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  1. 1. Phenomenology of Supersymmetry in the Minimal Supersymmetric SO(10) Grand Unified Theory Tatsuru Kikuchi (Ritsumeikan University)
  2. 2. Acknowledgment <ul><li>This work is based on the collaboration with my colleagues: </li></ul><ul><li>T. Fukuyama (Ritsumeikan University, Japan ) </li></ul><ul><li>D. Chang (NCTS & NTHU, Taiwan ) </li></ul><ul><li>S. Meljanac ( Rudjer Boskovic Institute, Croatia ) </li></ul><ul><li>A. Ilakovac (Zagreb University, Croatia) </li></ul><ul><li>Y. Koide (Shizuoka University, Japan) </li></ul><ul><li>H. Nishiura (Osaka Institute of Technology, Japan) </li></ul><ul><li>N. Okada (KEK, Japan) </li></ul><ul><li>K. Matsuda (Osaka University, Japan) </li></ul><ul><li>W. Naylor (Ritsumeikan University, Japan) </li></ul><ul><li>T. Osaka (Ritsumeikan University, Japan) </li></ul><ul><li>Y.Y. Keum (Academia Sinica, Taiwan) </li></ul>
  3. 3. This talk is partly based on my seminar given at Zagreb University, Croatia
  4. 4. Outline <ul><li>Introduction </li></ul><ul><li>Motivation </li></ul><ul><ul><li>Gauge hierarchy problem </li></ul></ul><ul><ul><li>Supersymmetry </li></ul></ul><ul><ul><li>Grand unification </li></ul></ul><ul><li>Minimal SO(10) Model and its predictions </li></ul><ul><ul><li>Neutrino Oscillation Data </li></ul></ul><ul><ul><li>Lepton Flavor Violation </li></ul></ul><ul><ul><li>Proton Decay </li></ul></ul><ul><li>Conclusion </li></ul>
  5. 5. New revolutionary era in particle physics from experimental point of view
  6. 6. Large Hadron Collider (LHC) <ul><li>Why we can say that now is so revolutionary era? Because LHC will start in 2007. </li></ul><ul><li>LHC is a proton-proton collider at CERN, Geneva. </li></ul><ul><li>The ring length is 27 km , energy is 14 TeV (total cost is over 300 billion yen). </li></ul><ul><li>It is expected to discover the Higgs boson and supersymmetry . </li></ul>Last Hadron Collider (LHC)
  7. 7. The LHC machine First full LHC cell (~ 120 m long) : 6 dipoles + 4 quadrupoles; successful tests at nominal current (12 kA) More than half of the 1232 dipoles are produced 8.4 Tesla
  8. 8. The last(8-th) Barrel Toroid coil was installed in August 2005.
  9. 9. What kinds of “new” physics are waiting for us?
  10. 10. Standard Model <ul><li>We have discovered all the staff of Standard Model. The exception is the last missing piece, Higgs boson . </li></ul><ul><li>Standard Model can fit all the data at the same time, that is, any consistency check has been passed by for now. </li></ul>
  11. 11. Electroweak precision measurement prefers a light Higgs boson <ul><li>(LEP-1/2+SLD+Tevatron): mH< 186 GeV @95% CL. </li></ul>
  12. 12. Why Beyond the Standard Model <ul><li>Standard Model is so successful, it has been tested by thousands of experiments for more than a decade. </li></ul><ul><li>However, it does not mean that the Standard Model can explain everything. </li></ul><ul><li>It leaves so many great questions unanswered. </li></ul><ul><li> Drive us to go beyond the Standard Model. </li></ul>
  13. 13. Great Questions <ul><li>Vertical questions </li></ul><ul><li>Charge quantization, anomaly cancellation, bizarre hypercharge assignments in the Standard Model </li></ul><ul><li>Why are there three seemingly unrelated forces yet all gauge forces? Is there a unified description of all forces? </li></ul><ul><li>Why is m W <<M Pl ? (Hierarchy Problem) </li></ul><ul><li>Horizontal questions </li></ul><ul><li>Why are there three generations? </li></ul><ul><li>What physics determines the pattern of masses and mixings? </li></ul><ul><li>What is the origin of CP violation? </li></ul>
  14. 14. Quantum numbers in the Standard Model <ul><li>Standard Model is gauge theory. </li></ul><ul><li>The model is constructed by assigning the following quantum numbers by hand . We cannot answer the question why U(1) hypercharges are so bizarre. </li></ul>
  15. 15. Outline <ul><li>Introduction </li></ul><ul><li>Motivation </li></ul><ul><ul><li>Gauge hierarchy problem </li></ul></ul><ul><ul><li>Supersymmetry </li></ul></ul><ul><ul><li>Grand unification </li></ul></ul><ul><li>Minimal SO(10) Model and its predictions </li></ul><ul><ul><li>Neutrino Oscillation Data </li></ul></ul><ul><ul><li>Lepton Flavor Violation </li></ul></ul><ul><ul><li>Proton Decay </li></ul></ul><ul><li>Conclusion </li></ul>
  16. 16. Hierarchy Problem
  17. 17. The Main Obstacle <ul><li>We look for physics beyond the Standard Model that answers these great questions </li></ul><ul><li>By definition, that is physics at shorter distances </li></ul><ul><li>Then the Standard Model must survive down to whatever shorter distance scale </li></ul><ul><li>Hierarchy problem is the main obstacle to do so  We can’t even get started! </li></ul>
  18. 18. Once upon a time, there was a hierarchy problem… <ul><li>At the end of 19 th century: a “crisis” about electron. </li></ul><ul><li>Like charges repel: hard to keep electric charge in a small pack </li></ul><ul><li>Electron is point like, at least smaller than 10 -17 cm </li></ul><ul><li>Need a lot of energy to keep it small. </li></ul><ul><li>Correction: </li></ul><ul><li>Breakdown of the theory of electromagnetism </li></ul><ul><li>⇒ c annot discuss physics below 10 -13 cm </li></ul>
  19. 19. Anti-particle come to rescue by doubling # of particles <ul><li>Electron creates a force to repel itself </li></ul><ul><li>Vacuum bubble of matter anti-matter creation/annihilation </li></ul><ul><li>Electron annihilates the positron in the vacuum </li></ul><ul><li>⇒ Only 10% of mass even for Planck size </li></ul>
  20. 20. Higgs repels itself, too <ul><li>Just like electron repelling itself because of its charge, Higgs boson also repels itself </li></ul><ul><li>Requires a lot of energy to contain itself in its point-like size! </li></ul><ul><li>Breakdown of theory of weak force </li></ul><ul><li>Can’t get started! </li></ul>
  21. 21. History repeats itself? <ul><li>Double #particles again  superpartners </li></ul><ul><li>“ Vacuum bubbles” of superpartners cancels the energy required to contain Higgs boson in itself </li></ul><ul><li>Theory of weak force made consistent with whatever physics at shorter distances </li></ul>
  22. 22. Opening the door <ul><li>Once the hierarchy problem solved </li></ul><ul><li>We can get started to discuss physics at shorter distances. </li></ul><ul><li>It opens the door to the next level: </li></ul><ul><li>Hope to answer great questions </li></ul><ul><li>The solution to the hierarchy problem itself, e.g. supersymmetry, provides additional probe to physics at short distances. </li></ul>
  23. 23. Supersymmetry in one page <ul><li>“ Supersymmetry ” unifies both fermions and bosons into a set of fields by introducing a fermionic coordinate. </li></ul><ul><li>Though it is interesting, unfortunately, we have not yet see any kinds of superpartners having the same mass of the ordinary particles. Hence, it should be softly broken so as to obtain larger masses than the ordinary particles. </li></ul>
  24. 24. Experimental signatures beyond the Standard Model
  25. 25. Neutrino masses & mixings <ul><li>Since the discovery of neutrino oscillations in SuperK (1998), we have a first evidence of physics beyond the SM. (lepton family number violation!) </li></ul><ul><li>Now is in the era of precision measurement for atmospheric & solar neutrino oscillations in SuperK, K2K, SNO and KamLAND. </li></ul><ul><li>These data show that we have two large mixing angles plus one small angle in the lepton sector. (cf. quark sector have three small mixing angles . ) </li></ul>
  26. 26. Muon g-2 <ul><li>There exist a 2.8σ discrepancy between the recent BNL result and the Standard Model prediction. </li></ul><ul><li>Hagiwara et al. (02’) </li></ul><ul><li>If this is real, it may be a second evidence of supersymmetry (or any physics beyond the Standard Model) </li></ul>
  27. 27. “ Powers of Supersymmetry” <ul><li>Electroweak scale is stabilized against quantum corrections, which is necessary to go beyond the Standard Model ( a natural solution to the gauge hierarchy problem ). </li></ul><ul><li>The lightest supersymmetric particle can provide a very natural candidate for the cold dark matter which was missing in the Standard Model. </li></ul><ul><li>It can provide an origin of the electroweak symmetry breaking , supported by the fact of the observed large top Yukawa coupling. </li></ul><ul><li>Low energy supersymmetry can naturally realize the gauge coupling unification . </li></ul><ul><li>We can explain some anomalous experimental results beyond the Standard Model, e.g. muon g-2. </li></ul>
  28. 28. Radiative Electroweak Symmetry Breaking (REWSB) <ul><li>To realize a “Mexican hat” type Higgs potential, we need to have a negative mass squared. </li></ul><ul><li>That was put by hand in the Standard Model. </li></ul><ul><li>REWSB : Starting from the universal soft SUSY breaking masses at the Planck scale, large top Yukawa coupling drives one of the Higgs mass parameters to the negative value at the weak scale through the renormalization group running (dynamical generation of the weak scale). </li></ul>
  29. 29. Gauge Coupling Unification <ul><li>When we input the observed values for three gauge constants, they converge with each other at a very high energy scale (assuming the SUSY around 1 TeV) </li></ul>
  30. 30. Unification of Electroweak Interactions <ul><li>The HERA collider experiment confirmed the unification of electroweak interactions at high energy by measuring the neutral and charged current cross sections in positron--proton scattering. </li></ul>
  31. 31. More theoretical motivations to consider the grand unification
  32. 32. Gauge Anomaly <ul><li>Gauge symmetry crucial to keep quantum field theories (including the SM) under control </li></ul><ul><li>Triangle diagrams: </li></ul><ul><li>May spoil the gauge invariance at quantum level  disaster </li></ul><ul><li>Anomalies must all vanish for three gauge vertices (not for global currents, e.g . B, L ) </li></ul><ul><li>Sum up all standard model fermions and see if they indeed vanish </li></ul>
  33. 33. Anomaly Cancellation <ul><li>U(1) 3 </li></ul><ul><li>U(1)(gravity) 2 </li></ul><ul><li>U(1)(SU(2)) 2 </li></ul><ul><li>U(1)(SU(3)) 2 </li></ul><ul><li>(SU(3)) 3 </li></ul><ul><li>(SU(2)) 3 , (SU(3)) 2 SU(2), SU(3)(SU(2)) 2 </li></ul><ul><li>SU(2) </li></ul><ul><li>Non-trivial connection between quarks & leptons </li></ul>
  34. 34. SU(5) GUT <ul><li>SU(3)  SU(2)  U(1)  SU(5) </li></ul><ul><li>U(1) must be traceless: try 5* : </li></ul><ul><li>Then the rest belongs to 10 : </li></ul><ul><li>Anomaly cancellation: </li></ul><ul><li>Traceless condition for 5* leads to explain the charge quantization: 3 Q(d*) = - Q(e) </li></ul>
  35. 35. SO(10) GUT <ul><li>SU(5)  U(1)  SO(10) </li></ul><ul><li>Come with right-handed neutrinos! </li></ul><ul><ul><li>anomaly-free for any multiplets </li></ul></ul><ul><ul><li>Smallest simple anomaly-free group with chiral fermions </li></ul></ul><ul><ul><li>Smallest chiral representation contains all standard model fermions </li></ul></ul>
  36. 36. Motivation of SO(10) GUT <ul><li>SUSY + GUT </li></ul><ul><li>Experimental evidence: three gauge couplings unification </li></ul><ul><li>with MSSM particle contents. </li></ul><ul><li>SO(10) GUT </li></ul><ul><li>SO(10) fundamental representation include all the matter in the MSSM plus right-handed neutrinos . </li></ul><ul><li>Experimental evidence: very tiny neutrino masses . </li></ul><ul><li>It can be explained via the “ seesaw mechanism ”, and it works well in SO(10) GUT in the presence of the right-handed neutrinos. ( Yanagida, Gell-Mann et al. (79’) ) </li></ul>
  37. 37. Seesaw Mechanism <ul><li>Why is neutrino mass so small? </li></ul><ul><li>Need right-handed neutrino to generate a neutrino mass, but is SM neutral, it can have the Majorana mass. </li></ul>To obtain m 3 ~(  m 2 atm ) 1/2 , m D ~ m t , M 3 ~10 15 GeV (GUT!)
  38. 38. Outline <ul><li>Introduction </li></ul><ul><li>Motivation </li></ul><ul><ul><li>Gauge hierarchy problem </li></ul></ul><ul><ul><li>Supersymmetry </li></ul></ul><ul><ul><li>Grand unification </li></ul></ul><ul><li>Minimal SO(10) Model and its predictions </li></ul><ul><ul><li>Neutrino Oscillation Data </li></ul></ul><ul><ul><li>Lepton Flavor Violation </li></ul></ul><ul><ul><li>Proton Decay </li></ul></ul><ul><li>Conclusion </li></ul>
  39. 39. Minimal SO(10) Model (Babu-Mohapatra (93’); Fukuyama-Okada (01’)) <ul><li>Two kinds of symmetric Yukawa couplings </li></ul><ul><li>Two Higgs fields are decomposed to </li></ul><ul><li>SU(4) adjoint 15 have a basis, so as to satisfy the traceless condition. Putting leptons into the 4 th color, we get, so called, ‘Georgi-Jarslkog’ factor, for leptons. </li></ul>
  40. 40. <ul><li>After the symmetry breakings, we have </li></ul>Yukawa Couplings <ul><li>Below the GUT scale, we assume MSSM is realized, and we have two Higgs doublet which are linear combinations of original fields. </li></ul>
  41. 41. Low-energy Superpotential <ul><li>Then the low-energy Yukawa couplings are given by </li></ul>
  42. 42. Mass Relation <ul><li>All the mass matrices are descried by only two fundamental matrices. </li></ul><ul><li>13 inputs : 6 quark masses, 3 angles + 1 phase in CKM matrix, </li></ul><ul><li>3 charged-lepton masses. </li></ul><ul><li>⇒ fix and </li></ul><ul><li>⇒ predictions in the parameters in the neutrino sector! </li></ul>
  43. 43. <ul><li>By making some linear combinations, we get a “GUT relation”, e.g. </li></ul><ul><li>Cf. GUT relation in minimal SU(5): </li></ul><ul><li>This is a good relation for 3 rd generation. So we can naively expect that is small. </li></ul>Charged Lepton Sector
  44. 44. <ul><li>Dirac neutrino mass matrix: </li></ul><ul><li>Right-handed Majorana mass matrix: </li></ul><ul><li>Light Majorana neutrino mass matrix is obtained by using a seesaw formula: </li></ul><ul><li>All lepton mass matrices are determined by only the quark mass matrices! </li></ul>Neutrino Sector
  45. 45. Seesaw Mass Matrix <ul><li>Type-I seesaw formula: </li></ul><ul><li>When we choose parameters to cancel the second line, this reduces to the type-II seesaw formula. </li></ul>
  46. 46. Bi-large Mixing Mass Matrix <ul><li>Bi-large mixing mass matrix is naturally obtained as a result of the fact that the bottom-tau mass unification at the GUT scale. </li></ul><ul><li>“ 33” element is suppressed by choosing a parameter near the value σ= π. It’s an essential point to produce the bi-large mixing structure of the neutrino mass matrix. </li></ul>
  47. 47. <ul><li>By using “trace” and “determinant”, we obtain two independent equations. </li></ul>Solving the GUT relation
  48. 48. Input data @ EW scale
  49. 49. Solution of the GUT relation <ul><li>We vary the input values of and to find a solution. </li></ul><ul><li>For </li></ul><ul><li>we find a crossing point as in the figure: </li></ul>
  50. 50. Seesaw Mass Matrix <ul><li>Type-I seesaw formula: </li></ul><ul><li>Once we determined the coefficients, and , we can predict all the oscillation parameters in terms of only one undetermined parameter, ( Matsuda et al. (‘00) ) </li></ul>
  51. 51. Predictions in Neutrino Sector <ul><li>We have only one parameter         , left free. So, we can make definite predictions. </li></ul>
  52. 52. <ul><li>Now, all the mass matrices have been determined! </li></ul><ul><li>For example, Neutrino Dirac Yukawa coupling matrix (in the basis where charged lepton mass matrix is diagonal): </li></ul><ul><li>We must check this model by proving the other phenomena related to the Yukawa couplings! ( LFV , muon g-2 , EDM , proton decay , etc.) </li></ul>Yukawa’s are determined!
  53. 53. Lepton Flavor Violation
  54. 54. Lepton Family Number <ul><li>Neddermeyer-Anderson discovered muon in 1937. </li></ul><ul><li>A very naïve question: </li></ul><ul><li>Why doesn’t muon decay    e   ? </li></ul><ul><li>Inoue-Sakata made up a new conservation law: </li></ul><ul><li>Lepton Family number must be conserved. </li></ul><ul><li>Neutrino oscillations (SuperK & SNO) have disproved lepton family number conservation! </li></ul>
  55. 55. <ul><li>Because we really see LFV as neutrino oscillations, we naturally expect LFV can also be seen in the charged lepton sector! </li></ul><ul><li>Current experimental bound: </li></ul><ul><li>How well motivated from theoretical point of view? </li></ul><ul><li>In the Standard Model (+ Right-handed neutrinos): too small rate (∵GIM suppression well works). </li></ul><ul><li>In SUSY models: New source of LFV, soft SUSY breaking terms (with No GIM suppression, in general) exist. </li></ul><ul><li>LFV processes are important sources for low-energy SUSY search! </li></ul>Lepton Flavor Violation (LFV)
  56. 56. Estimations of LFV and g-2 <ul><li>LFV and g-2 are originated from the same dipole moment operator </li></ul><ul><li>include the SUSY partners in the loop. </li></ul><ul><li>Chargino –sneutrino & Neutralino -charged-slepton loop </li></ul><ul><li>Hisano et al. PRD53 (1996) </li></ul>
  57. 57. Formula for LFV, g-2 and EDM <ul><li>For the estimation of LFV the decay rate is given by </li></ul><ul><li>For the estimation of g-2 the SUSY contribution is estimated by </li></ul><ul><li>For the estimation of EDM the SUSY contribution is estimated by </li></ul>
  58. 58. Soft SUSY breaking terms <ul><li>We consider the general soft SUSY breaking mass parameters at low-energy </li></ul>
  59. 59. Minimal Supergravity boundary condition for the soft SUSY breaking parameters <ul><li>We impose the universal boundary condition (mSUGRA) at the GUT scale : </li></ul><ul><li>So we have three free parameters in the soft mass terms : </li></ul>
  60. 60. RG induced Flavor Mixings <ul><li>Flavor mixing is induced by RG running from the GUT scale to the EW scale </li></ul><ul><li>In the basis where the charged lepton mass matrix is diagonal, LFV is induced through the neutrino Dirac Yukawa coupling matrix. </li></ul>
  61. 61. Approximate Formulae <ul><li>We present approximate formulae in order to see the parameters dependence. </li></ul>
  62. 62. prediction <ul><li>For fixed </li></ul><ul><li>Very close to the current experimental upper bound. </li></ul><ul><ul><li>-> It is testable in near future experiments. </li></ul></ul>
  63. 63. prediction <ul><li>For fixed </li></ul>
  64. 64. <ul><li>For fixed </li></ul><ul><li>Input parameters providing close to the present upper bound predict suitable magnitude for muon g-2. </li></ul>Predictions about Muon g-2
  65. 65. Light on the Dark Matter <ul><li>Recent WMAP satellite data show the very precision measurement of the cold dark matter (CDM) relic density </li></ul><ul><li>Because the Majorana mass term of the right-handed neutrino violate the lepton number by two units. So in the minimal SO(10) model, R-parity is automatically conserved . Then the LSP (lightest sparticle) is stable enough to provide a candidate for the CDM. </li></ul>
  66. 66. Cosmologically allowed parameters <ul><li>The mSUGRA parameter region is very restricted. (even to the “line”! ) </li></ul>
  67. 67. prediction
  68. 68. Prediction about Muon g-2
  69. 69. Prediction about electron EDM <ul><li>Leptonic EDM is important to explore the CP violation (T violation) in the lepton sector. </li></ul><ul><li>The experimental bound: </li></ul><ul><li>The predicted value is well below the present experimental bound, but it is in the range of near future experiment. </li></ul>
  70. 70. Semileptonic LFV processes <ul><li>The theoretical bound on the semileptonic LFV processes including electron. </li></ul>
  71. 71. <ul><li>The theoretical bound on the semileptonic LFV processes including muon. </li></ul>
  72. 72. Proton Decay smoking gun signature of GUT
  73. 73. Problem with Anti-Matter <ul><li>Anderson discovered positron e + , anti-matter of electron in 1932 </li></ul><ul><li>A very naïve question: </li></ul><ul><li>Why doesn’t proton decay p  e +  ? </li></ul><ul><li>Stückelberg (1939) made up a new conservation law: </li></ul><ul><li>Baryon number must be conserved </li></ul><ul><li>(later also by Wigner, 1949) </li></ul>
  74. 74. Baryon number as an accidental symmetry in the Standard Model <ul><li>In the Standard Model, the proton is absolutely stable. </li></ul><ul><li>Baryon number is an “accidental” symmetry, i.e., there is no renormalizable interaction you can write down that violate Baryon number with the minimal particle content. </li></ul><ul><li>But once beyond the Standard Model, there is no reason for Baryon number to be conserved. </li></ul><ul><li>Grand Unified Theories prime example of well-motivated theories that lead to proton decay. </li></ul><ul><li>Especially in SUSY GUTs', proton decay is easy to occur as we will see in the following transparencies. </li></ul>
  75. 75. Proton decay in SUSY GUT <ul><li>In the minimal SO(10) model, we have two kinds of Yukawa matrices, and the Wilson coefficients can be written as: </li></ul><ul><li>In SUSY models, the color triplet Higgsinos mediate the proton decay induced by the following baryon and lepton number violating dimension five operator </li></ul>
  76. 76. Proton decay rate formula
  77. 77. Parameters in Higgs sector-(i)
  78. 78. Parameters in Higgs sector-(ii)
  79. 79. Proton decay in SO(10) GUT-(i) The green region is the allowed region . In case of , there is large enough parameter space which cancels the proton decay rate, though it is very tiny region in case of .
  80. 80. Proton decay in SO(10) GUT-(ii) The green region is the allowed region . In case of , there is large enough parameter space which cancels the proton decay rate, though it is very tiny region in case of .
  81. 81. Conclusion <ul><li>Supersymmetry gives a natural way to stabilize the theory with Higgs field, and gives an opportunity to go in searching for physics beyond the Standard Model. </li></ul><ul><li>Grand Unified Theory combined with SUSY provides an explanation for many unanswered questions in the SM: charge quantization, anomaly cancellation, etc. </li></ul><ul><li>There are actually some indications of supersymmetry: (anomalous magnetic moment of the muon @ BNL, the light Higgs boson @ LEP-II, time dependent CP violation @ B-factory, etc.) </li></ul><ul><li>If SUSY is real, we can see a lot of supersymmetric particles @ LHC in 2007, even within a day. </li></ul>
  82. 82. <ul><li>A minimal SUSY SO(10) model is a very natural and predictive theory of grand unification. </li></ul><ul><li>Based on the Minimal SO(10) Model , w e estimated neutrino oscillation parameters , LFV rates, Muon g-2, electron EDM and Proton decay rates. </li></ul><ul><li>Results: </li></ul><ul><li>Neutrino masses & mixings can be well much described. </li></ul><ul><li>LFV rates can be well exceed the future bounds </li></ul><ul><li>Muon g-2 can be suitable for BNL E821 result </li></ul><ul><li>Combining with WMAP data </li></ul><ul><li>-> Cosmologically allowed region exists </li></ul>
  83. 83. <ul><li>Proton Decay: The decay rate in our model is within the experimental (SuperK) upper bound if we take the small tan β = 2.5, assuming the color triplet Higgs mass to be at the usual GUT scale. </li></ul><ul><li>Our SO(10) Model is very testable in the near future experiments! </li></ul>
  84. 84. Particle data book after 2007