CORE JHEP08(2010)115 brought to you by by you to brought Springer - Publisher Connector - Publisher Springer by provided Springer July 22, 2010 April 27, 2010 : : August 10, 2010 August 25, 2010 : : Revised Received 10.1007/JHEP08(2010)115 Accepted Published best fits, still allowing for nothing first proposed in b ¯ doi: ]. We show that the observed → Zb 4 A Published for SISSA by (2006) 039 04 flavor symmetry breaking scheme implemented 4 JHEP A must arise from higher order corrections. Without td V and [email protected] , ub V (or other versions of) custodial symmetry, the bulk mass parameter of 1004.0321 LR P Large Extra Dimensions, Beyond Standard Model, Quark Masses and SM We propose a spontaneous flavor model for quarks and leptons in warped

[email protected] 4 A

E-mail: Centre for Theoretical Physics, University9747 of AG, Groningen, Netherlands Open Access Parameters ArXiv ePrint: the left-handed quarks ina this Kaluza-Klein model scale is below constrainedscale 2 by TeV. implied Finally, the by we flavor briefly changingresidual discuss neutral little bounds current CP processes on problem in the is our Kaluza-Klein milder model than and in show flavor thatKeywords: anarchic the models. [X.G. He, Y.Y. Keum andquark R.R. mixing Volkas, patternviolating can phase, with be leading order explained cross-interactions,the while in the smallest observed CKM a difference between entries ratherimplementing economical way, including the CP mass hierarchies by wave function overlaps,and the emergence zero of quark tribimaximal mixing neutrinoflavor mixing at violations. the leading Quark orderfor mixing and “cross-brane” is the interactions induced absence and of byrealizing a tree-level “cross-talk” the the gauge between presence spontaneous mediated the of quark symmetry bulk and breaking flavons, neutrino which sectors, pattern allow Abstract: in a warped extramasses dimensional and setup to mixings. explain The the observed main pattern advantages of of quark this and choice lepton are the explanation of fermion Avihay Kadosh and Elisabetta Pallante An geometry View metadata, citation and similar papers at core.ac.uk at papers similar and citation metadata, View JHEP08(2010)115 – 12 22 12 (3 TeV), is now allowed O 10 14 18 24 26 8 10 15 3 – 1 – ], which have been proposed as an alternative solution to parameters, unless the lowest Kaluza-Klein (KK) mass scale 2 , 17 1 T 30 , 23 S ]. Having the zero mode fermions peaked at different points in the 6 – 1 3 28 properties 4 ]. However, letting the standard model (SM) fermion content propagate through A ] were constructed. Alternatively, large brane kinetic terms were introduced [ 10 11 – 7 5.1 Alternative solutions by model modifications 4.1 The quark4.2 and charged lepton The sector neutrino4.3 sector Obtaining the4.4 CKM matrix and Estimation fixing of the cross-talk scale and cross-brane contributions in the lepton sector 2.1 Leading order results in the neutrino sector 3.1 Cross-talk and3.2 cross-brane effects in Cross-talk the and neutrino cross-brane sector effects in the charged fermion sector ]. In both cases a mass of the first KK excited state as low as as the Peskin-Takeuchi is unnaturally pushed to valuesmore much realistic higher than models a involvingbranes TeV. a To [ suppress bulk these custodial contributions, symmetry,14 broken differently at the two explained by the overlap of theextra fermion dimension and Higgs [ wave functionsfifth in dimension, the the bulk exponentially of hierarchical the massesobtained warped of with quarks a and tiny charged hierarchy leptonsunity of can [ bulk be masses andthe all bulk 5D generally Yukawa couplings results being in of large order contributions to electroweak precision observables, such 1 Introduction Warped extra dimensions [ the gauge hierarchy problem, also provide a simple framework in which fermion masses are 7 Conclusions A Basic 5 Vacuum alignment 6 Flavor violation and the Kaluza-Klein scale 4 Numerical results for fermion masses and mixings 3 Higher order and cross-talk corrections Contents 1 Introduction 2 The model and leading order results JHEP08(2010)115 6 ]. ], ], K  38 20 45 [ – ]. It ] is at K 34 25 / 16 0 , ]. Even in  25 15 ] was used to , – 44 10 21 – 41 ]. In these settings, oscillation parameter 32 , 0 K 31 − 0 ] a shining mechanism is pro- K 33 well describes the lepton sector, ], where a mass of the first KK 4 19 A – family symmetry [ 17 4 A ]. In addition, tree-level leptonic FCNCs are ], the direct CP violation parameter 46 – 2 – 19 – ], a bulk ] and in the lepton sector [ 17 40 [ γ 30 to generate tribimaximal (TBM) neutrino mixing [ , ) 4 d ] that the mixing between fermion zero modes and KK ( 29 A s 28 – → 26 b ], see also [ 39 ] to produce stringent combined lower bounds on the KK gluon and the 28 – (3 TeV) gives rise to a NP contribution which is roughly twenty times larger than 26 O All above considerations suggest that a candidate for a realistic model of lepton and Additional flavor symmetries in the bulk can in principle allow to partially or fully and the radiative decays K scale of order a TeV.explain In masses [ and mixings inlepton the doublets SM form a lepton triplet sector.in of In agreement this with setting, the theabsent recent three in global this left-handed fit scheme. in While [ the simplest realization of that Higgs mediated FCNCs are eliminated2-3 to TeV leading seems order, to and a be lowest allowed, KK rendering scale of the about model testablequark at masses collider and experiments mixings [ inmodel a fields warped setup in shouldadditional the possibly flavor be symmetry, bulk, to realized avoid including with large all the new standard physics Higgs contributions and field, maintain a the KK bulk custodial symmetry and an the bulk mass matrices are alignedflavor with symmetry the 5D that Yukawa matrices is as broken aposed, in result where a of the controlled a suppression bulk manner. of [U(3)] In flavorobtained violation [ by in confining the effective the 4D sourcesits theory of effects on through the flavor IR gauge violation brane bosons to is of the the UV gauged bulk brane, flavor and symmetry. communicating There, it is also shown remove these constraints, by forbidding orNCs providing and a one further loop suppression contributionsremoves of or induced tree suppresses by level all the FC- tree presence levelvor of contributions violation KK is in modes. the the generalization quark One to sector example 5D [ that of minimal fla- modes generally induces a misalignmentmasses in the and 4D the effective Higgs theory Yukawa couplings. betweenchanging the neutral This SM misalignment currents, fermion leads once to theis Higgs fermion mediated found mass flavor matrix [ is diagonalized.standard model In Higgs particular, mass in flavor anarchic models. the current experimental bound —Stringent a constraints CP on problem the in KK itself,the scale referred are absence to also of as present neutrino little in masses, CPmediated the severe problem. lepton bounds by sector arise tree [ from level contributionswas to KK also FCNC recently gauge processes observed bosons [ with anarchical 5D Yukawa couplings [ Yukawa couplings, new physics contributions can alreadya be KK generated gauge at boson tree level exchange.work, through stringent Even constraints if on an the RS-GIM KK suppression scale mechanism come [ fromand the especially the neutronstate electric of dipole moment [ degenerate 5D bulk massnon parameters, degeneracy governing induces the new localization physics(FCNC) of (NP) processes bulk contributions mediated to zero by flavor modes. KK changinggauge excitations neutral The interactions of current in the the gaugegeneral fermion bosons case, and kinetic without fermions, terms imposing through any and additional 5D flavor symmetry Yukawa interactions. and assuming In anarchical 5D the most by electroweak precision data. Another problem arises, this time due to the presence of non JHEP08(2010)115 . , ), 5 4 7 11. (2.1) ' is the kπR 2 − ( Z kR . Two 3- R spontaneous k exp 2 custodial sym- Z ≡ LR → P = 0, the UV brane, 4 KK y A M with radius 2 and /Z SSB pattern associated with k 1 . In other words, we allow for 3 , S ν Z πR we discuss the vacuum alignment we briefly discuss constraints from dx → ] between the = µ 5 6 4 KK y 47 dx A M best fits in our model. The numerical we review the basic setup of the model µν 45 . η 2 b ¯ | y | Zb k 2 orbifold boundary conditions, where − 0 2 – 3 – e Z , namely two flavon triplets, reside in the bulk. + 4 The electroweak scale naturally arises for × 2 A 2 1 dy Z , the three generations of left-handed quarks transform 4 = A 2 is the reflection about ds 0 , compactified on an orbifold 2 we classify all higher order corrections, including cross-talk y Z curvature scale. The geometric warp factor sequestering the two family symmetry, and derive the leading order results for masses 5 3 ], which are usually associated with a rather richer flavon sector. 4 53 A – 48 [ = 0 and 0 ], and it is largely relaxed in models with (extended) y ; this assignment forbids tree level gauge mediated FCNCs and will allow T is the AdS 4 54 family symmetry, implemented in a slightly different setup, in an attempt to A ]. Pl , the IR brane. The resulting bulk geometry is described by the metric 4 M 56 A , πR ∼ 55 k = y All matter fields of our model, fermions and scalars including the Higgs field, live in The paper is organized as follows. In section An additional feature worth to mention is the constraint on the common left-handed Notice that the first KK gauge boson mass is about 2 1 the latter referred to as the KK scale. the bulk and we allowreflection for about arbitrary and where branes generates two characteristic scales within this setup, 2 The model andWe leading adopt the order RS1 results framework andwith thus the assume the extra bulk dimension, branes of our with model opposite to tension be are a located slice at of the AdS orbifold fixed points and cross-brane operators forcontains leptons our and numerical analysis quarks and andproblem results. and parametrize suggest In possible their section solutions, effect. whileflavor in violating Section section processes on the Kaluza-Klein scale in our model. We conclude in section metry [ and the various representationsymmetry assignments. and We a then bulk presentand a mixings. RS model In with custodial section symmetry, like quarks bulk mass parametersignificance implied of such by a the of constraint RS has models been [ thoroughly investigated in the minimal version mediator peaked towards the UVthe brane quark and — charged and lepton the sectorsAs — in with previous scalar models mediator peaked basedas towards on triplets the IR of brane. to obtain realistic massesalso and be almost instructive realistic to mixing compare angles this in pattern to the the quark case sector. of It larger will realizations of the flavor on a bulk describe both the quarkunder and non lepton sectors. trivial InConsequently, representations they this allow of for setup a the complete ”cross-talk”symmetry scalar [ breaking fields (SSB) that pattern transform associated with the heavy neutrino sector — with scalar it does not give rise to a realistic quark sector. In this paper, we propose a model based JHEP08(2010)115 00 ], ), Y × 1 , y 11 ) (2.5) (2.3) (2.4) (2.2) ⊕ − 00 cust SM Higgs 0 U(1) 1 π G 1 0 × ⊕ 2) L Ψ( 0 ⊕ , . 5 1 γ 1 2 0 ⊕ Z ) Z 3 1 ) × . doublet for each 3 4 ) ) = R 1) ( 1) ( 1 A y − 0) ( − notation is standard. , , , × + 0) ( 1 2 2 assignments for leptons L , , , , π 2 − 2 1 1 4 cust SM , , , , , so that zero modes will B 0 2 2 G , (1 (1 (1 Z (1 ∼ ∼ ∼ U(1) × L R 00 R 2 ) and Ψ( × ` e ν ], thus many of the leading order flavor symmetry plus an auxiliary y Z R 4 ,H ⊕ − 47 ) A , 0 R 3 Ψ( on the IR brane. e 5 to incorporate custodial symmetry [ 44 L – SU(2) ⊕ ! 0) ( L − Zγ , R − ¯ 41 × ξ ψ B 1 e B , and a Higgs field transforming under L

1 ) = χ , ) ) – 4 – y 00 00 U(1) (1 U(1) 1 1 × Ψ = SU(2) × ∼ ⊕ ⊕ D 0 0 R × 1 1 c , respectively. The 5D fermion corresponds to two Weyl ⊕ ⊕ 0 2 , χ ) or a triplet scalar VEV, while a bidoublet (2 is augmented by an ) Z 1 1 3 2 SU(2) ( ( ( 3 / ]. 1    × cust SM ]. In particular, the complete UV breaking pattern is achieved 0) ( 3 1 3 1 3 1 and 2) = SU(3) L G , 58 , , , , 11 2 , 2 1 2 2 1 , Z , , , Z 57 1 1 1 2 , , , , × 3 3 3 as in [ (1 4    0 2 A (4TeV). This symmetry is broken down to the SM group SU(2) ∼ Z ∼ ∼ ∼ O × doublet (1 Φ 1, under × L 00 R 00 R notation is explained in the appendix, and the 2 ± d R u , whereas the right-handed charged-fermions are each given a Q 4 SM cust 4 Z = ⊕ ⊕ A G A 0 R 0 0 R = d assignments will be specified later. Models with similar A u of 2 G ⊕ ⊕ 3 Z,Z Z Bulk fermions are assigned specific parities under We introduce two scalar flavons Φ and Both breaking patterns can be realized by orbifold boundary conditions on the gauge The symmetry group in our model is R as R , whose nature and role will be explained below. In addition, the electroweak gauge d u 4 2 the bulk fermion fieldwith Ψ transforms as Ψ( spinors of opposite chirality in 4D properties are shared with ourto model. a Notice that thestructure. right-handed neutrinos It are is assigned alsoright important handed to fermion. notice that we have a separateprovide SU(2) the standard model particle content. As implied by the invariance of the 5D action, where the The and scalar fields have been considered before [ bidoublet Higgs field lives in the bulk and itA is peaked towards the IR brane. The three families of quarks and leptons are assigned to the following representations: fields under via an SU(2) VEV induces the IR breaking.mass These limit fields as can in eitherand higgsless be leptons, models, decoupled by as or taking it be their is dynamical infinite true and in used our to case generate for masses the of Higgs quarks field. Notice also that, in our case, the group is extended to SU(2) and thus protect electroweak precisionbeing measurements as with light as the lighteston Kaluza-Klein the mass UV brane, and down to SU(2) Scherk-Schwarz twists [ The bulk gauge symmetry Z discontinuity of the bulk profiles at the orbifold fixed points by the presence of non trivial JHEP08(2010)115 . , , L . Pl . ` has ` L ! M (2.7) (2.8) (2.6) c ] ] ¯ ψ , while − − e, µ, τ doublet , , = R − πR +), h.c. , , [+ [ ` 2), the zero , + = / ! R 1 ] ] 0 R ˜ t 1 y , b ] − − c R has the opposite ˜ c, , , each. Again, the ) , with c < 0 R each. These fields H u ¯ − R , s ˜ ψ u, ] R ) = (+ [ [+ 0 ν 00 b R νR R ( c ˜ 1 0 R d R ν ˜ ` H d R ν ν 00

Φ) [ Z,Z ˜ and 1 H e

, share one common bulk L and = 4 and , while 00 M is naturally of order 2 (resp. R Q Φ) R = ξ / 1 s ( ` R R L + 1 00 u D , , b R τ 5 y Φ) i Q , c ν R R , ( L χ parameter which we label d 00 R + d ` ` L , s c > · , ( y c µ c ! R s 00 R 00 e R +) Weyl spinor. ] ] , d t 3 y + ] , R − − , c has parities ( e , , 00 R + ) ! H u R ] ] 0 c R − ξ 00 R [+ [ 1 ν ˜ , − − H d ( ], and we do this for quarks and leptons. , , R R 0 implies Neumann-like boundary conditions ˜ R Φ) H e u − 1 11 ν [ [+ L , τ 0 [ 1 R χ Q πR Φ) R ( y e,µ,τ L – 5 – 0 u b , µ ˜ Φ) ˜ ν , t = y Q + L R R ˜ ( s, y ` e 0 d ( + , c ˜ 0 e H y d,

R y R 1 u + ) = + R R

= 0 or H u R ν R 3. = L y 1 parities. Hence, if ) is the sign function. For , τ , ˜ ` H d y R 2 ˜ ( 0 R 2 H e ( Φ) , 1  D , t ν Z L 1 , µ y , they will share one common R Φ) h 4 Q R = 1 ) are given for the upper Weyl spinor Φ) ( 0 e , c L 2 parities. To get a massless zero mode from both components, we i u L / and R Q 1 y ` , and 2 D [ u ( (  , hence there are 6 different bulk mass parameters entering their zero 2 − 5 2 d e Z 4 . The right handed quarks are assigned to distinct one dimensional D ck , all fields propagate in the bulk and Λ Z,Z Z y y  5 − and ) q L ) bulk global symmetry: since the three left handed lepton doublets are ∗ is broken on the UV brane, the two components of each SU(2) +] c 2 y + + +Λ , ( H +] R Z  u,d i , L [+ = Λ c × 2 ). Even parity at ( = [+ 4 iτ L − invariant 5D Yukawa lagrangian at leading order reads  L m , and a single right handed zero mode in , ≡ Q G − = ˜  Yuk(5D) H and a single right handed zero mode in L L ` = L The Analogously, the boundary conditions for the quarks are chosen to be: The bulk profile of the would-be zero mode is shaped by the fermionic bulk mass term e, µ, τ L Q Q = where The Higgs and Φ fields are chosen to be peaked towards the IR brane at mode profiles, In this way wein have a left handedthree massless left zero handed quark mode doublets, formass being the assigned parameter, to three a left tripletrepresentations handed of of A doublets A conditions. Hence, there` is a lefthave handed bulk zero masses, in mode units of forand the AdS each we curvature, left given work by handed indue doublet the to in basis the A whereunified they into are a real triplet and of diagonal. A An important restriction is where the parities ( mode is exponentially localizedthat on since SU(2) the UVmust (IR) have brane. opposite Finally, itthus is need important to double toTaking the notice into account number the of above doublets considerations,to we [ leptons, assign in the the following absence boundary conditions of localized mass terms: parities ( on the bulk fermionfollows that profile, a while massless odd zero-mode only parity exists implies for Dirichlet awith boundary (+ mass conditions. It and with opposite JHEP08(2010)115 , , 4 = d L A ` , g , u (2.9) − L (2.10) h.c. , Q √ ) + ) ) are the y    ( 00 0 πkR R R R ), and follow- f f f |− L,R y | f    2.8 k 4(    e 2 and the electroweak 3 ), they read 1 . Φ − Φ 4 , and 00 Φ 00 4 f y 00 (1 2 y a πkR ωy ω 2 χ − triplet field Φ and the Higgs ( 3 3 GeV, the ZMA turns out to 2 ), the metric factor is . 4 ) = 1 Φ y symmetry, under which Φ 0 A 0 Φ ( exp y 0 2.9 2 a 2 y to the electroweak singlet and Z χ ωy ω = 171 χ t y 1 2 3 m = 0, for phenomenological reasons. The ) Φ Φ Φ y y y Yukawa invariants of eq. ( and the Higgs have acquired a VEV. The y πkR    |−  , χ y quark, | – 6 – L k u, d, e t 3 ) are from eq. ( 4( f y = e is absent from the Lagrangian. , ( 0 a L f R 2 H have a suppressed subscript f , 00 (1) in the construction of section component. The size of the SM fermion masses is thus Hν L ) = 1 O Φ 4 , y 0 y 03 for the masses of the zero mode fermions. f L ) respects an additional . A ( ` ) and Φ 0  y H y, y ( ) 2.8 ' y D . The VEV profiles for the scalar fields in our model are solu- H ( 2 5 4 Λ ) once the flavons Φ H KK ) g ) has a relatively simple structure. Each charged fermion sector M 2.8 t − πkR will be responsible for providing two distinct patterns of spontaneous , and a single Yukawa coupling on the UV brane. To leading order in 2.8 m √ |− χ y χ M | 3 denotes the k dy , invariant term 2 4( 4 ], an IR localized quartic double well potential for Φ and the Higgs, and a , e a πR is peaked towards the UV brane at A ), the Yukawas πR | 59 v − × y χ = 1 Z | . In total there are only twelve, a priori complex, Yukawa parameters to describe k χ a ) = = 4 SM cust y f − Writing out the charged-fermion All the SM fields are identified with the 4D components of the zero modes in the The lagrangian in eq. ( ( G and involves the Higgs only, while the right-handed Majorana sector contains one bare and Φ are odd, while all other fields are even. This non-flavor symmetry ensures that a M has three independent Yukawa terms, all involving the Φ D R ν where the scalar profiles exp( mass present in ourbe model as is accurate that as of the ing the rules in the appendix, one finds that each of the three mass matrices has the form symmetry, lead to boundary conditions thatare mix however all rather levels insensitive of to KKas fermions. the presence a The of light small modes these perturbation. boundaryobtained terms by and Thus, using can to the beeach zero leading treated specific mode order, case depends profiles the on of low the all energy lightness bulk of mass the fields. spectrum lowest lying The can KK accuracy be states. of Since the the ZMA largest in where determined by the amount ofcorresponding wavefunction overlap to of two the zero same modescorresponding of scalar Dirac opposite fields. fermion chirality, This ingood holds description 4D, as of far together the as with 4Dpotential the reduction the boundary zero of mode VEV terms our approximation for model. profiles (ZMA) the of In is general, scalar a the the fields presence will, of after kinetic and SSB of A tions of the bulkpurposes equations [ of motionsimilar with term for almost vanishing bulk mass for stabilization Kaluza-Klein decomposition of the bulkare fields. induced Masses by and eq. mixingsVEVs ( for of leptons Φ and quarks and symmetry breaking of A triplet masses and mixings of ninebe Dirac taken and to six be Majorana universal fermions. and All of of theseν parameters will the lagrangian in eq. ( e field. By construction, they neutrino Dirac term isMajorana governed mass by a single coupling constant the field JHEP08(2010)115 ) , | y | k , A.1 ) j (2.14) (2.15) (2.16) (2.11) (2.12) (2.13) , with R ] it was j symme- c kπR (0) R 8 − 3 47 f i Z |− L c y | − k ( 8 and e e ) i 1) f (0) L R − f , c flavor symmetry, i.e. flavor subgroup cycli- f components, as in the πkR 3 ) L 3 ) j c Z j 4 Z ( R R c A c F 2 2 . assignments, the Φ VEV of . − − πR (1 dy 4    2 e A 2 , )(1 ω ) = 1 i } 1)( πR πR ], L ω 2 − 3 denote c − ( , ω ω , Z ω 2 47 0 U 2 , c, a f † Φ 1 11 1 1 , 1 − y πkR ) ) { i ω ≡    (1 = ( L = c 3 3 2 f U v 1 3 ˜ y √ − C = = (1 – 7 – e d 2 ∼ = L ( v ) = V 3    † ω s = Z ( u v . We will show below that, if the remnant L 00 f 4 1 U V y v → 0 A 3˜ kπR = = 4 √ A included. This shows that the left-diagonalization matrices )= v triplet basis states with no change of signs, see eq. ( y 0 u,d,e f g L ( CKM y 4 0 0 j V V − 3˜ (0) A R √ representations transform under this subgroup in the same way √ f , and each of the above mass matrices translates into the effective ) 00 v D y 2 5 ( 1 f y i Λ 0 0 0 (0) 3˜ L / 0 √ and gf Φ 0 0 −    1 ) . H √ ω ( ≡ ≡ and the factor ) U v j denotes “isomorphism”, see the appendix. The remnant ) forces the CKM matrix to be the identity: R ]; in this case the mixing angles are independent of the mass eigenvalues. One = ]. The ∼ = for the up-quark, down-quark and charged lepton sectors, respectively, are identical , c nothing f 60 i 47 2.11 u, d, e L M c → ( = u,d,e 3 L F try remains unbroken, the CKM matrixis will thus remain needed trivial in to order allfirst to orders. produce suggested A deviations that further of breaking such theto CKM small induce matrix deviations from a unity. can relativelyZ In be weak [ generated subsequent by breaking higher-order of effects, the able residual where cally permutes theand three [ they do under the full flavor group, eq. ( It also induces the breaking pattern This diagonalization propertyity” of [ mass matricescan is easily see referred that, to at as this “form order diagonalizabil- and due to the above f V and equal to the unitary trimaximal mixing matrix [ product of the 5D profiles for the zero modes of the fermion fields, where we conveniently introduced the fermion overlap function appendix. For the special VEV pattern of Φ we define 4D mass matrix fermion bulk profiles. The numerical subscripts 1 JHEP08(2010)115 · ) R ν ] and (2.18) (2.19) (2.20) (2.17) , c R ν 47 , , c ) VEV ( R 44 to the quark . ν χ ] and the 5D – i 1 , c dy F 47 ), the 4D Dirac 41 χ R h D ν ν R c m A.5 ( M F ≡ ) ), thus allowing to ap- ) = 1 · , χ πR M ν , ! |− (Φ ]. The neutrino Dirac mass M y          | ) ( V χ R 39 k D ν ˜ ν 0 0 4 M , M e m ). Using eq. ( , c ` L − D ν c ˜ 0 0 0 0 is dimensionless. The right-handed 2.8 ). We now follow [ 6= 0 M ( m (1 0 D ν F ) χ 2.9 y χ D ν ˜ M πR dy M m πR ≡ 2 induced by the choice of the in eq. ( that induces a non trivial pattern in the |− 2 D ν y } 0 0 | R 2 ( χ m πR πR k 4 − , r , χ Hν D ν e – 8 – 1 Z 0 0 L { 2 m ` / D allows for the presence of higher dimensional oper- χ = 0 1 5 = πR dy y D ν 2 3 χ 0 0 0 00 00 0 0 0 0 0 0 0 0 Λ 2 χ m Z = πR πR =          . On the other hand, having these profiles exponentially − χ → 1 Z ˜ y = 4 χ 3.2 D 2 ν A / D y 1 5 0 total ν Λ , H M   

2 1 0 = χ χ is the effective 4D coupling and 6 neutrino mass matrix in 4D becomes 3 1 1 3 the VEV components of eq. ( 0 , D χ χ ν × D ν 2 y ˜ y 3 2 , 0 0 χ χ H    = 1 . = χ . It is the coupling to the flavon 5 y D 1 ν , a a = ˜ ˜ M χ M χ ν Our main goal is to implement this idea in our setup to obtain a realistic CKM ma- ≡ M so that the full 6 with assume the breaking pattern neutrino bare Majorana mass matrix1 is similarly trivial, being neutrino mass matrix, with contribution In this equation ˜ 2.1 Leading order resultsThis in is the an neutrino immediate sector warped generalization model to with our brane model localizedmatrix of scalars is the on derived 4D from an derivation the intervalmass in in Yukawa term matrix [ [ turns out to be proportional to the identity matrix localized on different branes, combined withsuppresses the the internal mixed symmetries interaction terms of in theproximately the model, preserve scalar the strongly potential original alignmentin between the section VEVs of these fields, as discussed trix, without spoiling the resultslepton that sector. will It be is obtainedoverlap for below between this the for purpose profiles the that of neutrino weators, Φ and choose which and charged communicate to the use symmetry bulk breakingsector, flavons. pattern as associated The explained with non in vanishing section JHEP08(2010)115 |  χ (2.21) (2.22) (2.23) in the M | 3 , | Z ˜ , M |      2 χ 2 χ χ M M 2 − , 2 − ˜ ˜ M MM 2 ˜ ) does not allow for M ˜     M ], those which preserve 6 − 2.8 6 2 0 0 47 iπ/ 2 iπ/ √ 0 − 5 √ 2 χ e − 2 χ χ e M − M 2 − 0 1 0 2 − ˜ ˜ . We will first show the pattern 3 3 3 2 M MM 1 2 ω ˜ ω χ √ √ √ M ˜ . M 6 6 − 2    ω 6 ω √ √ 2 1 √      − − − 2 )     2 0 D ν ˜ M in the charged-fermion sector, respectively √ = breaking to the neutrino sector via Φ. In our m ( 3 2 1 0 0 1 0 1 ν L Z Z − V    – 9 – in the neutrino sector. The latter communicate † ) ]. Notice that the Jarlskog invariant is vanishing = 2 → 2 1 ω Z T 4 ( √ ) 61 , and , A U χ D ν = 47 = ν are in general complex. In the see-saw limit M L ( ν V χ L 1 ) of each sector, call them “higher-order”, and those that V M − 3 † e
L Z and Φ, which are in charge of the symmetry breaking pattern χ ν V χ 3 light neutrino mass matrix is thus and or M = ˜ 2 × + M Z M ν flavor symmetry through the overlap of bulk scalar fields. It is these MNSP M 4 V , and 0 A D χ ν χ ˜ M y − ≡ in the neutrino sector and = χ ], as already concluded in [ 2 ν L Z M 46 M Higher order effects were naturally divided into two classes [ The bulk scalar fields , and the effective 3 → breaking to the charged sector via ν D 4 3 of all dominant higherviations order from corrections the to trivial the andstructure CKM tribimaximal and and forms, size MNSP respectively. in matrices, Weested will our producing in then model de- the estimate quark and their sector. comparefor The with the reason CKM existing is matrix results. that can within emerge We our with are setup a mainly an fairly almost inter- restricted realistic choice structure of the parameters involved. involve interactions between the twoquark sectors, and “cross-talk”. charged lepton The sectors,Z former and preserve context, a further way to isolateis the to dominant distinguish contributions between amongst brane all localizedtions higher order interactions, induced UV terms by or the IR, overlap and of “cross-brane” the interac- bulk profiles of Φ and a talking between thebreaking two of sectors, the higher dimensionaleffects operators that will we ensure are the interested in, complete in order tothe account flavor for subgroups a ( realistic CKM matrix. A are peaked on different branes.will be Thus, approximately, the but two notof distinct fully flavor these sequestered symmetry fields. from breaking one patterns another, Thus, due while to the the leading bulk nature order lagrangian in eq. ( which is tribimaximal updata to [ phases anddespite in the good presence of agreement these with phases, the and consequently neutrino CP oscillation violation is absent at this order. The MNSP matrix, at this order, is then whose diagonalization matrix is m where JHEP08(2010)115 . 2 3 3 , Z Z will 4.4 (3.2) (3.1) n and Φ talk − χ and ,  cross

3.2 talk    ) of the form − ∗ 2 11 2.8   cross Φ 3

+ ˆ + ˆ 
2 Φ 1 Φ 11 triplet part of Φ . The complete higher . Hence, the contribu-  ≥  4 4 -preserving sector come H ) and thus prevent quark A 3 1 1 A 22 , and since the VEV of Φ m,n ω −    Z 4 ) ( † χ R A + ˆ + ˆ + ˆ U Φ 3 Φ 2 11 Φ under Hν   =  m χ χ 2 11 Φ and  n 2) entries of both the neutrino Dirac  `,u,d 2 , L − Φ 2 + ˆ + ˆ Φ ) to all orders for charged leptons. V  ). Cross-talk is induced by all contribu- χ L 3 Φ ω Φ 11 ` (   † 2.8 U + (    . o 1 . operators will be absorbed in the leading order violating contributions. = 3) and (3 . + and by the amount of overlap of bulk profiles; h ≥ o ,

` . n 3 n L – 10 – 1 2 h . After breaking of D ) Z

V n 5 ≥ R R Λ m    ) / 1), (2 ∗ and Φ are IR peaked. Hence, a strong suppression is Hf , Hν n R . It is immediate to obtain the following textures for χ 13 0 χ 11 ) n n   G 2 H Φ Hν Φ L χ 22 0 0 ¯ in  m L f 2), (2 transforms effectively as ` , χ VEV 2 ( 3 χ 11 χ 13 L 0 Z χ   ` ( symmetric higher dimensional operators contributing to the neu- +     4 2 . + ) in the rest of this section, and postpone to sections A / o . ω l transforms as 1 + Φ. Given that only the (

† +1) 2    m U 1 preserving, +3 = n 2 D ` (6 5 L is UV peaked, while 1 0 0 0 1 0 0 0 1 Z V Λ operators to the (1 χ    is m -preserving sector, i.e. no cross-talk, leave unchanged the leading order result for = . The only higher order corrections allowed in the = χ 3 χ R 0 D ν Z symmetric, Φ D ν H L The leading order contribution comes from the operator in eq. ( Hf 3 ∆ D ν M Φ Z ˜ y L ¯ the above corrections to the neutrino Dirac mass matrix to all orders: where we separated theforbidden cross-talk by terms the from additional the rest. Notice that odd powers of Φ are recall that induced by the small overlaporder in contribution the to interference the of neutrino Dirac lagrangian can be written as follows tions of and right-handed Majorana mass matricestransforms will as be 1+Φ, zero the to contributions all ofcontributions, Φ orders. or effectively Analogously, since amount Φ tosize of the all operator higher order with contributionspowers one will of Φ be the insertion. suppressed relevant with scales In respect ( to general, the the leading order by We now identify all the trino sector in our model.into the These leading are order obtained terms by for additionaltions neutrinos insertions involving in of Φ. eq. the ( We fields VEV can of already anticipate a pattern in the corrections. Given that the mixing, so that the onlyWe way assume to allow for athe non analysis trivial of CKM the matrix suppressed is cross-talk to further3.1 break Cross-talk and cross-brane effects in the neutrino sector from the operators ofis the type contribute, it is clear thatall the orders corrections will to be massessymmetry and identical in mixings in the of structure charged the to fermion above sector the operators will leading to ensure order ones. This shows that the We first consider chargedin fermions, the to immediately showmass that and higher mixing matrices, order in contributions particular f 3 Higher order and cross-talk corrections JHEP08(2010)115 4 , can π/ . = 0 bulk (3.5) (3.3) (3.4)  = talk Φ 11 13 ) and can be H  − θ D 23 talk 3 5 22 θ 3 complex −  Λ cross / is vanishing,

and × 2 0 cross    χ ). Notice that 4 and χ

and ˆ (Φ 1 1 D  3 5 . This matrix is π/ ≥ † 2 11 Λ 0 ) ,n +   / 0 = ω 2 2 0 s, one can treat the ( ≥ 0  ∼ O  Φ 23 m U 1 2 . χ θ
  c 23 , ) M 0 ˜ Φ ii θ + + ( R 1 1 ν ,  ˜   ( Φ i brane R  2 and ∼ O we obtain the following texture  − ν , once rotated to the basis of i 1 ν 13 m factors in  L 0 ˜ +  m ), θ . If the bulk mass of χ 2 2 χ M , ω R n ˜  / D 2 3 5 no cross 12

Φ    Λ θ ) and / and    χHν 2 + 0 / D . , while for simplicity we have neglected ∗ ∗ 3 n 2 4 L + χ 9 5 o 2 ` δ δ δ . χ . ( h Λ o .

2 4 3 / M h δ δ δ 0

   2 χ ∗ 1 2 2 – 11 – ∗ 2 0 δ δ δ ≥ 0 13 0 11 0 ∼ O   Φ m , compared to the leading order Dirac mass term. .    ) χ , and similarly the coefficients ˆ c ˜ 0 22 χ 13 0 0 ) D ν M   M ), and assuming all real input parameters, will be to = ]; this is not surprising, since their model is the limit y χ 13 R ( ω  ν ν L ( 0 11 0 13 0 ( and deal with all of the other operators, we can have a 39 †   ˜ R M χ U ∼ O ν ),    i m D →  3 5 + χ . ν L ( Λ and o ), ˜ . l are real. We can conclude that for particular realizations of the / 

D M 2 0 2 4 3 5 H . The Majorana mass matrix is corrected by the operators χ ). Notice that in the above expression the coefficient /    δ ( Λ 2 is confined to the UV brane, while Φ and the Higgs are confined to 22 χ 2) χ / D are anyway complex due to the /  ˜ 9 5 0 2 0 − χ M i M n Λ χ δ and 1 / χ +6 ˜ 0 2 0 0 and ∼ O M δ M χ m D ( 2 0 χ (3 5 11 χ ˜ 0  M Λ (Φ M 22 , ∼ O =    χ 11 = 0, if  0 ij =  M ν ∼ O 13 L M θ ν We now recall that in general the effective Majorana Mass matrix is a 3 The most dominant cross-brane operator is If we neglect cross-brane interactions, induced by the overlap of Φ, can be absorbed into a redefinition of ii ∆ ˆ  M , 0 13 i ˆ set the exact profilegood of understanding of the deviations it induces to symmetric matrix and thusthe contains 3 12 mixing angles parameters. and 6 These phases, parameters out are of which the 3 3 can be masses, absorbed in the neutrino fields and remain protected from highercase order they brane-localized will corrections, be while corrected in by the naturally most suppressed general contributions. this operator is suppressedKeeping only the by perturbative expansiontextures associated linear with in each each operator of in the an additive various manner. Therefore, even before we identical to the oneof obtained our in model [ when the IR brane. Oneand can easily verify thatparameters, the it above matrix is is certainly diagonalized possible with that the leading order values where the entries diagonal contributions that redefine profiles, the correcteddiagonal light charged leptons neutrino with any mass order matrix, of the following form: where  Using again the transformationfor properties the of Majorana Φ mass matrix,  be absorbed intoabsorbed a in redefinition of ˜ where JHEP08(2010)115 . i ) ). ),  2 χ . χ   0 3.2 3.8 ( , the (3.9) (3.6) (3.7) (3.8) ) and H χ 4.4 O  D ν 3.4 ˜ y ) and we 4 + ∼ , 3.2 π/ , 22 ,    of eq. ( 3 = χ 11     i 0 iα θ is generated, and )  ) e χ ) χ in eq. (  χ 2  13  and θ ’s defined in eqs. ( 0 0 iα − ,  − 22 χ e , −  ) , iα 1 χ 11 0 iα ) δ e iα  0 0 0 2 iα e H χ 11 ωe e  ω sin | ( D ν ( ˜ y θ ˜    and 2 M | ω ∼ 2 ( ω    ). The resulting expressions for 2 χ 13 2 ) + ) √ sin 2  χ 13 √ 2 χ χ √  3.2  ˜  − M ) ) θ − χ ) χ  χ  2 2 +  iα Arg( iα √ √ e iα . After introducing the higher dimensional / 2 e (cos 2 − 2( χ ωe ω / (1 3 )) − 18 ∗ √ . χ 11 (1 + – 12 – 0 1 (1 +  (1 + | ] = ˜ ) 0    M 2 χ | 22 χ MNSP  6  V 1 V + parameters in eq. ( √ − ∗ 21 ˜ 2 Φ i 0 1 0 2 + V M =  √ ), it is clear that their contributions are of characteristic ∗ √ ν 12 L / 2( V V 1 3.4 / † ) and higher. In particular, ) 1 11 3 χ ω  = Arg( V breaking cross-talk effects should produce deviations of the CKM ( (    violation in neutrino oscillations. The MNSP matrix, to ) stands for contributions from δ 3 U 2 O    Im[ / D Z 5 3 in eq. ( = iδ ], CP Λ e i /  47 0 ). Consequently, the deviations from TBM induced by these effect are 3 , the left-diagonalization matrix is now corrected to: χ can be absorbed in a rotation of the neutrino fields, while the KM phase 1 0 0 0 1 0 0 0 ( − denote the entries of MNSP R i ) are complex. Thus, considering only the contributions of operators of the V    α ij deviate from their leading order bimaximal values. Defining (10 Hν ) and ˜ 3.2 V ∼ O = O 23 m ). However, considering the scales and wavefunction overlaps associated with ˆ θ ν 3.2 χ χ L  L V 3.4 ` To account for all possible deviations from tribimaximal mixing we should consider the and of eq. ( , given by 12 ij χ 3.2 Cross-talk and cross-braneAs suggested effects in in [ thematrix charged from fermion unity. sector Theour case details on of the the wavefunction overlap cross-talk of Φ depend and on the specific dynamics and in only contributions that need tothose be associated further with studied complex arethe those deviations encoded induced in bydeviations these are effects still turn almost an outThese order to contributions of will be magnitude anyway quite smaller be than cumbersome, taken those yet into described account the in in largest eq. the ( estimations of section fully perturbed effective neutrino mass matrixand to first ( order in all the in eq. ( strength negligible and actually below the model theoretical error. To complete our analysis, the Jarlskog invariant turns out to be where the where the middle columnθ does not receive corrections. A non zero will contribute to acquires a simple structure where have omitted terms of The phases δ  form the remaining are 2 Majorana and 1 KM phase. Notice also that, in general, the various JHEP08(2010)115 , u,d L V    (3.12) (3.10) (3.11) (3.13) (3.14) ) 3 , a sup- ω / ( breaking φ ) 3 q 3 3 U 4 / y / ) A 2 ) q 3 q 3 and schematically ω y ωy χ + R + q 3 + x 1. q 3 χ u q 3 x VEVs to obtain the . . Each operator in x ' +( Φ 4 i v L . A H 3 ,d 6= 1 00 q i R Q χ, χ, u y ) u y d Φ L Φ 3 ( 1 and ] V / 3 ˜ ˜ ) H † H , / 3 ( χ χ q 2 u ) / L 00 R 00 R a q 2 ) ) compared to the leading order. V u d    3 y q ωy 2 2 2 / D y L L 3 5 + ω u,d 3 u,d 3 = ( Φ) q 2 Q Q Λ + y x x L / +  q 2 , 0 q 2 x )] Q † χ +( x d χ, ( χ, ’s small enough compared to the mass L v u,d 2 q u,d i 2 u,d 2 V R Φ Φ y y x 0 q breaking to the quarks through these opera- ) V y 3 ˜ 'O H ω H ( to fit the observed CKM matrix, while still Z 3 (    δ 0 R 0 R / and [ ( 3 ( 0 0 0 u,d 1 U u,d 1 3 ˜ invariants; for example ) d – 13 – u t,b / [ y x q / 1 0 ) u,d L 4 L ) † L y ’s and q 1 m ] q R 1 q i    V A Q Q y + u u x 2 L ), we obtain the general corrections to the 4D quark q 1 c,s ωy = V 0 0 1 ω x ] ) m + χ, χ, + χ ω 2.19 u,d +( q 1 ( s q 1 Φ Φ v x u,d 3 M x 0 0 0 U ( 1 ( ˜ q [ communicates H H m ∆ ˜ y ]  Φ) ). The left-diagonalization matrices are promoted to χ R R    2 L d 47 ) and (    u textures associated with the above operators and conveniently = / D 3 5 L Q L 3 4 u,d Λ L Q Q √ A [( / 2.11 V 0 ) ) CKM ω ω V ( ( vχ i u, d q U U . Consequently, the CKM matrix will be given by y . Schematically, they are of the form = (˜ 2 ˜ yv = ≡ / D in what follows, since it transforms trivially under q 7 5 are nearly diagonal for q ∼ ∼ O H M i u,d ) represents two independent L , y V i +∆ q x 3.10 We focus on the The higher dimensional 5D operators relevant for quark mixing are generically sup- M eigenvalues There should beexplaining enough why freedom it in is nearly the identity. However, it is not obvious that an appealing with where where all entries arecorrected to, in general complex, and the leading order mass matrix is linearly Writing these terms according to theby decomposition the in VEVs the appendix, in andmass eqs. after matrices, ( as also in [ disregard eq. ( denotes the independent terms The VEV of the UV peaked tors, and they are suppressed byThey an are amount also suppressed bypression the that small amounts overlap to between a the multiplicative factor, bulk slightly profiles different of for the various operators. physical quark masses while maintaining the Yukawa couplings pressed by Λ cross-talk operators for quarks, we will set the values of Φ, JHEP08(2010)115 . is . u,d i 0 y GeV 18 4.4 for each and ˜ 10 . q,l L 2 × / c u,d i 3 P l 44 x are essentially . M 2 and comes from q,l L ' c q L 396 . c P l boson we can set the . However, all fermion M = 0 2 / 0 3 W P l H M . Also, the 4 , where 577 . A parameters are still constrained P l c M = 0 0 ' , we will first obtain the effective 4D D ] and by precision measurements. The 13 5 θ Λ , in terms of the 5D ones, ˜ 19 – ' u,d i to be all of order one, a well known pleasing 17 and y k range of the experimental values for the neutrino – 14 – 23 q,l,ν θ ), and the way they affect the neutrino mixing σ c and 34, such that the mass of the first KK excitation , 00 R singlet. For the same reasons, the scalar VEV Φ 12 , e ' 4 ). Therefore, if we take the 5D Yukawa couplings to u,d i θ ]; a large mass hierarchy is seeded by a tiny hierarchy 0 R x A e 9 ( – 2.13 . Using the known mass of the 7 R kπR P l M Hχe Φ ) and ( L ` 2.9 ]. The maximal deviations from TBM will be discussed in section in terms of the 5D weak gauge couplings to be 46 H parameters. c In this setting, fermion masses are determined by the overlap integrals in the By exploiting the warped geometry, we can match all the observed 4D fermion masses We take the fundamental 5D scale to be At this point, with all scales fixed in the quark sector, we will need to estimate the essentially also a free parameterzero and mode we set wave it functions toby associated be a Φ with few the importantmost various perturbativity stringent bounds constraint is [ the on bottom the sector, quark in left-handed particular bulk the parameter combined best fits for the ratio of the Z-boson decay VEV profiles of eqs.be ( universal and setmass spectrum. them to We remind one,left-handed the quark all reader and bulk that lepton there parameters doublet,free is being can parameters, only it since be a one we triplet matched can bulkof of always to parameter the set the corresponding the mass right observed of handed each fermion by tuning the bulk mass by taking the bulkfeature fermion of parameters the warpedof scenario the [ corresponding Yukawa terms, involving the fermion zero mode profiles and the scalar will always use valuesis around of a fewto TeV. acquire It a is natural VEVamplitude to of of expect order all of the scalars in our theory, being bulk fields, and neutrino oscillation data.various higher Once order these contributions, starting scales from are the set, quark we sector. is will the be reduced able Planck toexperiments, mass. quantify but To the keep satisfying the the scale constraints of from the IR the brane observed in S reach and of future T collider parameters, we 4 Numerical results for fermionWe first masses proceed and to mixings set all VEVs and mass scales, according to the observed mass spectrum size of theoperators analogous of cross-talk effects thematrix. back form in Clearly, we the wantthe charged to previous section, preserve lepton at the least sector, within appealingmixing the mediated neutrino angles 1 mixing [ by pattern described in with a minimal amountCKM of matrix, fine like tuning. thecouplings hierarchy To of account of the for above theSecondly, operators, we more search detailed for featuresto the of obtain minimal the a number realistic of CKM parameter matrix. assignments possible, in order solution can be found, that is an economical one, satisfying all perturbativity constraints JHEP08(2010)115 ) ] in ) in c (4.1) (4.2) 2.13 ( in the 56 f   , ) ) b   R 54 c ( ) 1 ( b L q L 2 g c 1 f ( ) of eq. ( i 2 y c ( f q L 1 has been recently (0) c with the tree-level f 1 1 + 2  LR 2 ,b 2 ) couplings | FB | 0 1+2 P . i q L q L b 3 ¯ 2 33 b 2 c ¯ A | c | ) ) 2 i ]. d 2 d , 3 33 Zb custodial is in place. The Zb b Y ) Y ) − ( 62 ( − d . d A | [ | , the bottom-quark left-right best fits, unless an extended ) Y Y 5 0 b LR , ( c (  | | 2(3 ,b 0 ( b b ¯ P d,s R FB ) 0 f = b R X i b − A c d,s Zb c 2 = X 2 + i kπR − 6= 1 corrections due to the presence of 3 2 constraints. + −  kπR b b ¯ ) 5  · c b ) L,R 2(3 2 q L c Zb L b Z q L c b ( Z c ω 2 2 − − kπR e ω ( f 2 3 ], we conveniently define the functions −  √ f 3 q L ) 54 – 15 – c kπR q L 1 + ) = 2 · c 1+ ( R 2 − − − b Z πR f ) ) 3 ω b q L custodial case and possibly close to the minimal RS = custodial, or extended c flavor symmetry might modify the non orthonormality c  1 ( 1 ( 2 show that the allowed window for new physics corrections 2 Z KK y b 2 4 2 ) ] take into account contributions induced by the complete summation ( custodial symmetry and extended c LR b f 2 LR f m A M 2 c P P 56 (0) 2 (  ,  2 − LR f b 54 f q L − c P 3 c 1 ], with the dominant 1 1 couplings in the minimal (non custodial) RS model can be found ]. Analogously to [ 2 2 Z KK 54 ]. We correct the contributions to the in our model, at tree level and in the ZMA, based on the recent   1+2 1 + 2 b ¯ m 56 M — is severely constrained by the 2 w     q L 3 2 56 s Zb c , b L − c 2 b 2 b 2 2 + KK KK 54 1 , and the forward-backward asymmetry, 1 2 m m  M M ]. These analyses b 2 2 − A 2 w 3 56 s −  + = = b L b R ], while the case of g g For the purpose of model building we provide here an approximate estimate of the 54 Notice that the analyses of [ more severe than in the 2 q L over KK states andand their turn non out orthonormality. to be These numerically corrections significant were in not the case considered of in previous bounds We obtain calculations in [ minimal RS model of [ custodial symmetry [ terms of the canonically normalizedevaluated fermion at zero the mode IR wave brane functions modes with KK states.allows Secondly, a for bulk further Higgs suppressions instead viafuture of overlap work a in the brane the analysis localized presence of Higgs of generally these mass two aspects insertions. in Weallowed the defer range context to of for symmetry, and it isc thus expected to bemodel. subject On to constraints thetwo on other respects. the hand, left-handed the The profile modelproperties additional also of differs bulk from fermions the and cases eventually analyzed suppress in contributions [ due to mixing of zero considered [ to the SMbulk prediction parameter — andcustodial consequently symmetry such the as model window considered for here is the an corresponding intermediate example, bottom which embeds non-extended custodial asymmetry, 4.1 The quarkA and thorough charged lepton comparison sector corrections of to the the combinedin best [ fits for width into bottom quarks and the total hadronic width JHEP08(2010)115 b b m m = 0 , with 41918 gauge . q L 5. The L . 0 b c Z towards R ω ]. b − c 42114 and = 0 . 56 0 s = c ) has a strong − ]. = 4.2 = exp 56 d 419, we obtain the and SU(2) , ) . c b L 0 L 54 g ]. SM − ) as a function of custodial has b L 56 . , b L g in the three different se- b L 54 58, and δg in the region of interest and g LR . . We disregarded the new 4 P ) set to 1 in magnitude and the . L,R − SM b Z = 0 ) ) ω 4.2 10 b R 8 TeV, and imposing a 99% prob- c 424 ( . . . Notice that eq. ( . b L 0 5. Notice that the latter is negative, g 1 b R ( − = 1 . Thus, lowering the value of anomaly. We have however verified that δg = 1, the − ∼ − , at the price of higher Yukawa couplings. d,s KK ) L q ,b c 2 w FB R 0 c R b = 150 GeV as in [ Z s ( M A 2 ω b L H / g satisfy 2 w ) we have disregarded corrections to the m = c – 16 – b R = 3 ) in the case of equal SU(2) g 4.2 q L ) 23, while the custodial case as in our model has − b Z . Q R ω ) is strongly dependent on the right-handed bottom 0 ( = 2 w b L s R ≈ 4.2 b Z δg − ω 2 w q s 3 L ] and the predicted SM values ( T ( 54 / 9 and ) . q 0 3 R ] at the reference Higgs mass of 150 GeV, to constrain the new 10 for T ∼ 62 ∼ + 3) q 090677 [ . However, it can be effectively suppressed in the particular case of / 2 w . 3 35, as it can be inferred from figure b L and only a mild dependence on . c 2 w T 0 /s b s flavor in our case, and weak isospin assignments of bulk fermions. The ( c 2 2 w custodial symmetry due to degeneracy of right-handed profiles [ 2 w 4 = 0 > c c 077345 [ − . A q L LR c = (1 P = 3 8 TeV, the down-type 5D Yukawa couplings in eq. ( exp / . An illustrative example. of the new physics contribution with the SM prediction computed at doublets; the exact form of the corrections depends on the symmetries of the ) q = 0 Z 2 w ) b R R ω c b Z R R g = 1 ( ω SM b For a Higgs mass of 150 GeV, a KK scale We used the combined best fit values for the couplings ( In the estimate provided by eq. ( L = ) g L b KK R b Z g constraint dependence on 0.5 will allow for significantly larger windowsThe for corrections to the SM predictionhave for been safely neglected. The perturbativity constraint on the 5D top Yukawa coupling and ( ( physics contributions definedphysics as corrections to the SM contributions in the lightability sector interval as for in the left-handed [ coupling given by model, also dependent contribution as inbulk eq. ( paramater extended and would go in the right directionits to numerical solve the impact is limited, as it is itsdependent positive contribution terms in due theSU(2) minimal to RS the setup. admixture of the KK partners in the zero modes of the where couplings. Ittups. is instructive The toand minimal compare RS the model valuesω has for right-handed bulk parameters setshaded horizontal to band the corresponds conservativefor to value the 99% probability interval allowed by the best fit values Figure 1 M JHEP08(2010)115 ] ˜ ' = 45 M 42. . 56 . e 770, 0 (4.3) (4.4) (4.5) 0 . top, is m & 5 MeV, R < . 635 and = 0 q L best fits. . 8 TeV) c q L . d b ¯ c c = 1 (1 t = 0 Zb 150GeV) [ u / changes signif- m µ c 790, m H . q L c m = 140 GeV. All 5D = 0 , , 803, ln ( . t . u   . For example, a mass 2 c 1 2 q L m # − ) c χ = 0 q − 10 1 e 2 M · − c ) , the partner of the SU(2) 1 q b − ˜ (1 92 1 . ˜ 52, − . M 42 in the most conservative case. . , (1 + 1 = 0 2 GeV and 0 32, within our estimate and using   . ˜ . 1 = 0 b R M 2 2 = 1, the bound on 0 .

g , 17, corresponding to . l L 2 2 χ = 2 q L c N ) ) 0 ) ) & c become accessible for a KK scale higher b D ν D ν ˜ ˜ − M M M L q L 1 is severely constrained by the ( ( . m c m m c + ( ( implies instead the upper bound 7. Another possibility is the one of a heavier = q L

MS top mass at the KK scale ˜ c 3 35 t M . ], with ), for which the eigenvalues are given by: c = = 2, – 17 – | ∼ 776 GeV. " , in order to constrain the possible choices of . t . 2 2 64 0 y | | [ should be produced in each version of the custodial | 2 sol × 2 3 2.21 − 2 = 1 m H N m m ) 150GeV) and ∆ & τ m D ν √ / t − | − | ]. = 550 MeV, m H 557 and c m 8. . π/ 2 2 ( . c 19 | | in eq. ( 4 m – 2 1 2 and ∆ − m ν L . m m = 0 17 , thus allowing for a larger range for ln ( = , | | ' M b t R 2 atm 3 b t 11 y g c ≡ | ≡ | − y [ | m | b ¯ diag. L 10 2 12 2 23 6 MeV and · Zb . and M m m 606, . b L 77 ∆ ∆ . = 50 MeV, g 52. Hence, one obtains 0 . 6= 150 GeV. However, a heavier Higgs mass in the custodial setup easily s 0 = 0 = 105 40, all the right-handed quark bulk parameters are chosen in order to yield 8 TeV. On the other hand, a KK scale as low as 1 TeV would force = 1 . m . H c µ < b L c ] and the constraint m g m q L = 0 = 1 c 63 q L c . Given , together with the matching to the 683, KK 5336, which reproduce the experimental value of the corresponding masses . . χ π M = 300 GeV would imply a lower bound M For the charged leptons we make the choice It should be added that lower values for For MS quark masses at the KK scale of 1.8 TeV. Their values are = 3 MeV, . This constraint ensures that the contribution through mixing from = 0 = 0 3 | d H 511 MeV, t . τ s y sufficiently suppressed in We now write the neutrino mass-squaredthe splittings, observed for values afterwards of we ∆ and would like to impose To obtain the neutrino masses we firstmass recall matrix the leading after order see-saw, structure of the light neutrino c 0 4.2 The neutrino sector the shifts ∆ induced by induces conflicts with electroweakactually precision allowed range measurements of values and for setup. a We careful defer estimate this point of to the future work on phenomenological applications. than and the top Yukawa coupling toHiggs. values A Higgs massbest larger fit than values 150 for GeVm would bring the model prediction closer to the the c m Yukawa couplings have been set tobreaks 1 universality in with magnitude, while the top Yukawa coupling slightly 140 GeV [ Notice that by requiring icantly to As expected, the allowed minimal value for | JHEP08(2010)115 2 2 ). + ) u,d i D ν y eV (4.8) (4.6) (4.7) M 5 m 3.13 , ( − ( u,d i † u,d 10 , we can ) ˜ x M/ R × is obtained ν M c 67 u,d . , L ]. Since at this 2 to match the + ∆ 7 V /    1 . Furthermore, we are constrained by 47 ) M i ' , ) q 3 q ,d 3 , the ratio ˜ ∼ i M 44 y q u ωy / – 2 sol from the quark mixing ˜ y χ + v + m χ q 3 3 . 41 M q 3 , x 2 M x √ ( / ( to absorb the relative factor 1 39 1 1 = − 3 , and the right diagonalization − and − 3 2. Given , we obtain the following cubic i u,d m i  † u,d , m ˜

y m > ) M 1 2 atm ) 1 | / q 3 q 2 M − m | ¯ ) y = 0 ) q 2 2 and 2 D ν y )  ω for 2 sol +∆ and extract q m 1 to a natural value = ∆ + u,d i + 1 x m R | x M q 2 − + 1 q 3 ν R ( x ν c 2 23 x x x ( (1 + c (¯ 1

u,d m 1  → − or ∆ ) − 2 − 3  ∆ 2 – 18 – x | m M m × − 2 atm − ) stands for the complex conjugate. In the above q m 2 2 sol y 3 )) 1 and +∆ ) (¯ q q 2 3 ] for the mass splittings, ∆ m D ν x y y 2, and − , in order to eventually match the three mixing angles M 2 sol 46 d ∆ 3 L m + ¯ + ¯ < ), to leading order in perturbation theory. The up and q ( , we find four possible solutions to the above equation, m V | q 2 q 3 q 2 † q x x 1 u | L (¯ (¯ , where the first two correspond to inverted hierarchy, while , and ¯ = eV 3.13 V 1 1 i } = ∆ 3 models with similar assignments [ − 2 − 3 2 ,d ˜ | for − . i M 4 1 u m m 2 12 , 10 A − − m m 2 atm from the same data. This is a nice feature of the light neutrino mass 79 × . ∆    m χ = | 0 , ∆ , 39 . Terms of this kind will be included in the complete expressions derived i = M . / ˜ q 99 2 m L M . u,d i 2 sol / 1 V y , : χ ' and q m , − is analogously obtained by the unitary diagonalization of ( , M ˜ u, d u,d i M 02 u,d x R 2 atm . = = ∆ . The entries of the CKM matrix are then derived in terms of the = 2 V 3 compared to the unperturbed mass eigenvalues m q x q u,d √ ) It is now straightforward to extract the estimations for the upper off-diagonal elements / ' {− M have omitted contributions thatlinear are in suppressed by quadraticbelow, for quark each mass of ratios the and interesting CKM still matrix elements. of the CKM matrix out of with matrices, for simplicity, weof have 1 redefined the ∆ parameters defined indown eq. left-diagonalization ( matrices turn out to be: 4.3 Obtaining the CKMWe now matrix analyze and the CKM fixing matrixUsing the resulting standard scale from the perturbative contributions techniques, introducedby in the the eq. unitary left ( diagonalization diagonalization of ( matrix matrix stage only the overall lightthe neutrino observed mass ratios, splittings, ( wedata. choose not It to will set neutrino mass be spectrum. possible afterwards to set and ∆ q the second two correspondconstrain to normalmatrix hierarchy. obtained in In all addition, once we set Imposing the measured values [ equation for where can be extracted either in terms of ∆ where JHEP08(2010)115 , , . ) y i π 1 y . = (4.9) 4.11 . Let ) and ˜ (4.13) (4.10) (4.11) (4.15) (4.14) (4.12) in the u 2 k and δ x )–( u,d i i , , y u,d x or ) (˜ ) . , . 4.9 d 3 d 2 j M ) y u,d i d 3 ωy 155 ˜ ) are given by x = y . + ts = 0) 0 i + ! d 2 + V ) ) and taking into u 3 x d 3 ) ' d 3 δ ( , x ( s x ( χ ) 4.9 πR ( 2 d b 2 s b m C (and 2 s ) and |− ⇐ u,d m m m i ] y m | ˜ 2 y m ⇒ k u,d i cb ) − − n ) + c ) entries of ∆ V d 1 4( 004 ) to be universal and equal ) + − 2 s 2 b ω i . ) + ¯ e u,d k y d 2 2 b d − 0 1 2 ¯ m m y + u,d i ¯ y m − 2257 ω q L m y ω ( . , these elements turn out to be ' ω c (˜ i , 0 u,d i + (1 2 ; using eq. ( χ + ) + ) x − u,d i d 1 , y ' d 2 C us i d 1 x x ) and (3 )(˜ x πR V u,d j χ i  x i (¯ x (¯ χ ) (¯ d (12 s |− C f 2 b m d y / χ | m  m [( k m ) C /m 2 s 8( 2 + + 2 s = 4 ) e + ) ) ) max i m ) χ /m u 2 u 3 u,d i ( u f 2 d 3 y ± u,d i y . The numerical results are reported in table O , m ωy m 2 + , c ( – 19 – 3 (( / + + q L u 2 3 + P l O c u 3 t to be 1 in magnitude, with a relative phase, χ x ( u 3 ( x ⇒ f u 2 + x c ( ) F /M t ( y ) 2 c u c 3 0 χ t 2 t 2 t m 2 ˜ y f m χ ) m u,d ) i m m m ω πR correspond to the (1 dy . To leading order in u y 2 2 and ˜ u,d k = − ) + y n − − + ) + u . The dominant contributions to 1 u 2 2 u ) + ω 2 c m u,d χ 2 u u i 1 ¯ u 3 y χ + ˜ x πR ( u 2 ¯ πR y 13 y CKM 2 C m x , ˜ m ¯ m y C + − u 2 δ (˜ ω d ω 2 − Z x ω y (˜ 2 − + 0 u,d i + , ˜ ) and + b d 2 χ x χ u 1 − 2 u 1 ( 0 2 u x f / D x u,d j x s χ ) 7 5 x (¯ (¯ Φ u,d i f d 3 (¯ u,d i u m 0 u Λ x ) c ˜ y ( d 2 m m H m ω m y ) we obtain: 408 it is possible to satisfy the constraints in both sectors, namely to have a

. + ' ' + ˜ according to the experimental value of ' 2, and where d 3 d 2 , ∗ ∗ ∗ χ 4.13 ts ub cd x 1 x ) = = 0 (˜ , while at the same time having a realistic neutrino mass spectrum with a normal C with the neutrino mass splittings and the bare Majorana mass scale. It turns out (˜ V V V ,   R χ us u,d i ν V y c C ' ' = 0 ( ' − ' − ' − together with a minimal number of relative phases between the remaining ˜ cb n us u,d i td χ us We recall that cb V V x V V V C realistic or inverted hierarchy. Atwith this small level deviations, the as we neutrino sawonce mixing in the section matrix scales is are obviously fixed tribimaximal by of parameters, are enough toelements. account Yet, we for first want thevalue to of magnitudes check the of consistency of thethat the remaining for scale associated observed with CKM the above account eq. ( in which we have fixed ˜ between the contributions from the up and down sectors. We want to see if the above value with us first set To narrow down the parameter space,to we one choose in all magnitude, the while relative ˜ due phases between to these the parameters mass will be hierarchyproportional allowed. of to the Hence, quarks, just which one keeps quarkeach the of mass denominators the to in CKM a eqs. good matrix ( elements approximation, are the of resulting the corrections generic to form, the integral for each of the above parameters. For the 4D couplings we thus obtain where it is important to observeThe that diagonal the elements of first the equality CKM is matrix exact remain to unchanged leading at order this in orderinteraction and equal basis, to respectively. one. This tells us which fermionic wave function overlaps enter and the CP violating phase JHEP08(2010)115 ) ), ub V 4.16 4.16 (4.16) ’s and u,d 3 ) with the x . 4.6 ) and ( 05 compared to . 4.15 = 0) 0 , but still outside eV. u 3 0415. The leading to eq. ( 3 . δ ≈ ( − . The minimal viable ), but failed to match χ ˜ 3 CKM M ub cd λ C = 0 ⇐ / = 1. Solving eqs. ( i V V χ χ | u 3 f y M cb 007 . V and = ˜ 0 ≡ χ (and 155 155 155 155 d 3 C cb q . . . . ' x us parameters. 0 0 0 0 V | ' | V χ ts C P l u,d 3 V | y  077 077 . . ) 202 135 , ˜ . . 2 b 0 0 0 0 ˜ − − u,d 3 , is to break the universality assumption M/M | /m x 2 d ts 1 3 4 3 . . . V , to match | m 50 m u 2 ( 17 17 49 δ , while setting ˜ O – 20 – 8 8 5 d 3 2 4 . . . . y and parameter space, we still require small deviations, + 9 m 51 51 10 | t χ and find their values that match the experimental td 7 3 f u,d 1 3 . We are going to elaborate on this possibility once we 8 3 . . and ˜ ) . . V y . The masses are given in units of 10 | u 3 5 4 m u,d 3 u 3 , ˜ 52 50 u,d i y us y x y V , ˜ u,d 3 + ˜ (1) universality assumption. It is obvious that assignments 99 02 , turn out correctly to be of order . . x 79 19 u 3 q . . O 1 2 td u,d 3 and x 0 1 V x (˜ − − u,d i − , without any relative phase assignments, and with the ˜ x b χ ub f V ) d 3 y + ˜ 155 arising from , and thus . d 3 ub x ). In general, one may still expect them to modify the relatively small values , especially in the presence of strong cancellations at leading order, and given ) to their central experimental values (˜ | 2 = 0 V ) cb  ts χ V V C | u,d i ' ], will not be arbitrarily modified. Therefore, while trying to find the minimum 408 has been chosen to match the four solutions for . Approximate numerical values of the neutrino masses and relevant UV scales, where , and the related values of . , y 15 ub and cb V u,d i V In addition the only choice of parameter assignments that maintains all coefficients of The only way to obtain a realistic prediction for the independent magnitudes of The next to leading order corrections to the various CKM elements enter at (and = 0 ub ’s set to 1, is x V (1) is to break universality for ˜ (( R cb u,d 3 ν ˜ and will hence fail againchoice to consists account for of realistic atuniversality values of assumption least for 2 two parameter out of assignments. the four Namely, ˜ weO will have to break the contributions to varioussetup flavor [ violating processes,number which of assignments are in present thein ˜ general in complex, any from the RS-flavor in terms of one parameter will yield results proportional to those of eq. ( made an attempt to obtain an almost realistic CKMand matrix, using the firstfor order results. the Yukawa couplings,data. ˜ However, we areassumption interested in which the smallest assumes possible all deviations from of the universality the Yukawa couplings to be of order one, so that O of that each independent contribution isthe effectively corrections linear suppressed in by We see that the experimental error. Up till now, we introducedV only one phase, order contribution to y Table 1 c constraint JHEP08(2010)115 , ), 3. ub 05 , . V one 2 0 ) are 0 , CKM 0087. 4.16 (4.17) (4.18) . λ T ≈ χ = 1 3 CKM and from = 0 must rely i C λ | i ( χ 0 . The first is f td u,d ) and ( i O T V y induced phase 0407. We also td | 2, which is well . . V 4 1 , with 4.15 A and holds exactly, and = 0 and ˜ ' u,d i | | and 4 y ts 13 A cb u,d i δ V ub V | x | V and ˜ i . = | u,d i 23 , . ts x 0 V | , offering an elegant and simple − 0039 . 60 CKM . λ 0 = 0 | ' ub d 3 ˜ y V | ]. Interestingly, we are able to match also the 63 pattern with other flavor symmetry groups, in – 21 – i, 4 19 are generically suppressed by a factor A . 0415 , hence a cancellation pattern must again be in place. 0 . 3 u,d i − − y = 0 Obviously, at this order | 67 . 4 cb 0 and ˜ V | ' close to the central experimental value u,d i u 3 | we obtain: x ˜ x ts d 3 V , using the same assignment. We find it to be y of order one and two non zero relative phases; however at this order, | i 13 ]. The Wolfenstein parametrization would suggest the existence of an , and thus fail to match the central experimental value δ y | and ˜ and contributions beyond the ZMA, must be responsible for the deviation 53 , with all parameters of order one stems from the presence of built-in ub – 2 u 3 V ) and ˜ | x 48 can easily arise from the subleading corrections in ˜ [ i , the latter of order 10 3 CKM u,d i 0 = x 2 ˜ y λ td | − T , V ) for ˜ td are degenerate. i u,d V | and x to be the unit matrix, a rather good first step in the description of quark mixing. td 4.15 V It is instructive to compare this We notice that the possibility of producing hierarchical CKM entries, of order We have thus shown that at leading order in the VEV expansion the model predicts At a higher level of accuracy one should obviously satisfy the full set of constraints implied by the 4 also produces a pattern in the corrections. In this framework, subleading corrections of 2 CKM CKM description of quarkbased mixing in on the otherwiseon standard appealing more model. discrete complicated flavor patterns On to symmetries the produce such other a as hand, realisticmeasured CKM flavor Jarlskog invariant. matrix. models In the case of from one of the CKMof diagonal order entries 10 and the non degeneracy of particular expansion parameter to be naturally identified with and λ cancellations induced by theω hierarchical masses. Theorder presence (˜ of the unity, parametrized in terms ofWe have twelve shown complex that, parameters linearly ˜ be in obtained these within parameters, the realisticwith model values all of theoretical the the error ˜ CKM inno entries a can corrections finite to portion of the the diagonal parameter unit space, entries is produced and the two smallest entries corrections quadratic in ˜ with respect to the linear contributions. V At the next to leading order, cross-brane and cross-talk operators induce deviations from obtain Notice, however, that corrections ofbelow the size the of model the smallest theoreticalvalue CKM error for entries, i.e. induced byhigher the dimensional zero operators mode beyond approximation. the zero A mode realistic approximation. We remind that the which are the central experimental valuesCP violating [ phase within the experimental error. this gives a value for These parameters are almost degenerate,of in particular the if zero one mode considerswe the approximation, obtain overall and accuracy substituting these values in eqs. ( and ( JHEP08(2010)115 , ) σ ub R are V 4.16 4 are ) and R (4.20) (4.19) Hχν ) to be π/ ) of the L ¯ ` ω CKM 3.7 ( Hχν = λ L ) and ( U ( ` 23 O θ 4.14 case, at the price 4 ) and are of approximate A 00 R . Taking its phase to , e 23 χ 11 . = 0 and θ 0 R  ) and with characteristic , defined in eq. ( 0 e ( , we are only interested in 13 δ ' R χ 07 θ . 3.13 0 12 , we get that the contribution and ∆ θ e i ' Hχe y χ Φ 12  θ L ` and ˜ ⇒ e i R 04 ∆ we also obtain . ν x c 0 χ  − ' 4 e L 23 c – 22 – θ − 8 from their experimental values. The other class of χ ). Given σ C ) have the same structure as the operators in charge 0 00 R 3.6 05 ∆ H . 028, which is of the same order of the model theoretical , e ν . 0 ˜ 0 R y 0 e 04, comparable to the model theoretical error. Higher order parameters, and therefore we expect the maximal deviations . ' ( ' 0 ' R χ ij in the worst scenario where its coefficient is purely imaginary. 13  ) χ 13 ) we can now estimate the deviations from TBM arising from the θ `  R ). This provides | ' ∆ , c Hχe 3.8 23 e L 3.2 Φ θ c ( Hχν L ∆ ` χ L ) ` f 2 ) χ / D 7 5 D C | ' | 2 5 Λ 12 Λ / ' θ / ` was introduced in eq. ( ∆ is vanishing, while the contributions to ∆  | ) entries, and a hierarchy of specific VEVs to induce the splitting between χ 11. Using eq. ( . Similar hierarchies can in principle also be postulated in the .  13 0 2 we get the largest possible contribution to the phase td θ V CKM 2 as defined in eq. ( coefficients based on the results of the previous section. As we are interested only in π/ λ ( ' − χ ij χ 13 cross-talk operators arecan not conclude considered, that as thecross-brane their most operators contribution on significant lies the deviations safelythese three from below quantities. mixing TBM 1%. angles induced Thisparameters stay by can We of within cross-talk the be the model and experimental obtained and errors without maintaining for all making of any them further naturally of assumption order on one. the error. We couldthe have proceeded quarks, to yet explicitlydeduce since write the the effect all of of structure theseand these small is using corrections terms. practically as no For example, identical we additionalto in did in analogy phase ∆ for with both assignments eqs. for cases ( strength ˜ we can easily of quark mixing.as it The is perturbative donerotation diagonalization in matrix procedure the for quark caninduce sector, the thus perturbations in left to be order the handed carried tostrength mass charged determine out matrix leptons. the in deviations the form from Generically, of these eq. ( operators will These turn out to be All of these deviationsoperators are (1 within 1 where be δ operator (1 from TBM when they are purely imaginary.the All dominant said, contributions, we associated estimate with the one magnitude insertion of of the by cross-talk operatorssuppressed of and the keep characteristic therange forms predictions of for thealready the experimental explored neutrino error. in mixing sectioninduced parameters We only III. within for first Recall the complex consider that 2 the deviations from cross-brane operator O and of an increased fine tuning of the4.4 input parameters. Estimation of cross-talkTo and complete cross-brane contributions our in the analysis lepton sector we want to ensure that the deviations from TBM induced needs to postulate a hierarchy of Yukawa couplings to distinguish between JHEP08(2010)115 ) , χ (5.2) (5.3) (5.4) (5.1) (Φ ]. V 65 00 are switched 1 ) χ χχ ( ) can be omitted 0 1 , χ ) 00 Φ 1 1 ) χχ ( H, χ 2 ( χχ ) is a global minimum of ( λ V 0 (ΦΦ) . 1 0 1 + ) a 3 1 ) 2.19 ). The self interaction terms 1 , 3 up to quartic order is displayed ) ) ]. It is then easy to check that χχ (ΦΦ) ( χχ χ 5.4 , χ ( χ 00 χχ 59 (ΦΦ) a ( Φ 1 1 (ΦΦ) Φ 2 3 (Φ 1 λ a λ ) 3 V + ], which is the limit of our model when + ] to explain the fermion mass hierarchy. χχ (ΦΦ) and gives rise to contributions that can χ ( (ΦΦ) 1 39 ∗ ] a ) + χ 1 66 χ χ 4 (ΦΦ) 3 χ λ Φ 4 Φ 2 47 ( A Φ 4 are completely sequestered. In our model, the λ λ iλ + V (ΦΦ) are essential in order to obtain realistic results χ + – 23 – . 1 1 + (ΦΦ) + a ) χ 00 χ s 3 3 1 Φ (Φ), and that eq. ( a 3 ) . ) (Φ) + V iδ 3 (ΦΦ) ) are approximately preserved also in the presence of χχχ ) χχ ( V χχ Φ 1 ( + ( (ΦΦ) χ λ 0 s (ΦΦ) s δ χχ = χ s 1 3 2.19 ( 3 , as Φ and s + 3 + 3 V 3 ) 1 1 ] and many others, was to prohibit the problematic ) (ΦΦ) (ΦΦ) (ΦΦ) χχ (ΦΦ) χ χ ( is a singlet under 65 Φ 5 (ΦΦ) ) and ( χχ Φ 2 Φ 3 Φ 3 χ 3 (ΦΦ) ( χ λ λ λ iλ λ 2 Φ 2 χ Φ H s tout court δ + + µ + + µ + 2.11 -invariant scalar potential in Φ and G ) = ) = χ ( , χ (Φ) = ). The problem is that the extremal conditions yield a larger number of V V in eqs. ( (Φ , χ i V χ (Φ ) is a global minimum of h V 2.11 and To solve this problem extremely hierarchical fine tuning has to be imposed on the The complete ). This situation drastically changes once interactions between Φ and χ i and Φ are strictly localized on the UV and IR brane respectively, the vacuum alignment ( Φ various parameters offine the tuning, scalar adopted byinteraction potential. [ terms by The construction.use most of These the direct models Froggatt-NielsenExplaining are approach (FN) the usually mechanism observed to features [ supersymmetric of avoid and fermion this mixings make within these setups usually requires a are assumed to beeq. confined ( on theV two branes ason in via [ independent equations than there are unknown VEVs, as was demonstrated in [ Notice that thein additional this interactions context, withbe since the Higgs absorbed field in the corresponding coefficients of eq. ( below, and we conveniently separate its terms as follows with the single contributions also derived in [ χ problem is eliminated cross-brane interactions between Φin and the quark sector. Thebe question sufficiently is suppressed, whether while their still modifications protecting to the the results scalar in potential the can lepton and quark sectors. We are still left withh one important challenge: tohigher ensure order that corrections. the alignments Thesethe of VEV above the patterns results. VEVs were thesolutions. In key It this ingredient is in section, obvious obtaining we that all briefly in of the discuss scenario the of challenge [ and suggest possible 5 Vacuum alignment JHEP08(2010)115 , χ χ χ 2 C 2 and and (5.5) Φ η χ u,d i Φ δ x , we assign . 8 6 singlet α πi/ 4 2 e A ⇒ ) . It turns out that = 00 R R α ν c , e ) while preserving the 0 R 05 compared to the self . ). This factor can easily , e terms. Most importantly, 5.4 0 ). However, we have an R , with R 2.9 e 00 R 4 ' ( α 3 , d / 0 R Hχν χ is in charge of the bare Majorana L , d C , ` , its VEV profile will become more η to be R 2 χ is set according to the experimental ' α η , d χ χ and ). 00 R a C ⇒ 00 R R , u and ) ν , d 0 R R symmetry we imposed. We know that this Φ 0 R u H ( , ν 2 , H , d R L Z χ L ` R – 24 – ` ( . The singlet χu 8 , d 2 Z 00 R Φ L , u , Q 0 R 4 and accordingly, the matching of α χ , u ). After the scale R C 00 R ⇒ u charges of Φ, ( ) , d ) interaction terms are obviously further suppressed and lie 8 00 R smaller than the theoretical error we only need to suppress 0 R Z interaction term is also prohibited in this setting. The operators , χ χH χ , d , d µ L symmetry into 0 R χ R (Φ C 2 Q 2 ). In the first suggested setup, we use an additional , d χ V , d Z R in front of the original expression in eq. ( C . If we switch on the bulk mass of , χ 00 R 2 , d χ 3) , u (Φ µ / 00 R 0 R − V e , u , u 0 R = (1 R = u , u χ ( χ a L µ H ), while they forbid the unwanted Q C ( Φ parameters by at most a factor two, without breaking the universality assumption. 2.8 L The latter will obviously dominate over the contributions of operators involving Φ Q , in order to eliminate problematic terms from the superpotential. The drawback is , giving rise to the operators 8 n u,d i interactions. This is clearly so,the given leading that the order above operators operators incross-brane are terms, the of they the Yukawa will lagrangian same still of dimension beof as the suppressed compared quark to sector. the IR However, dominated being contributions eq. ( the dangerous cubic Φ in charge of quarkZ mixing are now supplemented withextra an source extra of insertion quarkoperators of mixing of Φ allowed the to by form preserve the above assignments, arising from cross-brane the rest of the fields according to The above assignments allow the presence of all the operators in the Yukawa lagrangian of We offer two alternativeforbidding setups, cubic in which mixedinteractions the interaction in desired terms, vacuum alignmentmodify and is the allowing protected external by onlymass for term. Assigning quartic the (and higher) y Quartic and higher safely below the model theoretical error, originated by5.1 the zero mode approximation. Alternative solutions by model modifications suppress the induced shift offactor the enters scalar VEV all belowmodify the the the model calculations numerical theoretical value performed error. of to The so make same far, howeverby a its factor effect of 1/2, only which amounts can be to compensated by a global rescaling of the various results in the quark andwhich lepton is sectors. not The most eliminatedterm problematic by cross-brane is the term typically is additional suppressedinteraction by term an Φ overlap factor sharply localized on thefactor UV brane, an effect that we can parametrize by a multiplicative Z that one usuallymake ends ad hoc up assumptions with toassumptions, account a we for large experimental can data. parameterin try In order space to this to without case, exploit reduce using avoiding the no the the further suppressed impact need of overlap to the of interaction the terms flavons in bulk eq. profiles ( significantly larger flavon content, and additional higher permutation symmetries, typically JHEP08(2010)115 3 ]. φ π Z χH 69 and = , for (5.6) – ) are c to be 2 R ) ν ud χ, 08 acts , where φ R 67 2.8 2 . δ , ν singlet 0 ( u,d χ,i ). Each of φχ 4 a R 47 ' L , and ν A α , ` 3 η 44 3.12 χ , both of which – ⇒ 577 . ) and 41 u,d R 0 [ 00 R q / 045, which in turn R 2 . 4 , e ν 0 χ to the CKM elements. A 2 0 R 045 Φ . Φ ' L , e 0 , with the newly defined φ R χH Q L χ e ` ' u,d i ( C z Φ and . Consequently, we can match /C and ˜ , χ u,d R 3.2 3 C , the above operators involving α χq χ u,d i 2 y ' Φ ⇒ ) compared to the ones associated with , ˜ 2 L ) . Differences will stem from redefinitions − u,d i Q , φ mod. x 4 being swallowed into Φ, and the Dirac mass  L (10 ` ( O H . This results in . The dominant higher order corrections in the – 25 – us R V , φν 2 L ` α , we choose the other fields to transform according to , it turns out that we still need a relative phase . This means that, in total, we have 4 non degenerate preserving VEV of 4 ⇒ 2 α ) Z 4.3 CKM 13 R δ ν ( discrete symmetry in this slightly simplified setup. Given that 8 are suppressed by extra discrete symmetry, where the two complex parameters turn Z , to account for χ 2 , 2 2 Z 4 d χ, α a ⇒ ) and and consequent rescaling of fermion bulk masses. The resulting mixing data L , we are able to tell if this perturbative expansion is justified. Due to the | transform again as χ 2 Q us ( C u χ, η V a , for which the resulting textures were also inspected in the same section. | c R ν and R parameters entering at the second row of the up and down mass matrices in the , and Turning back to the quark sector we see that the most dominant cross-talk interac- We again assign a The second solution we suggest is based on the simplifying assumption that the field 0 . It turns out that we need two independent and non degenerate complex parameter χ ην 2 specifies the generation. When matching the observed magnitudes of the CKM elements u,d χ,i u,d i ˜ give similar contributions tothe those CKM described matrix in as section of we Φ already did inin section the quark sectorz will be now governed by ˜ Dirac neutrino mass matrixwhich arise the from associated operators contributionshigher of order were the corrections already form to inspected theΦ heavy in Majorana section mass matrix III. will The consist dominant of tions, leading to quark mixing, are of the form and importantly the scalarwhich sector is in is charge nowUV of supplemented and the with IR neutrino an localized, Diracstill additional allowed mass respectively. by term. the All above Weterm terms assignment naturally for with in expect the the neutrinos Yukawa of lagrangian the of form eq. ( the 4D effective theory with the SM Higgs. Φ, out to be degenerate to a good approximation. Φ can also play theIt role is not of clear, the at Higgssetup this as we stage, in use, to many however which it previous extent this seems works assumption possible on can to be identify justified the in lightest the mode warped associated with Φ in a assignments for the above coefficients,at in leading order order to as obtainreal in an parameters section almost governing the realisticthan CKM mixing the matrix data one in with the a quark sector, a less appealing situation i and the CP violating phase, between validates the perturbative expansion,as where the small expansionoperators involving parameter. Φ The contributions to quark mixing arising from the preserving VEV of Φwill and generate the the same kindHowever, of contributions the as corrections those involving induced Φ up by and these down operators massthese will matrices contributions enter in will in the be the interaction characterized basis, by second one differently row coefficient from of which eq. the we ( define as value of JHEP08(2010)115 . In ]. 1 19 × – Q f 17 ) = 3 ], the direct CP ,Q ]. More recently, 2 19 flavor symmetry is ,Q 70 – 1 4 Q 17 A [ f ( K  diag discrete bulk flavor symmetry. 4 , i.e. A Q f ] apply to the general case of flavor an- 20 – 17 can be performed, yet the parameter space 4 – 26 – are irrelevant to the vacuum alignment problem, φ ] that FCNC processes can in general produce more 4 TeV. A generalization of that analysis to a wider set 28 invariant interaction terms in the scalar potential with ∼ – and 8 Z ] and the neutron electric dipole moment (EDM) [ η 26 , × 20 ] that custodial symmetry in the bulk of RS warped models is [ 20 4 – 11 K A 17 10 TeV to / × 0  ∼ cust SM G The predictions and constraints derived in [ These bounds can slightly be improved if the Higgs field is allowed to propagate in the It has been shown [ We should also add that in both solutions offered above to protect the desired vacuum imply an increased alignmentgauge between couplings, the thus suppressing 4D the amount fermionwith of mass flavor KK violation matrix induced states. by and the Inthe the interactions our degeneracy Yukawa of case, and the the left-handed most fermionaddition, bulk relevant the profiles distribution consequence of of phases, the CKM and Majorana-like, in the mixing matrices might straints. As we already observed,heaviest this fermion is zero particularly mode relevant and for the thecustodial most top symmetry IR quark, with localized. being a it For bulk these the reasons, Higgs, our in model addition realizes to an archical 5D Yukawa couplings. The conclusionscouplings may is differ assumed if to hold a in flavor the pattern 5D of theory the due Yukawa to bulk flavor symmetries. They typically violation parameter bulk. In this case allserving zero the mode same 4D fermions mass can and be havinga a pushed consequence reduced further the overlap towards 5D with the Yukawa the couplings UV IR can localized brane, be KK pre- raised modes. without As violating perturbativity con- measurements from of scenarios and includingit higher has order been corrections observedstringent can bounds [ be than the found observedCP in S, problem [ T remains parameters in on the the KK form scale, of and excessive that contributions a to residual scale of order a fewthe TeV. exchange of In the other KK words, excitationswill once are force taken new a into physics lower account, bound (NP) the on agreement contributions the with induced KK observations by scale, and we demandable it to be naturally reduce of order the a lower few TeV. bound on the first KK mass imposed by electroweak precision 6 Flavor violation andAll the models Kaluza-Klein with scale extra dimensionsgrees of will freedom have of to the effective face 4Din the theory the and presence their construction of KK mixing excitations. of betweenmixing these One the of do models, the de- not crucial is tasks spoil thus the to agreement guarantee with that observations corrections for induced a by natural this value of the lowest KK insertions of thesince new they fields aremore both complicated flavor flavor symmetriesarbitrariness singlets. of are the obviously model. Further possible constructions at with the price additional of fields an and increased assignments analogous to theis one in still section larger.identification As of already the said 5D another flavon possible Φ with drawback the of bulk thisalignment, Higgs. proposal the may lie in the interaction basis. A matching of an almost realistic CKM matrix by 4 real parameter JHEP08(2010)115 , ) γ R ) s d ( (6.1) (6.2) ( R s d quarks. ) → d k 11 ( L b i u d L γ V ) ± , 3 H ,Q ) l 2 coming from a KK ( L = 0 u ,Q ) K 1 n 2 12  ( R 2 ) Q u d f L ) V L † b ( d , center diagram in figure 1. L L diag( V d µν † £ is released, leaving ) d . L G V Im( K ( )  will vanish. We leave this analysis 4 = 0

F − Q ) K j R f d,s,b R 11 d s i / ( m 0 = d R µν R  d σ V 2 12 ) i L i ) 3 ¯ d d k diag( L ( L ,d d d 2 R V = ) ,d V 3 ) 1 ) – 27 – γ 2 g d 3 ( ,Q

f H ,d 2 ij γ, 2 ) ,Q O ,d l 2 1 ( L 1 2 d − . d Q diag( ) f f † n K ( R will disappear from all down-type contributions to the d R d / 0 V d )  L h L diag( V b diag( ( † † from a KK gluon exchange (left). Dipole contributions to the neutron d d L Im R L and d d ], we observe the following facts, consequence of the degenerate

V ¢ K V  γ h h m ) 19 flavor symmetry can only improve upon the residual CP violation 2 d ], this contribution vanishes as follows Q – ( Im f Im 4 s 19 17 A – ∝ ∝ = → 17 b ¯ d NP K  type − n s d d C ) n ( . Contribution to Im G , the neutron EDM and Higgs mediated FCNCs as possible candidates to produce the ¯ s d K /

0 ¡ and the studypresence of of Higgs a mediated bulk problem FCNCs that for in general future affectsconstraint work. warped induced models by with We tree flavor conclude level anarchy. KK We here have gluon that seen exchange that the to the Contributions from up-type KKleft- fermion and exchange, right-handed rightmost matrices diagram and aresize in thus figure as expected 2, in to be involve anyinteresting non flavor zero, cancellation anarchic generally of of model. observable the phases,to same However, the so a neutron that electric bulk dominant dipole flavor new moment symmetry physics and, contributions might or, induce to an Again following [ in the basis where theitself fermion profiles vanishes are and real and notleft-handed diagonal. only rotation We notice its matrix that thedipole imaginary amplitude effective part. operators of the Second,A form and pleasing for resultneutron the is electric same the dipole reason, vanishing moment, the of induced the by down-type the same new diagram physics with contributions external to the left-handed fermion profiles. First,gluon the exchange, new the physics leftmost contribution diagram to in figure 2 vanishes, since induce zeros in theviolating imaginary quantities. components We of canstate straightforwardly the some identify Wilson results, a while coefficients few we contributingspurion properties defer to analysis to of a in our CP separate [ model work a and more complete study. Following the Figure 2 EDM from KK down-quarks (center)also and contribute KK to up-quarks (right). The same type of dipole diagrams JHEP08(2010)115 ]. nothing 47 , → . 44 4 – 13 A θ 41 flavor model for 4 A in the charged fermion in the neutrino sector. 3 2 Z Z → → 4 4 A A 3. It turns out that, with all these , 2 , = 1 i – 28 – , with u,d i ˜ y , u,d i flavor symmetry is induced by the VEVs of two bulk flavon x 4 A is expected in our model due to the vanishing of down-type dipole , would obviously be a welcomed feature of the model; it would K K ]. In this construction all standard model fields, including the Higgs / / 0 0   47 is responsible of the breaking pattern and on one side, charged fermions with the IR-peaked Φ on the other. If the : Φ is responsible of the breaking pattern χ χ χ K  ] on the UV and IR brane by orbifold boundary conditions. The spontaneous 11 The cross-talk/brane induced quark mixing, to leading order in the perturbative Using this realization we have obtained an almost realistic CKM matrix, including its Alternatively, a cancellation of observable phases, and a consequent vanishing of the from the experimental values, with small non zero contributions also to with charged fermions are switched off, tribimaximal mixing for neutrinos is exactly σ 1 diagonalization of thein mass the matrices, up is andparameters expressed down of sectors, in order ˜ terms one of and six allowing complex for parameters at least two relative phases, one obtains an CP violating phase, withlarge hierarchy almost of degenerate standard orderbulk model one fermion fermion mass complex masses parameters, Yukawa is athe couplings. generated well same by known The time a pleasing the feature tinytribimaximal contributions of hierarchy mixing warped in of pattern constructions. the all in the At cross-talk neutrino and sector, cross-brane where effects they do produce deviations not within spoil the reproduced, while no quark mixingin is the generated. bulk In are ourthe responsible model charged for the fermion cross-brane two and flavons interactions neutrino propagating sectors.is and a As generated a complete consequence, by cross-talk quarkwith between contributions mixing respect on which to the IR are the brane leading naturally order suppressed pattern in by the the quark and warped lepton geometry sectors [ By taking the twothe flavons to two be sectorsUV-peaked peaked and on different the branes,two associated we sectors approximately symmetry do sequester not breakingχ communicate, patterns: that is neutrinos when with the interactions the of Φ with neutrinos and field, propagate inways the [ bulk andsymmetry a breaking bulk of the custodialfields symmetry Φ and is brokensector, in while two different 7 Conclusions We have constructed aquarks and warped leptons, and extradimensional implementedfirst realization the suggested flavor of symmetry in breaking an [ pattern imaginary parts of flavorthe violating EDM, amplitudes suchrelease as the the most new stringentand physics lower solve contributions bounds the to residual on CP the problem. KK scale from CP violating observables from the EDM and contributions. On the otherexpected hand, to the not degeneracy belevel. of sufficient This left-handed to might fermion produce require bulk a additional profiles constraints suppression on is of the Higgs right-handed mediated fermion FCNCs profiles. at tree most stringent lower bounds on the KK scale. In the worst scenario, a milder lower bound JHEP08(2010)115 and and also 4 3 , offer- K A ]. Z / 0 19 inevitably  → – CKM χ λ 4 17 , implies that A 4 are degenerate. A td pattern with other V 4 induced cancellation 4 A and ] and their contribution A 28 ub – V 26 vanishes. For the same reason, K  field. Obviously, this implies the need to ]. The Wolfenstein parametrization would symmetry setup, as suggested in section VI, 53 χ – parameters entering quark mixing, a rescaling 8 Z 48 – 29 – [ u,d i 0 , with all parameters of order one stems from the y T , ˜ u,d i 3 CKM ) can be pushed below the model theoretical error by x λ , χ (Φ and V 2 CKM λ , , would obviously be a welcomed feature of the model, removing the also produces a pattern in the corrections. Analogous cancellations are K ω in a warped extra dimension and with minimal field content. The main CKM / λ 4 0 flavor symmetry is also welcomed in order to suppress the amount of flavor  A 4 flavor symmetry still appears to be the most elegant and economical way to A 4 and , leading to the well known vacuum alignment problem. However, in this case A 2 K  Z at tree level, since they involve both left- and right-handed fermion profiles. Their The Finally, the presence of cross-brane interactions of the flavon fields Φ and A bulk We have also noticed that the possibility of producing hierarchical CKM matrix ele- K → induced phase seem to rely on more complicated patterns in order to produce a realistic CKM matrix.  4 4 0 that it is alsoembedding possible of to obtainadvantage an of almost realistic this quarkcross-talk construction mixing, effects remains using the sufficiently aaffecting rather one large the simple of to other having account results, cross-brane for or interactions spoiling the and the observed vacuum quark alignment. mixing, A without dynamical completion rescale by a global amountthat all should the ˜ anyway maintainbounds. all On parameters the of otherdirectly hand, order forbids employing the one a most and dangerous satisfy terms and all seems perturbativity toaccount provide for a the more elegant nearly solution. tribimaximal mixing pattern of neutrinos. We have shown here A such corrections arebranes. naturally In particular, suppressed, wein have being shown the that the interaction the potential twointroducing contribution from a flavons the bulk most peaked mass dominant on for term the different UV-peaked of observable phases andEDM, the consequent vanishingmost stringent of bounds new on physics the KK contributions scale to and the resolvinginduces the deviations little from CP the problem [ VEVs that realize the two breaking patterns all down-type dipole contributionsvanish. to The the situation is neutron different electricto for Higgs dipole mediated moment FCNCs [ and suppression might require further constraintsfuture on work. the right-handed Even in sector, the to presence be of explored non in vanishing amplitudes, an violation induced by the mixing5D of theory the — standard withbulk model their profiles, Kaluza-Klein particles due excitations. — to the having The assignedthe zero degeneracy the tree modes of left-handed level of fermions contribution left-handed to from the fermion triplets a of KK gluon exchange to expected to occur at higherflavor orders. symmetry groups, It in is instructive particular suggest to the existence compare of this an expansioning parameter an to elegant be and naturally simple identifiedhand, description with flavor of models quark based mixing on in otherwiseT the appealing standard discrete model. flavor symmetries On such as the other CKM entries remain equal to one, and the two smallestments, entries of order presence of built-in cancellationsA induced by the hierarchical masses. The presence of the almost realistic CKM matrix within the model theoretical error. At this order the diagonal JHEP08(2010)115 ) ), ≡ 3 a ( 3 , y best c r 2 (A.3) (A.1) (A.2) b ¯ ]. , y 1 Zb y 72 3 identity × 1) and . This would are non-trivial 4 − , 00 A ) and ( 1 1 3 , , 1 ) , , x , 1 00 − 2 and y 1    0 2 , x as a remnant spacetime 1 x 1 = 4 x 0 diag( + A 1 2 should be produced in each 0 1 0 0 0 1 1 0 0 ≡ y ⊗ 1 0    H ] into warped 2 1 r m , x ≡ 55 3 1 y − 1), 1 c , the tetrahedral group. It has a real is a complex cube root of unity, with x and − ] or having , . T ratios and asymmetries, allowing for a = 3 is trivial, while i + 1 , is defined as the set of all twelve even 71 r , a b ¯ π/ 1 1 4 − 00 2 y , and three inequivalent one-dimensional , i A 1 3 3 e Zb are conveniently taken to be the 3 ⊕ , x = 0 3 and 2 – 30 – 1 y ω diag(1 3 ⊕ x . Under the group element corresponding to    ≡ i 1 + 1 ar ⊕ 3 i r y r a ’s. Then 2 , where 0 0 1 1 0 0 0 1 0 3 3 00 x 1 ⊕    ) and s ω = ( ≡ i . The representation 3 ( s 00 2 1 cr 3 1 = i ω − ) r a 3 3 → = and ⊗ ⊗ 00 0 c 3 3 1 1 ( , properties 1 4 and 1), the cyclic and anticyclic matrices 0 A (or other versions of) custodial symmetry [ , 1 1 ) ) denotes symmetric (antisymmetric) product. Let ( 2 − LR a ω , ( P ( 1 s ω − The basic non-trivial tensor products are The twelve representation matrices for It is worth to mention two additional points. It is appealing to explore the effects model. It is interesting and phenomenologically relevant to consider the possibility to → 4 0 where denote the basis vectors for two respectively, as well as 1 both representations being unchanged under the matrix 1, thediag( reflection matrices The alternating group ofpermutations order of four, four denoted objectsthree-dimensional and is irreducible isomorphic representation to representations and complex conjugates of each other. We thank Yuval Grossmansupported and in part Gilad by the Perez Ubbo for Emmius scholarship useful program at discussions. the UniversityA of Groningen. The work of Basic A.K is embed release the most stringentfits constraint and on could the provide new model appealing parameter features space alternative due toAcknowledgments to flavor anarchic the models. the best fits forlarger certain parameter observables, space. sucha However, as as custodial discussed setup in easilymore the induces careful literature, conflicts estimate a with of heavier electroweakversion the Higgs of precision allowed the mass measurements range custodial and in ofA setup. a values The for final point concerns possible extensions of the warped desirable. Possible scenarios already describedmetry in breaking the of literature a include a continuoussymmetry flavor spontaneous of symmetry sym- a [ toroidal compactification scheme of a six-dimensionalof spacetime a [ heavier Higgs in this context. Some of the model predictions would get closer to of this, as of other flavor models involving a discrete flavor symmetry would certainly be JHEP08(2010)115 , ]. , B (A.4) (A.5) (A.6) (A.7) ]. ]. (1999) Phys. SPIRES , Nucl. Phys. 83 ][ , Phys. Lett. SPIRES SPIRES , ]. ]. ][ ][ ]. , Warped fermions and ) 1 y 2 SPIRES SPIRES x ][ SPIRES ]. ][ Phys. Rev. Lett. − Bulk standard model in the hep-ph/9912498 , ][ 2 [ y 1 Opaque branes in warped hep-ph/0005286 hep-ph/0212279 ]. , x , custodial isospin and precision [ [ SPIRES ]. 1 3 ]. ][ y , , ]. 1 3 3 RS x y y 3 3 SPIRES − x , SPIRES hep-ph/0410344 (2000) 084025 hep-ph/0104293 3 2 1 ][ ω x [ SPIRES y [ y ][ ω ]. hep-ph/0212307 3 SPIRES 3 + ][ [ Brane localized kinetic terms in the Bulk gauge fields in the Randall-Sundrum model x + ][ ]. 2 (2001) 045010 (2003) 045002 , x 2 y D 62 + 2 y 2 – 31 – 2 2 y x y 3 SPIRES 2 hep-ph/0010195 2 x D 63 D 68 [ x ω x ω (2001) 365 ][ SPIRES − + + + ][ 3 (2005) 015010 ]. Bulk fields and supersymmetry in a slice of AdS 1 1 1 y Neutrino masses and mixings in non-factorizable geometry y y y 2 hep-ph/9912408 (2003) 096006 Phys. Rev. 1 1 1 hep-ph/9911262 x [ A large mass hierarchy from a small extra dimension An alternative to compactification , B 512 x x x [ hep-ph/0308036 hep-ph/9905221 D 71 [ (2001) 256 = = ( = = [ Higgs mechanism and bulk gauge boson masses in the Fermion masses, mixings and proton decay in a Randall-Sundrum Neutrino oscillations and rare processes in models with a small Phys. Rev. Phys. Rev. SPIRES D 67 0 , , a 00 1 ][ 1 ) 3 1 ) ) ) 3 3 3 3 hep-ph/0003129 (2000) 361 (2000) 43 B 498 ⊗ [ ⊗ ⊗ Phys. Lett. ⊗ hep-ph/9911294 3 (2003) 050 , 3 ( Phys. Rev. 3 3 [ ( This article is distributed under the terms of the Creative Commons ( ( , (1999) 3370 Phys. Rev. Gauge bosons in a five-dimensional theory with localized gravity 08 , B 474 B 473 83 (2000) 141 Phys. Lett. hep-th/9906064 JHEP , (2000) 153 [ , Randall-Sundrum model backgrounds precision tests B 586 tests Phys. Lett. model extra dimension Randall-Sundrum background Randall-Sundrum model 4690 Phys. Lett. 486 Rev. Lett. S.J. Huber and Q. Shafi, S.J. Huber and Q. Shafi, S. Chang, J. Hisano, H. Nakano, N. Okada and M.S.J. Yamaguchi, Huber and Q. Shafi, Y. Grossman and M. Neubert, H. Davoudiasl, J.L. Hewett and T.G. Rizzo, A. Pomarol, L. Randall and R. Sundrum, L. Randall and R. Sundrum, M.S. Carena, E. Ponton, T.M.P. Tait and C.E.M. Wagner, M.S. Carena, A. Delgado, E. Ponton, T.M.P. Tait and C.E.M. Wagner, T. Gherghetta and A. Pomarol, K. Agashe, A. Delgado, M.J. May and R. Sundrum, H. Davoudiasl, J.L. Hewett and T.G. Rizzo, [8] [9] [5] [6] [7] [3] [4] [1] [2] [13] [14] [10] [11] [12] References Open Access. Attribution Noncommercial License whichand permits reproduction any in any noncommercial medium, use, provided distribution, the original author(s) and source are credited. in an obvious notation. JHEP08(2010)115 ]. 12 , ] JHEP Phys. Phys. , , , 10 ]. mass Phys. SPIRES Phys. Rev. , 0 s JHEP , ][ , ¯ (2009) B , - 0 s JHEP (2008) 006 SPIRES , B ][ ]. D 80 04 ]. Nucl. Phys. (Proc. (2003) 269 hep-ph/0606021 , [ JHEP SPIRES , SPIRES ][ Flavor physics in the B 666 ][ arXiv:0905.3264 Phys. Rev. [ , ]. ]. ]. arXiv:0804.2503 (2006) 053011 [ ]. ]. SPIRES ]. SPIRES Nucl. Phys. ]. ][ (2009) 200 ]. ][ SPIRES , D 74 Next to minimal flavor violation ][ SPIRES Flavor alignment via shining in RS arXiv:0711.3376 hep-ph/0604112 SPIRES SPIRES ][ Probing the Randall-Sundrum geometric origin [ [ (2009) 253 [ ][ ]. Flavor from minimal flavor violation & a viable B 682 SPIRES SPIRES ][ – 32 – ][ ]. ]. Phys. Rev. Solving the flavour problem with hierarchical fermion B 672 Combining direct & indirect kaon CP-violation to Implications of the measurement of the ]. , Higgs mediated FCNC’s in warped extra dimensions SPIRES (2008) 73 Flavor structure of warped extra dimension models B-factory signals for a warped extra dimension Flavour physics of the RS model with KK masses reachable ][ arXiv:0906.1990 arXiv:1001.2693 SPIRES SPIRES Phys. Lett. [ hep-ph/0602155 [ (2006) 101801 , ][ ][ [ ]. SPIRES Composite Higgs-mediated FCNC B 663 ]. Minimal flavor violation in the lepton sector of the 97 hep-ph/0408134 arXiv:0907.0474 ]. ][ Natural neutrino masses and mixings from warped geometry Phys. Lett. arXiv:0710.1869 [ [ hep-ph/0406101 , , hep-ph/0002279 A GIM mechanism from extra dimensions [ [ SPIRES (2010) 185 SPIRES (2006) 090 ][ SPIRES (2009) 035016 [ ][ Phys. Lett. 03 arXiv:0805.4652 The hunt for new physics at the Large Hadron Collider , [ (2000) 39 Minimal flavor protection: a new flavor paradigm in warped models Flavor violation and warped geometry arXiv:0807.4937 arXiv:0806.1230 (2010) 075025 (2005) 016002 D 80 Lepton flavor violation in the Randall-Sundrum model with bulk neutrinos Phys. Rev. Lett [ [ , JHEP ]. (2004) 201804 arXiv:0906.1542 B 200-202 , [ B 481 93 D 81 D 71 (2009) 077 hep-ph/0303183 arXiv:0709.1714 SPIRES Suppl.) 01 Rev. Randall-Sundrum model (2008) 046 Randall-Sundrum model 075016 Randall-Sundrum model: I. Theoretical(2008) setup 094 and electroweak precision tests of flavor with lepton[ flavor violation Phys. Rev. at LHC wave functions constrain the warped KK scale Lett. [ hep-ph/0509117 difference Lett. [ Rev. G. Perez and L. Randall, C. Cs´aki,G. Perez, Z. Surujon and A. Weiler, P. Nath et al., J. Santiago, M.-C. Chen and H.-B. Yu, S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, A.L. Fitzpatrick, G. Perez and L. Randall, A. Azatov, M. Toharia and L. Zhu, K. Agashe and R. Contino, G. Moreau and J.I. Silva-Marcos, S. Davidson, G. Isidori and S. Uhlig, K. Agashe, A.E. Blechman and F. Petriello, R. Kitano, S.J. Huber, K. Agashe, M. Papucci, G. Perez and D. Pirjol, Z. Ligeti, M. Papucci and G. Perez, O. Gedalia, G. Isidori and G. Perez, G. Cacciapaglia et al., K. Agashe, G. Perez and A. Soni, K. Agashe, G. Perez and A. Soni, [32] [33] [34] [30] [31] [28] [29] [26] [27] [23] [24] [25] [21] [22] [18] [19] [20] [16] [17] [15] JHEP08(2010)115 ]. ] 836 ]. Phys. , ] Summer SPIRES (1999) 79 ][ (2007) SPIRES ]. ]. ][ ]. symmetry ]. B 458 symmetry in Erratum ibid. D 75 ]. [ 4 hep-ph/0601001 [ SPIRES A U(2) SPIRES , talk given at SPIRES ][ ]. ][ SPIRES ][ arXiv:0907.3963 SPIRES [ ][ hep-ph/0409075 (2004) 031901 LHC signals from warped ]. What we (would like to) ][ Phys. Lett. Phys. Rev. , (2007) 120 , hep-ph/0206292 (2006) 039 SPIRES [ ]. D 70 ][ 04 SPIRES [ B 775 A model of lepton masses from a symmetry for the neutrino mass matrix ]. (2010) 036004 hep-ph/0612015 SPIRES arXiv:0705.0714 4 hep-ph/0606293 [ [ JHEP [ (2003) 207 A [ , Tri-bimaximal neutrino mixing and quark flavor physics without Phys. Rev. arXiv:0806.0356 hep-ph/9409330 Top quark spin correlations in the , [ A redetermination of the neutrino mass-squared symmetry for nearly degenerate neutrino [ D 81 A viable Randall-Sundrum model for quarks and flavour symmetry breaking scheme for Neutrino masses from an 4 SPIRES 4 Nucl. Phys. A B 552 ][ hep-ph/0106291 A , – 33 – [ (2007) 34 ]. CKM and tri-bimaximal MNS matrices in a Underlying arXiv:1001.5151 (2008) 015003 Simple non-Abelian finite flavor groups and fermion , (2008) 055 ]. (2007) 015002 ]. Collider signals of top quark flavor violation from a warped Phys. Rev. (1995) 4689 , Flavor physics constraints for physics beyond the standard B 652 10 SPIRES arXiv:0809.2936 Phys. Lett. , D 77 ][ D 75 , Softly broken ]. ]. A 10 SPIRES SPIRES (2001) 113012 [ ][ JHEP hep-ph/9910392 , Fuji-Yoshida Japan August 12–19 2004 [ , [ ) Phys. Lett. D 64 SPIRES SPIRES , Phys. Rev. 2004 ][ ][ Phys. Rev. , , (SI model (2000) 170 hep-ph/0702194 T origin of the neutrino mass matrix ) 4 2004 d ]. ]. Int. J. Mod. Phys. Phys. Rev. hep-ph/0701155 ( A Non-Abelian discrete family symmetries of leptons and quarks arXiv:1002.0900 , , [ × , B 474 hep-ph/9904297 hep-ph/0404199 SPIRES SPIRES masses Lett. SU(5) leptons with T’ family[ symmetry understanding quark and neutrino[ mixing angles masses from a discrete(2010) flavour 127] symmetry [ difference in tri-maximal mixing[ with terrestrial matter effects know about the neutrino mass and the quark mixing matrix [ institute holographic composite Higgs models masses Randall-Sundrum model at the095008 CERN Large Hadron Collider warped extra dimension model extra dimension extra dimensions P.H. Frampton and T.W. Kephart, A. Aranda, C.D. Carone and R.F. Lebed, U(2) M.-C. Chen and K.T. Mahanthappa, M.-C. Chen, K.T. Mahanthappa and F. Yu, X.-G. He, Y.-Y. Keum and R.R. Volkas, F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, P.F. Harrison, D.H. Perkins and W.G. Scott, G.L. Fogli, E. Lisi, A. Marrone, A. Palazzo and A.M. Rotunno, E. Ma, E. Ma, F. del Aguila, A. Carmona and J. Santiago, E. Ma and G. Rajasekaran, K.S. Babu, E. Ma and J.W.F. Valle, M. Arai, N. Okada, K. Smolek and V. Simak, C. Cs´aki,C. Delaunay, C. Grojean and Y. Grossman, K. Agashe, G. Perez and A. Soni, K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, G. Isidori, Y. Nir and G. Perez, [51] [52] [49] [50] [47] [48] [45] [46] [43] [44] [40] [41] [42] [38] [39] [36] [37] [35] JHEP08(2010)115 ]. ]. 83 A 20 Nucl. B 630 10 Phys. , Phys. B 153 Z , , SPIRES ] b [ ¯ SPIRES [ Zb (2003) 033007 JHEP , (2010) 071 ]. (2005) 037301 Phys. Lett. Phys. Rev. Lett. D 68 02 , Nucl. Phys. ]. , , ]. Mod. Phys. Lett. , D 72 ]. SPIRES hep-ph/0701055 JHEP ][ [ Flavor physics in the The custodial , arXiv:1005.4315 hep-ph/0507217 SPIRES 4 , SPIRES , A ][ Phys. Rev. ][ , SPIRES Electroweak constraints on warped → Review of particle physics ][ Phys. Rev. , ]. A custodial symmetry for ]. SO(3) (2007) 035006 ]. hep-ph/0312247 ]. [ SPIRES D 76 [ hep-ph/0002044 SPIRES hep-ph/0504165 [ SPIRES Maximal neutrino mixing from a minimal flavor [ ][ – 34 – ][ ]. ]. ]. Precision electroweak measurements on the hep-ex/0509008 SPIRES [ ]. [ Tri-bimaximal neutrino mixing from orbifolding Modulus stabilization with bulk fields (1979) 277 Hierarchy of quark masses, Cabibbo angles and Phys. Rev. (2004) 115013 (2005) 64 SPIRES SPIRES SPIRES , ]. Holographic theories of electroweak symmetry breaking without ][ ][ ][ SPIRES Tri-bimaximal neutrino mixing from discrete symmetry in extra ]. Model of leptons from Spontaneous breaking of supersymmetry through dimensional How to get masses from extra dimensions (2000) 016009 (1979) 60 (2006) 257 ]. ]. ][ Tri-bimaximal mixing, discrete family symmetries and a D 69 B 147 Model of geometric neutrino mixing collaboration, C. Amsler et al., B 720 hep-ph/0610165 hep-ph/0605341 427 [ D 62 SPIRES [ B 82 [ SPIRES SPIRES SPIRES ]. ][ ][ ][ Phys. Rev. Nucl. Phys. , (2007) 31 hep-ph/0508099 hep-ph/9907447 (2008) 1 (2006) 62 , Nucl. Phys. arXiv:0807.4937 [ [ Phys. Rept. , Phys. Rev. SPIRES hep-ph/0508278 [ Phys. Lett. , , collaboration, S. Schael et al., [ [ , ]. Obtaining the neutrino mixing matrix with the tetrahedral group Aspects of the tetrahedral neutrino mass matrix Tetrahedral family symmetry and the neutrino mixing matrix B 775 B 667 B 641 arXiv:0910.4392 hep-ph/0505209 hep-ph/0305243 SPIRES Phys. models with custodial symmetry [ [ [ (2005) 2601 dimensions CP-violation (2005) 58 Particle Data Group Lett. a Higgs boson conjecture connecting the quark and[ lepton mixing matrices ALEPH resonance (1979) 61 (1999) 4922 Randall-Sundrum model: from precision tests to Higgs physics reduction symmetry Randall-Sundrum model: I. Theoretical(2008) setup 094 and electroweak precision tests Lett. J. Berger and Y. Grossman, G. Altarelli, F. Feruglio and Y. Lin, E. Ma, E. Ma, M.S. Carena, E. Ponton, J. Santiago and C.E.M. Wagner, C.D. Froggatt and H.B. Nielsen, A. Zee, G. Burdman and Y. Nomura, G. Altarelli and F. Feruglio, K.S. Babu and X.-G. He, J. Scherk and J.H. Schwarz, W.D. Goldberger and M.B. Wise, C.I. Low and R.R. Volkas, S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T.J. Pfoh, Scherk and J.H. Schwarz, S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A. Aranda, C.D. Carone and R.F. Lebed, [71] [72] [68] [69] [70] [66] [67] [63] [64] [65] [61] [62] [58] [59] [60] [56] [57] [54] [55] [53]