SO(10) SUSY GUTs with family symmetries: the test of FCNCs

SO(10) SUSY GUTs with family symmetries: the test of FCNCs Outline Diego Guadagnoli Technical University Munich The DR Model: an SO(10) SUSY GUT with D 3 family symmetry Top down approach to the MSSM+ Successful fit to quark & lepton masses, CKM & PMNS matrices Including FCNCs: the only way to test the pattern of SUSY particles masses & mixings predicted by the model Details on the analysis: global fit to low energy observables, FCNCs directly in the 2 function

The Model The model by Dermíšek & Raby (DR) is an SO(10) SUSY GUT with an additional D 3 [U(1)Z 2 Z 3 ] family symmetry Dermíšek & Raby PLB ( 05), PRD( 00)

The Model The model by Dermíšek & Raby (DR) is an SO(10) SUSY GUT with an additional D 3 [U(1)Z 2 Z 3 ] family symmetry Dermíšek & Raby PLB ( 05), PRD( 00) Why SUSY GUTs Tantalizing unification of LEP measured SM couplings after MSSM running to high energies. Maybe just a coincidence. Maybe not. Why SO(10) Complete quark lepton unification: single 16 representation for each family Natural inclusion of R in each 16. See saw mechanism easily incorporated. Can explain the pattern of quark/lepton masses and mixings, through family symmetries Dermíšek & Raby or (few) extra fermion multiplets Babu & Barr ( 95) many other authors

Why (discrete) family symmetries Global symmetries: are believed not to arise in string theory Local (i.e. gauge) symmetries: typically enhance FCNCs Discrete symmetries can arise e.g. as the remnant of spontaneously broken gauge symmetries directly from compactifications in string theory Family symmetries: isospin example We know that in SO(10) the 16 i contains the fermions of the i th generation Let {16 1, 16 2 } transform as an isospin doublet and 16 3 as a singlet Then let us introduce: flavon fields : transform under the family isospin, are SO(10) singlets Froggatt Nielsen fields : transform under the family isospin, are 16 s of SO(10)

Now one can build up the following interactions: 16 1,2 [Higgs], 16 1,2, 16 1,2 [Higgs], Yukawa unification only for 3 rd generation fermions 16 3 [Higgs]16 3

Now one can build up the following interactions: 16 1,2 [Higgs], 16 1,2, 16 1,2 [Higgs], Yukawa unification only for 3 rd generation fermions 16 3 [Higgs]16 3 One then breaks spontaneously the family symmetry through = vev and integrates out the, with M GUT scale. Mass terms for, say, quarks are generated through diagrams like: Higgs 16 i 16 i q M q q q M Higgs q FN states implement a sort of see saw mechanism to make quark masses GUT scale Quark mass hierarchies are understood in terms of the sequential breaking of the family symmetry through = vev The DR model realizes the above mechanism with the smallest (non Abelian) discrete analogue of isospin, i.e. the D 3 group. With 11 family symmetry (real) parameters, it successfully describes quark & lepton masses and mixings. With a total of 24 parameters (less than in the SM+) the whole MSSM+ parameter space is fixed.

It is worthwhile to perform a more detailed analysis of the DR model. The aim is to test the SUSY mass spectrum and mixings predicted by the model. The SUSY spectrum will affect flavor changing neutral current (FCNC) processes. Albrecht, Altmannshofer, Buras, D.G., Straub, JHEP 07 Strategy: perform a global fit to the model parameters, including FCNCs among the observables in the fit. One step back: how a GUT scale model is tested at the EW scale. scale Y s, soft SUSY pars, i, M Ri The DR model is specified in terms of coupling and unified scale: G, M G initial conditions M G soft SUSY breaking params at M G M Ri textures entering the Yukawa s at M G EW scale

It is worthwhile to perform a more detailed analysis of the DR model. The aim is to test the SUSY mass spectrum and mixings predicted by the model. The SUSY spectrum will affect flavor changing neutral current (FCNC) processes. Albrecht, Altmannshofer, Buras, D.G., Straub, JHEP 07 Strategy: perform a global fit to the model parameters, including FCNCs among the observables in the fit. One step back: how a GUT scale model is tested at the EW scale. scale Y s, soft SUSY pars, i, M Ri The DR model is specified in terms of coupling and unified scale: G, M G initial conditions M G MSSM+RH RGEs soft SUSY breaking params at M G M Ri integrate out RH textures entering the Yukawa s at M G right handed neutrino masses M Ri define see saw scale EW scale

It is worthwhile to perform a more detailed analysis of the DR model. The aim is to test the SUSY mass spectrum and mixings predicted by the model. The SUSY spectrum will affect flavor changing neutral current (FCNC) processes. Albrecht, Altmannshofer, Buras, D.G., Straub, JHEP 07 Strategy: perform a global fit to the model parameters, including FCNCs among the observables in the fit. One step back: how a GUT scale model is tested at the EW scale. scale Y s, soft SUSY pars, i, M Ri The DR model is specified in terms of coupling and unified scale: G, M G initial conditions M G MSSM+RH RGEs soft SUSY breaking params at M G M Ri integrate out RH textures entering the Yukawa s at M G right handed neutrino masses M Ri define see saw scale MSSM RGEs term and tan at the EW scale Compute observables enter EWSB EW scale integrate out SUSY SM RGEs

A closer look to the strategy We test the model, through the following observables O i : EW obs. quark masses lepton masses CKM & PMNS M W M Z G F e.m. s M Z M h 0 M t m b m b m c m c m s 2GeV m d 2 GeV m u 2 GeV M M M e 2 m 31 2 m 21 V us V ub V cb sin 2 sin 2 2 12 sin 2 2 23 sin 2 2 13

A closer look to the strategy We test the model, through the following observables O i : EW obs. quark masses lepton masses CKM & PMNS FCNCs M W M Z G F e.m. s M Z M h 0 M t m b m b m c m c m s 2GeV m d 2 GeV m u 2 GeV M M M e 2 m 31 2 m 21 V us V ub V cb sin 2 sin 2 2 12 sin 2 2 23 K BR [ B s + - ] BR [ B X s ] BR [ B X s l + l - ] BR [ B u ] M s / M d sin 2 2 13 These observables O i enter a 2 function, defined as 2 [ model pars] i=1 N obs f i [model pars] O i 2 i 2 exp i 2 theo f i : model prediction for O i The 2 function is then minimized upon variation of the model parameters.

Detailed chart of the fitting procedure scale M G Set initial conditions: {Y s, soft SUSY pars, i, M Ri } Variation of: textures soft SUSY pars [all but m Hu, m Hd ] MSSM+RH RGEs M G, G, 3 M Ri Integrate out Ri MSSM RGEs M Z Get all MSSM pars: {Y s, soft SUSY pars, i, M } Compute: SUSY spectrum EWSB conditions [including one loop corr. to masses and mixings] SM RGEs. Variation of: m Hu, m Hd,, tan [obtain correct EWSB] m b Compute: FCNC observables Evaluate 2 function

FCNCs considered in the analysis: Main features The DR model is characterized by tan50 because of SO(10). Hence all the FCNC observables need be computed in the MSSM at large tan.

FCNCs considered in the analysis: Main features The DR model is characterized by tan50 because of SO(10). Hence all the FCNC observables need be computed in the MSSM at large tan. BR [ B s + - ] For large tan (and sizable A t ), dominated by double penguins with neutral Higgses Enhancement going as: BR [ B s + - ] A t 2 tan 6 M A 4 (Old) upper bound from CDF BR [ B s + - ] exp 1.0 10 7 M A > 450 GeV Generic bound valid for all the heavy Higgs masses

BR [ B X s ] exp BR [ B X s ] E 1.6GeV SM BR [ B X s ] E 1.6GeV = 3.55±0.26 10 4 = 3.15±0.23 10 4 HFAG average Misiak et al., PRL 07 The theory prediction for b s must be SM like

BR [ B X s ] exp BR [ B X s ] E 1.6GeV SM BR [ B X s ] E 1.6GeV = 3.55±0.26 10 4 = 3.15±0.23 10 4 HFAG average Misiak et al., PRL 07 The theory prediction for b s must be SM like Very rough b s formula [ B X s ] G 2 F e.m. 32 V * 4 ts V tb 2 m b5 C eff 7 b 2.... Subleading corr s & contrib s negligible in the DR model with C eff eff 7 b = C 7, SM b C 7, DR b In order to end up with a SM like prediction, one must have either or eff C 7, DR b C 7, SM b eff C 7, DR b 2 C 7,SM b Notes This solution is highly conspired SUSY is here not a correction to the SM result The theoretical control on the SUSY part should then be at least as good as in the SM In absence of it, we find e.g. a strong sensitivity to the SUSY matching scale

BR [ B X s ] [continued] Within the DR model, dominant NP contributions are from charginos and Higgses. Gluinos play a minor role. C 7, DR b C 7 + b C 7 H + b small

BR [ B X s ] [continued] Within the DR model, dominant NP contributions are from charginos and Higgses. Gluinos play a minor role. C 7, DR b C 7 + b C 7 H + b small Main features: Higgs contrib s add up to the SM ones. However, Higgs contrib s are made small by the lower bound on M A placed by B s + - Contributions from charginos are the dominant ones, and behave like SM H + At 0 A t 0 C 7 + A t tan signc 7 SM

BR [ B X s l + l - ] At variance with b s, the decay b s l + l is sensitive to the sign of C 7 eff s= p + p - 2 /m b 2 d [ B X s l + l - ] d s 12 s C eff 9 s 2 C eff 10 s 2 4 12 s C eff 7 2 12C 7 eff Re C 9 eff s

BR [ B X s l + l - ] At variance with b s, the decay b s l + l is sensitive to the sign of C 7 eff s= p + p - 2 /m b 2 d [ B X s l + l - ] d s 12 s C eff 9 s 2 C eff 10 s 2 4 12 s C eff 7 2 12C 7 eff Re C 9 eff s BaBar & Belle average SM C 7 eff C 7 eff 10 6 BR[ B X s l + l - low s ] exp = 1.60±0.51 1.57±0.16 3.30±0.25 Gambino, Haisch, Misiak, PRL 05 The sign of C 7 eff is the same as in the SM, unless C 9 and C 10 are significantly affected by NP

Some reference fits univ. scalar term m 16 = 4 TeV, univ. trilinear A 0 2 m 16, > 0 To fit m b, a cancellation between these terms is required: A t m g Helped by A0 2 m 16 The solution A 0 2 m 16 helps 3 rd generation Yukawa unification [ 0 m b M Z = m 1 tan 2 s b 3 m g 2 t 2 m b 16 2 A t m t 2 m b log] The solution A 0 2 m 16 leads also to inverted mass hierarchy: m t m b Blazek, Dermisek, Raby, PRL & PRD ( 02)

Some reference fits: continued m 16 = 4 TeV, < > 0 A 0 2 m 16 Easy to fit m b, since in this case these two terms are both small In this case one has NO inverted mass hierarchy: One typically finds solutions with both heavy, and A t small m t, m b [ 0 m b M Z = m 1 tan 2 s b 3 m g 2 t 2 m b 16 2 A t m t 2 m b log]

Some reference fits: continued m 16 = 4 TeV, < > 0 A 0 2 m 16 Easy to fit m b, since in this case these two terms are both small In this case one has NO inverted mass hierarchy: One typically finds solutions with both heavy, and A t small m t, m b m b M Z = m b 0[ 1 tan 2 s 3 m g 2 t 2 m b 16 2 A t m t 2 m b log] Now b s is OK But typical masses are m t 2.6 TeV M A 1.5 TeV In this case EWSB finds generically very large masses for heavy Higgses

The Big Picture Fit strategy: choose m 16 [4,10] TeV, then let the fit determine the other param s. Benchmark Cases Dictionary m 16 = univ. soft scalar term A 0 = univ. trilinear term Fit Details Remarks sign(c 7 ) [GeV] b s b s l + l m t m 16 = 4 TeV, > 0 A 0 2 m 16 Inverted mass hierarchy (IMH) C 7 C 7 SM 400 OK 3 too large [Gambino et al.] m 16 = 4 TeV, > 0 Like, but C A 0 2 m 16 forcing C 7 > 0 7 0+ 600 5 too low OK m 16 = 6 TeV, > 0 Like, but try C A 0 2 m 16 increase m 7 > 0 1200 2.3 too low OK 16

BR [ B u ]: a possible additional problem The DR model fits successfully quark & lepton masses and mixings. However, among the predictions one gets: V DR ub 3.26 10 3 which is somehow too small The B u mode is a way to display the problem

BR [ B u ]: a possible additional problem The DR model fits successfully quark & lepton masses and mixings. However, among the predictions one gets: V DR ub 3.26 10 3 In the SM which is somehow too small The B u mode is a way to display the problem The B u decay is affected by a large error due to the poor knowledge of F B + F B d One considers one of the Ikado ratios BR [ B u ] SM SM B + M d, s with reduced hadronic uncertainties [mostly ] B Bd Correspondingly, one predicts 10 4 BR B u SM = 0.87±0.11, with V ub UTfit =3.6615 10 3 1.31±0.23, with V ub incl =4.4933 10 3 versus 10 4 BR B u exp = 1.31±0.48 Belle & BaBar average

BR [ B u ]: a possible additional problem The DR model fits successfully quark & lepton masses and mixings. However, among the predictions one gets: V DR ub 3.26 10 3 In the SM which is somehow too small The B u mode is a way to display the problem The B u decay is affected by a large error due to the poor knowledge of F B + F B d One considers one of the Ikado ratios BR [ B u ] SM SM B + M d, s with reduced hadronic uncertainties [mostly ] B Bd Correspondingly, one predicts 10 4 BR B u SM = 0.87±0.11, with V ub UTfit =3.6615 10 3 1.31±0.23, with V ub incl =4.4933 10 3 In the DR model versus 10 4 BR B u exp = 1.31±0.48 Belle & BaBar average suppression: Hou; Akeroyd+Recksiegel; Isidori+Paradisi BR B u DR BR B u SM [ = 1 m 2 + B 2 m + H tan 2 1 0 tan ]2 V DR ub SM 2 V ub further suppression Typical prediction: 10 4 BR B u DR 0.6

Conclusions The DR model, an SO(10) SUSY GUT with a D 3 family symmetry, provides detailed, testable predictions for the low energy MSSM. It successfully describes quark and lepton masses and mixings. The DR model is however challenged when probed against the simultaneous description of quark FCNC data. This test is accomplished through a global fit, with FCNCs appearing directly in the 2 function. FCNCs offer a unique probe to the SUSY mass spectrum predicted by the model. They turn out into a discriminating test for the model itself. Outlook The most evident FCNC problems should actually already arise when just considering 3 rd generation new physics.