B. Bajc, The Still Available Parameter Space of the Minimal Supersymmetric SU(5)

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Balkan Workshop BW2013
Beyond the Standard Models
25 – 29 April, 2013, Vrnjačka Banja, Serbia

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B. Bajc, The Still Available Parameter Space of the Minimal Supersymmetric SU(5)

  1. 1. Borut BajcThe Still Available ParameterSpace of the MinimalSupersymmetric SU(5)Borut BajcJ. Stefan Institute, Ljubljana, SloveniaBB, Stephane Lavignac and Timon Mede, work in progressBW13, Vrnjaˇcka Banja, Serbia 1
  2. 2. Borut BajcOutline• The minimal susy SU(5)• RGEs and proton decay• Fermion mass constraint• Higgs mass• Electroweak symmetry breaking scale• An upper limit• More ambitious? Neutrino mass and dark matter• ConclusionsBW13, Vrnjaˇcka Banja, Serbia 2
  3. 3. Borut BajcThe minimal susy SU(5)It is made of• 3 generations of matter in ¯5i + 10i• Higgses in 24H and 5H + ¯5H• gauge superfield in 24VFurthermore we will assume• renormalizability• susy broken above MGUT , soft terms SU(5) symmetric• vacuum (global) stabilityBW13, Vrnjaˇcka Banja, Serbia 3
  4. 4. Borut BajcRGEs and proton decayFrom RGE’s and known exp values of αi(MZ):mT ≈ 1015GeVm3m85/2msusy1 TeV5/6m3,8 . . . masses of weak triplet and color octet in 24H.In minimal renormalizable susy SU(5):m3 = m8 → mT ≈ 1015GeVmsusy1 TeV5/6In low-energy susy T too light, mediates too fast proton decay!WT = Y ij10 QiQj + uci ecj T + Y ij5 uci dcj + QiLj¯TBW13, Vrnjaˇcka Banja, Serbia 4
  5. 5. Borut Bajcτd=5p ≈ 4.1033yrs4tan β2˜m21,2m ˜w 10 TeV2mT1017 GeV2Possible solution split supersymmetry: m ˜w ˜m1,2This same solution kills also all needed corrections to fermionmasses (will see later)Increase msusy = ˜m1,2 ∼> m ˜w a bit (mT ∝ m5/6susy) !For example this works for msusy ≈ 20 TeV ≈ 3 m ˜wNotice that τd=5∝ m22/5T ≈ m4T similar to τd=6∝ m4VBW13, Vrnjaˇcka Banja, Serbia 5
  6. 6. Borut BajcFermion mass constraintIn minimal renormalizable susy SU(5) most general YukawasWSU(5)Y = Y ij10 10i10j5H + Y ij5¯5i10j¯5Hi, j = 1, . . . 3 (generation indices)MSSM Yukawas parametrized byWMSSMY = Y ijU QiucjHu + Y ijD QidcjHd + Y ijE LecHdBW13, Vrnjaˇcka Banja, Serbia 6
  7. 7. Borut BajcEasy to derive in our GUT thatMU = MTU (∝ Y10)BAD → MD = MTE (∝ Y5)3rdgeneration (mb = mτ at GUT scale) OK1stand 2ndgeneration bad after RGE’s from GUT scale to EWscaleBW13, Vrnjaˇcka Banja, Serbia 7
  8. 8. Borut BajcMore precisely at MZ (tan β ≈ 3):δmd/md ≈ 2δms/ms ≈ −0.75δmb/mb ≈ 0.1In this minimal renormalizable model• no extra rep’s like for ex. 45H, extra vector like pairs• no non-renormalizable terms 101,2¯51,2¯5H24H/Λthe only way to improve → susy threshold correctionsBW13, Vrnjaˇcka Banja, Serbia 8
  9. 9. Borut BajcGluino exchange dominates (maximized for common soft mass˜m = m˜g ≈ ˜m1,2)δmDi = −αs3πv˜m(ADi cos β − µyDi sin β)Vacuum stability:ADi ≤ yDi√3 m2Hd+ 2 ˜m2 1/2Only possibility in mHd>> ˜mi:δmDimDi≈αs3πµ tan β − aDi√3mHd˜mwith |aDi | ≤ 1BW13, Vrnjaˇcka Banja, Serbia 9
  10. 10. Borut Bajcµ term cannot dominate (different generations have opposite sign)mHd/ ˜m1,2 ≈ O(100) must overcome loop factorBW13, Vrnjaˇcka Banja, Serbia 10
  11. 11. Borut BajcHiggs massm2h = m2tree + m2log + m2mixm2tree = m2Z cos2(2β)m2log =3 sin2βy2t m2t4π2logm˜t1m˜t2m2tm2mix =3 sin2βy2t m2t4π2f Xt, m˜t2/m˜t1For any choice of m˜t1,2 ∼> 1 TeV (both from ( ˜m10)3 at GUT scale)the Higgs mass can always be mh ≈ 125 GeV for someXt ≡ At sin β − µyt cos βBW13, Vrnjaˇcka Banja, Serbia 11
  12. 12. Borut BajcVery preliminary:tan β ≈ 2, sign(µ) > 0, At = 00 200 400 600 800 100002004006008001000m103GUTTeVmHGUTTeVmh mhexpmHu2MZ 0BW13, Vrnjaˇcka Banja, Serbia 12
  13. 13. Borut BajcElectroweak symmetry breaking scaleTo minimize the 1-loop effect one solves the RG improved tree levelHiggs potential at the scaleMEW SB = m˜t1(MEW SB)m˜t2(MEW SB)At this scale (neglecting small MZ)µ2=m2Hd− m2Hutan2βtan2β − 1and similarly for Bµ.In our case (large mHd= mHu≈ ( ˜m10)3)→ µ ≈ O (few hundreds) TeV (modulo cancellations)BW13, Vrnjaˇcka Banja, Serbia 13
  14. 14. Borut BajcAn upper limitAt GUT scaleWH = ¯5H (η 24H + m5) 5H + m24 242H + λ 243HSU(5) → SU(3)C × SU(2)L × U(1)Y24H = v242 0 0 0 00 2 0 0 00 0 2 0 00 0 0 −3 00 0 0 0 −3BW13, Vrnjaˇcka Banja, Serbia 14
  15. 15. Borut BajcDoublet-triplet splitting fine-tuning:m5 = η v24Mass spectrum:mT = η v24mΣ = m3 = m8 = λ v24mX = g5 v24It follows:mT ∼< mV (perturbativity)mΣ could be also much smaller in principle (if λ 1)BW13, Vrnjaˇcka Banja, Serbia 15
  16. 16. Borut BajcFrom RGE:mΣ1016 GeV3 mV1016 GeV6=103GeVmsusy2Since mT ∼< mV and proton decay needs as large mT as possiblemT ≈ 1015GeVmsusy1 TeV5/6→ larger msusy allowed by smaller mΣ (i.e. small coupling λ)Maximum msusy reached when mT ≈ mV ≈ MP lanck→ maximum µmax≈ mmaxsusy ≈ 104TeVFor higher msusy SU(5) becomes non-perturbative (η ∼> 1)BW13, Vrnjaˇcka Banja, Serbia 16
  17. 17. Borut BajcMore ambitious? Neutrino mass and darkmatterAlthough not really necessary to explain (different sector), whatabout neutrinos and dark matter?In this minimal renormalizable model• no extra representations 1F , 15H, 24F (type I, II, III resp.)Without adding anything the only source of ν mass could beR-parity violating couplingsBW13, Vrnjaˇcka Banja, Serbia 17
  18. 18. Borut Bajcν massSU(5) relations→ λ ≈ λ ≈ λ →• either in conflict with d = 4 p-decay τ ≈ 1/(λ λ )2• or not enough for neutrino mass mν ∝ λ2, λ 2Only possibility bilinear R-parity violation µ LHudark matterneutralino decays too fast → only dark matter candidate: gravitinodue to diffuse photon background constraintsmgravitino ∼< O(1) GeVBW13, Vrnjaˇcka Banja, Serbia 18
  19. 19. Borut BajcConclusionsThe minimal renormalizable susy SU(5) (probably) still alive (oralmost alive) providing• p decay → small tan β ≈ O(2 − 5)• correct md,s → m˜g ≈ ˜md,s ∼< O(10) TeV at MZ→ ( ˜m10,5)1,2 ≈ O(10) TeV at MGUT• SU(5) relations at low scale → m ˜w ≈ m˜g/3 at MZ• vacuum stability + Higgs mass →mHd= mHu≈ ( ˜m10)3 ∼> O(100) TeV at MGUT• ( ˜m5)3(MGUT ) constrained only by stability (not too small)• Higgsino mass µ ≈ O(10 − 100) TeVBW13, Vrnjaˇcka Banja, Serbia 19

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