Neutrino Mass Physics at LHC

R. N. MohapatraUniversity of MarylandNO-VE, 2008, Venice

Neutrino mass Physics

Neutrino masses and mixings are now facts: we are entering the era of Precision Neutrino Mass Science (PNMS era)

There is surely a great deal of physics beyond the standard model associated with this.

How can LHC help us to unravel this physics ?

Two broad new kinds of physics for neutrino mass:

(i) Why ? (new scale, new particles, ..)

(ii) Why two mixing angles are so large ?

(new flavor symmetries or GUTs ?)

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Small neutrino mass and Seesaw mechanism

Why ? Seesaw solution: Add right handed

neutrinos to SM with Majorana mass:

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Breaks B-L : New scale, new symmetry and new physics beyond SM.

After electroweak symmetry breaking

leads to seesaw formula:

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Seesaw Mechanism After Electroweak Sym Breaking mass matrix is given by

which gives (type I seesaw)

Minkowski,Gell-Mann, Ramond, Slansky,Yanagida,R.N.M.,Senjanovic,Glashow

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Seesaw and B-L symmetry SM Higgs boson represents physics of the

electroweak symmetry breaking and its discovery will complete understanding of SM symmetry.

Seesaw mechanism tells us that there is a new symmetry breaking scale associated

with RH neutrino mass: B-L symmetry . This talk discusses how to search for the

Higgs fields associated with this symmetry and improve our understanding of B-L symmetry.

Testing the seesaw idea and B-L symmetry.

Important for testing seesaw are two considerations:

(i) How big is the seesaw or B-L scale ?

(ii) What is the new physics associated with this new scale ? –are there new forces, new Higgs fields, etc ?

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Seesaw with no new forces at LHC

If there is no new interaction: Only way to test seesaw is to produce N; This can happen only through mixing if is in sub-TeV range and further only if mixing is > (del Aguila,Aguilar-Savedra,

Pittau; Han, Zhang…) – However Tiny and 100 GeV implies and ; can only be

large under highly contrived cases:(Kersten, Smirnov) ; Unlikely to test seesaw this way!

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Situation changes drastically with new interactions: With new gauge forces coupled to RH

neutrinos, seesaw can be tested despite tiny ;

A simple possibility is where there is a

B-L gauge force coupling to matter as part of an

gauge symmetry. RH neutrino mass in this case is associated with the

breaking of this new symmetry . This provides new signals for seesaw

at LHC.

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Two well motivated scenarios:

(i) Large Grand unification is an independently well motivated

hypothesis which suggests for Yukawa coupings:

implying GeV

Gauge coupling unification scale High scale seesaw goes well with GUT s; e.g. SO(10).

However in this case, few signals of seesaw: One direct test is search for assuming susy ! GUTs have problems too: doublet triplet splitting; vs

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Lower scale non-GUT type seesaw: Subject of this talk: (ii) Small Yukawas: Note the dependence of in the seesaw formula compared to linear on for ; so not too small

Yukawas can lead to e.g. Implies seesaw or B-L physics scale in few TeV range. In general scale far below GUT scale- Simple example is - low scale left-right model.

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SUSY LR attractive for other reasons: Supersymmetric left-right model: (i) Expialns the origin of parity violation: (ii) Solves gauge hierarchy problem (as in

MSSM); (iii) Gives automatic R-parity (unlike

MSSM) and hence natural neutralino dark matter and naturally stable proton.

(iv) Solves susy CP and strong CP problem (unlike MSSM).

(v) Helps in understanding a supersymmetry breaking mechanism (unlike MSSM).

SUSYLR DETAILS:

Gauge group: Fermion assignment

Higgs fields

(R.N.M., Senjanovic, 79)

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SUSY essential for lower scale left-right seesaw

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Without SUSY neutrino mass too large since v_L~GeV. (type I+II seesaw) , SUSY implies ; (pure type I seesaw) nu-mass in the eV range even for TeV seesaw.

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SUSY breaking constraints and sub-TeV - Higgs An important question in supersymmetry

is: how is supersymmetry broken ? Scenarios: (i) Minimal Supergravity: FCNC problem (ii) Gauge mediation (needs many

particles, does not have cold dark matter etc.) (iii) Anomaly mediation: (potential to solve

both these problems.)(Randall, Sundrum; Giudice, Luty, Murayama, Rattazzi)

Consistency of case iii with electric charge conservation requires sub-TeV - Higgs

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Two cases with LHC signal (i) Multi-TeV scale WR: In this case, Sub-TeV to TeV scale WR, Z’, which can be searched for

in colliders: (ii) Higher scale B-L (or WR): New result: If , one will have in the sub-TeV range and

observable. Searching for Higgses can probe

B-L scale upto .

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TeV mass WR case: (A): Direct production at LHC Looking for TeV scale at LHC : Signal: Very little background; already used in

D0, CDF ; Present limits: 780 GeV (Keung, Senjanovic, 83) (Does not depend on )

LHC reach 4 TeV (Azuelos et al)

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(B): Neutrinoless double beta decay

TeV scale WR contributes to nu-less double decay regardless of how small nu- Majorana mass mass is .

(P. Vogel’s talk)

Dependence on WR mass is M^-5 – Present bound is ~1 TeV can go up to2

TeV.

(C): New Relaxed Upper bound on light Higgs mass

MSSM: Light Higgs mass: GeV For Low scale WR, new contribution from

D-term+ 1-loop

Zhang,RNM,Ji,An arXiv:0804.0268

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TeV and Higher scale Seesaw and Higgs

A generic prediction of all these models: doubly charged Higgs and Higgsinos, triplet Higgses

( , )in the TeV range – without fine tuning.

Different from triplet Higgs of type II seesaw models discussed in Perez,Han, Huang, Wang,Li, Si, Akeroyd,Aoki, Sugiyama; ……

Different from usual SUSY models which only have neutral and singly charged Higgs

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Doubly charged Higgs: Very different from known Higgs in that it couples

only to leptons and not to quarks: Coupling not small.

One coupling to left and another to the right sector:

Both decay to lepton pairs (from coupling)

For left Delta,

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Difference from type II models

In type II models, it is only the triplet that is present; its coupling f to leptons depends on

the < >=v since

So only for eV vev for f is measurable; Pro: it tracks neutrino mass matrices; Measuring

different branching ratios gives neutrino mass matrix

Con: such small vevs come out naturally only if triplets are superheavy and beyond the reach of LHC. One needs to do a severe fine tuning (~ )

The models I discuss are not fine tuned:

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Difference of type II models from type I: Type II: decays:

Whereas for type I models we discuss:

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Present lower bounds on doubly charged Higgs mass:

Drell-Yan pair production main mechanism at hadron colliders: Signal: pp --> or all muon

Collider: CDF, D0: GeV HERA > 141 GeV Low energy: Muonium-anti-muonium osc. (PSI)

For , M++ >250 GeV. g-2 of muon: 100 GeV order.

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Production process: Drell-Yan via exchange;

Signal: peak in like sign lepton invariant

mass plot for double charged case;

trilepton + missing E in case.

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LHC prospects: Gunion, Loomis and Petit; Akyroid, Aoki; Azuelos et al.,

Mukhopadhyaya,Han,Wang,Si; Huitu,Malaampi,Raidal; Dutta..

Main Bg ZZ production: LHC Mass Reach ~TeV

with 300 fb^-1.

Doubly charged Higgs and muonium-antimuonium Osc.:

Muonium-anti-muonium can provide better probe for some models:

If SUSY is broken by anomalies: and also M < 10 TeV.

Lower limit on

PRISM expt. Reach:

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Doubly charged Higgs atCollider ee

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collider at 1 TeV cm E can probe doubly charged Higgs upto 900 GeV mass. (Mukhopadhyay, S. Rai)

The relevant processes:

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Singly charged signal Properties of singly charged

different from MSSM singly charged couples only to leptons- has L=2

Present bound on mass comes from wrong kind of muon decay:

and nuTeV expt looking for

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Bounds on NuTeV bound (Formaggio et al, 2001)

Mass bound in 100 GeV range for reasonable values of f-couplings.

New proposal NUSONG expt (Conrad et al. 2007) will improve this limit by a factor of 4 .

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AT LHC LHC signal: pp + missing E K. Wang et al.

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Why are naturally light even for high scale seesaw ?

(i) If LR scale is less than few TeV , clearly these Higgs can have in the sub-TeV mass.

(ii) For higher scale seesaw accidental global symmetry leads to sub-TeV

as long as or less. (iii) If SUSY is broken by anomaly

mediation, these fields with sub-TeV to TeV masses become essential to avoid electric charge non-conservation. Strongest case for light .

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Basic point is the constraint of supersymmetry:

SM Minimum corresponds to: Conserves electric charge. Higgs mass prop to and hence Higgs mass arbitrary. Bring in Supersymmetry: and

hence an upper limit on Higgs mass <130 GeV.

For SUSYLR seesaw models, SUSY constrains the Higgs potential so much that

Necessary consequence is light below 10 TeV . Otherwise, electric charge broken by vacuum.

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Light Higgs for High seesaw scale

Naïve logic: Higgs mass is of the order of symmetry breaking scale; breaks down when there are accidental symmetries.

SUSYLR superpotential:

Has U(6,c) global symmetry which breaks down to U(5,c) (in the absence of higher dim term.)

eleven massless complex Higgs bosons: 3 absorbed in gauge sym. breaking from SU(2)xU(1) to U(1). Eight left are two doubly charged Higgs bosons and two SM triplets;

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How do get masses ? The nonrenormalizable term

Where could be the new physics scale above WR scale or Planck scale.

Breaks this enhanced global symmetry and give mass to fields.

Mass is of order: ;

implying for Delta mass sub-TeV. (Aulakh, Melfo, Senjanovic; Chacko, RNM, 97)

Observation of probes seesaw scale far below GUT scale.

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So for the case of MSSM+AMSB, slepton mass squares negative-vacuum breaks electric charge:

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Squark and slepton masses in AMSB:

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Where f is the Yukawa coupling and g is the generic gauge coupling: slepton masses become positive if

SUSYLR cures the tachyonic slepton problem of AMSB without fine tuning assumptions:(Setzer, Spinner, RNM, Phys. Rev. D and arXiv:0802.1208- JHEP )

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Limit on Higgs mass, couplings from detailed study: For AMSB cure to work, we must have

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(ii) ;also triplets.

This implies Prism proposal:

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Summary and Conclusion: Minimal SUSY seesaw in conjunction with

a way to understand SUSY breaking (AMSB) predicts the existence of sub-TeV

They can be observable in LHC as well as in muonium-anti-muonium oscillation

experiments. In particular it predicts:

Search for Delta Higgses can probe seesaw below

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Summary and Conclusion: (i) < few TeVs or

(ii) > GeV ;

(iii) If SUSY is broken by anomaly mediation, then

GeV (iii) In these models, there are 100 GeV to TeV scale SU(2)-triplet and doubly charged Higgs fields. (iv) Case (i)- Upward shift of light Higgs mass

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Range of Double charged Higgs masses

Upper limit for AMSB to work:

Lower limit on muonium-anti-muonium oscillation amplitude for this model (PSI)

Higher precision search for important. TeV scale WR models have many collider

tests: e.g. Higher Higgs mass, like sign dilepton

events and of course sub-TeV scale doubly charged Higgs

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Dark matter issue: Neutralino unstable ! But gravitino though unstable due to R-P

breaking but still quite long lived to be dark matter:

Decay diagram:

Longer than the age of the universe ! (Ibarra,

et al)

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Displaced vertices: Neutralino decays but with a nano to pico sec.

lifetime; hence leads to displaced vertices:

(Zhang, Nussinov, et al. to appear)

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Constraints on WR in SUSYLR : Theory details

Higgs superfields break SU(2)_R

V=V_F+V_D+V_S (V_F,V_D >0)

Look for minimum of the potential

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What is the smallest value of the D-term ?

When is =0

Since in general

If RP conserved i.e. V is minimum when V_D vanishes and that occurs

when: since

But this breaks electric charge !

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Charge conservation-> RP violation

So only choice left to get a charge conserving minimum is when

It breaks R-parity and Lepton number but not

Baryon number. So proton stability is guaranteed. Corollary: Seesaw scale has an upper limit

of a few TeV. (Kuchimanchi, RNM, 95)

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Why GeV ? As the seesaw scale increases, higher dim

terms in superpotential become important : restore R-parity and give a stable charge conserving vacuum:

Typically, they are (if no new physics till Planck-otherwise replace by new Phys scale)

+

Lower limit on WR when above terms are of order weak scale i.e. >

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How do they get masses ?

The second nonrenormalizable term

breaks this enhanced global symmetry and give mass to fields.

Mass is of order: ; LEP bound then implies

GeV implying v_R

(Aulakh, Melfo, Senjanovic; Chacko, RNM, 97)

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Range of Double charged Higgs masses

Upper limit for AMSB to work:

Lower limit on muonium-anti-muonium oscillation amplitude for this model (PSI)

Higher precision search for

important.

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LHC signals of low scale seesaw (i) TeV scale : Signal: Very little background; already

used in D0, CDF ; Present limits: 780 GeV (Keung, Senjanovic, 83)

(ii) I will focus on Higgs boson tests

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Signals for TeV scale WR’s etc.

First issue: Is there a dark matter ? Yes. It is the gravitino; it is unstable due

to R-P breaking but still quite long lived. Decay diagram:

Longer than the age of the universe !

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