1. March 2005 Theme Group 2 Left Right Symmetry around a TeV Scale R. N. Mohapatra University of Maryland

2. March 2005 Theme Group 2 SKETCH OF STANDARD MODEL

3. March 2005 Theme Group 2 Origin of Parity violation Standard model has parity violation built in from the beginning making it different from all other interactions. Left-right models were introduced in 1974-75 primarily as a way to understand the origin of P-violation: (R. N. M., Pati, Senjanovic: 74-75) Later on many interesting properties of LR models were discovered:

4. March 2005 Theme Group 2 Left-Right models Gauge group : Fermion assignment Higgs fields:

5. March 2005 Theme Group 2 Detailed Higgs content and Sym Breaking Break symmetry

6. March 2005 Theme Group 2 Symmetry breaking

7. March 2005 Theme Group 2 Comparision with standard model LR model quark-lepton symmetric whereas SM not. Standard model; electric charge is given by Y is arbitrary parameter with no physical meaning. Situation different in left-right models Davidson; Marshak,RNM’79 Every term has a physical meaning

8. March 2005 Theme Group 2 Asymptotic Parity conservation Weak interaction Lagrangian in LR model: For E >> M_WL,R, theory conserves parity. Low energy weak Lagrangian: V-A theory for M_WR >> M_WL.

9. March 2005 Theme Group 2 Another consequence of LR models: Under Parity: This implies that the Yukawa coupling matrices defined by: h are hermitean to be parity invariant. This implies that the quark mass matrices are hermitean provided the vacuum expectation values are real. This has several consequences:

10. March 2005 Theme Group 2 Consequences of hermitean m 1.Left and Right CKM are same. 2.Solves the strong CP problem Without need for an axion. Note that strong CP parameter vanishes Unfortunately in the minimal non-SUSY LR Vevs are complex. SUSYLR they are real.

11. March 2005 Theme Group 2 Spontaneous CP and P Breaking Spontaneous CP breaking mean complex vevs and real Yukawas (T. D. Lee). Minimal LR model has complex vevs. In LR models CP implies Yukawa’s are real and symmetric; Then i.e. CKM angles But the total number of right handed phases: # = n(n+1)/2. Thus for 2 gen.,3 total phases; three gen. 7 total phases in weak currents.

12. March 2005 Theme Group 2 Attractive Grand Unification of LR Natural GUT group of the Left-right model is SO(10) : its spinor rep contains all 16 needed fermions (including RH neutrino) in a single rep. Georgi; Fritzsch, Minkowski (74) Natural Partial Unif. Group is SU(2) L X SU(2) R X SU(4) C of Pati and Salam (74)

13. March 2005 Theme Group 2 SO(10) down to Std Model via LRS SO(10) Nu mass Left-Right Sym. Theory Standard Model-> seesaw

14. March 2005 Theme Group 2 Unification of Couplings: two examples Weak scale susy Non SUSY SO(10) with seesaw Low WR Unif OK too. Chang, Parida et al (85)

15. March 2005 Theme Group 2 Compare with SU(5)

16. March 2005 Theme Group 2 Neutrino Mass, Seesaw AND LR Neutrino Naturally Majorana in LR model: Recall Above the WL scale, Implying: Parity violation implies B-L violation and B-L violation means Majorana neutrino. Connects small neutrino mass to the scale of parity violation.

17. March 2005 Theme Group 2 How does one see it in practice ? Effect of symmetry breaking on neutrino mass: SU(2) R XU(1) B-L and Parity broken by the vev This gives large Majorana mass to N R: gives mass connecting nu L and N R (the Dirac mass m D )- the seesaw mechanism:

18. March 2005 Theme Group 2 Seesaw Formula: Neutrino mass matrix Diagonalizing this gives a heavy and light eigenstate; Heavy is NR with mass And light state with mass: Minkowski (77); Gell-Mann, Ramond, Slansky; Yanagida: Glashow; RNM, Senjanovic (79).

19. March 2005 Theme Group 2 Small nu mass Due to suppressed V+A Seesaw formula in terms of scale of parity restoration: Strength of V+A currents: AS NU MASS GOES TO ZERO, WEAK INT BECOMES PURE V- A; SMALL NU MASS AND SUPPRESSION OF V+A INTIMATELY CONNECTED VIA SEESAW.

20. March 2005 Theme Group 2 Type II seesaw and LR symmetry True seesaw formula in LR models is: The connection between small nu mass and suppressed V+A remains. First term pretty much says that in nonSUSY models eV neutrino mass implies that v_R=10^13 GeV. But it is not there in some models. E.g SUSYLR

21. March 2005 Theme Group 2 Seesaw and Parity Scale Known But Dirac mass mD unknown. So apriori Parity breaking scale unknown. (i)GUT assumption: Atmospheric data then implies: Which implies (ii) However if << due to some symmetries, can even be TeV range. (see models by Perez, Khasanov; Soni, Kiers, et. Al. where only type I dominates.) (iii) 3 rd possibility: = (Setzer, Spinner, RNM-06)

22. March 2005 Theme Group 2 Theory Summary so far: LR symmetric models address the following issues: i) Restoration of party at high scale ii) Natural framework for small neutrino mass via the seesaw mechanism, which connects small neutrino mass to the suppression of V+A currents. iii) Solve the strong CP problem; iv) Easy grand unification into SO(10) A priori, the W_R mass could be low; RH neutrino would then have a low mass. There are new Higgs bosons at low mass. We now discuss the phenomenology of these models.

23. March 2005 Theme Group 2 What is the lower limit on M_WR ? Depends on the nature of neutrinos and mass of nu_R. First analysis for Dirac nu or m_nuR << MeV: (Beg, Budny, RNM, Sirlin (75)) Two new parameters characterize muon and beta decay processes: and WL-WR mixing Pol Muon decay: at TRIUMPH (Strovnik et al) yield: -0.05 432 GeV)

24. March 2005 Theme Group 2 WR mass limit from beta decay WR mass limit from beta decay Search in In107, N12 by Leuven group: J. Deutsch et al. -Longitudinal pol of positrons From pol nuclei; -

25. March 2005 Theme Group 2 TWIST expt on muon decay MWR>325 GeV; Ultimate goal ~900 GeV

26. March 2005 Theme Group 2 Polarized neutron decay PERKEO II collaboration (M. Schuman et al, hep- ph/0705.3769) Limits on electron and neutrino asym. Coeff.- MWR>270 GeV,

27. March 2005 Theme Group 2 Collider searches: D0 and CDF Production cross section at Tevatron

28. March 2005 Theme Group 2 Limits on WR mass from Tevatron search Depends on mass of nuR: Vacuum stability requires (RNM,86) Look for a pick in the hard spectrum of e in WR decay or look for eejj from Bound: > 720 GeV (D0, CDF) For nuR much lighter, combining e and mu, CDF bound is: > 786 GeV.

29. March 2005 Theme Group 2 WR->mu+N (Goldsmit, thesis) W_R signal: pp->lljj; like sign leptons

30. March 2005 Theme Group 2 W_R cross section at LHC Collot, Ferrari et al. (2002)

31. March 2005 Theme Group 2 WR search at LHC (Datta, Guchait and Roy, 92) Heavy Majorana RH neutrinos

32. March 2005 Theme Group 2 LHC Discovery Reach for WR

33. March 2005 Theme Group 2 Z’ Mass limit (Cvetic, Godfrey (95); Leike (98); Godfrey’s talk.) Different sources for the limits: LEP data Atomic parity violation Roughly MZ’ > 630 GeV Possible at ILC with polarized beams: 7.2 TeV with 500 GeV and L=1000 fb^-1.

34. March 2005 Theme Group 2 WR mass limits independent of nuR mass K_L-K_S mass difference has WL-WR box graph contribution: (Beall, Bender, Soni’82) M_WR > 1.2-1.6 TeV Can be lowered however if g_L is not equal to g_R To the sub-TeV range.

35. March 2005 Theme Group 2 More recent comprehensive analysis Zhang, An, Ji and RNM, 2007 Ji’s talk. M_WR > 2.5 TeV from a combination of KL-KS, epsilon, d_n together.(uncertainty from long distance contribution)

36. March 2005 Theme Group 2 A bound on M_WR for Majorana RH nu Neutrinoless double beta decay receives new contributions if LR sym scale is in the TeV range: (RNM,86) M. Hirsch Review Neutrino 2006

37. March 2005 Theme Group 2 Doubly Charged Higgs bosons A distinctive signal of LR models is the presence of doubly charged Higgs bosons: Recall Couples to two charged leptons: Gives rise to a variety of experimental signatures: a) Double beta decay b) Muonium-Anti-muonium Osc. c) Colliders (ILC, LHC)

38. March 2005 Theme Group 2 Double beta decay without neutrinos (RNM, Vergados, 1981): 100 GeV for Higgs mass is OK.

39. March 2005 Theme Group 2 Muonium-Anti-muonium Oscillation (Feinberg, Weinberg) In left-right models, Delta ++ exchange gives rise to this process (Herczeg, RNM,92) Mass of Delta 100 GeV also OK. SEARCH FOR DOUBLY CHARGED HIGGS BOSON WILL BE A SIGNAL OF UNDERLYING LR SYM.

40. March 2005 Theme Group 2 Doubly charged Higgs at LHC Romanenko and Maalampi (02)

41. March 2005 Theme Group 2 Other consequences of low WR i) For M_L/M_R\sim 30, M_N\sim 300 GeV Observable at MEG till MWR=20 TeV.

42. March 2005 Theme Group 2 Two models with Sub-TeV W_R How to avoid the K_L-K_S bound: With supersymmetry there are new graphs involving gauginos, squarks: can lower the bound from cancellation.

43. March 2005 Theme Group 2 Avoiding KL-KS Bound Make gR<< gL. Non-manifest LR: (Datta, Raichoudhuri, 83; Langacker and Uma Sankar, 90) Susy LR (Has other advantages-solves strong CP problem)

44. March 2005 Theme Group 2 WR mass limits-SUSY LR Case IN SUSY LR, K_L-K_S mass difference has WL-WR box graph contribution as well as gaugino contributions: For s-squark mass >400 GeV cancellation possible to lower M_WR below TeV. (Gangopadhyay,85; Frank,Nie)

45. March 2005 Theme Group 2 Theoretical upper bound on WR in SUSYLR Model: Higgs superfields: V=V_F+V_D+V_S (V_F,V_D both positive)

46. March 2005 Theme Group 2 What is the smallest value of the D-term ? Since in general V_D is smallest when it vanishes and that occurs when: But this breaks electric charge: The only charge conserving vev is: For V_D to take the smallest value of zero, there must be cancellation between the Delta-vev and nu_R-tilde vev. But nu_R-tilde vev is zero if $M_WR >M_SUSY. Therefore electric charge conservation implies that M_WR< TeV in SUSYLR models. (Kuchimanchi and RNM,95)

47. March 2005 Theme Group 2 Two Other advantages of SUSYLR (i) There is no type II contribution and low WR scale is more easily compatible with small neutrino masses. (ii) There is range of parameters of the potential where the vevs of bi-doublets are real. This then gives natural solution to strong CP problem via left-right symmetry.

48. March 2005 Theme Group 2 Absence of type II term in SUSYLR Origin of type II term in LR models: Higgs potential has the term: When LR and EW symmetry break, becomes nonzero due to the following diagram:

49. March 2005 Theme Group 2 SUSYLR Supersymmetry does not allow V’ and hence in this case = 0 Hence low W_R is achieved if symmetries suppress Dirac neutrino mass. Similarly, SUSY restriction also makes vevs real and hence hermitean quark mass matrices and solves strong CP problem. A viable alternative to axion models. (RNM, Rasin; Kuchimanchi (96))

50. March 2005 Theme Group 2 Conclusion LR and SUSY LR theories have a number of attractive features and they solve a number of problems of the standard model: origin of P-violation, nu mass, strong CP problem. TeV scale WR allowed by neutrino masses and other low energy constraints. Tevatron limits are 650 GeV. LHC can push limits to 5-6 TeV range. For non-manifest and SUSY LR theories, WR can be below TeV and can be searched at ILC.

51. March 2005 Theme Group 2 Extra D LR and Sub-TeV W_R Extra dimension and Breaking SU(2)_R by orbifolding so that W_R is a KK mode and does not connect SM fermion to SM fermions whereas W_L connects SM to SM fermions: (R. N. M. and Perez-Lorenzana, 2003) d U,C.T s s U,C,T d DOES NOT GO SINCE WR IS A KK MODE WHEREAS WL IS ZERO MODE.