Left Right Symmetry around a TeV Scale

March 2005Theme Group 2

Left Right Symmetry Left Right Symmetry around a TeV Scalearound a TeV Scale

R. N. Mohapatra

University of Maryland


SKETCH OF STANDARD MODELSKETCH OF STANDARD MODEL

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RRR due ,,Higgs

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No R .0 m


Origin of Parity violationOrigin 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:


Left-Right modelsLeft-Right models

• Gauge group:

• Fermion assignment

• Higgs fields:

LBRL USUSU )1()2()2(

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u

R

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)0,2,2( )2,1,3()2,3,1(; LR


Detailed Higgs content and Sym BreakingDetailed Higgs content and Sym Breaking

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Break symmetry


Symmetry breakingSymmetry breaking

LBRL USUSU )1()2()2(

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Comparision with standard modelComparision 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

23

YIQ L

233

LBIIQ RL


Asymptotic Parity conservationAsymptotic 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.

]..[ ,,

RRLLwk WJWJgL

..2

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Wwk JJ

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Another consequence of LR models: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:

..chQQhL bRaLabY ii

i

i i


Consequences of hermitean Consequences of hermitean mm

0.. duMMDetArg

1.Left and Right CKM are same.

2.Solves the strong CP problemWithout need for an axion.

Note that strong CP parameter vanishes

Unfortunately in the minimal non-SUSY LRVevs are complex. SUSYLR they are real.

0.. duMMDetArg


Spontaneous CP and P BreakingSpontaneous 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.

Tlduldu MM ,,,,

RL


Attractive Grand Unification of LR 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)


SO(10) down to Std Model via LRSSO(10) down to Std Model via LRS

• SO(10) Nu mass

• Left-Right Sym. Theory

• Standard Model-> seesaw

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0

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Unification of Couplings: two examplesUnification of Couplings: two examples

Weak scale susyWeak scale susyNon SUSY SO(10) with seesawNon SUSY SO(10) with seesaw

Low WR Unif OK too.Low WR Unif OK too.Chang, Parida et al (85)Chang, Parida et al (85)


Compare with SU(5)Compare with SU(5)


Neutrino Mass, Seesaw AND LRNeutrino 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.

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How does one see it in practiceHow 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 nuL and NR

• (the Dirac mass mD)- the seesaw mechanism:

..)( chfhL RRRLLLRLlY

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Seesaw Formula: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).

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Small nu mass Due to suppressed V+ASmall 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.

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Type II seesaw and LR symmetryType 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

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DT

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Seesaw and Parity ScaleSeesaw 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) 3rd possibility: =(Setzer, Spinner, RNM-06)

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Theory Summary so farTheory 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.


What is the lower limit on M_WR ?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 < < 0.035 0.035 (MWR>432 GeV)

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WR mass limit from beta decayWR mass limit from beta decay

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Search in In107, N12 by Leuven Search in In107, N12 by Leuven group: group: J. Deutsch et al.J. Deutsch et al.

-Longitudinal pol of positrons-Longitudinal pol of positronsFrom pol nuclei;From pol nuclei;--


TWIST expt on muon decayTWIST expt on muon decay

MWR>325 GeV; Ultimate goal ~900 MWR>325 GeV; Ultimate goal ~900 GeVGeV


Polarized neutron decayPolarized neutron decay• PERKEO II collaboration (M. Schuman et al,

hep-ph/0705.3769)

• Limits on electron and neutrino asym. Coeff.- MWR>270 GeV,


Collider searches: D0 and CDFCollider searches: D0 and CDF

Production cross section at Tevatron


Limits on WR mass from Tevatron searchLimits 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.

RR WMM

eNW RR ejj

RWM

RWM


WR->mu+N WR->mu+N (Goldsmit, thesis)(Goldsmit, thesis)

W_R signal: pp->lljj; like sign leptons


W_R cross section at LHCW_R cross section at LHC

• Collot, Ferrari et al. (2002)


WR search at LHC WR search at LHC

• (Datta, Guchait and Roy, 92) Heavy Majorana RH neutrinos


LHC Discovery Reach for WRLHC Discovery Reach for WR


Z’ Mass limitZ’ 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 .


WR mass limits independent of nuR massWR 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.

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More recent comprehensive analysisMore 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)


A bound on M_WRA bound on M_WR for Majorana RH nufor Majorana RH nu

• Neutrinoless double beta decay receives new contributions if LR sym scale is in the TeV range: (RNM,86)

M. Hirsch ReviewNeutrino 2006


Doubly Charged Higgs bosonsDoubly 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)

..chllfL baab

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Double beta decay without neutrinosDouble beta decay without neutrinos

• (RNM, Vergados, 1981): 100 GeV for Higgs mass is OK.

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Muonium-Anti-muonium OscillationMuonium-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.

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ffA ee

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Doubly charged Higgs at LHCDoubly charged Higgs at LHC

• Romanenko and Maalampi (02)


Other consequences of low WROther consequences of low WR

• i)

• For M_L/M_R\sim 30, M_N\sim 300 GeV

• Observable at MEG till MWR=20 TeV.

,, ee

29 )cos(sin104)( eB


Two models with Sub-TeV W_RTwo 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.


Avoiding KL-KS BoundAvoiding 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)


WR mass limits-SUSY LR CaseWR 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)

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Rg

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Theoretical upper bound on WR in SUSYLRTheoretical upper bound on WR in SUSYLR

• Model: Higgs superfields:

• V=V_F+V_D+V_S (V_F,V_D both positive)

0

)2,1,3(


What is the smallest value of the D-term ?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)

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Two Other advantages of SUSYLRTwo 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.


Absence of type II term in SUSYLRAbsence 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:

RLV '

L


SUSYLRSUSYLR• 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))

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ConclusionConclusion

• 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.


Extra D LR and Sub-TeV W_RExtra 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.

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Left Right Symmetry around a TeV Scale