Supersymmetry

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

2. In the MSSM, electroweak symmetry does not get broken Only after supersymmetry is broken, Higgs can obtain a VEV v~mSUSY Regard EWSB as a consequence of supersymmetry breaking EW symmetry and hierarchy “protected” by supersymmetry Electroweak Symmetry Breaking

3. Origin of Hierarchy • v<<MPl because v~mSUSY<<MPl • Why mSUSY<<MPl? • Idea: dimensional transmutation • SUSY broken by strong gauge dynamics with • “Dynamical supersymmetry breaking”

4. Simplest example: SO(10) with one 16 No moduli space, can’t analyze with Seibergian techniques “non-calculable” (Affleck-Dine-Seiberg) Add one 10, make it massive and decouple When M10=0, moduli space spanned by 161610, 102, generically SO(10)SO(7) SO(7) gaugino condensation generates dynamical superpotential Add W=M10102, lifts moduli space, breaks SUSY Decouple 10 smoothly(HM) Dynamical Supersymmetry Breaking

5. Izawa-Yanagida-Intriligator-Thomas model • Sp(Nc) gauge theory with Nf=Nc+1 • Quantum modified moduli space Pf M = L2Nffor mesons Mij=QiQj • Add superpotential with singlets Sij W=Sij QiQj forces Mij=0 • Contradiction  no SUSY vacua

6. Issue of mediation • Many gauge theories that break SUSY dynamically known • The main issue: how do we communicate the SUSY breaking effects to the MSSM? “mediation”

7. Spurion • Supersymmetry is broken either by an F-component of a chiral superfield fi=q2Fi0 or a D-component of a vector superfield V=q2D0 • Once they are frozen at their expectation values, they can be viewed as spurions of supersymmetry breaking order parameters

8. Soft supersymmetry breaking • Purpose of supersymmetry is to protect hierarchy • Arbitrary terms in Lagrangian that break supersymmetry reintroduce power divergences • “Soft supersymmetry breaking” classified: mll, m2ijfi*fj, Aijkfjfjfk, Bijfjfj, Cifj • Dark horse terms (not always allowed): fj*fjfk, lyj, yiyj

9. Spurion operators • Spurion z =fi/M=q2Fi/M generates soft terms • M is the “mediation scale” where the effects of SUSY breaking are communicated m ll = d2q z c Wa Wa m2ijfi*fj = d4q z*z cijfi*fj Aijkfjfjfk = d2q z cijkfjfjfk Bijfjfj = d2q z cijfjfj Cifj = d2q z cifj • Coefficients c are random at this point

10. Supersymmetric flavor problem • Random SUSY breaking excluded by FCNC constraints • Consider scalar down quarks • Take the off-diagonal terms to be perturbation:

11. Supersymmetric flavor problem • Random SUSY breaking excluded by FCNC constraints • Want a reason why off-diagonal terms are suppressed _ K0 K0

12. Two possible directions • Develop a theory of flavor that predicts not only the pattern of Yukawa matrices (masses, mixings), but also soft masses • Develop a theory of mediation mechanism of supersymmetry breaking that predicts (approximately) flavor-blind soft masses

13. Gravity Mediation

14. Supergravity • Specify Kähler potential K and superpotential W • Minimal supergravity K=|z|2+i|fi|2 W=Wh(z)+Wo(f) • SUSY broken if Fz=zW*+Wz0, W0 Universal scalar mass, trilinear couplings etc

15. Lore • Got universal scalar mass! • “Of course, because gravity doesn’t distinguish flavor” • Wrong! • “Minimal” is a choice to obtain canonical kinetic terms with no Planck-suppressed corrections • But in general there are such corrections in non-renormalizable theory and SUGRA not minimal

16. Problems with Minimal SUGRA • There is no fundamental reason to believe that Kähler potential in effective theory of quantum gravity is strictly minimal • In many string compactifications, it isn’t • Direct coupling of observable fields with moduli in Käler potential that depend on their modular weights • Thought to be an ad hoc convenient choice, not a theory of mediation • But phenomenologically excellent start point, explaning EWSB, dark matter, absence of FCNC

17. Problems with general SUGRA • There may be arbitrary coupling between hidden and observable fields in Kähler potential under no control • Generically, soft masses expected to be arbitrary, with flavor violation m2ijfi*fj = d4q z*z cijfi*fj • Phenomenogically disaster

18. Remedy by flavor symmetry • We need theory of flavor anyway • The issue of flavor-violating soft masses is intimately tied to the origin of flavor, Yukawa couplings • Seek for a common theory that solves the problem

19. Flavor-blind Mediation Mechanisms Gauge Mediation Gaugino Mediation Anomaly Mediation

20. Gauge Mediation

21. Dynamical supersymmetry breaking sector Take SU(5) with 10+5* (“non-calculable DSB model” add massive 5+5* and can show DSB; HM) break it to SU(4)U(1) with non-anomalous global U(1)m (6+2+4-3+1-8)+1 +(4*-1+1+4)-3 W= 4*-1 4-3 1+4+ 1+4 1+4 1-8 breaks supersymmetry dynamically gauge global U(1)m as “messenger U(1)” Problem with FY D-term for messenger U(1)  solved by changing the DSB model to SU(6)U(1) (Dine, Nelson, Nir, Shirman) Dine-Nelson-Shirman model

22. Messenger sector a pair f charged under messenger U(1) NF pairs of F+F* (5+5*) under SU(5) SU(3)SU(2)U(1) W=l1Sf+f-+l2SFF*+l3S3 f acquire negative mass-squred from two-loops in messenger U(1) interaction triggers S to acquire both A- and F-component VEVs gives both mass and B-term to F+F* M=l2<S>, MB=l2<FS> Dine-Nelson-Shirman model

23. Because F+F* are charged under the standard model gauge groups, their one-loop diagrams generate gaugino masses, and two-loop diagrams generate scalar masses Generated scalar masses flavor-blind, because gauge interactions do not distinguish flavor Dine-Nelson-Shirman model

24. Dine-Nelson-Shirman model • Lightest Supersymmetry Particle: gravitino • In general, a cosmological problem (overclosure) (de Gouvêa, Moroi, HM) • Collider signatures may be unique: • Bino  gravitino + photon • Decay length may be microns to km • Should not have any new flavor physics below the mediation scale to screw-up flavor-blindness of soft masses

25. Too many sectors to worry about! DSB sector: Sp(4) with 5 flavors charged under SU(5) (HM) Direct Gauge Mediation

26. (Kaplan, Kribs, Schmaltz) (Chacko, Luty, Nelson, Ponton) DSB in another brane Gauge multiplet in the bulk Gauge multiplet learns SUSY breaking first, obtains gaugino mass MSSM at the compactification scale with gaugino mass only Scalar masses generated by RGE Gaugino Mediation

27. Gaugino Mediation • Phenomenology similar to minimal supergravity with zero universal scalar mass • Gravitino heavy: less harmful • Needs high (~GUT scale) compactification to jack up slepton mass high enough • Should not have any new flavor physics below the compactification scale to screw-up flavor-blindness of soft masses

28. (Randall, Sundrum) (Giudice, Luty, HM, Rattazzi) Try not to mediate Zen of SUSY breaking If no coupling between DSB and MSSM, there is no supersymmetry breaking at tree-level But divergence of supercurrent in the same multiplet as the trace of energy momentum tensor Conformal anomaly induces supersymmetry breaking Anomaly Mediation

29. Weyl compensator formalism • Conformal Supergravity “fixed” by Weyl compensator F • The only communication of SUSY breaking is through the auxiliary component of F=q2F d4q F*Ff*f +d2q F3(M f2+l f3) • Scale ff/F d4q f*f +d2q (FM f2+l f3) • Only dimensionful parameters acquire SUSY breaking • Massless theory  no SUSY breaking

30. Conformal Anomaly • Any (non-finite) theory needs a regulator with an explicit mass scale • Pauli-Villars with heavy regulator mass • DRED with renormalization scale m (Boyda, HM, Pierce) • Regulator receives SUSY breaking • SUSY breaking induced by regulator effect: anomaly

31. Anomaly mediation predicts SUSY breaking with theory given at the scale of interest UV insensitivity Can be checked explicitly by integrating out heavy fields that their loops exactly cancel the differences in b-functions & anomalous dimensions (Giudice, Luty, HM, Rattazzi) (Boyda, HM, Pierce) SUSY breakings always stay on the RGE trajectory Anomaly Mediation

32. Too predictive! • Anomaly mediation highly predictive with only one parameter: overall scale • Slepton mass-squareds come out negative • Phenomenologically dead on start • Remedies: • Add uinversal scalar mass • Cause symmetry breaking via SUSY breaking • Destroys UV insensitivity

33. Add U(1)B-L and U(1)YD-terms Three SUSY-breaking parameters now Can show that UV-insensitive (Arkani-Hamed, Kaplan, HM, Nomura) Viable UV-insensitiveAnomaly Mediation

34. Conformal sequestering • Inspiration from AdS/CFT correspondence • Make hidden sector nearly superconformal • Dangerous coupling between hidden and observable fields suppressed because Kähler potential of hidden fields flow to IR fixed point (Luty, Sundrum) • Can be extended to include U(1) breaking sector to make the scenario phenomenologically viable (Harnik, HM, Pierce)

35. U(1) breaking sector • SO(5) theory with 6 spinors, no mass parameters • Gauge SU(4)SU(2)U(1) subgroup of global SU(6) symmetry • Quantum modified moduli space breaks U(1) (and also SU(4)Sp(2)) • D-term “non-calculable” because compositeness scale L~v U(1)-breaking scale • Can be made calculable within the same universality class by (1) additional flavor L>>v or (2) additional color&flavor L<<v to show D0 • Can be used to generate right-handed neutrino mass (Harnik, HM, Pierce)

36. SUSY spectra

37. Models of Flavor

38. Question of Flavor • What distinguishes different generations? • Same gauge quantum numbers, yet different • Hierarchy with small mixings:  Need some ordered structure • Probably a hidden flavor quantum number  Need flavor symmetry • Flavor symmetry must allow top Yukawa • Other Yukawas forbidden • Small symmetry breaking generates small Yukawas

39. Broken Flavor Symmetry • Flavor symmetry broken by a VEV ~0.02 • SU(5)-like: • 10(Q, uR, eR) (+2, +1, 0) • 5*(L, dR) (+1, +1, +1) • mu:mc:mt~ md2:ms2:mb2~ me2:mm2:mt2 ~4: 2:1

40. Not bad! • mb~ mt, ms ~ mm, md ~ me @MGUT • mu:mc:mt~ md2:ms2:mb2~ me2:mm2:mt2

41. New Data from Neutrinos • Neutrinos are already providing significant new information about flavor symmetries • If LMA, all mixing except Ue3 large • Two mass splittings not very different • Atmospheric mixing maximal • Any new symmetry or structure behind it?

42. Is There A StructureIn Neutrino Masses & Mixings? • Monte Carlo random complex 33 matrices with seesaw mechanism (Hall, HM, Weiner; Haba, HM)

43. Anarchy • No particular structure in neutrino mass matrix • All three angles large • CP violation O(1) • Ratio of two mass splittings just right for LMA • Three out of four distributions OK • Reasonable  Underlying symmetries don’t distinguish 3 neutrinos.

44. Anarchy is Peaceful • Anarchy (Miriam-Webster): “A utopian society of individuals who enjoy complete freedom without government” • Peaceful ideology that neutrinos work together based on their good will • Predicts large mixings, LMA, large CP violation • sin22q13 just below the bound • Ideal for VLBL experiments • Wants globalization!

45. More flavor parameters • Squarks, sleptons also come with mass matrices • Off-diagonal elements violate flavor: suppressed by flavor symmetries • Look for flavor violation due to SUSY loops • Then look for patterns to identify symmetries  Repeat Gell-Mann–Okubo! • Need to know SUSY masses

46. To Figure It Out… • Models differ in flavor quantum number assignments • Need data on sin22q13, solar neutrinos, CP violation, B-physics, LFV, EWSB, proton decay • Archaeology • We will learn insight on origin of flavor by studying as many fossils as possible • cf. CMBR in cosmology

47. More Fossils:Lepton Flavor Violation • Neutrino oscillation  lepton family number is not conserved! • Any tests using charged leptons? • Top quark unified with leptons • Slepton masses split in up- or neutrino-basis • Causes lepton-flavor violation (Barbieri, Hall) • predict B(tmg), B(meg), me at interesting (or too-large) levels

48. Barbieri, Hall, Strumia

49. Now also large mixing between nt and nm (nt, bR) and (nm , sR) unified in SU(5) Doesn’t show up in CKM matrix But can show up among squarks CP violation in Bs mixing (BsJ/y f) Addt’l CP violation in penguin bs (Bdf Ks) (Chang, Masiero, HM) More Fossils:Quark Flavor Violation

50. Conclusions • Dynamical supersymmetry breaking successfully produces hierarchy • Various mediation mechanisms • Gravity mediation + flavor symmetry • Gauge mediation • Anomaly mediation • Gaugino mediation