JHEP09(2004)004 a of of .pdf and 2004 2004 to fixed 2, dimen- 15, er forbidden leads six presence July quarks /jhep092004004 SISSA/ISAS in orbifold are 04 suppression 40 This the Septemb or 200 f ysical rbifold the 09 to three ep des. theory o ph jh erators Received: s/ due mo the er op ccepted: The pap y at A gauge 6D e/ zero iv particular Publishing ch deca in ar in t/ bulk , enhanced calised . .i y SO(10) y o lo ssa are proton Physics subgroups. deca GUT ecnic ´ are T deca of additional GUT http://jhep.si erators erior proton ersymmetric families op and in Sup sup dimension-5 three Physics roton Dimensions, Institute a p of its states in ratios The by DESY DESY y to Instituto on on Higher de de a, hing dimension-6 en and quark-lepton deca brane de h y. y. otr otr artment in ısic ´ F the orbifold. tial brok Dep branc Published these de is an proton of of Theories on sequen CERN de. onen-Synchr onen-Synchr whereas ¨ uller study , mo SO(10) e pattern 0 Field structure artamento 2004 W Elektr Elektr Three Germany Germany mixtures K Switzerland [email protected]. [email protected] [email protected] [email protected] + Portugal g, g, Dep Division, Buchm µ ct: where are ers. Emmanuel-Costa Wiesenfeldt Covi ords: w on, ory → compactified ts, to p R-symmetry Hambur E-mail: Deutsches E-mail: Geneva, CFTP, The Lisb E-mail: Hambur E-mail: Deutsches SISSA/ISAS oren oin y haracteristic c p leptons c KK Keyw Abstra the ° b S¨ sions David Laura GUTs Flavour Wilfried JHEP09(2004)004 e 7 6 8 a 1 2 6 ]. v 12 10 ts. 15 10 via the e the the has 24 nat- v ha , y in It t higher strong fron is ha erators On mediat- [23 strongly t that y ]. structure in enhanced op deca ery tion ]. can v ed urthermore, [8 ]–[6 erimen deca a w F our are [1 dels v ]. atten leptons differen y sho yrs exp fla particles mo proton h o mixing 33 w uc predictions and vy t ]–[24 of proton deca the 10 erators m ande dimension-6 [22 hea on GUT × op on , so constitutes 9 analyses y . tly b 1 quarks the wn leptonic proton studies end ≥ states of GUTs. ed is for ) dra ed theoretical ] h erKamiok dep These ¯ ν Recen absence dimension-5 20 + suc ]. revitalised , not the ]. 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Con 1 3 literature. strong ha reac dimension-5 theoretical On 5 JHEP09(2004)004 ], y ], w of at in or on 4D [1 our F and and and and and and and 1 The [25 elo This v (2.1) large , ψ . -plets . deca b y 6 Φ Quark gg y gg proton ]. fla in H ectation O 16 ely O ]. usual , of couplings , erformed. , [25 erators SU(2) U(1), . additional deca . generation del deca . p 27 dimensions ps place a ps exp leptons . cancellation structure × , × op osed tial haracteristic the , O ectiv w is proton O an c y Mo 1 a , are distances alues i b . 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Conclusions w’ The in study giv à of electro in the strongly 3, rate en, con in GUT fourth erm ]. and , SU(5) SU(5) to yields gauge h = U(1) ximately effects . brok is three 6 29 yp ws: ‘pillo . dels. c aluate is lopsided compactifications del , h . Hence, ed × proton brane is The brok H 4D a L , total ev , three hange . 1 the in whic . er mo bulk is theory [28 mo 5 of mixing ∗ follo The of in 4D appro L t anomalies ) doublet = flipp groups H − exc . bulk with its ectorial) M the theory del for i and pap as , B gg SU(2) the via 2 ps , (v arise of the are t i as to Z SO(10) ! O × and GUT and gauge SUSY a del mo those ψ , the del discuss 4 × 4 to ] oson c brane GUT deals scale U(1) ν e en corners differen at b φ ps e 2 as [2 of mo 3 mo duced where à 3 w Z scale. (10) only presen φ, t with X where ψ generations calculate SU(3) , the and , × parities -plets brok 4 = four 6D i c act organised I GUT these 2 SO naturally matrices orbifold ten cutoff = Φ O in L is 16 the repro Z gauge GUT , 0 is ( ti-doublet U(1) will and t the brane e all the the des an / Φ Section bulk con sm compared of three can surviving A b e 2 fl a the an × results er (10) branes (5) G of as at w (10) mass T O mo ose section ). three ratios to del on 1 the SO (5) the SU can the from pap ell the field ho goal SO at in c orbifold orbifold del, w -plets, mo 2 SU three of , zero e widths. cated ψ hing factor, of 16 as lepton with mo = y also The W The The lo ecific cated , 6D start compactification figure orbifold break taining 6D difications the , , irreducible lo e sp tersection fl gg fl c gg alues the Φ v U(1) These in G (cf. of four to O mix O con W the compared O a 2. kind structure case branc Finally the mo is this and therefore compare deca JHEP09(2004)004 3 β ]. ts in six six for the × [25 This with (2.3) (2.2) (2.4) tan Latin 3 fields, These to / the the orbifold hical ortional D elemen mass of symmetry m the een while leads brane form prop w , of c 4 t eak et hierarc , and ν diagonal c i terms b w jorana e unification e are symmetries oin The wn-quarks. n = b m in N i are c 4 , do Ma suppression. . d n to fixp m off-diagonal (branes) N c i electro m m e no h ottom GUT hies no n , v m ts mixings 1 2 ≡ β is matrices with , the haracteristic eac ha oin c and ect + structure,      p    ] top-b and the c i tan at 4 t-handed N 3 2 1 the 3 suppressed. ] ps u hierarc 0 0 / fl and u exp v e e e the µ µ µ f µ u i M G there u G [ of states are [ e m 2 m 3 fixed righ 3 0 0 m i fl ps µ w 0 0 underlying µ D f u M ws O O tially mass 1 of ximate scale couplings h that common 0 0 m 2 bulk ro + µ 2 and a 0 0 ts assume µ f the β couplings M    w diagonal onding onen the ν the whic a the 1 a and 1 appro to ∼ ultiplet. Note 0 0 D αβ lepton w at µ f three uk e M exp a – N for m Y The an terms elemen m 3. also with c α 3 leptons      erm uk m corresp . due , and n are . – Y first d ∼ ). ∗ yp des . matrices. + T h e m 1 the of 2 N mass M β v mo 1 m e breaking onding The GU at implies v = quark include 6D ∼ e αβ the i L . ] matrices (Λ mass ∼ 3 d mixings , 4, of relations gg m zero 4 i O − . e µ u off-diagonal of the c α 2 G m left-handed . This , [ e . × matrices 2 B m strength corresp = H states. ∼ gg e 1 µ h 4 [SO(10)] + eral fields, β i and , i O bulk D 1 subgroups c β Direct = = 1 the from f O one. M e µ d sev The m are 2 after bulk ersal α tan among pattern v of the d αβ ), o ], D β (10) , 1 brane i w m and and 1 c m 1 t univ order fields. α [25 /v SO 3 ) diagonal only tan er d 2 scale. H a 1 with µ satisfy v h v of in parametrisation v , o the indices, = and ( 2 feature of originates the . = a = ts µ e eak O three 00 ed 2 Higgs 1 , mix W h β place of w 1 Z m v run and = µ e , and haracteristic × d The c Greek i 0 2 can via whic β (tan bulk matrices crucial e µ m tak othesis a efficien Z , only describ 1: c 4 i electro the states co × ν er, yp to µ tan the 2 h As The tification ev = Z to these the / w 2 c 4 breaking mixings leads up matrices iden Here The of indices n ho parameters large whereas where Figure T with brane to JHEP09(2004)004 t < the 1 this final e (2.6) (2.9) (2.8) (2.7) (2.5) µ , , (2.11) (2.10) fourth 1 are , phases) µ mixings, tegrated the 3 ¶ consisten in V 2 The 2 theory e a v dels. f M b e large and µ mo transformation erform 3 giv O p hical. U then (neglecting to + parameters tains orbifold. y ). complete mass y b and           can a a f con M 4 4 4 unitary w the / en f f f hical 4 M M M In v a 3 2 1 , V ( . that e e e µ µ µ on 2 2 2 the giv h O 1 ¶ non-hierarc + + + ˜ ˜ ! f M M M 3 2 1 fermion indices y ts 2 . 1 0 b f f f f suc v M M M M are , hierarc 3 2 1    oin 0 b t 4 µ µ µ V µ in masses. our j j j V 4 4 4 m v for 4 general, à O ) ) ) , : fixp 4 4 4 f M assume, fla † c + = 3 4 eigenstate, V V V lopsided In and e e µ ( ( ( 2 V 3 m 1 2 3 ! corrections † 4 + w the 3 lepton V . f : M 1 0 0 3 e e e µ µ µ SM 2 U V β 0 Hence, f f u M M to of as – mass + + + diagonalised 3 from f D . M m µ i 3 and j j j 0 4 b e parameters the m , 1 2 3 e µ , up U + vy b ) − ) ) part, ∼ – , 4 4 4 4 i à 2 particular           α and, ! 3 4 3 U on V V V µ the 1 2 3 4 cation hea ( ( ( 0 1 µ f f = M M in f f f f can 1 2 3 M M M M e × f f f f : 2 M M M M quark = lo 4 subspace. familiar e µ µ µ µ 2 q 3 2 t ose lik )) scale the † + 0 matrix of 3 m only f ckm 23 23 µ M 0 1 0 2 14 14    14 14 mV h = 23 23 V : f f ho × M M f f f † M M M 4 f f c M M f f 1 4 = 2 3 1 M M (2.4 out à U 2 3 act µ f f eac M M µ f f unit matrix, αβ M M f f M M b f f M M m 3 = − = differen f eq. − − can M V ectrum 0 3 structure 4 , the e 2 U 3 23 m scale f sp single a non-trivial M 3 w 23 the f 1 (cf. unification M CKM U 0 0 f M 4 f and e a M µ b f 2 M m ], V + to − m 2 remaining f , α M 1 0 0 1 4 of the [25 and f 1 M f 14 M U 1 only obtain 4 f M 14 the f due M µ α in ws 0 0 ximately realistic f e e M f M e v ro a in P w − − matrices b order matrix diagonalise 3 ha q y                     e µ of pattern the appro , the = matrices 3 ma is = = is that mass µ obtain , they y 4 4 discussed 4 α f that , M h V mass the < U U to f M while 2 As The e µ , w, 2 quark matrices while hierarc Clearly Notice where order where ro µ where out, diagonalisation JHEP09(2004)004 wn ex- de- the This mass mass third do (2.14) (2.17) (2.12) (2.15) (2.16) (2.13) (2.18) unless to second . the erimen- eak the w the the ely parameter one the , Exp een for w and           . . and ectiv parameterized i from 3 et wn-quark es 0 e 14 23 − b order f M do f M = giv cating corrections resp 3 10 . of 2 f , lo M , f it M 4 × d 1 remaining second the 3 3 2 ts states the f µ 4 ¯ M µ 1 2 µ m 14 23 ], analysis 3 2 f f f as M M M f f . 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The The The relev other data to a to consisten ys 1 y e pression matrix consisten the Within where the is The and up tal matrix, eigen ca quark b matrix µ JHEP09(2004)004 3 to X . on PS . een not one e eing . (3.1) (3.5) (3.2) (3.4) (3.3) b osons b mass, 1 es lepton the e b erators the ) v last scale = do Y tegrating op of i , ha on and in e parameters it sensitiv X the , ( gauge . GUT on . the neutrino = not h.c. hange , cated y t indices X h.c b is h.c. effectiv the lo simply bary + erator, tation, exc + SU(5) ¤ e it + h.c. y ligh of (2) op k ¤ b b ¤ the k the generations, + with k L the SU L the i µ L to the get ∗ k γ µ ,i y the 5 γ γ e b represen the t for fields > w α,k Q ,k yields determined endence ) with c γ therefore , c ,i a d obtained 10 d β X relation. family c and T SM coun are − 10 ( dep u is − M dimension-5 µ This and e of the γ ,j α,i α,k , m c γ relation mass ∗ k eak third and mediated Q i d the as ¯ 5 Q w µ Φ ertex ∗ − µ is v indices γ from + and freedom U(1). V 5 terms to masses γ the i 2 ,j d ¢ e c j e the c γ i × of in partners i – e SU(5) e del m Q ¯ £ Φ dels 6 10 erators + erators with ,i for come Latin ed trary a ,i – β mo successful ,i β op c γ tations T reps X mo op Q effectiv SU(2) µ u Q requires 2 the tations Con ¯ θ γ brane, degrees flipp µ µ , × α,i 2 osons i the The c γ θ γ 4D terms a b ]. u Z The ,i SU(5) eV (except j 10 y o GG c β . α,i ¡ c in b e ∗ ersymmetric [17 w represen 01 Q u £ t . 5 colour tr write SU(3) γ the γ 0 γ the represen gauge 2 sup scale brane. of coupling; αβ h αβ of αβ ∼ in ² the on ² ² can first a µ osons £ vy SU(5) terms, related ectrum). 2 N y b 2 A 2 X dimension-6 X 2 5 erators 2 5 αµ SU(5) g y hea sp 2 /v those the one g 5 M M gauge X SU(5) ∗ osons. the g op tation 2 not √ 3 deca 2 family − b through 5 via denote i the . M breaking the g − deca . √ ed of 2 t gauge = . kinetic that i y = are mass terms = m 1 first − eff SU(5) out h L SU(5) eff flipp ∼ gauge = L = represen proton L indices e their the deca 3 Note express k quark dressing proton the L reordering, . whic vy , y 6) ∗ the M w y , b / is / 5 couplings e 2 for 10 2 t 5 violating no hea 5 an µ ersymmetry erparticle , lepto on With t en g Greek include m e tegrating 2 of Fierz e er the , an Y h Effectiv b W In The ∗ the sup sup ∼ giv Proton and olv 3 3 ( v d 2 um relev those from where With where m family a brane. suppressed. n µ and in 3.1 3. Dimension-6 the the whic are out JHEP09(2004)004 t of of in as ta- are des, oin bulk only (3.9) (3.8) (3.7) (3.6) case, clear p (3.11) (3.10) SU(5) but mo osons 6D alid erator b finds the v their fixed represen coupling op KK y oson, Y is the b to e b 6) therefore . corrections / one in the del easily en 1 and y is ¶ due at − er ¶ mo giv , v It X vit 2 ∗ gauge effectiv o 2 violating One , . √ as M ∗ gra X . our , 6 1 er ∗ 3 5 the ], / one. ( b sum 5 h.c. calised . M . 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SU(5) states symmetry Numerically Note 10 op the more breaking m dence and flipp and these JHEP09(2004)004 e y ts of a- on on for the the the the can can KK KK term ativ osons result deca (3.18) (3.20) (3.21) (3.19) (3.17) (3.16) (3.15) of of b for deriv ting the the efficien they hange again erators the X deriv of co endence same erators o op exc kinetic obtain of hange single w 0 op instead t e accoun only dep X Using , w osons: The exc ersal our the n obtained or , a one , b v . branes. ∗ ergence GG—PS. GG—fl, Therefore ertices. 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R 575. 10 Phys. for , , ersymmetric de , ett. ev. Phys. (2004) p. ersymmetric D ay L R ch , c ons gaton sup oton minimal ar Phys. ay angian de sup ersymmetric oton pr ev. ouble hep-ph/9808255 a c 595 , [ se R hep-ex/0110005 pr tr hadr 1975, de es sup Phys. , in lagr enormalizable Phys. B c r and . of , oton the The a ay and for Multi-me pr NY, c (5), onsistent ett. ]. oton Phys. 855 del hep-ph/0107055 , c out 115009 minimal hep-ph/0311330 ctive [ L in on de [ , al., ories pr SU al., a titanic) mo and minimal - ay effe et AIP the c 304 et olor in 105 ge: article save ator c leptons d oton p in de Phys. (2001) SU(5) nti (1999) er the (10) sie ay , ed., of an Pr A c name: SU(5) c ay op ]. ]. c ay 59 SO de d On c unifie 5 (2001) oton Suzuki (2004) de fourth Ganezer Ng, – de D pr . under for 16S1B Y. oulos, S. Flipping d and oton hep-ph/0302272 actions the 523 Carlson 16 unifie [ 587 ev. oupling (former A oton gr oulos, elementary S.-P c K. Pr oton R – er, B as l B 62 , Pr de diate pr inter attern GUTs and al (5) C.E. Nanop alk er p c, dimension ´ 6 and d gr ett. , me ett. oration, of Phys. W vi titand Nanop r SU L tion Phys. = L r even , r d. hep-ph/0204311 hep-ph/0108104 J. the (2003) in [ [ D.V. numb ]. D r SUSY 1974 aking ch: Nasri Unifie e del , in collab Mo D.V. Not y Unity ar of Gauge vs Phys. br and Phys. S. . 661 Wiesenfeldt, and Senjano ]. mo se , J. , ct w, epton es Rab and S. B oup ter, wski, Fields mixing 320 075005 055009 L G. ay o h c Effe Int. Kim S. oulos Collabora . Pierce, Gr GUT mixings de , and mixings and Ric and a Glasho mixings matric Phys. A. Mink 401 symmetry J.E. ent (1979) Flavor (2002) (2002) ]. . Salam, M. Mafi, Gaillard oton Nihei, P Nanop Mohapatra, sugr erez hep-ph/0007213 S.L. [ and 88 66 65 pr A. . P A. new mass orking T. ermion Nucl. and Inher a F and B , (1979) D D A Particles uel-Costa W hep-ph/0205336 M.K. D.V. R.N. . . 193 and .F. neutrino [ and h ama P SU(5) og, del and for y 82 ev. ev. ett. 035001 99 219 438 alistic for erez, ´ ati er-Kamiokande R R L jc, mo e himan Mohapatra, B Barr, Goh, r P Ellis, Ellis, P Derendinger, ritzsc AND ctor . . (1975) . Emman F Georgi, Georgi Mura Ac Dermisek, Goto Jarlsk Ba del Sup .F. ett. hep-ph/0403286 Phys. GUT Phys. 893 Phys. (2001) mo minimal [ L (2002) with at 170 (1982) dete 93 (1974) T. TIT Super-Kamiokande J.P H. S.M. J.C. H. H. D. H. B. J.R. C. R.N. H.S. J.R. Y. R. P [9] [7] [8] [6] [4] [5] [1] [3] [2] [13] [11] [12] [17] [15] [16] [14] [19] [18] [10] [20] References JHEP09(2004)004 , , , om a , 370 fr by B ay B c Phys. (2002) d and extr e (2004) de Nucl. ept. Phys. (2001) ett. ett. , 6 65 , , R ories Part. L L 64 with Nucl. asymmetry D ators g. induc the oton CP-violation , bulk o er dimensions D d world pr ]. Phys. Pr Phys. ev. Phys. family op des Phys. ories , , and R , six and , ev. e J. aryon ane and mo b R unifie the physics ac dimensions ays in ane br c ]. guts ay br anes New the c de Phys. six leptons angles and , br field ]. , ¯ otic de ν Phys. mine ories o gr in ν oset-sp , in and c en π and dimensions . on the ep erfield orbifold Heter d abibb de → dimensions c six 105 hep-ph/0112230 etwe mixings sup [ of k a b dels: chies nucle orbifold for in e, ar es quarks to dimensions mo unifie of and extr 101 nomalies ac anomalies 5D dimensions of hep-ph/9809307 A [ hier (1983) in masses, ation leptons ersp ane esaw hep-th/0403163 angian Wingerter, [ ]. higher 293 br se signatur 229 (2002) elations SO(10) masses sup ]. ]. mass r higher and A. ation lagr in unific in – quark B ay Serone, alculation schemes c 2579 c and in 4D al 632 of and 17 de and ]. M. (1999) ]. unific in ]. B Smith, ation Constructing lepton – Chir Phys. Gauge Bulk Quarks chy neutrino mixing ation mixing and (2004) oton ory ange and angian ar of vi, vi, vi, system D.R. unific gr Pr Phys. the Hall, 19 Suppl.) . Quark lagr Nucl. Co Co Co ]. ]. unific Zhang, B Hier hep-ph/0108071 ls [ , lepton c. dels (5) A flavor and and al hep-ph/9810308 hep-ph/0102301 audrev o L. L. L. [ [ . L.J. Scrucca the V gr ge Nucl. Mo SU ]. R.-J. (Pr , ators d ar and Chir 277 in Gauge and and and 399 257 L Okui hep-ph/0209144 and er Phys. hep-ph/9912358 ]. ]. h-Russell, [ anagida, ang-Mil 035008 hep-ph/0304142 [ Nielsen, C.A. 77 [ .K.S. guts Y and Y op 1 d. T. P ouple ura, ]. y c Mass ¨ ¨ ¨ uller uller uller 231 eruglio, eruglio, see er T. Sato, Marc 209 Wise (1979) Mo F F H.B. (1999) (2001) Daniel, . hm hm hm Phys. ura, (2002) J. Rab hep-ph/0403065 J. sup Nom . J. hep-ph/0108021 hep-ph/0204037 F. F. , [ [ and (2000) M. Nilles, ongly orbifold Xing, 147 S. and 297 445 511 65 M.B. Buc Buc Buc . Y. (2003) 5D CP-violation Nom and and (2003) review, to Str Int. B 45 Z. and and hep-ph/0207108 Nucl. 199 119 B B D [ and t , ¨ uller , W. W. W. H.P er, er ersymmetric Y. h, and ashi, strings k k 648 her, y hep-ph/0103125 hep-ph/0108170 563 a, a, a, ev. ura, [ [ ett. ett. hm (1982) ec ec 537 sup roggatt L R B L Phys. Phys. recen ations ation F B 5 otic hep-ph/0405048 (2001) (2002) Hall, Hall anagida ritzsc [ orste, a Buc Claudson, Altarelli Altarelli Heb F Nom Heb Fleisc Y Asak Asak Asak Koba 195 Chadha F¨ = ett. or B Phys. D Nucl. unific 106 hep-th/0406208 Phys. 523 applic Nucl. Phys. L dimensions (2002) 055003 heter 085036 Phys. 539 M. W. S. C.D. G. T. T. L.J. S. T. A. F G. R. H. L.J. T. T. Y. A. [39] [38] [40] [37] [36] [35] [28] [29] [27] [30] [34] [31] [21] [32] [33] [22] [25] [26] [23] [24] JHEP09(2004)004 , ay Nucl. c de QCD ev. e R oton nn. lattic pr A , the om fr ays of c de on er elements alculation . hyp c matrix QCD ]. ay e c de – attic Semileptonic L on 18 ]. – al., hep-lat/0402026 , Nucle et Winston, al., limit hep-lat/9911026 [ et R. Tsutsui and Aoki N. 014506 hep-ph/0307298 w [ S. ontinuum c allo 39 the Sw (2000) oration, in oration, 62 (2003) E.C. collab D 53 o, collab ev. CS element R Sci. A Cabibb matrix Phys. Part. JLQCD CP-P N. [43] [42] [41]