motivations basics models experimental constraints and ...pgl/talks/pgl-atlas-exotics.pdf · models...

Z′/W ′ Theory Overview

• Motivations

• Basics

• Models

• Experimental constraintsand prospects

• Implications

The Physics of Heavy Z′ Gauge Bosons, RMP 81, 1199 (0801.1345)

Z′ Physics at the LHC, 0911.4294

ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)

http://arXiv.org/abs/0801.1345

http://arxiv.org/abs/0911.4294

[TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B [

pb

]σ

410

310

210

110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

ll→Z’

1 = 13 TeV, 3.2 fbs

M [GeV]500 1000 1500 2000 2500 3000 3500

+

X)

→Z

+X

→(p

pσ

+

X)

/ →

Z'+

X→

(pp

σ

7−10

6−10

5−10

4−10Median expected

68% expected

95% expected

(LOx1.3)ΨZ'

95% CL limit

)µµ (13 TeV, -1 (13 TeV, ee) + 2.8 fb-12.6 fb

CMSPreliminary

llllll

[TeV]W’

m

1 2 3 4 5 6

B [pb]

σ

4−10

3−10

2−10

1−10

1

10Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMW’

PreliminaryATLAS

1 = 13 TeV, 3.3 fbs

νl→W’

Ru

nI L

imit

[GeV]W'M1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

B (

fb)

× σ

1−10

1

10

210

310

410

510sα PDF+ ⊗ SSM W' NNLO σ

Observed

Expected

σ 1 ±

σ 2 ±

miss

T+Eµe,

(13 TeV)-12.2 fb

CMSPreliminary


Motivations for a Z′ or W ′

• Strings/GUTS (large underlying groups; U(n) in Type IIa)

– Harder to break U(1)′ factors than non-abelian (remnants)

– Supersymmetry: SU(2)×U(1) and U(1)′ breaking scales bothset by SUSY breaking scale (unless flat direction)

– µ problem

– Larger MH than MSSM

• Alternative electroweak model/breaking (TeV scale): left-rightsymmetry, extra dimensions (Kaluza-Klein excitations, M ∼ R−1 ∼2 TeV × (10−17cm/R)), composite Higgs

• Connection to hidden sector (dark, SUSY breaking/mediation)

• Extensive physics implications, especially for TeV-scale Z′, W ′


Standard Model Neutral Current

−LSMNC = gJµ3 W3µ + g′JµYBµ = eJµemAµ + g1J

µ1 Z

01µ

Aµ = sin θWW3µ + cos θWBµ

Zµ = cos θWW3µ − sin θWBµ

θW ≡ tan−1

(g′/g) e = g sin θW g1 = g/ cos θW

Jµ1 =∑i

fiγµ[ε1

L(i)PL + ε1R(i)PR]fi PL,R ≡ (1∓γ5)

2

ε1L(i) = t3iL − sin2 θW qi ε1

R(i) = − sin2 θW qi

M2Z0 =

1

4g2

1ν2 =

M2W

cos2 θWν ∼ 246 GeV


Standard Model with Additional U(1)′

−LNC = eJµemAµ + g1Jµ1 Z

01µ︸︷︷︸

SM

+

n+1∑α=2

gαJµαZ

0αµ

Jµα =∑i

fiγµ[εαL(i)PL + εαR(i)PR]fi

• εαL,R(i) are U(1)α charges of the left and right handed componentsof fermion fi (chiral for εαL(i) 6= εαR(i))

• gαV,A(i) = εαL(i)± εαR(i)

• May specify left chiral charges for fermion f and antifermion fc

εαL(f) = Qαf εαR(f) = −Qαfc

Q1u = 12 −

23 sin2 θW and Q1uc = +2

3 sin2 θW


Mass and Mixing

• Mass matrix for single Z′

M2Z−Z′ =

(M2Z0 ∆2

∆2 M2Z′

)

• Eg., SU(2) singlet S; doublets φu =

(φ0u

φ−u

), φd =

(φ+d

φ0d

)M

2Z0 =

1

4g

21(|νu|2 + |νd|2)

∆2

=1

2g1g2(Qu|νu|2 −Qd|νd|2)

M2Z′ =g

22(Q

2u|νu|

2+Q

2d|νd|

2+Q

2S|s|

2)

νu,d ≡√

2〈φ0u,d〉, s =

√2〈S〉, ν

2= (|νu|2+|νd|2) ∼ (246 GeV)

2


• Eigenvalues M21,2, mixing angle θ

tan2 θ =M2Z0 −M2

1

M22 −M2

Z0

• For MZ′ � (MZ0, |∆|)

M21 ∼M

2Z0 −

∆4

M2Z′�M2

2 M22 ∼M

2Z′

θ ∼ −∆2

M2Z′∼ C

g2

g1

M21

M22

with C = 2

[Qu|νu|2 −Qd|νd|2

|νu|2 + |νd|2

]

• Kinetic mixing also possible


Anomalies and Exotics

• Must cancel triangle and mixed gravitationalanomalies

• No solution except Q2 = 0 for family universalSM fermions

f

V1 V2

V3

– Typeset by FoilTEX – 1

• Must introduce new fermions: SM singlets like νR or exotic SU(2)(usually non-chiral under SM)

DL +DR,

(E0

E−

)L

+

(E0

E−

)R

• Supersymmetry: include Higgsinos and singlinos (partners of S)

• 750 GeV diphoton?


Z′ Models

• Enormous number of models, distinguished by gauge coupling g2,mass scale, charges Q2, exotics, mass/kinetic mixing, couplings tohidden sector · · ·

• No simple general parametrization

• Benchmark models: TeV scale MZ′ with electroweak strengthcouplings

– Sequential ZSM

– Models based on T3R and B − L– E6 models

– Anomaly cancellation + miscellaneous assumptions(universality? Yukawas? Gauge unification? SUSY? Seesaw? # Exotics?)


Sequential ZSM

• Same couplings to fermions as the SM Z boson

– Reference model

– Hard to obtain in gauge theory unless complicated exotic sector[e.g., “diagonal” embedding of SU(2) ⊂ SU(2)1 × SU(2)2]

– Kaluza-Klein excitations with TeV extra dimensions


Models based on T3R and B − L

• Motivated by minimal fermions (only νR needed for anomalies), SO(10),and left-right SU(2)L × SU(2)R × U(1)BL

• TBL ≡ 12(B − L), T3R = Y − TBL = 1

2[uR, νR], −1

2[dR, e

−R]

• For non-abelian embedding and no kinetic mixing

QLR =

√3

5

[αT3R −

1

αTBL

]

α =gR

gBL=

√(gR/g)2 cot2 θW − 1 −−−→

gR→g1.53

g2 =

√5

3g tan θW ∼ 0.46


The E6 models

• Example of anomaly free charges and exotics, based onE6 → SO(10)× U(1)ψ and SO(10)→ SU(5)× U(1)χ

• 3× 27: 3 S fields, 3 exotic (D +Dc) pairs, 3 Higgs (or exotic lepton) pairs

• Supersymmetric version forbids µ term except χ model (SO(10))

SO(10) SU(5) 2√

10Qχ 2√

6Qψ 2√

15Qη

16 10 (u, d, uc, e+) −1 1 −2

5∗ (dc, ν, e−) 3 1 1νc −5 1 −5

10 5 (D,Hu) 2 −2 45∗ (Dc,Hd) −2 −2 1

1 1 S 0 4 −5

• General: Q2 = cos θE6Qχ + sin θE6Qψ


Other Z′ Models

• TeV scale dynamics (composite Higgs, un-unified, strong tt coupling, · · · )

• Kaluza-Klein excitations (large dimensions or Randall-Sundrum)

• Decoupled (leptophobic, fermiophobic, weak coupling, low scale/massless)

• Hidden sector “portal” (e.g., SUSY breaking, dark matter, or “hidden

valley”) [kinetic or HDO mixing, Z′ mediation]

• Secluded or intermediate scale SUSY (flat directions, Dirac mν)

• Family nonuniversal couplings (FCNC)

• String derived (may be T3R, TBL, E6 or “random”)

• Stuckelberg (no Higgs)

• Anomalous U(1)′ (string theories with large dimensions)


Precision Electroweak

• Low energy weak neutral current: Z′ exchange and Z − Z′mixing (still very important)

• Z-pole (LEP, SLC, Tevatron, LHC)

– Z − Z′ mixing (vertices; shift in M1)

Vi = cos θg1V (i) +

g2

g1

sin θg2V (i), Ai = cos θg

1A(i) +

g2

g1

sin θg2A(i)

• LEP2 (and future e+e−): four-fermi operator interfering with γ, Z


-0.004 -0.002 0 0.002 0.0040

1

2

3

4

5

6

x

0.6 0.2

CDFD0LEP 2

MZ’

[TeV]

Zχ

sin θzz’

0.4 00.81

-0.004 -0.002 0 0.002 0.0040

1

2

3

4

5

6

x

CDF

MZ’

[TeV]

Z ψ

sin θzz’

00.50.751 0.25

D0LEP 2

Erler et al., 0906.2435; 95%


The Tevatron and LHC

• Resonance in pp, pp→ e+e−, µ+µ−, · · · AB → Zα in narrow width:

dσ

dy=

4π2x1x2

3M3α

∑i

(fAqi(x1)f

Bqi

(x2) + fAqi(x1)fBqi

(x2))

Γ(Zα→ qiqi)

Γαfi ≡ Γ(Zα→ fifi) =g2αCfiMα

24π

(εαL(i)2 + εαR(i)2

)x1,2 = (Mα/

√s)e±y

Cfi = color factor

• Also dijet, tt, etc: strongly coupled resonances

• Corrections for QCD/width/interference, etc


[TeV]Z’M0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B [

pb

]σ

410

310

210

110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

ll→Z’

1 = 13 TeV, 3.2 fbs

M [GeV]500 1000 1500 2000 2500 3000 3500

+

X)

→Z

+X

→(p

pσ

+

X)

/ →

Z'+

X→

(pp

σ

7−10

6−10

5−10

4−10Median expected

68% expected

95% expected

(LOx1.3)ΨZ'

95% CL limit

)µµ (13 TeV, -1 (13 TeV, ee) + 2.8 fb-12.6 fb

CMSPreliminary

llllll

• LHC discovery to ∼ 4− 5 TeV at 100 fb−1

– Spin-0 (Higgs), spin-1 (Z′), spin-2 (Kaluza-Klein graviton) by angulardistribution, e.g.,

dσfZ′

d cos θ∗∝

3

8(1 + cos2 θ∗) +AfFB cos θ∗ [for spin-1]


Discovery Reach (GeV)

310 410

χE6 Model -

ψE6 Model -

ηE6 Model -

LR Symmetric

Alt. LRSM

Ununified Model

Sequential SM

TC2

Littlest Higgs

Simplest LH

Anom. Free SLH

331 (2U1D)

Hx SU(2)LSU(2)

Hx U(1)LU(1)

7 TeV - 50 pb-1

7 TeV - 100 pb-1

10 TeV - 100 pb-1

10 TeV - 200 pb-1

14 TeV - 1 fb-1

14 TeV - 10 fb-1

14 TeV - 100 fb-1

1.96 TeV - 8.0 fb-1

1.96 TeV - 1.3 fb-1

Diener ea, 0910.1334; 5 events/dilepton channel

] (TeV)+e-m[e2.8 2.85 2.9 2.95 3 3.05 3.1 3.15 3.2

)-1

] (Te

V+ e-

/dm

[eσ

dσ

1/

0

2

4

6

8

10

12

14 χ

ψ

η

LRB-LSSM

Han et al, 1308.2738

• Mass, width?

• Rates (total width) dependon open sparticle/exoticchannels

• σZ′B`ΓZ′ probes absolutecouplings


Diagnostics of Z′ Couplings

• LHC diagnostics to 2-2.5 TeV at 100 fb−1 (at least)

• Forward-backward (or charge) asymmetries and rapiditydistributions in `+`−

[GeV]llM1000 1100 1200 1300 1400 1500 1600 1700 1800

FB

lA

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2χZ’

ψZ’

ηZ’

LRZ’-1, L=100fbηZ’

Forward backward asymmetry measurement

|>0.8ll|y=1.5TeVZ’M

=14TeVsLHC, a)

|ll|Y0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

dn

/ d

y

0

500

1000

1500

2000

2500

-1, 100fbη Z’

u: fit uη Z’d fit d

sum

ψ Z’

<1.55 TeVll1.45 TeV<M

Rapidity distributionb)

LHC/ILC, 0410364


*)θcos(-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

*)θ/d

cos(

σ dσ

1/

0.3

0.4

0.5

0.6

0.7

0.8χ

ψ

η

LRB-LSSM

Han et al, 1308.2738] (fb)+e-[eσ

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

]+ e-[e

FBA

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

= 42χ∆, 3 TeV Z’, -1LHC 14 TeV 300(3000) fb

χ

ψη

LR

B-LSSM


http://arxiv.org/abs/1308.2738

• Lineshape: MZ′, σZ′B`, ΓZ′ (σZ′B`ΓZ′)

• Other two body decays (jj, bb, tt, eµ, τ+τ−)

• Polarization ( τ , t)

• Associated production Z′Z,Z′W,Z′γ [f -line filter]

• Rare (but enhanced) decays Z′→Wf1f2 (radiated W , f filter)

• Z′→W+W−, Zh, or W±H∓: small mixing compensated bylongitudinal W,Z

Γ(Z′ →W

+W−

) =g2

1θ2MZ′

192π

(MZ′

MZ

)4

=g2

2C2MZ′

192π

• Exotic decays: multileptons (` ¯ ¯ via RPV; 6` via ZH′);ggg, ggγ (loops); same-sign dileptons (heavy Majorana νR); invisible;sparticles/exotics (SUSY factory)


W ′

• Less motivated than Z′, but possible

• WL: diagonal SU(2) ⊂ SU(2)1 × SU(2)2 (e.g., un-unified, Little Higgs);large extra dimensions (Kaluza-Klein excitations)

• WR: SU(2)L × SU(2)R × U(1)

• Hybrid models: couplings to both L and R

• Family nonuniversal (stronger coupling to third family)

• Leptophobic


SU(2)L × SU(2)R × U(1)

• Stringent constraints: β, µ decay, universality, MW , mKL−mKS

• But constraints/LHC signatures very model dependent

– Light Dirac νR? β, µ decay

– Heavy Majorana νR? (seesaw)

– Intermediate scale Majorana νR?: W ′ → νR `;Z′ → νRνR

νR → ν`+1 `−2 or νR → `qq (Z′ → `+

1 `+2 +X)

– UR? (right-handed CKM)

– W −W ′ mixing? (Higgs SU(2)L doublets)

(MW , W ′ →WZ)


• SU(2)R breaking (for MW ′,Z′ �MZ and gR/g = (1− 0.7))

δR =

(δ+R

δ0R

), ∆R =

∆++R

∆+R

∆0R

︸︷︷︸

seesaw

, χR =

χ+R

χ0R

χ−R

MZ′

MW ′= (1.2− 1.6) (1.7− 2.3) 0

• Distinguishing WL from WR

– νR

– AFB (charge) asymmetries the same (except hybrid)

– Associated pp→WW ′, W ′→ ffW (fermion-line filters)

– τ polarization

– W −W ′ interference

– β, µ decays; mKL −mKS


Implications of a TeV-scale U(1)′

• Natural Solution to µ problem W ∼ hSHuHd → µeff = h〈S〉(“stringy version” of NMSSM)

• Extended Higgs sector

– Relaxed MH limit, couplings, parameters

– Higgs singlets needed to break U(1)′

– Doublet-singlet mixing, extended neutralino sector→ non-standard collider signatures

• Extended neutralino sector

– Additional neutralinos, non-standard couplings, e.g., lightsinglino-dominated, extended cascades

– Enhanced cold dark matter, gµ − 2 possibilities


• Exotics (anomaly-cancellation)

– Non-chiral wrt SM but chiral wrt U(1)′

– May decay by mixing; by diquark or leptoquark (B → D(∗)`ν`?)

coupling; or be quasi-stable

– 750 GeV diphoton resonance?

S

G

G

�

�



• Z′ decays into sparticles/exotics (SUSY factory)

• Flavor changing neutral currents (for non-universal U(1)′ charges)

– Tree-level effects in B decay competing with SM loops(B → K`+`−, Bs − Bs mixing, Bd penguins )

• Constraints on neutrino mass generation

– Various versions allow or exclude Type I or II seesaws, extendedseesaw, small Dirac by HDO; small Dirac by non-holomorphicsoft terms; stringy Weinberg operator, Majorana seesaw, orsmall Dirac by string instantons

• Large A term and possible tree-level CP violation (no new EDM

constraints) → electroweak baryogenesis


Conclusions

• New Z′, W ′ are extremely well motivated

• TeV scale likely, especially in supersymmetry and alternative EWSB

• LHC discovery to 4-5 TeV, diagnostics to 2-2.5 TeV at 100 fb−1

(or more)

• Also: precision; ILC, CLIC, FCC-ee, CEPC, FCC-hh, SPPC

• Implications profound for particle physics and cosmology

• Possible portal to hidden/dark sector (massless, GeV, TeV)


Kinetic Mixing

• General kinetic energy term allowed by gauge invariance

Lkin→ −1

4F 0µν

1 F 01µν −

1

4F 0µν

2 F 02µν −

sinχ

2F 0µν

1 F 02µν

• Negligible effect on masses for |M2Z0| � |M2

Z′|, but

−L→ g1Jµ1 Z1µ + (g2J

µ2 − g1χJ

µ1 )Z2µ

• Usually absent initially but induced by loops,e.g., nondegenerate heavy particles, inrunning couplings if heavy particles decouple,or by string-level loops (usually small)

f

f

Z1 Z2



The µ Problem

• In MSSM, introduce Higgsino mass parameter µ: Wµ = µHuHd

• µ is supersymmetric. Natural scales: 0 or MPlanck ∼ 1019 GeV

• Phenomenologically, need µ ∼ SUSY breaking scale

• In Z′ models, U(1)′ may forbid elementary µ (if QHu +QHd6= 0)

• If Wµ = λSSHuHd is allowed, then µeff ≡ λS〈S〉, where 〈S〉contributes to MZ′

• Can also forbid µ by discrete symmetries (NMSSM, nMSSM, · · · ),but simplest forms have domain wall problems

• U(1)′ is stringy version of NMSSM


Models based on T3R and B − L

• More general: QY BL = aY + bTBL ≡ b(zY + TBL)

T3R TBL Y√

53QLR 1

bQY BL

Q 0 16

16

− 16α

16(z + 1)

ucL −12−1

6−2

3−α

2+ 1

6α−2

3z − 1

6

dcL12

−16

13

α2

+ 16α

13z − 1

6

LL 0 −12−1

21

2α−1

2(z + 1)

e+L

12

12

1 α2− 1

2αz + 1

2

νcL −12

12

0 −α2− 1

2α12


The E6 models

• General: Q2 = cos θE6Qχ + sin θE6Qψ

g2 =

√5

3g tan θWλ

1/2g , λg = O(1)

SO(10) SU(5) 2QI 2√

10QN 2√

15QS16 10 (u, d, uc, e+) 0 1 −1/2

5∗ (dc, ν, e−) −1 2 4νc 1 0 −5

10 5 (D,Hu) 0 −2 15∗ (Dc,Hd) 1 −3 −7/2

1 1 S −1 5 5/2

• GUT Yukawas violated (proton decay), e.g., by string rearrangement


• Gauge unification requires additional non-chiral Hu +H∗u

• Can add kinetic term −εY (Qχ − εY ⇒ QY BL)


Minimal Gauge Unification Models

• Supersymmetric models with µeff and MSSM-like gaugeunification

• 3 ordinary families (with νc), one Higgs pair Hu,d and n55∗ pairs(Di + Li) and (Dc

i + Lci)

Q55∗ Qψ Q55∗ QψQ y 1/4 Hu x −1/2uc −x− y 1/4 Hd −1− x −1/2dc 1 + x− y 1/4 SD 3/n55∗ 3/2L 1− 3y 1/4 Di z −3/4e+ x+ 3y 1/4 Dc

i −3/n55∗ − z −3/4νc −1− x+ 3y 1/4 SL 2/n55∗ 1

S 1 1 Li5−n55∗4n55∗

+ x+ 3y + 3z/2 −1/2

Lci −2/n55∗ −QLi −1/2


Stuckelberg Mass

• For U(1)′ can generate massive Z′ without breaking gaugeinvariance

L = −1

4CµνCµν −

1

2(mCµ + ∂µσ)(mCµ + ∂µσ)

– Cµν is field strength, ∆Cµ = ∂µβ

– σ is axion like scalar, ∆σ = −mβ

• Gauge fixing terms cancels cross term, leaving massive vector anddecoupled σ (Higgs without a Higgs)

• Can occur for U(1) in 5D; as (µ2, λ) → ∞ limit of Higgs modelwith(−µ2/λ) fixed; or in strings/brane models with Green-Schwarzmechanism


Z′ MZ′ [GeV] sin θZZ′ χ2min

EW CDF DØ LEP 2 sin θZZ′ sin θminZZ′ sin θmax

ZZ′Zχ 1,141 892 640 673 −0.0004 −0.0016 0.0006 47.3

Zψ 147 878 650 481 −0.0005 −0.0018 0.0009 46.5

Zη 427 982 680 434 −0.0015 −0.0047 0.0021 47.7

ZI 1,204 789 575 0.0003 −0.0005 0.0012 47.4

ZS 1,257 821 0.0003 −0.0005 0.0013 47.3

ZN 754 861 −0.0005 −0.0020 0.0012 47.5

ZR 442 0.0003 −0.0009 0.0015 46.1

ZLR 998 630 804 −0.0004 −0.0013 0.0006 47.3

ZSM 1,401 1,030 780 1,787 −0.0008 −0.0026 0.0007 47.2

Zstring 1,362 0.0002 −0.0005 0.0009 47.7

SM ∞ 0 48.5

Erler et al., 0906.2435; 95%


• Future: JLab and other (Qweak, Moller, SOLID); Giga-Z

0.0001 0.001 0.01 0.1 1 10 100 1000 10000μ [GeV]

0.228

0.23

0.232

0.234

0.236

0.238

0.24

0.242

0.244

0.246

0.248

0.25

sin2 θ

W(μ

)

Q

Q

W

QW

(Ra)

(Cs) SLAC E158

W(e)

QWeak

QWeak

NuTeVν-DIS

LEP 1

SLC

Tevatron

CMSSOLID

MOLLER

JLab

JLabMainz

KVI

Boulder

JLabPVDIS 6 GeV

JLab

screeningan

ti-sc

reen

ing

SMpublishedongoingproposed

Z

γW W

Z

γf

-1 0 1

α cos β

-1

0

1

β

x

x

x

Zψ

x

x

x

x

MOLLER (2.3%)

SOLID (0.6%)

ZR1ZI

ZR

Z χ

Zη

ZN

ZS

x

xZd/

xZL1

xZp/

xZB-Lx

ZLR

xZn/

ZALR

xZYx

x

Zu-int+

Qweak (4%)

x

APV

E158

68% exclusion limits

x ZSOLID

ZL/

MZ’ = 1.2 TeV

Erler, 1209.3324; Z′ = cosα cosβZχ + sinα cosβZY + sinβZψ


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