Left Right Symmetry around a Te V Scale
- Slides: 51
Left Right Symmetry around a Te. V Scale R. N. Mohapatra University of Maryland Theme Group 2 March 2005
SKETCH OF STANDARD MODEL Theme Group 2 March 2005
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: Theme Group 2 March 2005
Left-Right models • Gauge group: • Fermion assignment • Higgs fields: Theme Group 2 March 2005
Detailed Higgs content and Sym Breaking Break symmetry Theme Group 2 March 2005
Symmetry breaking Theme Group 2 March 2005
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 Theme Group 2 March 2005
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. Theme Group 2 March 2005
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: Theme Group 2 March 2005
Consequences of hermitean m 1. Left and Right CKM are same. 2. 2. Solves the strong CP problem 3. Without need for an axion. 4. Note that strong CP parameter vanishes 5. Unfortunately in the minimal non-SUSY LR 6. Vevs are complex. SUSYLR they are real. 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. Theme Group 2 March 2005
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)LXSU(2)RXSU(4)C of Pati and Salam (74) Theme Group 2 March 2005
SO(10) down to Std Model via LRS • SO(10) Nu mass • Left-Right Sym. Theory • Standard Model-> seesaw Theme Group 2 March 2005
Unification of Couplings: two examples Weak scale susy Non SUSY SO(10) with seesaw Low WR Unif OK too. Chang, Parida et al (85) Theme Group 2 March 2005
Compare with SU(5) Theme Group 2 March 2005
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. Theme Group 2 March 2005
How does one see it in practice ? • Effect of symmetry breaking on neutrino mass: • SU(2)RXU(1)B-L and Parity broken by the vev • This gives large Majorana mass to NR: • gives mass connecting nu. L and NR • (the Dirac mass m. D)- the seesaw mechanism: Theme Group 2 March 2005
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). Theme Group 2 March 2005
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. Theme Group 2 March 2005
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 non. SUSY models e. V neutrino mass implies that v_R=10^13 Ge. V. But it is not there in some models. E. g SUSYLR Theme Group 2 March 2005
Seesaw and Parity Scale • Known But Dirac mass m. D 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 Te. V range. (see models by Perez, Khasanov; Soni, Kiers, et. Al. where only type I dominates. ) (iii) 3 rd possibility: = (Setzer, Spinner, RNM-06) Theme Group 2 March 2005
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. Theme Group 2 March 2005
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_nu. R << Me. V: (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 < < 0. 035 (MWR>432 Ge. V) Theme Group 2 March 2005
WR mass limit from beta decay Search in In 107, N 12 by Leuven group: J. Deutsch et al. -Longitudinal pol of positrons From pol nuclei; - Theme Group 2 March 2005
TWIST expt on muon decay MWR>325 Ge. V; Ultimate goal ~900 March 2005 Theme Group 2 Ge. V
Polarized neutron decay • PERKEO II collaboration (M. Schuman et al, hep- ph/0705. 3769) • Limits on electron and neutrino asym. Coeff. - MWR>270 Ge. V, Theme Group 2 March 2005
Collider searches: D 0 and CDF Production cross section at Tevatron Theme Group 2 March 2005
Limits on WR mass from Tevatron search • Depends on mass of nu. R: • 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 Ge. V (D 0, CDF) • For nu. R much lighter, combining e and mu, CDF bound is: > 786 Ge. V. Theme Group 2 March 2005
WR->mu+N (Goldsmit, thesis) W_R signal: pp->lljj; like sign leptons Theme Group 2 March 2005
W_R cross section at LHC • Collot, Ferrari et al. (2002) Theme Group 2 March 2005
WR search at LHC • (Datta, Guchait and Roy, 92) Heavy Majorana RH neutrinos Theme Group 2 March
LHC Discovery Reach for WR Theme Group 2 March 2005
Z’ Mass limit • (Cvetic, Godfrey (95); Leike (98); Godfrey’s talk. ) • Different sources for the limits: • LEP data • Atomic parity violation • Roughly MZ’ > 630 Ge. V • Possible at ILC with polarized beams: 7. 2 Te. V with 500 Ge. V and L=1000 fb^-1. Theme Group 2 March 2005
WR mass limits independent of nu. R mass • K_L-K_S mass difference has WL-WR box graph contribution: (Beall, Bender, Soni’ 82) • M_WR > 1. 2 -1. 6 Te. V • Can be lowered however if g_L is not equal to g_R To the sub-Te. V range. Theme Group 2 March 2005
More recent comprehensive analysis • Zhang, An, Ji and RNM, 2007 • Ji’s talk. M_WR > 2. 5 Te. V from a combination of KL-KS, epsilon, d_n together. (uncertainty from long distance contribution) Theme Group 2 March 2005
A bound on M_WR for Majorana RH nu • Neutrinoless double beta decay receives new contributions if LR sym scale is in the Te. V range: (RNM, 86) M. Hirsch Review Neutrino 2006 Theme Group 2 March 2005
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) Theme Group 2 March 2005
Double beta decay without neutrinos • (RNM, Vergados, 1981): 100 Ge. V for Higgs mass is OK. Theme Group 2 March 2005
Muonium-Anti-muonium Oscillation • • (Feinberg, Weinberg) In left-right models, Delta ++ exchange gives rise to this process (Herczeg, RNM, 92) • Mass of Delta 100 Ge. V also OK. • SEARCH FOR DOUBLY CHARGED HIGGS BOSON WILL BE A SIGNAL OF UNDERLYING LR SYM. Theme Group 2 March 2005
Doubly charged Higgs at LHC • Romanenko and Maalampi (02) Theme Group 2 March 2005
Other consequences of low WR • i) • For M_L/M_Rsim 30, M_Nsim 300 Ge. V • Observable at MEG till MWR=20 Te. V. Theme Group 2 March 2005
Two models with Sub-Te. V 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. Theme Group 2 March 2005
Avoiding KL-KS Bound • Make g. R<< g. L. • Non-manifest LR: (Datta, Raichoudhuri, 83; Langacker and Uma Sankar, 90) • Susy LR (Has other advantages-solves strong CP problem) Theme Group 2 March 2005
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 Ge. V cancellation possible to lower M_WR below Te. V. (Gangopadhyay, 85; Frank, Nie) Theme Group 2 March 2005
Theoretical upper bound on WR in SUSYLR • Model: Higgs superfields: • V=V_F+V_D+V_S (V_F, V_D both positive) Theme Group 2 March 2005
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< Te. V in SUSYLR models. (Kuchimanchi and RNM, 95) Theme Group 2 March 2005
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. Theme Group 2 March 2005
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: Theme Group 2 March 2005
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 <phi> vevs real and hence hermitean quark mass matrices and solves strong CP problem. A viable alternative to axion models. (RNM, Rasin; Kuchimanchi (96)) Theme Group 2 March 2005
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. • Te. V scale WR allowed by neutrino masses and other low energy constraints. • Tevatron limits are 650 Ge. V. LHC can push limits to 5 -6 Te. V range. • For non-manifest and SUSY LR theories, WR can be below Te. V and can be searched at ILC. Theme Group 2 March 2005
Extra D LR and Sub-Te. V 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 s U, C. T U, C, T s d DOES NOT GO SINCE WR IS A KK MODE WHEREAS WL IS ZERO MODE. Theme Group 2 March 2005
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