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Quark masses from Gaugino Condensation in String Theories

Quark masses from Gaugino Condensation in String Theories. Talk at Corfu Summer Institute, Theory-Cosmology-Phenomenology, September 8, 2009. Christos Kokorelis. Based on : C.K, 0812.4804[hep-th] ; C.K , V.E.Mayes, D,V. Nanopoulos, 0907.4028  [hep-th ]. Basic Idea.

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Quark masses from Gaugino Condensation in String Theories

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  1. Quark masses from Gaugino Condensation in String Theories Talk at Corfu Summer Institute, Theory-Cosmology-Phenomenology, September 8, 2009 Christos Kokorelis Based on : C.K, 0812.4804[hep-th]; C.K, V.E.Mayes, D,V. Nanopoulos, 0907.4028 [hep-th]

  2. Basic Idea • Generate masses for all generations, reproduce hierarchical Q+L masses • Examples: Toroidal orientifolds IIA/IIB: 1 family get a mass, 2 massless one’s ≈ factorization of Yukawa’s ≈ Non-zero Iab in 2 different tori [Cremades, Ibanez, Marchesano] Additional Higgs evade the problem for specific values of the moduli [Cvetic, Langacker, Shiu, Chen, Li, Mayes, Nanopoulos] in Pati-Salam GUTS SU(4)c x SU(2)L x SU(2)R like D-brane string models

  3. Basic Idea continued • However, e.g. in SU(5)/flipped SU(5) GUTS missing up-quark masses do not get generated perturbatively! • Possible Non-perturbative solutions » D-brane Instantons [Blumenhagen, Cvetic, Lust, Richter, Weigand] • Perturbative Solution » Gaugino Condensates [ C.K, Mayes, Nanopoulos]

  4. OutLine • Part I – Missing mass terms for SU(5) GUTS • Part II – Perturbative solution to missing quark masses in SU(5), flipped SU(5) orientifolds • Part III – Instanton solutions inspired from the perturbative solution • OutLook

  5. PART I Missing mass terms for SU(5) Orientifold GUTS

  6. Missing mass terms for u-quarks in orientifolds • SU(5)/FSU(5) GUTS in (IIA, IIB)/ΩR orientifolds are missing up/down quark masses ~ 10 10 5 coupling does not exist from U(1) charge conservation • A typical SU(5)/FSU(5) U/D quark mass term : 10 (2, 0) 10 (2, 0) 5 H(1, 1)

  7. A typical SU(5) GUT Bachas, Blumenhagen, Kors, Lust, Ott, Ellis, Kanti, Nanopoulos, Axenides, C.K, Floratos, Bianchi, Weigand

  8. Historical facts SU(5) GUT Flipped SU(5) GUT Yukawa mass terms SU(5) 10 10 5H = εijklm 10i 10j 5Hm = u c3 u3 <h0> Yukawa massterms FSU(5) 10 10 5H = εijklm 10i 10j 5Hm = dc3 d3 <h0>

  9. Part II Perturbative solution to missing quark masses in SU(5), flipped SU(5) orientifolds

  10. The coupling “exists” from charge and gauge invariance gets charged ~SU(5) x U(1) The or ~ SU(5) x Sp(2) x..

  11. The condenses • In the case of chiral symmetry breaking as SU(3) symmetry is not spontaneously broken we take the vacuum to be SU(3) symmetric • <0|QL UR|0>= μ3 ~ (1,2)-1/2 Ibanez, Marchesano,Rabadan

  12. SU(5)/FSU(5) • In our case, the “condensate” ~(1,2) and provides masses to U/D quarks • When it is charged under SU(5) x Sp(2) Or (FSU(5) x Sp(2)) :

  13. Sp(2) strongly coupled

  14. b<0 , ~ 0 1016 < Ms < 1018

  15. Conclussions/Outlook We have presented evidence for the existence of condensates able to give masses to the missing up/down quark masses in SU(5)/FSU(5) GUTS in toroidal orientifolds The mechanism may be applied to F-theory constructions

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