Z0 Physics - University of Pennsylvania€¦ · Other Models TeV scale dynamics (Little Higgs,...

Z′ Physics

χE6 Model -

ψE6 Model -

ηE6 Model - LR Symmetric

Alt. LRSM

Ununified Model

Sequential SM

TC2

Littlest Higgs Model

Simplest Little Higgs

Anom. Free SLH

331 (2U1D)

Hx SU(2)LSU(2)

Hx U(1)LU(1)

RS Graviton

Sneutrino

7 TeV - 100 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

7 TeV - 1 fb-1

Discovery Reach (GeV)

310 410

• Motivations

• Basics

• The standard TeV scale case

• Nonstandard cases

• Experimental constraintsand prospects

• Implications

Reviews: The Physics of Heavy Z′ Gauge Bosons, RMP 81, 1199 [0801.1345]

The Standard Model and Beyond (CRC Press)

Talk at: www.sns.ias.edu/~pgl/talks/zprime_10.pdf

Penn, October 2010 Paul Langacker (IAS)

http://arXiv.org/abs/0801.1345

http://www.crcpress.com/product/isbn/9781420079067

http://www.sns.ias.edu/~pgl/talks/

Additional References

• Z′ Physics at the LHC, from P. Nath et al., The Hunt for New Physics

at the Large Hadron Collider, Nucl. Phys. Proc. Suppl. 200-202, 185 (2010)[arXiv:1001.2693 [hep-ph]]

• The Physics of New U(1)′ Gauge Bosons, SUSY09, AIP Conf. Proc. 1200,55 (2010) [arXiv:0909.3260 [hep-ph]]

• J. Erler, PL, S. Munir and E. Rojas, Z′ Searches: From Tevatron to LHC,arXiv:1010.3097 [hep-ph]

• J. Erler, PL, S. Munir and E. R. Pena, Improved Constraints on Z′ Bosons

from Electroweak Precision Data, JHEP 0908, 017 (2009) [arXiv:0906.2435[hep-ph]]







Motivations

• 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

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

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

• Extensive physics implications, especially for TeV scale Z′


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 g

21 = g

2/ cos

2θW

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

• 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

– Typeset by FoilTEX – 1


Anomalies and Exotics

• Must cancel triangle and mixed gravitationalanomalies

f

V1 V2

V3

– Typeset by FoilTEX – 1

• No solution except Q2 = 0 for family universal SM fermions

• Must introduce new fermions: SM singlets like νcL 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)


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

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

• No simple general parametrization

• “Canonical” models: TeV scale MZ′ with electroweak strengthcouplings

– Sequential ZSM

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

– Minimal Gauge Unification Models


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 νcL 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 g2 =

√5

3g tan θW ∼ 0.46

• 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

• Example of anomaly free charges and exotics, based on E6 →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√

15Qη16 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

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


Other Models

• TeV scale dynamics (Little 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, apparent CPT violation)

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

• Stuckelberg (no Higgs)

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


Experimental constraints and prospects

• Tevatron (CDF, D0): resonance in pp→ e+e−, µ+µ−, · · ·

AB → Zα in narrow width:

dσ

dy=

4π2x1x2

3M3α

∑i

(fAqi(x1)fBqi

(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


(TeV)Z’M0 0.2 0.4 0.6 0.8 1 1.2 1.4

) (

pb

)µµ

→ B

R(Z

’× σ

95%

C.L

. Lim

its

on

-210

-110

SE Median68% of SE95% of SEData

IZ’

secZ’

NZ’ψZ’

χZ’

ηZ’

SMZ’

(TeV)Z’M0 0.2 0.4 0.6 0.8 1 1.2 1.4

) (

pb

)µµ

→ B

R(Z

’× σ

95%

C.L

. Lim

its

on

-210

-110

(CDF dimuons: PRL 102, 0918905)


-1 0 1

-1

0

1

x

x

x

Zψ

x

x

xx

ZI

ZR

Z χ

Zη

ZL-B

ZN

ZS

x

x

xZ

dph

d-xu10+x5*q+xu

Zη*

0.8

0.85

β

1

1.1

0.2

0.5

0.7

0.8

0.85

1

1.1

0.9 0.9

α Cos β0 1 2 3 4 5 6

MZ’

-1[TeV

-1]

0.01

0.1

1

g2

g2 = 0.461

This analysis (68% C.L.)



CDF analysis (95% C.L.)

Zχ

– From 1010.3097 [hep-ph]:

Z′ = cosα cosβZχ + sinα cosβZY + sinβZψ

– Interference with γ, Z included in second plot


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

−Leff =4GF√

2(ρeffJ

21 + 2wJ1J2 + yJ

22)

ρeff =ρ1 cos2θ + ρ2 sin

2θ w =

g2

g1

cos θ sin θ(ρ1 − ρ2)

y =

(g2

g1

)2

(ρ1 sin2θ + ρ2 cos

2θ) ρα ≡M2

W/(M2α cos

2θW )

• Z-pole (LEP, SLC): Z − Z′ mixing (vertices; shift in M1)

Vi = cos θg1V (i) +

g2

g1

sin θg2V (i)

Ai = cos θg1A(i) +

g2

g1

sin θg2A(i)

• LEP2: 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


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


Future Prospects

• Tevatron and LHC: pp(pp)→ Z′→ e+e−, µ+µ−, jj, bb, tt, eµ, τ+τ−

• Rates (total width) dependent on whether sparticle and exoticchannels open (ΓZ′/MZ′ ∼ 0.01→ 0.05 for E6)

• LHC discovery to ∼ 4− 5 TeV

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

dσfZ′

d cos θ∗∝

3

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

• ILC: 5σ intererence effects up to ∼ 5 TeV


χE6 Model -

ψE6 Model -

ηE6 Model - LR Symmetric

Alt. LRSM

Ununified Model

Sequential SM

TC2

Littlest Higgs Model

Simplest Little Higgs

Anom. Free SLH

331 (2U1D)

Hx SU(2)LSU(2)

Hx U(1)LU(1)

RS Graviton

Sneutrino

7 TeV - 100 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

7 TeV - 1 fb-1

Discovery Reach (GeV)

310 410

(Courtesy: Steve Godfrey)


Diagnostics of Z′ Couplings

• LHC diagnostics to 2-2.5 TeV

• Forward-backward asymmetries and rapidity distributions 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, hep-ph/0410364)


• Other two body decays (e.g., tt)

• Lineshape: σZ′B`, ΓZ′

• τ polarization

• Associated production Z′Z,Z′W,Z′γ

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

• 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

• LHC/ILC diagnostics complementary


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 mass limits, couplings, parameters (e.g., tanβ ∼ 1)

– 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 (even small tanβ)


• Exotics (anomaly-cancellation)

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

– May decay by mixing; by diquark or leptoquark coupling; or bequasi-stable

• 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 (or with

enhanced loops in MSSM with large tanβ)

– Bs − Bs mixing, Bd penguins

• Non-universal charges: apparent CPT violation (MINOS)


• 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


W ′

• Less motivated than Z′, but possible

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

• WR: SU(2)L × SU(2)R × U(1)

• Issues

– Light Dirac or heavy Majorana νR

– UR (right-handed CKM)


Conclusions

• New Z′ 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

• Implications profound for particle physics and cosmology

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


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