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Weak Mixing Angle and Higgs Mass in Gauge-Higgs Unification Models with Brane Kinetic Terms

Weak Mixing Angle and Higgs Mass in Gauge-Higgs Unification Models with Brane Kinetic Terms. 2012. 2. 21 @YongPyong2012 Jubin Park. Collaboration with Prof. Sin Kyu Kang and Prof. We-Fu Chang. arXiv:1111.5422 [ hep -ph] submitted to JHEP . Contents.

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Weak Mixing Angle and Higgs Mass in Gauge-Higgs Unification Models with Brane Kinetic Terms

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  1. Weak Mixing Angle andHiggs Mass in Gauge-Higgs Unification Models withBrane Kinetic Terms 2012. 2. 21 @YongPyong2012Jubin Park • Collaboration with Prof. Sin Kyu Kang and Prof. We-Fu Chang arXiv:1111.5422[hep-ph] submitted to JHEP

  2. Contents • The Standard Model(SM) and Hierarchy problem – Higgs mass • Solutions about the Hierarchy problem • Brief introduction to Gauge Higgs unification(GHU) • A toy example – 5D SU(3) GHU model on S1/Z2. • Problems in the toy model • Goals • Possible answers for these problems • Phenomenologically viable GHU models • Higgs potential in 6D • Numerical results. • Summary Jubin Park @YongPyong2012

  3. Standard Model A fundamental scalar field (Higgs) is introduced to explain spontaneous symmetry breaking of gauge group of electroweak symmetry. The same field is also responsible for masses of all matter fields through Yukawa interactions. Radial modes ~ Massive Jubin Park @YongPyong2012

  4. Moreover, The Higgs potential is written by HAND. Unknown origin Without symmetry protection, So the Higgs sector is very sensitive to the UV scale of the theory Hierarchy Problem Jubin Park @YongPyong2012

  5. For example : Significant Higgs loop corrections in the standard Model h h top W,Z h h h h h Jubin Park @YongPyong2012

  6. ‘Little’(low mass) Higgs and Fine Tuning Cutoff scale Λ = 10TeV Tree = Gauge Higgs Needed Tree Contribution Higgs mass Top Jubin Park @YongPyong2012

  7. So we need incredible fine tuning to explain why the Higgs mass (~Weak scale order) is so much lighter than other mass parameter scales (Planck, GUT or Heavy Majorana scale) when we take the Cutoff scale Λ as P or G or H. This is not NATURAL. (NATURALNESS problem) In order to solve the hierarchy problem naturally (without fine tuning), we can expect that there exist at least the new physics beyond the Standard Model if we accept the big-desert between weak energy scale and P or G or H. . LEP and Tevatron have probed directly up to a few hundred GeV, and indirectly between 1 and 10 TeV through the precision measurements. Jubin Park @YongPyong2012

  8. Energy scales 10 TeV 1 TeV 200 MeV 5 GeV 80 GeV 172 GeV Weak scale B physics scale Theory cutoff scale Hadronization scale Compactification scale 10 ^19 GeV 10 ^17 GeV Planck scale- strong gravity Heavy right-handed Majorana for Seesaw Mechanism GUT- coupling unification Jubin Park @YongPyong2012

  9. One well-known solution • Supersymmetry h h top Cancellation condition: stop h h Jubin Park @YongPyong2012

  10. Alternative models I • Composite Higgs - Little Higgs (from UV completion) - Tecnicolor (new Strong-type interation) • Extra dimension- Large extra dimension (ADD) - Universal extra dimension (UED)- Small extra dimension - With the warped spacetime (RS) Jubin Park @YongPyong2012

  11. Alternative models II • - Higgsless no zero modes SM gauge bosons = First excited modes • - Gauge Higgs Unification(GHU) Jubin Park @YongPyong2012

  12. Brief introduction to GHU • - Gauge Higgs Unification SM gauge bosons = Zero modes Needs Higgs mechanism in order to break the EWSB. but there is no Higgs potential in 5D. or Hosotani mechanism. too low Higgs mass (or top quark mass) with VEV which is proportional to 1/R. Jubin Park @YongPyong2012

  13. Unification of gravity (s=2) & electromagnetic (s=1) Kaluza-Klein gravity theory Unified theory of gauge (s=1) & Higgs (s=0) Gauge-Higgs unification The pioneer works of GHU : ・N.S. Manton, Nucl. Phys. 58(’79)141. ・Y.Hosotani, Phys. Lett. B126 (‘83) 309 ``Hosotani mechanism” Higher dimensional Gauge Theory extra dimension 5D gauge field Higgs 4D gauge-field Zero mode 4D space-time Jubin Park @YongPyong2012

  14. Kaluza-Klein gravity theory Gauge-Higgs unification Jubin Park @YongPyong2012

  15. Advantage of the GHU ・ The quantum correction to mH is finite because of the higher dimensional gauge symmetry.An interesting solution to solve the hierarchy problem without thesupersymmetry. In addition the scenario may also shed some light on the arbitrariness problem in the interactions of Higgs. Jubin Park @YongPyong2012

  16. Toy example – 5D SU(3) ORBIFOLD BOUNDARY CONDITIONS Pure higher-dimensional Gauge theory Jubin Park @YongPyong2012

  17. We only focus on the zero modes, After we integrate out fifth dimension, Volume factor And rescale the gauge field, Relation between 4d and 5d gauge couplings Jubin Park @YongPyong2012

  18. Adding to brane kinetic terms SU(2) U(1) We can easily understand that these terms can give a modification to the gauge couplings without big change of given models. From the effective Lagrangian, we can expect this relation Similarly, for the U(1) coupling Jubin Park @YongPyong2012

  19. Final 4D effective Lagrangian No mass term of the Higgs because of higher dimensional gauge symmetry Weak mixing angle This number is completely fixed by the analysis of structure constants of given Lie group (or Lie algebra) regardless of volume factor Z if there are no brane kinetic terms in given models. Jubin Park @YongPyong2012

  20. Problems in the toy model • Wrong weak mixing angle( , , ) • No Higgs potential (to trigger the EWSB). - may generate too low Higgs mass (or top quark) even if we use quantum corrections to make its potential. • Realistic construction of Yukawa couplings Jubin Park @YongPyong2012

  21. Goals • Stability of the electroweak scale (from the quadratic divergences – Gauge hierarchy problem) • Higgs potential - to trigger the electroweak symmetry breaking • Correct weak mixing Jubin Park @YongPyong2012

  22. Possible answers for these problems • Wrong weak mixing angle- Brane kinetic terms - Violation of Lorentz symmetry ( SO(1,4) -> SO(1,3) ) - Graded Lie algebra (ex. ) - Using a non-simple group. an anomalous additional U(1) (or U(1)s) Abandon the gauge coupling unification scheme . Jubin Park @YongPyong2012

  23. No Higgs potential (to trigger the EWSB). - Using a non-simply connected extra-dimension ( the fluctuation of the AB type phase – loop quantum correction) - Using a 6D (or more) pure gauge theory. - Using a background field like a monopole in extra dimensional space. Jubin Park @YongPyong2012

  24. Phenomenologically viable models Alfredo Arandaand Jose Wudka, PRD 82, 096005 • To find phenomenologically viable models they demand following 4 constraints:(1) three massive gauge bosons W+,W, Z0 at the electroweak scale(2) rho =1 at tree level (3) existence of representations that can contain all Standard Model(SM) particle, especially hyper charge 1/6.(4) correct weak mixing angle. (0) simple group ~ the gauge coupling unification. Jubin Park @YongPyong2012

  25. Possible all groups that satisfy (0), (1), (2), (3) constraints except (4) – weak mixing angle Any GHU model can not explain correct weak mixing angle. Simple rootscor. to SU(2) One cartan generator cor. to U(1) Jubin Park @YongPyong2012

  26. Higgs potential in 6D notations of Lie Algebra SU(2) and U(1) SU(2) generators U(1) generator Commutation relations Orthonormal basis Jubin Park @YongPyong2012

  27. A General form of Zero modes in terms of generators of lie algebra We focus on the mass term, and the mixing angle, From previous toy example, we can easily expectthat our brane kinetic terms can modify the coupling constants, that is, the mixing angle, Jubin Park @YongPyong2012

  28. From experimental value of weak mixing angle, Values of c1and c2 which are consistent with the present experiment value of the weak mixing angle and each group theoretic numerical factor in 6 dimensional SU(3) and E6gauge Higgs unification models on S2/ Z2. Straight, dashed and dotted lines correspond to the compactification scales 5, 10 and 20 TeV, respectively. Jubin Park @YongPyong2012

  29. Higgs potential, Radial modes ~ Massive Nambu-goldstone boson modes ~ Massless (flat direction) Finally, we can get this relation ( with brane Kinetic terms ), We can rewrite the equation with previous relation, Jubin Park @YongPyong2012

  30. Numerical results. 1. Possible gauge groups and Higgs mass under presence of Brane kinetic terms All masses are smaller than 114.4 GeV. Jubin Park @YongPyong2012

  31. 2. The Higgs mass of each group as a function of c2 on the compactification scale Mc=1, 5 and 10 TeV| in the 6 dimensional GHU model on S2/ Z2. Jubin Park @YongPyong2012

  32. Jubin Park @YongPyong2012

  33. 3. The Higgs mass of each groupas a function of c2 On the compactification scale Mc=1, 5 and 10 TeV in the 6 dimensional GHU model on T2/ Z3. Jubin Park @YongPyong2012

  34. Jubin Park @YongPyong2012

  35. 4. Volume factors and slopes of Several examples in 6D, 7d and 8d Jubin Park @YongPyong2012

  36. 3. The Higgs mass of each groupas a function of c2 On the compactification scale Mc=1, 5 and 10 TeV in the 7 dimensional model on S3/ Z2(top) and 8 dimensionalT4/z2(bottom) . Jubin Park @YongPyong2012

  37. Summary Jubin Park @YongPyong2012

  38. Jubin Park @YongPyong2012

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