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 S0(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 16th state

● Similarly the two Higgs doublets fit into a massless 10

● Gauge couplings unify

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

Trojuholníková anomália

kalibračná symetria SM je pokazená (narušená) procesmi, ktoré obsahujú diagram

Vμa

Vρb

Vσc

Vμa

Vρb

Vσc

+

Symetriu možno zachrániť iba ak

∑ Tr{ TaTbTc} + Tr{ TaTcTb} = 0 fermióny

Vμa = Bμ, Wμ

a, alebo Gμ

a

Príklad: nech sú všetky tri bozóny hypernábojové B-éčka. Potom Ta = yf1.Tieto komutujú, ľavá strana je preto ∑ 2(yf)3 fermióny

Hodnoty yf =2(Q-T3) 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

α2

α1

αS

100 GeV 1016 GeV |q|

q = prenesená hybnosť

α

Veľké zjednotenie v Minimálnom supersymetrickom štandardnom modeli:zbiehanie väzbových konštánt (nábojov) pri veľkej prenesenej hybnosti

Tieto hodnoty α1, α2 a α3≡αs

sú vypočítané z experimentálnenameraných veličín pri energií 100 GeV

V poruchovej teórii vieme z kvantových slučkových procesovvypočítať sklon kriviek α1, α2 a α3.Sklon závisí od častíc v slučkách: ak vynecháme SUSY častice, krivky sa nepretnú.

αS(MZ)=0.118

α2(MZ)=0.036

α1(MZ)=0.010

α (|q|→0) = 1/137 = 0.0073

α (MZ) = 1/128 = 0.0078

Well-Known SO(10) Virtues cont’d

●The 163 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 163 10 163 operator gives order one yukawa

coupling:

Prediction yt ≈ yb

implies large amount of fine tuning at EWSB scale: must get vd≈3GeV, as mt(MZ)/mb(MZ)≈50,

i.e., need large tanβ Moreover, scalar higgs masses run very steep –

Fig. 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

●UV completion ?

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

●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

OR

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 massesFace 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 C7(MZ):

chargino diagramenhanced by tanβ

picks up the sign of the μ parameter

SUSY CKM contribnon-negligible

C7

orT.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

mb(mb) Constraint

Large SUSY Threshold Contributions to mb(MZ):

both diagrams enhanced by tanβ and proportional to μmust be of opposite signs: need negative At

still potentially too large: pushes μ to low values ... get low mass higgsino-like charginos and neutralinosfor the same reason the global analysis best fits prefer heavy gluino. That means rather large M1/2

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+μ-

There 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 GeV

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 GeV

●the rest of the higgs spectrum above ≈ 250-300 GeV

●light higgsino-like charginos and neutralinos close to 100 GeV, 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 TeV 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