Obmedzenia MSSM z SO10 zjednotenej terie a implikcia

Obmedzenia MSSM z SO(10) zjednotenej teórie a implikácia pre kolajdre Tomáš Blažek Univerzita Komenského, Bratislava SK-CZ Atlas workshop, Košice, 5. marec 2009

Contents ●Why SO(10) ●Main Experimental Constraints and Their Effects ●Examples of Best Fits from the Global Top-Down Analysis ●Implications for SUSY searches

Well-Known SO(10) Virtues ●SM fermionic multiplets of one family (15 Weyl fermions) × 3 colours + fit nicely into the 16 of SO(10): the 16 is a chiral rep -> mass term M 16 16 is not allowed by S 0(10) gauge symmetry -> the 16 is massless if SO(10) is exact anomaly canceled automatically, since SO(10) is anomaly free, unlike SU(3)c×SU(2)L×U(1)Y or SU(5) the extra 16 th state right-handed neutrino quantum numbers, not protected against geting massive below MGUT setting stage for the L number violation and see-saw mechanism after EWSB ● Similarly the two Higgs doublets fit into a massless 10 ● Gauge couplings unify

Trojuholníková anomália kalibračná symetria SM je pokazená (narušená) procesmi, ktoré obsahujú diagram V ρb Vμa + V ρb Vμa Vσc Symetriu možno zachrániť iba ak Vσc Vμa = Bμ, Wμa , alebo Gμa ∑ Tr{ Ta. Tb. Tc} + Tr{ Ta. Tc. Tb} = 0 fermióny Príklad: nech sú všetky tri bozóny hypernábojové B-éčka. Potom Ta = yf 1. Tieto komutujú, ľavá strana je preto ∑ 2(yf)3 fermióny Hodnoty yf =2(Q-T 3) pre ec, L, dc, uc, Q sú 2, -1, 2/3, -4/3, 1/3. Suma z (yf)3 je 23+2(-1)3+3(2/3)3+3(-4/3)3+2· 3(1/3)3 = 0

Veľké zjednotenie v Minimálnom supersymetrickom štandardnom modeli: zbiehanie väzbových konštánt (nábojov) pri veľkej prenesenej hybnosti Tieto hodnoty α 1, α 2 a α 3≡αs sú vypočítané z experimentálne nameraných veličín pri energií 100 Ge. V αS αS(MZ)=0. 118 α 2(MZ)=0. 036 α 1(MZ)=0. 010 α (|q|→ 0) = 1/137 = 0. 0073 α (MZ) = 1/128 = 0. 0078 α α 2 α 1 100 Ge. V V poruchovej teórii vieme z kvantových slučkových procesov vypočítať sklon kriviek α 1, α 2 a α 3. Sklon závisí od častíc v slučkách: ak vynecháme SUSY častice, krivky sa nepretnú. 1016 Ge. V |q| q = prenesená hybnosť

Well-Known SO(10) Virtues cont’d ●The 16 3 10 163 operator gives order one yukawa coupling: get a heavy top quark EW symmetry broken radiatively (for universal scalar masses) prediction yt ≈ yb ≈ ytau ≈ yνtau includes successful idea of b-tau unification ● The see-saw mechanism then predicts about the right hierarchy between the charged fermions and much lighter neutrinos ●. . . and there is more that is less well-known and is coming in this talk

SO(10) Troubles ●proton decaying too rarely (unobserved, in fact) . . . dim 5 operator due to the coloured triplet higgs vs. the sign of the MGUT correction to αs ●The 16 3 10 163 operator gives order one yukawa coupling: Prediction y t ≈ yb implies large amount of fine tuning at EWSB scale: must get vd≈3 Ge. V, as mt(MZ)/mb(MZ)≈50, i. e. , need large tanβ Moreover, scalar higgs masses run very steep – Fig. ● UV completion ? Since mc/mt « ms/mb, mmu/mtau and also mu/mc « md/ms, different higher-dimensional operators generate fermion masses of the two lighter generations

Running MSSM mass parameters

SO(10) studies ●Approach 1: study a particular model, which can be more or less complete, generating higher dimensional operators, and filling in the 3× 3 yukawa matrices at MGUT by reading out the individual entries from the Frogatt-Nielsen diagrams OR ● Approach 2: be less specific and study „SO(10)-like models“ in an MSSM analysis below MGUT which just takes into account the large yukawa couplings of the third generation

SO(10) studies Approach 1: Implemented in and a number of follow-up papers. Strategy: Do pure top-down global analysis evaluating χ2 from the comparison with the available low energy data. See Table. Important details: Include GUT threshold correction to αs Gravity mediated SUSY breaking with non-universal scalar higgs masses Face fine tuning with an embedded minimisation procedure, separately minimising χ2 using the non-universal higgs masses for each set of the GUT parameters

Table of Low Energy Observables

Table of Low Energy Observables MSSM analysis only

BR(b sγ) Constraint Effective Hamiltonian: ~ where η = αs(MZ) / αs(μ) Contributions to C 7(MZ): chargino diagram enhanced by tanβ picks up the sign of the μ parameter C 7 or T. B. + S. Raby: b --> s gamma with large tan. BETA. in a MSSM analysis constrained by a realistic SO(10) model Phys Rev D, 59 (1999) 095002 SUSY CKM contrib non-negligible

mb(mb) Constraint Large SUSY Threshold Contributions to mb(MZ): both diagrams enhanced by tanβ and proportional to μ must be of opposite signs: need negative At still potentially too large: pushes μ to low values. . . get low mass higgsino-like charginos and neutralinos for the same reason the global analysis best fits prefer heavy gluino. That means rather large M 1/2 which through the RGEs feeds into large scalar masses.

Constraint from the muon anomalous magn moment SUSY Contributions to aμ: no freedom to choose the sign: could have gone the opposite way than the BNL measurement, but it has not the low value of μ and heavy scalar masses tend to prefer lesser contribution than what is measured in the e+e- exp. If the result stays, it could be a hint for a non-universal SUSY breaking mechanism. both diagrams enhanced by tanβ and proportional to μ, chargino contribution typically greater T. B. + S. F. King : Muon anomalous magnetic moment and. TAU. -->. MU. GAMMA. in a realistic string-inspired model of neutrino masses Phys. Lett B. 518, (2001), 109

Constraint from non-observation of Bs to μ+μThere are SUSY contributions to this decay amplitude that are enhanced by (tanβ)3. These contributions are mediated by the pseudoscalar higgs exchange -> sensitivity to its mass: need pseudoscalar higgs mass typically greater than 300 Ge. V T. B. , S. F. King, J. Parry: Implications of B_s -->. MU. +. MU. - in SO(10)-like models Physics Letters B. - Vol. 589, (2004), 39

Examples of Global Analysis Best Fits T. B. , R. Dermíšek, S. Raby: Predictions for Higgs and supersymmetry spectra from SO(10)Yukawa unification with. MU. > 0 Physical Review Letters. - Vol. 88, (2002), 111804

Examples of Global Analysis Best Fits

Examples of Global Analysis Best Fits

Another Example of Global Analysis Best Fits

Implications from the SO(10)-like models best fits ●the lightest CP even higgs very close to the current limit mh ≈ 115 -120 Ge. V ●the rest of the higgs spectrum above ≈ 250 -300 Ge. V ●light higgsino-like charginos and neutralinos close to 100 Ge. V, the LSP is most of the times a higgsino-like neutralino ●possibly a light stop and stau (and maybe sbottom) due to the large left-right splittings ●the rest of the MSSM sparticle spectrum at/above the Te. V scale ●CDM is formed by a mixture of bino/higgsino-like neutralino LSP and should be observed in the near future, or the LSP is higgsino-like LSP that annihilates too rapidly to form the dominant CDM component