solved for the mass squared parameters these are A.1 Tadpole equations The vev configuration introduced in section pole equations. In theto following be we will real. consider Defining all the parameters in the scalar potential FPA2014-61478-EXP. We have used of our results, and A Details of the model an “Atraccióde Talent” scholarshipsupport from from the VLC-CAMPUS. “Juan A.V.MINECO as de acknowledges well la as financial from Cierva” theSEV-2014-0398 program Spanish and grants (27-13-463B-731) PROMETEOII/ FPA2014-58183-P, Multidark 2014/084 funded CSD2009-00064, (Generalitat by Valenciana).the the J.V. Swiss is Spanish National funded Science by Foundation. J.V. acknowledges support from Explora project Physics, of INFN I.S.is TASP2014, supported and by of thein Alexander MultiDark von part CSD2009-00064. Humboldt by Foundation. The theCentro The work Spanish de work of of Excelencia Government, A.C. J.F. ERDF Severo53631-C2-1-P, is Ochoa from PROMETEOII/2013/007 supported Programme the and [Grants EU SEV-2014-0398]. No. Commission FPA2011-23778, J.F. and FPA2014- is the also Spanish supported by We thank SébastienDescotes-Genon, Thorstenand the Feldmann, participants Martin of Jung,discussions. the Admir June We 2016 Greljo, also BaBaranalysis thank Collaboration of Adam Meeting electroweak Falkowski at precision for SLACfor data. providing the for numerical Research helpful S.M.B. results Projects acknowledges of used support National in of Interest our PRIN the 2012 MIUR No.2012CP-PYP7 grant Astroparticle embeddings of the model within aarise larger from gauge spontaneous group, where symmetry the breaking. mass of the heavy fermions Acknowledgments extension of our framework. It would be interesting to pursue the investigation of possible JHEP12(2016)059 (A.8) (A.6) (A.7) (A.3) (A.4) (A.5) , , + Φ . Φ , ,A + 0 + φ 0 = 0), the mass matrix H , . , ξ , ϕ ,A , 2 H 6 , φ 3 + 5 λ λ λ ϕ A      2 M 2 2      u Φ u Φ Φ u T , Φ Φ Φ A A ≡ ≡ A S 0 + S S + 0 φ , Φ − φ 0 . φ Φ + 3 4 φ T T 2 A 2 A 4 φ 2 A 2 S ) 2 S ) 2 S λ ) H 6 P λ φ 2 + φ 0 Φ λ M M 0 M 2 M i A v φ M M H 2 φ + v i A 0 ( 0 0 i A v 0 Φ + + φ Φ φ φ φ P + 0 A + S A 2 S A S 0 + 0 + , 0 0 φ 2 P 1 φ λ φ φ φ φ φ φ µ , µ , 0 5 S 0 Φ 2 S λ 2 S 2 A 2 A 2 S φ S 2 A 2 uµ , φ λ φ ∗ 2 φ S M v v 1 2 + 2 v φ v + M T M 3 1 2 M M M 0 M v 3 1 2 + + φ φ + P 0 – 30 – 0 Φ φ v Φ + φ v u Φ φ 1 2 φ 1 2 1 2 4 + 1 2 ( ( S S S A A 6 A , λ φ φ 5 φ φ φ 0 φ 2 2 2 + + 2 S + 2 S ∗ + 2 S φ 1 1 1 2 A 2 A , 0 2 A uλ √ √ √ v uλ 0 2 φ 2 φ 2 Φ S + M φ φ φ M M 0 2 S M M , is identified with the recently discovered SM-like Higgs M m v v m v m Φ = = = ϕ h      0 0 0 M      ======0 ,S , 0 ϕ ≡ T Φ 0 0 ϕ = ∗ φ φ Φ Φ Φ = φ φ 1 S S S S S S S 2 S 0 φ φ S 0 1 2 Φ ,S + 2 P φ φ 2 S φ 2 S 2 S φ 2 S 2 S ϕ 2 S M = S M M M M M M M s m 125 GeV. Similarly, in the Landau gauge ( ≡ ≡ ∼ T T − L ) S − H ( for the CP-odd scalars is given by The lightest CP-even state, boson with a mass with The mass matrix for the CP-even scalars is given by which allow us to obtain the scalar mass Lagrangian Since we assume that CPdo is not conserved in mix. the In scalar this sector, case, the one CP-even and can CP-odd define states the bases The neutral scalar fields can be decomposed as A.2 Scalar mass matrices JHEP12(2016)059 (A.9) gauge (A.11) (A.10) 0 W and W , , , . by the . , , , 1) bosons. Finally, the mass 6 6 0 3 3 − 5 5     λ λ , λ λ λ λ Z 2 2 2 2 2 2 2 + + + u u / u u u u Φ Φ Φ ] are given by: 1 + + + + + 0 + + and + + − eaten-up 2 ϕ 2 Φ 84 2 ϕ 4 4 ( 6 6 4 4 λ λ Z = 0) is given by f λ λ λ λ after applying the tadpole equations M ), it is straightforward to show that M 0 0 2 2 M φ φ 0 0 ξ 2 2 φ φ 2 2 v φ v φ − v v + v v + + 0 0 2 H A.2 + + Φ ϕ 0) ϕ + + + + 2 , + 2 + + 0 0 M 5 5 1 2 1 λ λ 2 ϕ 2 ϕ 2 ϕ 0 0 λ -pole observables λ / λ λ 2 2 φ φ 2 2 φ φ 2 2 φ φ v v M (1 M v v M v v W f + – 31 – + 1 2 1 2 + 0 1 2 , 1 2 µ , 1 2 1 2 + µ , ϕ 0 Φ ϕ 2 φ φ µ , 0 + + + + + + ` ii µ , + 0 + + v v g 2 ϕ 0 2 ϕ 0 2 ϕ φ φ 2 1 2 2 φ 2 φ 2 Φ 1 2 ∆ 2 φ 2 φ 2 Φ 0 uµ , v uµ , v - and − 4 1 g 4 2 M M 1 2 1 2 1 2 1 2 M m − m m m − m m g n 2 Z g 2     ======0 0 φ Φ Φ Φ + + + + + + = δv ζ φ φ 0 0 A ϕ A A A Φ Φ Φ ϕ ϕ A A 0 − − φ φ 0 Φ + + + + φ φ + + 0 φ 0 2 A 2 A 2 ϕ 2 ϕ 2 A 2 H 2 Φ 2 A 2 ϕ 2 A 2 ϕ = = 2 ϕ 2 A i M M M M M M M M M M M M M δm W ` L δg has two vanishing eigenvalues. These correspond to the Goldstone bosons 2 P ). These correspond to the Goldstone bosons M A.2 In our model, the pseudo-observables considered in ref. [ in eqs. ( bosons. B Pseudo-observables for Again, one can find two vanishing eigenvalues in with After application of thethe tadpole matrix equations in eq.that ( constitute the longitudinal modesmatrix for for the the massive charged scalars in the Landau gauge ( with JHEP12(2016)059 , ]. i D Zu R (B.1) (B.2) δg ] SPIRE IN [ Averages of Phys. Rev. Phys. Rev. Phys. Rev. , , . , 02. However, the 2 couplings that are . 0 0 g decays Non-Abelian gauge 2 , 0 W (2010) 035011 processes − − . g ` 3) 2 s ]. arXiv:1604.03088 ζ / + g ` [ 2 and 84 → , + arXiv:1412.7515 Q 2 D 82 b ]. Z K / + 3 (1 → 2014, f T + , SPIRE + B (2016) 214 , ]. 3) IN ii δv / ]. ) 1) 1 Phys. Rev. − − , − , Global analysis of general collaboration, Y. Amhis et al., , † SPIRE 2 CKM 2 B 760 ) = ]. / IN SPIRE V / . We also neglect loop contributions, which Ununifying the Standard Model 1 q 1 IN ][ 3 ,Q − ∆ [ − 3 ( ( f T f (1989) 1540] [ – 32 – SPIRE ( IN + f CKM + , 63 V ][ ` ii q ii ( Phys. Lett. , , 3) 4 1 ∆ , ∆ 4 / 2 3) n 4 1 Left-right gauge symmetry and an isoconjugate model of 4 1 (1975) 566 1 1) g 4 2 4 / and 2 2 n n g 2 − − g 2 2 2 ]. ), which permits any use, distribution and reproduction in , , , 2 2 ζ (0 (0 (0 ` 22 arXiv:1406.6482 D 11 More model independent analysis of -lepton properties as of summer − f ζ f ζ f ∆ [ τ 4 1 models with precision data 4 2 SPIRE ======Erratum ibid. g n Test of lepton universality using i i i i i i IN [ 1 2 hep-ph/0310219 ][ Z` Z` L R Zd Zd 2 L R Zu Zu L R U(1) [ CC-BY 4.0 -decay anomalies δg δg ζ δg δg δg δg for these shifts covers the three fermion generations except for × B Phys. Rev. − i This article is distributed under the terms of the Creative Commons , = -hadron and 2. We neglect corrections to the right-handed c (2014) 151601 , ]. (1989) 2789 SU(2) δv × ’s in that case would be below the limits quoted in [ = 1 113 62 i δg (2004) 074020 SPIRE -hadron, arXiv:1003.3482 IN b Lett. 69 [ extensions for [ Heavy Flavor Averaging Group (HFAG) CP-violation Lett. SU(2) LHCb collaboration, G. Hiller and F. Krüger, S.M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicente and J. Virto, H. Georgi, E.E. Jenkins and E.H. Simmons, K. Hsieh, K. Schmitz, J.-H. Yu and C.P. Yuan, R.N. Mohapatra and J.C. Pati, [6] [7] [4] [5] [2] [3] [1] any medium, provided the original author(s) and source are credited. References we estimate to beresulting comparable to the tree-level contributions for Open Access. Attribution License ( The family index for which suppressed by the fermion masses, see section where JHEP12(2016)059 , and − ` in a , 1, C 74 B , τ + (2014) ] ` D 93 τν τν ∗ and ) ∗ K and ( (2014) 097 112 → K ]. anomalies D − R → B anomaly µ 04 → s`` + B − µ µ B and SPIRE 0 , → ∗ + Phys. Rev. Erratum ibid. IN b µ , [ K τν JHEP ∗ ][ ∗ , K ]. ]. → ]. − D arXiv:1407.8526 data and signs for lepton (2015) 054035 ` 0 [ → ]. + → B ` Phys. Rev. Lett. ]. ∗ s`` B , B SPIRE SPIRE ]. SPIRE ]. K , ]. D 92 → transitions after LHC run IN measurements IN IN (2014) 2897 SPIRE b → s s ][ ][ SPIRE Long-distance weak annihilation ][ IN Dτν IN B → ][ (2014) 125 → SPIRE SPIRE SPIRE ][ b Global analysis of On the impact of power corrections in b → C 74 IN IN IN arXiv:1206.2634 ]. 12 ][ ][ B [ ][ Calculation of Phys. Rev. , SPIRE On the anomalies in the latest LHCb data Global fits to JHEP Hint of lepton flavour non-universality in Understanding the ]. IN ]. , ]. Comprehensive Bayesian analysis of rare Sensitivity to charged scalars in ][ decays arXiv:1410.4545 arXiv:1210.8443 On the Standard Model predictions for – 33 – Explaining − Eur. Phys. J. [ [ arXiv:1605.07633 ` New physics in Implications of , SPIRE SPIRE arXiv:1408.4097 [ (2012) 054014 + ]. [ ` SPIRE IN IN ) [ arXiv:1512.07157 Reassessing the discovery potential of the IN decays at large recoil in the Standard Model: a theoretical ][ arXiv:1307.5683 [ arXiv:1411.3161 observables ][ arXiv:1603.00865 [ decays − [ D 86 [ ,K SPIRE ` ]. − On the LHCb anomaly in ]. ]. B + µ IN (2014) 053 (2013) 054 ` π + ∗ ( ][ (2016) 440 µ (2014) 131 ∗ 12 K 01 Resonances gone topsy turvy — the charm of QCD or new physics SPIRE → SPIRE K (2016) 116 SPIRE arXiv:1510.04239 IN 12 → [ IN IN (2015) 382 C 76 [ ][ (2016) 737 → B 06 B Phys. Rev. ][ (2013) 074002 , JHEP JHEP B , , arXiv:1406.0566 arXiv:1412.3183 JHEP , observables using form factors from lattice QCD C 75 [ arXiv:1310.2478 ? , B 909 JHEP − − D 88 ` , µ (2016) 092 decays + + ]. arXiv:1310.3887 τ s` 06 [ φµ Eur. Phys. J. τν , → → ∗ b → SPIRE 0 K s HDM of type-III arXiv:1312.5267 IN arXiv:1503.06890 reappraisal 2 B [ in the prediction of [ decays in the large-recoil region:(2016) SM 014028 challenges and BSM opportunities Nucl. Phys. (semi)leptonic and radiative (2014) 3179] [ arXiv:1503.06199 JHEP meson decays non-universality Eur. Phys. J. Phys. Rev. B 212003 contribution to the [ R A. Crivellin, C. Greub and A. Kokulu, A. Celis, M. Jung, X.-Q. Li and A. Pich, T. Hurth and F. Mahmoudi, J. Lyon and R. Zwicky, M. Ciuchini et al., S. Jägerand J. Martin Camalich, F. Beaujean, C. Bobeth and D. van Dyk, S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, W. Altmannshofer and D.M. Straub, S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, T. Hurth, F. Mahmoudi and S. Neshatpour, T. Hurth, F. Mahmoudi and S. Neshatpour, W. Altmannshofer and D.M. Straub, R.R. Horgan, Z. Liu, S. Meinel and M. Wingate, D. Ghosh, M. Nardecchia and S.A. Renner, S. Descotes-Genon, J. Matias and J. Virto, M. Bordone, G. Isidori and A. Pattori, A. Guevara, G. Castro, López P. Roig and S.L. Tostado, [9] [8] [24] [25] [21] [22] [23] [20] [18] [19] [15] [16] [17] [13] [14] [11] [12] [10] JHEP12(2016)059 ] , 02 ) ] B 01 ]. ) ∗ Phys. D 92 ( Phys. , (2016) D , with Phys. ( 116 JHEP , SPIRE τ R ]. JHEP Phys. Rev. ¯ , ν (2016) IN , , τ τν ) ) D 93 ][ ∗ ∗ τν ( ( data SPIRE D Phys. Rev. ]. D − D 93 , IN µ ¯ ν → → ]. arXiv:1605.09308 + ][ ]. models with flavored τ arXiv:1306.6493 [ Probing the R-parity ¯ ) B 0 B [ ∗ sµ SPIRE ( ]. Phys. Rev. IN D → decays into , SPIRE Phys. Rev. Lett. U(1) SPIRE ][ b , IN → B IN Phys. Rev. decay with lattice QCD SPIRE ][ ¯ , B ][ arXiv:1206.1872 IN (2016) 054 decays [ (2013) 084 ]. ][ Testing leptoquark models in ` Dτν ¯ 08 ν in chiral 11 − ]. ]. Sterile neutrinos in leptonic and → c` τν SPIRE arXiv:1511.03290 Implications of lepton flavor universality B anomalies FCNC quark couplings facing new ]. [ excesses in ALRSM constrained from IN → Minimally flavored colored scalar in JHEP → b ¯ Z b ν SPIRE SPIRE ][ JHEP , τ B , arXiv:1309.0301 IN IN ) models facing new ∗ [ and ( (2012) 161801 ]. ]. ][ ][ SPIRE and leptons in nonuniversal left-right models arXiv:1212.4607 -parity violation in mesons via on-shell sterile neutrinos arXiv:1311.2830 τ D Flavor models for IN 0 and [ τ R [ Z ][ B (2016) 117 109 arXiv:1309.2466 ]. ]. → – 34 – τν ]. [ ) SPIRE SPIRE ¯ ]. ]. ∗ B A perturbed lepton-specific two-Higgs-doublet model Revisiting the one leptoquark solution to the 01 ( IN IN D Correlating new physics signals in ][ ][ SPIRE SPIRE Hints of SPIRE → IN IN (2013) 151 (2013) 094012 SPIRE SPIRE (2014) 091 IN arXiv:1206.4992 New physics in the weak interaction of [ JHEP ][ ][ decays with B IN IN [ Left-handed 03 , (2013) 009 02 ][ ][ B arXiv:1211.0348 arXiv:1212.1878 Rare decays of [ [ D 88 12 Phys. Rev. Lett. , mixing arXiv:1606.04140 JHEP JHEP [ , 0 , ¯ Refining new-physics searches in D JHEP - , 0 decays arXiv:1507.07567 arXiv:1506.08896 (2012) 071802 D [ [ Phys. Rev. and the mass matrices constraints B , data arXiv:1311.6729 arXiv:1208.4134 Scalar doublet models confront (2013) 014014 (2013) 034028 ¯ ¯ ν ν [ [ 109 arXiv:1605.07191 − τ τ ) ) , ]. ]. µ arXiv:1602.06491 arXiv:1512.02210 ∗ ∗ τ ( ( + [ [ (2016) 053001 D D τν D 87 D 87 sµ decays and → → → SPIRE SPIRE → IN IN ¯ ¯ D 94 (2014) 112 b Rev. semileptonic decays violating supersymmetric effects in094023 the exclusive anomalies and its phenomenological implications [ B [ D (2013) 025 Rev. B B violations in 075017 (2015) 054018 Rev. Lett. multi Higgs doublets facing experimental hints for(2016) physics 081801 beyond the Standard Model A.J. Buras, F. De Fazio and J. Girrbach, 331 A.J. Buras and J. Girrbach, X.-G. He and G. Valencia, A. Abada, A.M. Teixeira, A. Vicente and C. Weiland, G. Cvetiˇcand C.S. Kim, J. Zhu, H.-M. Gan, R.-M. Wang, Y.-Y. Fan, Q. Chang and Y.-G. Xu, X.-Q. Li, Y.-D. Yang and X. Zhang, I. Dorˇsner,S. Fajfer, N. Koˇsnikand I. Niˇsandˇzić, C. Hati, G. Kumar and N. Mahajan, M. Tanaka and R. Watanabe, Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, S. Nandi, S.K. Patra and A. Soni, S. Fajfer, J.F. J. Kamenik, Zupan, I. Niˇsandˇzićand N.G. Deshpande and A. Menon, J.M. Cline, M. Freytsis, Z. Ligeti and J.T. Ruderman, P. Ko, Y. Omura and C. Yu, A. Crivellin, J. Heeck and P. Stoffer, J.A. Bailey et al., [43] [44] [40] [41] [42] [38] [39] [36] [37] [34] [35] [31] [32] [33] [29] [30] [27] [28] [26] JHEP12(2016)059 ] , , ] τ D 02 L Phys. muon - ]. , µ 2 L − Phys. ] and -meson − , ]. g JHEP in scalar ` − , B SPIRE models with + µ − Phys. Rev. ` IN 0 ]. + Phys. Rev. , s` anomalies with decay processes ]. + µ τ Z ][ , ` s ∗ SPIRE ]. L ∗ − → - ]. ` ]. IN K arXiv:1505.03079 b µ K → arXiv:1409.0882 + SPIRE [ ][ L b [ ]. SPIRE → anomalies IN → ]. K` SPIRE IN 0 d − B ][ SPIRE SPIRE ` IN ][ , B → IN + IN flavor anomalies ∓ ][ SPIRE arXiv:1503.03477 ][ B ` τ s` ][ ]. meson decays SPIRE [ IN boson within minimal flavor s` IN 0 µ → (2015) 142 ][ B and Z ][ b → → (2015) 015007 ]. ]. ¯ ν b arXiv:1509.01249 SPIRE 02 Quark flavor transitions in ]. h models for the LHCb and [ Family nonuniversal IN sν 0 ][ ]. physics beyond the Standard Model Z arXiv:1507.02070 → D 92 SPIRE SPIRE [ b JHEP SPIRE ]. Explaining the lepton non-universality at IN IN Shedding light on the s`` arXiv:1503.06077 (2015) 075006 arXiv:1408.1627 , IN Composite leptoquarks and anomalies in [ [ ][ ][ model for SPIRE Lepton flavor non-universality in → ][ arXiv:1511.07447 0 (2015) 173 IN A dark matter relic from muon anomalies arXiv:1503.09024 b Addressing the LHC flavor anomalies with Explaining arXiv:1602.08107 [ Z [ SPIRE [ ][ ]. D 91 arXiv:1403.1269 11 Constraints on a IN arXiv:1412.1791 [ – 35 – Clues for flavor from rare lepton and quark decays Phys. Rev. Lepton flavor nonuniversality in [ ][ , (2016) 034018 SPIRE Stringy explanation of JHEP IN arXiv:1509.06248 and future , (2015) 015001 (2014) 054014 [ ][ Phys. Rev. K D 93 (2016) 055045 , (2015) 014016 in a two-Higgs-doublet model with gauged R (2015) 006 (2016) 095009 Scalar leptoquarks and the rare Study of the rare semileptonic decays Leptoquark effects on arXiv:1507.06660 arXiv:1601.07328 D 92 (2014) 095033 D 90 − arXiv:1501.00993 [ [ e 05 [ + D 93 arXiv:1503.01084 D 92 D 93 [ flavor model Ke D 89 arXiv:1501.05193 Phys. Rev. JHEP (2016) 013032 [ → , , U(2) Phys. Rev. Phys. Rev. 18 /B , , arXiv:1512.02218 − (2015) 055021 (2016) 074003 Phys. Rev. [ µ (2015) 072 Phys. Rev. (2015) 151801 Phys. Rev. , , + ]. ]. ]. , Phys. Rev. 06 , Kµ 114 D 92 D 93 (2015) 094019 → SPIRE SPIRE SPIRE -meson decays IN IN IN 91 leptoquark model New J. Phys. JHEP processes the LHCb and CMS[ within a unified framework B Rev. violation opportunities decays from a anomalies [ Rev. (2016) 007 Lett. a dark sector protected flavor-changing interactions models horizontal gauge symmetries [ B S. Sahoo and R. Mohanta, S. Sahoo and R. Mohanta, I. de Medeiros Varzielas and G. Hiller, D. Fajfer and Beˇcirević,S. N. Koˇsnik, S. Sahoo and R. Mohanta, S. Biswas, D. Chowdhury, S. Han and S.J. Lee, B. Gripaios, M. Nardecchia and S.A. Renner, C.S. Kim, X.-B. Yuan and Y.-J. Zheng, G. Hiller and M. Schmaltz, A. Falkowski, M. Nardecchia and R. Ziegler, B. Allanach, F.S. Queiroz, A. Strumia and S. Sun, C.-W. Chiang, X.-G. He and G. Valencia, G. Bélanger,C. Delaunay and S. Westhoff, A. Celis, W.-Z. Feng and D. Lüst, D. Aristizabal Sierra, F. Staub and A. Vicente, A. Celis, J. Fuentes-Martin, M. Jung and H. Serodio, A. Crivellin, G. D’Ambrosio and J. Heeck, A. Crivellin, G. D’Ambrosio and J. Heeck, W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, [62] [63] [59] [60] [61] [57] [58] [55] [56] [52] [53] [54] [50] [51] [48] [49] [46] [47] [45] JHEP12(2016)059 g ]. B K 2) ]. and B R 2 − D 92 , g ) − ( ∗ ( SPIRE flavour Phys. g SPIRE ] D IN , ]. Phys. Lett. (2016) IN R and ][ , ][ ]. (2016) 013003 U(2) K ]. (2015) 094015 R ]. SPIRE Phys. Rev. D 94 , , ) IN puzzles ]. D 94 ∗ SPIRE and muon ( ) ][ ]. IN ∗ D − ( SPIRE D 92 ` SPIRE ][ R D IN + ]. IN ` SPIRE R ][ ) -decays and ][ ∗ IN SPIRE ( B Simultaneous explanation of arXiv:1505.05164 Phys. Rev. IN ][ [ and , K arXiv:1412.7164 ]. Phys. Rev. SPIRE ][ ]. [ optimised observables in the arXiv:1607.04857 , K IN → [ Phys. Rev. − R Leptoquark patterns unifying ]. ][ , B µ SPIRE + SPIRE Toward a coherent solution of diphoton µ IN and neutrino masses ∗ IN arXiv:1510.07658 (2015) 184 ][ SPIRE Lepton universality violation and lepton [ ][ K K ]. (2015) 370 Anomalies in arXiv:1511.01900 IN R 10 [ → Linear flavour violation and anomalies in ][ Towards a unified explanation of arXiv:1503.03865 ]. arXiv:1604.03940 [ B [ (2016) 115005 SPIRE arXiv:1512.01560 arXiv:1401.2145 B 742 [ IN [ JHEP Explanation of Direct and indirect signals of natural composite Violation of lepton flavour universality in composite On the breaking of lepton flavor universality in – 36 – , ][ SPIRE ]. D 94 arXiv:1508.00569 IN [ (2016) 251801 ][ (2015) 182 (2016) 141802 (2016) 035 (2016) 67 SPIRE arXiv:1509.05020 116 ]. ]. arXiv:1506.01705 Phys. Lett. IN [ 08 [ Lepton flavor and nonuniversality from minimal composite (2014) 2927 , Common origin of 116 Flavor anomalies at the LHC and the R-parity violating Minimal leptoquark explanation for the ][ arXiv:1601.02457 B 747 Phys. Rev. [ C 76 Vector leptoquark resolution of (2016) 119 -meson decays , SPIRE SPIRE B JHEP C 74 IN IN puzzles 01 , ][ ][ ) arXiv:1511.06024 (2016) 083 ) (2015) 142 [ ∗ ( 06 arXiv:1510.08757 D 07 Phys. Lett. JHEP ( [ Phys. Rev. Lett. anomalies in a left-right model with leptoquarks , , R , (2016) 075002 Phys. Rev. Lett. µ Eur. Phys. J. , , 2) ]. Explaining the diphoton excess in alternative left-right symmetric model JHEP arXiv:1605.06313 and Eur. Phys. J. JHEP (2016) 270 , − [ , , K g D 93 ( R SPIRE arXiv:1603.07672 IN arXiv:1509.08599 and flavor anomalies the decays [ and 055034 symmetry Rev. neutrino masses, flavor anomalies and the diphoton excess anomalies B 755 MSSM flavor conservation in [ Higgs setups physics implications at the LHC Higgs models Higgs models (2015) 114025 supersymmetric model extended with vectorlike[ particles B. Bhattacharya, A. Datta, D. London and S. Shivashankara, A. Greljo, G. Isidori and D. Marzocca, D. Das, C. Hati, G. Kumar and N. Mahajan, D. Buttazzo, A. Greljo, G. Isidori and D. Marzocca, C. Hati, F.F. Deppisch, S. Kulkarni, H. Päsand E. Schumacher, M. Bauer and M. Neubert, S. Fajfer and N. Koˇsnik, R. Barbieri, G. Isidori, A. Pattori and F. Senia, R. Alonso, B. Grinstein and J. Martin Camalich, A. Carmona and F. Goertz, B. Gripaios, M. Nardecchia and S.A. Renner, F. Mahmoudi, S. Neshatpour and J. Virto, C. Niehoff, P. Stangl and D.M. Straub, C. Niehoff, P. Stangl and D.M. Straub, W. Huang and Y.-L. Tang, C.-H. Chen, T. Nomura and H. Okada, H. Päsand E. Schumacher, [80] [81] [78] [79] [76] [77] [73] [74] [75] [72] [69] [70] [71] [67] [68] [65] [66] [64] JHEP12(2016)059 , , ] ), Chin. (2015) γ , ( 113 JHEP ]. decays ]. τ , (2016) (1958) 267 Eur. Phys. B 115 πν , , ) 0 ( SPIRE → Phys. Rev. 112 SPIRE decays , D 93 IN τ branching s`` IN (2011) 036004 3 ` ][ − ][ Phys. Rev. → ` K -mixing matrix , ) b + arXiv:1310.7922 (1999) 093006 s ` 0 ( [ in chiral perturbation ]. s D 83 B ) X 4 Phys. Rev. p Phys. Rev. , D 60 2 → Phys. Rev. Lett. (2004) 081802 , e SPIRE , Kaon decays in the Standard ( B IN O 93 (2014) 41 ]. Review of particle physics ][ ]. Phys. Rev. 75 hep-ex/0503044 , [ arXiv:1502.07488 [ Phys. Rev. ]. SPIRE SPIRE , IN IN ]. mixing ][ ][ ¯ B SPIRE - Electromagnetic effects in ]. IN B SPIRE Phys. Rev. Lett. ][ , IN Measurement of the (2005) 092005 Improved measurement of the electroweak penguin Revisiting lepton flavour universality in branching ratios to arXiv:1107.6001 – 37 – ][ (2015) 094009 [ Electroweak constraints on flavorful effective theories e ]. ]. scalar form factors in the Standard Model SPIRE Discerning new physics in charm meson leptonic and ¯ ν Effective field theory approach to ]. e 3 IN ` D 72 ][ K → collaborations, A. Bazavov et al., D 91 Prog. Part. Nucl. Phys. SPIRE SPIRE with third generation couplings Short and long distance effects in the decay hep-ph/9403385 ]. , Electroweak radiative corrections to tau decay arXiv:0707.4464 SPIRE IN IN [ ]. ]. [ The (2012) 399 Radiative corrections to Fermi interactions IN π/K ]. ]. τν ][ ][ ) [ ∗ collaboration, K.A. Olive et al., MILC ( 84 SPIRE D SPIRE SPIRE Phys. Rev. arXiv:1503.07872 IN SPIRE SPIRE ]. and , [ Phys. Rev. arXiv:0805.2222 IN IN [ → [ (1995) 17 IN IN − , [ ][ ` (2007) 005 B ][ ][ + Fermi constants and ‘new physics’ ` arXiv:0807.4507 Anatomy of new physics in s SPIRE Radiative corrections to muon and neutron decay 10 [ and X IN (2014) 090001 B 438 [ ¯ ν (2015) 018 → ν ) Precision tau physics ]. ]. (2008) 541 (1988) 1815 collaboration, B. Aubert et al., arXiv:1602.03560 arXiv:1506.02661 ∗ B ( JHEP collaboration, M. Iwasaki et al., Rev. Mod. Phys. 07 [ [ C 38 , , K 61 (2008) 006 C 57 → SPIRE SPIRE hep-ex/0404006 arXiv:1008.1593 hep-ph/9903451 IN IN BaBar fraction with a sum[ over exclusive modes Belle process [ Fermilab Lattice elements from lattice QCD113016 for the Standard Model and beyond Model J. semileptonic decays Nucl. Phys. 11 Lett. [ theory (1959) 1652 [ JHEP [ Particle Data Group Phys. B 181801 arXiv:1606.00524 A. Lenz et al., A. Kastner and H. Neufeld, S. U. Fajfer, Rojec, I. Niˇsandˇzićand R. Decker and M. Finkemeier, V. Cirigliano, M. Giannotti and H. Neufeld, V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, W.J. Marciano, V. Cirigliano and I. Rosell, T. Kinoshita and A. Sirlin, S.M. Berman, W.J. Marciano and A. Sirlin, A. Pich, F. Feruglio, P. Paradisi and A. Pattori, A. Efrati, A. Falkowski and Y. Soreq, L. Calibbi, A. Crivellin and T. Ota, [99] [97] [98] [95] [96] [92] [93] [94] [90] [91] [87] [88] [89] [85] [86] [83] [84] [82] [100] JHEP12(2016)059 − ¯ ]. ν ]. ` + , D` ` `` ) ∗ ] → SPIRE SPIRE JHEP K Kπ ¯ , IN IN B region (2015) 045 of → ][ ][ → 2 Phys. Rev. 1 ]. ( q 04 , B − 0 ∗ decays ¯ ]. K 3 fb ]. − Phys. Rev. Lett. SPIRE (2009) 012002 µ → , JHEP IN + d decay from the , ][ ¯ SPIRE B ]. SPIRE − Kµ arXiv:1411.4413 ]. IN (2013) 048 D 79 µ IN [ ]. ][ + → mixing angles in presence of ][ (2012) 034010 decays µ 01 decay using arXiv:1303.5794 SPIRE effective lifetime B decay in the low- arXiv:1503.04849 [ d,s SPIRE ]. → IN − − − [ SPIRE : complete angular analysis and V `` B 0 µ IN s e branching fraction at low dilepton µ ][ − D 85 IN + ]. + B ` + ][ (2015) 68 JHEP → − Implications from clean observables µ e ][ µ + Phys. Rev. e , 0 0 Optimizing the basis of ` SPIRE ∗ ∗ ]. , B + s → e IN ]. K K 522 X 0 arXiv:1202.4266 0 s SPIRE ∗ ][ (2013) 137 [ B (2015) 176 → → IN → ]. K SPIRE 0 0 05 ][ arXiv:1403.8044 ¯ Complete anatomy of Phys. Rev. B IN SPIRE 06 → [ B B , arXiv:1512.04442 Nature An analysis of 0 ]. IN ∗ ][ [ final states 0 , SPIRE B ][ at large recoil ¯ ¯ ν K Measurements of the semileptonic decays IN arXiv:1304.6325 JHEP ∗ – 38 – (2012) 104 − [ 0 JHEP , ][ µ arXiv:1305.2168 arXiv:1506.08777 SPIRE , K Inclusive + [ [ DX` 04 IN (2014) 133 µ ∗ → ][ Time dependence in Observation of the rare (2016) 104 s K 06 arXiv:1502.05509 B 02 ]. ]. ]. JHEP arXiv:1304.3035 → (2013) 131 , [ B arXiv:1204.1737 (2013) 084 (2015) 179 08 JHEP [ , SPIRE SPIRE SPIRE arXiv:1501.03038 JHEP 07 09 Angular analysis of the Differential branching fraction and angular analysis of the decay Angular analysis and differential branching fraction of the decay Angular analysis of the Differential branching fraction and angular analysis of the decay Measurement of the Differential branching fractions and isospin asymmetries of Angular analysis of charged and neutral [ , IN IN IN Probing new physics via the arXiv:1311.0903 [ ][ ][ ][ (2015) 049] [ JHEP collaborations, (2013) 159 decays , using a global fit to arXiv:1403.8045 JHEP JHEP 07 − − ¯ [ ν , , in the Standard Model with reduced theoretical uncertainty µ 05 µ ` − − + ∗ + CMS − µ µ µ (2015) 064 ` (2012) 041801 µ D 0 + + ) ]. + ∗ collaboration, B. Aubert et al., ∗ ` ( 04 → φµ φµ K JHEP K 109 ¯ , → (2014) 101801 B → → → (2014) 082 → SPIRE 0 0 0 s s s,d Erratum ibid. arXiv:0809.0828 arXiv:1111.4882 arXiv:1207.2753 IN [ [ BaBar and new physics and an[ update of Lett. B B JHEP B integrated luminosity observables in the full kinematic range B mass and its angular distribution for the binned analysis[ of B 112 05 a thorough study of collinear photons combined analysis of CMS[ and LHCb data S. Descotes-Genon and J. Virto, S. Descotes-Genon, J. Matias and J. Virto, K. De Bruyn et al., LHCb collaboration, LHCb collaboration, LHCb collaboration, LHCb collaboration, LHCb collaboration, LHCb collaboration, LHCb collaboration, S. Descotes-Genon, J. Matias, M. Ramon and J. Virto, S. Descotes-Genon, T. Hurth, J. Matias and J. Virto, LHCb collaboration, J. Matias, F. Mescia, M. Ramon and J. Virto, LHCb and C. Bobeth, M. Gorbahn, T. Hermann, M. Misiak, E. Stamou and M. Steinhauser, T. Huber, T. Hurth and E. Lunghi, [117] [118] [115] [116] [113] [114] [110] [111] [112] [108] [109] [106] [107] [104] [105] [102] [103] [101] JHEP12(2016)059 ]. , τ | , ¯ ν , ]. cb , − V ¯ , ν | 2 τ ` Phys. SPIRE ∗ q ) ] ] , ]. ∗ IN ( D SPIRE decays ][ D Phys. Rev. IN → Phys. Rev. τ , ]. Addendum decays in the ¯ , ν ][ → ¯ | B SPIRE [ − τ ¯ cb B IN τ V ) | ∗ ][ (2005) 1 cτν ( ]. SPIRE D IN → ]. ][ b → C 41 SPIRE ¯ (2013) 054002 arXiv:1206.3760 ]. B decay distributions IN arXiv:1503.07237 [ ¯ SPIRE (2015) 111803 ν [ arXiv:1412.3761 sensitivity to new physics ][ τ ]. [ emcee: the MCMC hammer IN c τ ¯ ν D 87 ][ SPIRE X arXiv:1505.03925 Probing new physics with τ 115 ∗ IN ][ → ]. D ]. SPIRE arXiv:1302.1042 ][ CP violation and the CKM matrix: [ B IN Eur. Phys. J. → ]. ][ , form factors at nonzero recoil and arXiv:0802.3790 (2012) 034027 B SPIRE [ (2015) 034506 SPIRE Phys. Rev. (2015) 114028 IN IN , On the anomalous enhancement observed in D`ν hep-ph/9712417 τ ][ ][ lepton polarization in the decay SPIRE ¯ ν Measurement of the branching ratio of [ D 86 decays with a semileptonic tagging method IN τ τ → D 92 factories (2016) 119906 On the ) ` decays with hadronic tagging at Belle Phys. Rev. Lett. ∗ D 91 ¯ arXiv:1202.3665 ][ ν Diagnosing new physics in branching ratios: opportunity for lattice QCD and Dispersive bounds on the shape of ( Measurement of the branching ratio of B ` B [ (2013) 074010 – 39 – − Evidence for an excess of ), ¯ ν D ` µ − arXiv:1205.5442 + ¯ ν ` D 93 ∗ ) → [ Dτν − (2008) 014003 ∗ D ( µ ¯ (1998) 153 D 87 arXiv:1203.2654 B → Phys. Rev. + D [ ∗ Phys. Rev. → , Precise predictions for B , Phys. Rev. 0 D → (2013) 306 ]. ]. ]. D 78 , ¯ ]. B ¯ ¯ ν arXiv:1406.7013 Constraints on the charged scalar effects using the B → B 530 arXiv:1506.08614 τ [ form factors at nonzero recoil and extraction of ) 0 125 ∗ ][ ¯ ( B SPIRE SPIRE SPIRE collaboration, J. Charles et al., Measurement of the ( Phys. Rev. Erratum ibid. arXiv:1507.03233 (2012) 101802 D SPIRE Measurement of the ratio of branching fractions IN IN IN , B D`ν [ [ [ [ IN / ][ → ) (2012) 094025 ][ → τ Phys. Rev. 109 relative to ¯ ¯ ν B , relative to B τ − decays ¯ τ Nucl. Phys. ν τ ¯ ν , τ − + (2014) 034021 D 85 ¯ ν − ∗ τ -flavor lattice QCD collaboration, H. Na, C.M. Bouchard, G.P. Lepage, C. Monahan and (2015) 159901 τ τ + ) ) D ]. ]. collaboration, J.P. Lees et al., ∗ ∗ ∗ collaboration, A. Abdesselam et al., collaboration, M. Huschle et al., ( ( collaboration, J.A. Bailey et al., D (2015) 054510 (2015) 072014 → D D 2 + 1 115 D 90 0 → ¯ → → SPIRE SPIRE B 0 ( arXiv:1205.4908 IN hep-ph/0406184 IN ¯ ¯ [ B distributions in light of the recent BaBar[ result forward-backward asymmetry on CKMfitter Group assessing the impact of[ the asymmetric Publ. Astron. Soc. Pac. D 92 Rev. form-factors MILC from [ HPQCD J. Shigemitsu, arXiv:1608.06391 hadron colliders Phys. Rev. B ibid. Belle B arXiv:1603.06711 Phys. Rev. Lett. Belle B D 92 BaBar P. Biancofiore, P. Colangelo and F. De Fazio, Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, A. Datta, M. Duraisamy and D. Ghosh, Y. Sakaki and H. Tanaka, D. Foreman-Mackey, D.W. Hogg, D. Lang and J. Goodman, Z. Ligeti and F.J. Tackmann, I. Caprini, L. Lellouch and M. Neubert, J.F. Kamenik and F. Mescia, S. Fajfer, J.F. Kamenik and I. Niˇsandˇzić, A. Abdesselam et al., LHCb collaboration, [134] [135] [132] [133] [130] [131] [128] [129] [126] [127] [124] [125] [122] [123] [120] [121] [119] JHEP12(2016)059 , ]. (2015) ]. ] New J. SPIRE 02 Phys. Rev. , Phys. Lett. , ]. IN ]. , ][ SPIRE ]. ]. IN decays JHEP SPIRE ][ , b decays? SPIRE Lepton-flavour IN Λ arXiv:1011.0352 [ IN SPIRE s`` B ]. , SPIRE ][ (2016) 074038 IN [ IN → angular distribution with b ][ τ ¯ Violation of lepton flavor ν arXiv:1602.07671 SPIRE ]. D 93 [ − (2016) 075 IN [ τ polarization as a probe to ∗ (2015) 054013 arXiv:1509.07259 10 Assessing lepton-flavour ∗ (2015) 075022 D decay anomalies related to Angular distributions of [ SPIRE D → B ]. IN arXiv:1503.07099 decay in the Standard Model and with ]. meson decays via a scalar leptoquark [ D 92 B ][ τ JHEP D 92 arXiv:1606.09300 ¯ decays to excited charmed mesons with ν Phys. Rev. B arXiv:1405.3719 , τ , ) [ ), c s (2016) 094021 New physics in the kinematic distributions SPIRE arXiv:1602.03030 ]. ( SPIRE Λ ∗∗ , Are the IN arXiv:1502.07230 B IN [ D ][ → ( Lepton flavor violation in Optimal-observable analysis of possible new ][ (2016) 034011 b R (2015) 367 D 94 Azimuthal SPIRE Phys. Rev. arXiv:1606.03164 Phys. Rev. , , IN – 40 – Belle II technical design report , ¯ ν τ ][ τ D 93 L ∗ - (2014) 074013 B 750 µ D angular analyses ]. arXiv:1512.04657 Predictions for lepton flavor universality violation in rare models Semileptonic L [ 0 → `` (2015) 115003 Phys. Rev. ]. ]. ]. ]. ∗ Z Charged-lepton mixing and lepton flavor violation , D 90 B τ Diagnosing lepton-nonuniversality in K Lepton flavor violating Effects of scalar leptoquark on semileptonic ν SPIRE )¯ Phys. Rev. arXiv:1411.0565 arXiv:1607.04449 IN → τ D 91 , [ SPIRE SPIRE SPIRE SPIRE ν [ Phys. Lett. τ ][ ` B IN IN IN IN ¯ ν , τν − ][ ][ ][ ][ ) ` ∗ arXiv:1507.01412 ( (2016) 114001 Phys. Rev. [ → D , ( − decays and search of new physics → Phys. Rev. τ decays in generic ` , ) D 93 ¯ ν ∗ B collaboration, T. Abe et al., (2015) 091801 ( ` (2016) 093051 B ) ]. ]. D ∗ (2015) 54 ( and searching for new physics with 18 D 114 → arXiv:1411.4773 [ ¯ B decays in models with gauged → SPIRE SPIRE arXiv:1601.00970 arXiv:1504.07928 arXiv:1605.03156 arXiv:1508.07009 IN IN ¯ Phys. Rev. and lepton flavor universality[ in rare kaon decays violating [ B 751 [ Lett. neutrino oscillations? B [ non-universality from e, µ, τ Belle-II [ 055 of [ discriminate new physics in B Phys. tensor operators new physics physics in S. Sahoo and R. Mohanta, A. Crivellin, G. D’Ambrosio, M. Hoferichter and L.C. Tunstall, A. Crivellin, L. Hofer, J. Matias, U. Nierste, S. Pokorski and J. Rosiek, D. Guadagnoli and K. Lane, S.L. Glashow, D. Guadagnoli and K. Lane, S.M. Boucenna, J.W.F. Valle and A. Vicente, W. Altmannshofer and I. Yavin, B. Capdevila, S. Descotes-Genon, J. Matias and J. Virto, G. Hiller and M. Schmaltz, A.K. Alok, D. Kumar, S. Kumbhakar and S.U. Sankar, F.U. Bernlochner and Z. Ligeti, A.D. Fajfer, Tayduganov, I. Beˇcirević,S. Niˇsandˇzićand S. Sahoo and R. Mohanta, R. Alonso, A. Kobach and J. Martin Camalich, S. Shivashankara, W. Wu and A. Datta, Λ S. Bhattacharya, S. Nandi and S.K. Patra, M. Duraisamy, P. Sharma and A. Datta, [152] [153] [150] [151] [148] [149] [146] [147] [144] [145] [142] [143] [139] [140] [141] [137] [138] [136] JHEP12(2016)059 ] W b (2016) , ] ] collisions ]. TeV pp D 94 ]. decays into (2016) 442 in − = 8 ]. ]. ]. (2015) 150 τ − s SPIRE τ SPIRE √ IN arXiv:1405.4123 C 76 + 10 collisions at IN [ τ ][ SPIRE SPIRE SPIRE TeV with the ATLAS ][ Phys. Rev. pp IN IN IN ]. , TeV with the ATLAS ][ ][ arXiv:1412.6302 ][ = 8 JHEP arXiv:1502.07177 [ s , [ = 8 √ ]. (2015) 080 s SPIRE ]. √ IN Eur. Phys. J. 06 ][ (2014) 052005 Lepton flavor violation in exclusive , quarks in proton-proton collisions at SPIRE (2015) 025 SPIRE T IN hep-ex/0703009 (2015) 157 arXiv:1403.5781 3 IN / ][ [ [ JHEP D 90 04 2 ][ , collisions at 07 -jets and a pair of leptons of the same b arXiv:1602.00881 arXiv:1509.04177 collisions at arXiv:1605.05718 More lepton flavor violating observables for pp [ [ quarks decaying to top quarks and Higgs bosons [ Vector-like leptons: Higgs decays and collider pp JHEP T JHEP , Search for lepton flavor violating Model-discriminating power of lepton flavor , (2007) 341 – 41 – Phys. Rev. arXiv:1312.5329 ]. , TeV [ (2014) 095014 (2016) 134 (2016) 442 = 8 TeV with the ATLAS detector B 648 s arXiv:1409.5500 arXiv:1505.04306 SPIRE (2016) 012003 D 89 [ [ ]. ]. ]. √ IN = 8 C 76 s ][ (2014) 092 B 760 TeV with the ATLAS detector √ D 93 SPIRE SPIRE SPIRE Search for high-mass dilepton resonances in Search for production of vector-like quark pairs and of four top Analysis of events with Search for single production of vector-like quarks decaying into A search for high-mass resonances decaying to Search for pair and single production of new heavy quarks that decay 05 , CERN, Geneva Switzerland (2012). = 8 IN IN IN Phys. Lett. Search for high-mass resonances and large extra dimensions with Search for physics beyond the Standard Model in dilepton mass spectra Search for vector-like charge Search for vector-like s ][ ][ ][ , (2014) 104 (2015) 105 Phys. Rev. 0 √ , π JHEP 11 08 − Phys. Lett. , ` Eur. Phys. J. Phys. Rev. collisions at , 2, , Constraints on a scalar leptoquark from the kaon sector decays and TeV with the ATLAS detector pp τ JHEP JHEP collaboration, collaboration, collaboration, collaboration, collaboration, collaboration, 0 ]. ]. ]. arXiv:1603.00346 , , η TeV with the ATLAS detector TeV collaboration, Y. Miyazaki et al., boson and a third-generation quark in [ decays = 8 collaboration, collaboration, collaboration, − collaboration, collisions at ` Z s s , = 8 = 8 pp √ η SPIRE SPIRE SPIRE s s → -lepton pairs decaying into final states with an electron and a muon at − IN IN IN arXiv:1503.01952 arXiv:1602.05606 arXiv:1504.04605 CMS τ CMS-PAS-EXO-12-046 CMS in proton-proton collisions at [ [ ATLAS √ [ [ CMS √ ATLAS at ATLAS in [ CMS in the all-hadronic channel using jet substructure ATLAS quarks in the lepton-plus-jetsdetector final state in ATLAS charge in [ phenomenology ATLAS to a detector violating Belle ` b 014022 LHCb’s run A. Celis, V. Cirigliano and E. Passemar, A. Falkowski, D.M. Straub and A. Vicente, G. Kumar, D. Guadagnoli, D. Melikhov and M. Reboud, SumensariD. and Beˇcirević,O. R. Zukanovich Funchal, [168] [169] [167] [165] [166] [163] [164] [161] [162] [160] [157] [158] [159] [155] [156] [154] JHEP12(2016)059 , . ] 07 ] (2016) 302 (2003) 275 JHEP 153 (2007) 90 , B 754 9 Comput. Phys. Commun. arXiv:1512.01224 , arXiv:1104.1573 [ [ Phys. Lett. ]. , Parton distributions for the LHC SPIRE Comput. Sci. Eng. IN , ][ (2012) 2458 Comput. Phys. Commun. (2016) 071801 , ]. 183 116 ]. SPIRE – 42 – colliders IN − : extensions including flavour, CP-phases and models e ][ 1 . + SPIRE 3 e arXiv:0901.0002 IN graphics environment [ ]. ][ TeV with the ATLAS detector D ]. 2 Phys. Rev. Lett. , SPheno = 13 SPIRE Search for new phenomena in dijet mass and angular distributions s IN TeV SPIRE √ Search for narrow resonances decaying to dijets in proton-proton (2009) 189 : a tool for (not only SUSY) model builders ][ IN Comput. Phys. Commun. 4 , arXiv:1309.7223 ][ [ = 13 The automated computation of tree-level and next-to-leading order s C 63 Matplotlib: a √ arXiv:1405.0301 SPheno, a program for calculating supersymmetric spectra, SUSY particle decays [ SARAH collaboration, ]. ]. collisions at collaboration, pp (2014) 1773 SPIRE SPIRE IN hep-ph/0301101 arXiv:1512.01530 IN beyond the MSSM [ 185 and SUSY particle production at [ [ CMS collisions at [ differential cross sections and their(2014) matching 079 to parton shower simulations Eur. Phys. J. ATLAS from J.D. Hunter, W. Porod, W. Porod and F. Staub, F. Staub, A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, J. Alwall et al., [177] [175] [176] [173] [174] [171] [172] [170]