Supersymmetry I

1. Supersymmetry I Hitoshi Murayama Taiwan Spring School March 29, 2002

2. Why Beyond the Standard Model • Standard Model is sooooo successful. But none of us are satisfied with the SM. Why? • Because it leaves so many great questions unanswered  Drive to go beyond the Standard Model

3. Great Questions–Vertical– • Charge quantization, anomaly cancellation, bizarre hypercharge assignments in the Standard Model • Why are there three seemingly unrelated forces yet all gauge forces? • Is there a unified description of all forces as Einstein dreamed about? • Why is mW<<MPl? (Hierarchy Problem)

4. Great Questions–Horizontal– • Why are there three generations? • Why physics determines the pattern of masses and mixings? • What is the origin of CP violation? • What is the origin of matter anti-matter asymmetry in Universe?

5. Supersymmetry • Great questions = ambitious questions • Stablizing hierarchy is mandatory to start talking about physics beyond the SM • Supersymmetry stabilizes the hierarchy • It also addresses some of the great questions • But it also creates new problems

6. Outline • Introduction • Hierarchy Problem • Supersymmetric Lagrangian • Dark Matter • Grand Unification • Electroweak Baryogenesis • Conclusion

7. Hierarchy Problem

8. The Main Obstacle • We look for physics beyond the Standard Model that answers these great questions • By definition, that is physics at shorter distances • Then the Standard Model must survive down to whatever shorter distance scale • Hierarchy problem is the main obstacle to do so  We can’t even get started!

9. Once upon a time,there was a hiearchy problem... • At the end of 19th century: a “crisis” about electron • Like charges repel: hard to keep electric charge in a small pack • Electron is point-like • At least smaller than 10-17 cm • Need a lot of energy to keep it small!

10. Need more than GeV of energy to pack electric charge tightly inside the electron But the observed energy of the electron is only 0.5 MeV Electron cannot be smaller than 10–13 cm?? Breakdown of theory of electromagnetism E=mc2

11. Energy-Time Uncertainty Principle: You can violate energy conservation if it is only for a short time Vacuum is full of quantum bubbles! Uncertainty Principle Werner Heisenberg

12. Electron creates a force to repel itself Vacuum bubble of matter anti-matter creation/annihilation Electron annihilates the positron in the bubble  only 10% of mass even for Planck-size Weisskopf Anti-Matter Helps

13. Anti-Matter Helps • “Anti-matter attraction” cancels “Like-charge repulsion” • It does not cost too much energy to tightly pack the electric charge inside the electron • Needed anti-matter: double #particles • Theory of electromagnetism (QED) now works at very short distances (12 digits accuracy!)

14. Just like electron repeling itself because of its charge, Higgs boson also repels itself Requires a lot of energy to contain itself in its point-like size! Breakdown of theory of weak force Can’t get started! Higgs repels itself, too

15. Double #particles again superpartners “Vacuum bubbles” of superpartners cancels the energy required to contain Higgs boson in itself Theory of weak force made consistent with whatever physics at shorter distances History repeats itself?

16. Opening the door Once the hierarchy problem solved, • We can get started to discuss physics at shorter distances. • It opens the door to the next level: Hope to answer great questions • The solution to the hierarchy problem itself, e.g., SUSY, provides additional probe

17. Superpartners • Partners of fermions: “s”+name • e.g., selectron, sneutrino, stop, sup, sstrange • Partners of bosons: name+“ino” • e.g., wino, gluino, higgsino • But mass eigenstates are mixtures due to EWSB • Neutralinos: mixture of bino, wino3, two neutral higgsinos • Charginos: mixture of wino and charged higgsino

18. Where are the superpartners? • They need to cancel self-repelling energy of the Higgs boson • Cannot be too heavy to do this job • Have to be below ~1TeV or “Fermi energy” • We are getting there this decade • Tevatron (Fermilab, Illinois) 2001– • LHC (CERN, Switzerland) 2006– • But it may be everywhere now

19. Supersymmetric Lagrangian

20. Players _ • Superspace (x, q, q) • Supersymmetry: translation in q • Chiral superfields that contain spinless boson (sfermion) and spin 1/2 fermion f(x,q)~A(x)+ qy(x)+q2F(x) • Vector superfields that contain spin 1 gauge bosons and spin 1/2 gauginos V(x,q)~qsmqAm(x)+ q2q l(x)+c.c.+ q2q2D(x) _ _ _

21. Lagrangian _ d4qf*eVf=|Dmf|2+ysDy+|F|2 +A*Tayla+ A*TaADa define Wa=D2e-VDaeV d2qWaWa=Fmn2+lsl+D2 superpotential d2qW(f)=yyW´´+FW´ solve forF and D |F|2 +D2=|W´|2+g2 (A*TaA)2/2 _ _

22. Grand Unification

23. Quantum Numbers in the Standard Model • I didn’t become a physicist to memorize these weird numbers...

24. Anomaly Cancellation • U(1)3 • U(1)(gravity)2 • U(1)(SU(2))2 • U(1)(SU(3))2 • (SU(3))3 • (SU(2))3, (SU(3))2SU(2), SU(3)(SU(2))2 • SU(2) Non-trivial connection between q & l

25. Quantum Numbers in the Standard Model • To treat them on equal footing, make all particles left-handed using CP

26. SU(5) GUT • SU(3)SU(2)U(1)SU(5) • U(1) must be traceless: try 5*: • 55 matrices SU(3) SU(2) U(1)

27. Anomaly cancellation & chirality require Then the rest belongs to 10 All quantum numbers work out this way SU(5) GUT

28. Gauge Coupling Unification

29. SO(10) GUT • SU(5)U(1)SO(10) • Come with right-handed neutrinos! • anomaly-free for any multiplets • Smallest simple anomaly-free group with chiral fermions • Smallest chiral representation contains all standard model fermions

30. Most exciting thing about superpartners beyond existence: They carry information of small-distance physics to something we can measure “Is Unification true?” Superpartners as probe

31. Proton Decay • Quarks and leptons in the same multiplet • Gauge bosons can convert q to l • Cause proton decay!

32. Supersymmetric Proton Decay Suppressed only by the second power of GUT scale vs fourth in X-boson exchange

33. RGE analysis SuperK limit MHc>7.6 1016 GeV Even if 1st, 2nd generation scalars “decoupled”, 3rd generation contribution (Goto, Nihei) MHc>5.7 1016 GeV (HM, Pierce) Rest In PeaceMinimal SUSY SU(5) GUT

34. Avoiding Proton Decay • Unfortunately, proton decay rate/mode is highly model-dependent • more threshold corrections (HM, Pierce) • Some fine-tuning (Babu, Barr) • GUT breaking by orbifolds (Kawamura; Hall, Nomura) • Depends on the triplet-doublet splitting mechanism, Yukawa (non-)unification

35. Don’t give up! • Still, proton decay unique window to physics at >1015 GeV • Suppression by fine-tuning: pK+n may be just around the corner • Flipped SU(5): pe+p0 possible • We still need SuperK! (50kt) • Eventually with ~1000kt detector

36. Baryogenesis

37. Two Main Directions • BL0 gets washed out at T>TEW~174GeV • Electroweak Baryogenesis(Kuzmin, Rubakov, Shaposhnikov) • Start with B=L=0 • First-order phase transition  non-equilibrium • Try to create BL0 • Leptogenesis(Fukugita, Yanagida) • Create L0 somehow from L-violation • Anomaly partially converts L to B

38. Electroweak Baryogenesis • Two big problems in the Standard Model • First order phase transition requires mH<60GeV • Need new source of CP violation because J det[Mu† Mu, Md† Md]/TEW12 ~ 10–20<< 10–10 • Minimal Supersymmetric Standard Model • First order phase transition possible if • New CP violating phase e.g., (Carena, Quiros, Wagner), (Cline, Joyce, Kainulainen)

39. Scenario • First order phase transition • Different reflection probabilities for chargino species • Chargino interaction with thermal bath produces an asymmetry in top quark • Left-handed top quark asymmetry partially converted to lepton asymmetry via anomaly • Remaining top quark asymmetry becomes baryon asymmetry

40. Chargino mass matrix Relative phase unphysical if tanb Need fully mixed charginos  M2 (Cline, Joyce, Kainulainen) Parameters

41. SUSY Mass Spectrum • To avoid LEP limit on lightest Higgs boson, need left-handed scalar top ~ TeV • Light right-handed scalar top, charginos • Need with severe EDM constraints from e, n, Hg  1st, 2nd generation scalars > 10 TeV cf. Carena, Quiros, Wagner claim enough EDM constraint is weaker, but rest of phenomenology similar

42. Signals of Electroweak Baryogenesis • 20–30%enhancements to Dmd, Dms with the same phase as in the SM • Bs mixing vs lattice fBs2BBs • Bd mixing vs Vtd from Vub and angles • Find Higgs, stop, charginos (Tevatron?) • Eventually need to measure the phase in the chargino sector at LC to establish it (HM, Pierce)

43. Enhancement in B mixing (HM, Pierce)

44. Dark Matter

45. Theoretical Argumentsfor Dark Matter • Spiral galaxies made of bulge+disk: unstable as a self-gravitating system  need a (near) spherical halo • With only baryons as matter, structure starts forming too late: we won’t exist • Matter-radiation equality too late • Baryon density fluctuation doesn’t grow until decoupling • Need electrically neutral component

46. Observe galaxy rotation curve using Doppler shifts in 21 cm line from hyperfine splitting Galactic Dark Matter

47. Galactic Dark Matter • Luminous matter (stars) Wlumh=0.002–0.006 • Non-luminous matter Wgal>0.02–0.05 • Only lower bound because we don’t quite know how far the galaxy halos extend • Could in principle be baryons • Jupiters? Brown dwarfs?

48. Search for microlensing towards LMC, SMC When a “Jupiter” passes the line of sight, the background star brightens MACHO & EROS collab. Joint limit astro-ph/9803082 Need non-baryonic dark matter in halo Primordial BH of ~M ? MAssive Compact Halo Objects(MACHOs)

49. Galaxies form clusters bound in a gravitational well Hydrogen gas in the well get heated, emit X-ray Can determine baryon fraction of the cluster fBh3/2=0.0560.014 Combine with the BBN Wmatterh1/2=0.380.07 Agrees with SZ, virial Dark Matter in Galaxy Clusters

50. Cosmic Microwave Background