non-standard gauge bosonspgl/talks/newgauge_pgl.pdf · 2013-02-19 · non-standard gauge bosons...

Non-Standard Gauge BosonsDiscovery 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

• Motivations

• Basics

• The standard TeV scale case

• Nonstandard cases

• Experimental constraints,prospects, and diagnostics

• Implications

Snowmass Workshop (Duke), 2013 Paul Langacker (IAS, Princeton)

References

• CLIC: Physics and Detectors at CLIC: CLIC Conceptual Design Report,L. Linssen et al., [arXiv:1202.5940 [physics.ins-det]]

• ILC: ILC Physics DBD

• LHC: 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]]

• LHC/ILC: Physics Interplay of the LHC and the ILC, G. Weiglein et al.,Phys. Rept. 426, 47 (2006) [arXiv:0410364 [hep-ph]]

• Theory: The Physics of Heavy Z′ Gauge Bosons, PL,Rev. Mod. Phys. 81, 1199 (2009) [arXiv:0801.1345 [hep-ph]]


http://arXiv.org/abs/1202.5940

http://ific.uv.es/~fuster/DBD-Chapters/ILCPhysicsVolume.pdf


http://arxiv.org/abs/hep-ph/0410364


Non-Standard Gauge Bosons

• Precision W , Z (perturbations from mixing, oblique, vertex, DSB)

– MW , triple gauge, Higgs, top; Giga-Z

• TeV scale electroweak extensions (remnants, L-R symmetry, extra

dimensions, DSB, continuous flavor symmetries, AttFB, Z′ mediation)

• Strongly coupled gauge bosons (axigluons (AttFB), colorons, strong DSB)

• High scale physics (GUTs, intermediate scale models)

• Very weak coupling (dark sector, SUSY breaking sector)

• Will focus on TeV-scale Z′, W ′


Motivations for a Z′

• 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 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


Models

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

• No simple general parametrization

• Benchmark models: TeV scale MZ′ with electroweak strengthcouplings

– Sequential ZSM

– E6 models

– Models based on T3R and B − L– 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


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)


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)


Precision Electroweak

• 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, 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)

– Precision MW ,mt,MH


• 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

Erler et al., 0906.2435; 95%


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


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/interference, etc(e.g., Petriello ea, 0801.4389; Erler ea, 1103.2659)


[TeV]Z’M0.5 1 1.5 2 2.5 3

B [

pb

]σ

410

310

210

110

1Expected limit

σ 1±Expected

σ 2±Expected

Observed limit

SSMZ’

χZ’

ψZ’

PreliminaryATLAS

ll→Z’

= 8 TeVs

1 L dt = 6.1 fb∫: µµ

1 L dt = 5.9 fb∫ee:

8 TeV, ee (3.6 fb

-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 β

Z′

= cosα cosβZχ

+ sinα cosβZY + sinβZψ

Erler et al, 1103.2659


• LHC discovery to ∼ 4− 5 TeV

– 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]

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

(Kang ea 0412190, Chang ea 1107.1133)


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 channelSnowmass Workshop (Duke), 2013 Paul Langacker (IAS, Princeton)

e−e+ Linear Colliders: ILC, CLIC

• e−e+ → ff (γ, Z, Z′ interference in σ,AF,B, Pe−,e+, mixed )

εαL,R(f)→ ε

αL,R(f)

Mα√M2

α − s

• Possible window for resonance at CLIC?

• Regimes

– Discovery/mass at LHC (4-5 TeV)

– Too heavy for LHC (sensitive to 7-10√s)

– Also: Z-pole (Giga-Z)


0 5 10 15

Ψ

Η

Χ

LRS

SSM

ALR

MZ’ HTeVL

DISCOVERY

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

HP-;P+L ILC 0.5 TeV

HP-;0L ILC 0.5 TeV

H0;0L ILC 0.5 TeV

LHC

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

1 TeV

Osland ea, 0912.2806; 95%


1.5 Z0, CONTACT INTERACTIONS AND EXTRA DIMENSIONS

0 20 40 60 80 100 � /g !TeV"

LL

RR

RL

LR

VV

AA

V0

A0

V1

CLIC 3 TeV, 1 ab-1 e#e�� $+$-

P- = 0.8, P+ = 0.6

P- = 0.8, P+ = 0 P- = 0, P+ = 0

0 20 40 60 80 100 � /g !TeV"

LL

RR

RL

LR

VV

AA

V0

A0

V1

CLIC 3 TeV, 1 ab-1 e#e�� $+$-

P- = 0.8, P+ = 0.6

P- = 0.8, P+ = 0 P- = 0, P+ = 0

0 50 100 150 200 250 300 350

�/(g/p

4�) [TeV]

�/g [TeV]

0 20 40 60 80 100 0 20 40 60 80 100 � /g !TeV"

LL

RR

RL

LR

VV

AA

V0

A0

V1

CLIC 3 TeV, 1 ab-1 e#e�� b b-

P- = 0.8, P+ = 0.6

P- = 0.8, P+ = 0 P- = 0, P+ = 00 50 100 150 200 250 300 350

�/(g/p

4�) [TeV]

�/g [TeV]

0 20 40 60 80 100

0 20 40 60 80 100 � /g !TeV"

LL

RR

RL

LR

VV

AA

V0

A0

V1

CLIC 3 TeV, 1 ab-1 e#e�� b b-

P- = 0.8, P+ = 0.6

P- = 0.8, P+ = 0 P- = 0, P+ = 0

Fig. 1.15: Limits on the scale of contact interactions (L/g) that can be set by CLIC in the µ+µ� (left) andbb (right) channels with

ps = 3 TeV and L = 1 ab�1. A degree of polarisation P� = 0,0.8 (P+ = 0,0.6)

has been assumed for the electrons (positrons). The various models are defined in Table 6.6 of [20],except the model V1 which is defined as {hLL = ±, hRR = ⌥, hLR = 0, hRL = 0}.

withp

s = 3 TeV for leptonic final states. In this case the mass of the Z0 is assumed to be unknown,being well beyond the reach of the LHC.

Besides the models considered in the right panel of Figure 1.16, we have studied two other scenar-ios in detail. The first is a general and model-independent parametrisation of a Z0 boson and its couplingsproposed in [68] and generally referred to as minimal Z0 model. Its phenomenology at the LHC has beenrecently studied in [30]. The basic assumption in the model description is the presence of a single Z0

boson originating from an extra U(1) gauge group broken at the TeV scale, and no additional exoticfermions, apart from an arbitrary number of right-handed neutrinos. The requirement of anomaly can-cellation and the assumption of flavour universality of the U(1) charges then fix the couplings of the Z0 tothe fermions in terms of just two arbitrary parameters, gY and gBL. Several Z0 models considered earlierin the literature can be incorporated in this framework for specific choices of gY and gBL.

The second scenario is one in which more than one heavy neutral spin-1 particle exists. This is typ-ical of extra-dimensional extensions of the SM. In particular, we consider the warped/composite two-sitemodel of [69], which represents a qualitatively different scenario where third-generation fermions playa special role. The model can be described as being a “maximally deconstructed” version – i.e. with theextra dimension discretised down to just two sites – of the 5-dimensional Randall–Sundrum custodialmodel first studied in [70]. In the neutral sector there are three heavy Z0 bosons. Their couplings arecontrolled by composite-elementary mixing angles, which are generation-dependent. The right-handedtop quark, in particular, is fully composite, which implies that the extra spin-1 resonances are stronglycoupled to top pairs and are generally broad. The main signatures of the model are large deviations ofthe top sector observables from their SM expectations. In our analysis we have assumed a universal newvector boson mass M⇤ and composite coupling g⇤. Also, we have assumed that the composite fermionshave the universal mass scale m⇤ = 1.5M⇤, so that decays of the Z0 particles to the new heavy fermionsare forbidden. Our analysis is thus carried out with just two free parameters: M⇤ and g⇤. We found only

27

CLIC, 1202.5940 (g ∼ 0.46 for comparison)


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 (jj, bb, tt, eµ, τ+τ−)

• 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

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

• Upgrade to hadronic polarization would be useful


lRC

-0.5 0 0.5

l LC

-1

0

1

LH

LR

KK

χSLH

lRC

-0.5 0 0.5

l LC

-1

0

1

LH

LR

KK

χSLH

Godfrey ea, 0511335

MZ′ = 2(4) TeV; ILC at 500 GeV, 1000 fb−1, Pe−,e+ = 80(60)%; 95%


1 CLIC PHYSICS POTENTIAL

) (GeV)-µ+µM(1500 2000 2500 3000

-1En

trie

s / 1

ab

0

500

1000

1500

-0.2

-0.1

0

0.1

0.2

-0.2 -0.1 0 0.1 0.2

�s = 3 TeVmZ' = 10 TeVLint = 1 ab-1

�P = 0.5%Pe- = 80%Pe+ = 60%

aNl

vN l

�

�

�

LRSSM

LH

SLH

Fig. 1.16: Left: Observation of new gauge boson resonances in the µ+µ� channel by auto-scan at 3 TeV.The two resonances are the Z1,2 predicted by the 4-site Higgsless model of [67]. Right : Expectedresolution at CLIC with

ps = 3 TeV and L = 1 ab�1 on the “normalised” leptonic couplings of a

10 TeV Z0 in various models, assuming lepton universality. The couplings can be determined up to atwofold ambiguity. The mass of the Z0 is assumed to be unknown. c,h and y refer to various linearcombinations of U(1) subgroups of E6; the SSM has the same couplings as the SM Z; LR refers toU(1) surviving in Left-Right model; LH is the Littlest Higgs model and SLH, the Simplest Little Higgsmodel. The two fold ambiguity is due to the inability to distinguish (a,v) from (�a,�v). The degeneracybetween the y and SLH models might be lifted by including other channels in the analysis (tt, bb, . . .).

a mild dependence of the final results on the value of the composite Yukawa coupling Y⇤U33 that controlsthe top mass and the degree of compositeness of tL and bL.

We study the sensitivity of the two models in terms of the discovery regions in their parameterspace [71]. The anticipated experimental accuracy on the electroweak observables (total production crosssection, sff, forward-backward asymmetries and left-right asymmetries, ALR) for the process e+e� ! ff(f = µ, b, t) is determined from the analysis of fully simulated and reconstructed events, using the sameCLIC_ILD detector model and the event reconstruction software adopted for the benchmark analysesdiscussed in Chapter 12. Beamstrahlung effects are taken into account in the luminosity spectrum, butmachine-induced backgrounds are not overlaid on the e+e� ! ff events. For polarised observables weassume 80% and 60% polarisation for the e� and e+ beam respectively. Quark charge is determined usingsemi-leptonic decays, which are robust against the effect of machine-induced backgrounds. In particular,for tt events we tag the top production using the hadronic decay of one top quark and determine thecharge using the W± ! `±n decay in the opposite hemisphere. The deviations of the nine electroweakobservables from their SM predicted values are computed by varying the model parameters in a multi-dimensional grid scan. The sensitivity to a model is defined as the region of parameters for which thec2 probability that all the observables are compatible with their SM expected values is below 0.05.Results for the Z0 minimal model and the warped/composite model are shown in Figure 1.17 assumingp

s = 3 TeV. We find that CLIC data are generally sensitive to a mass scale of order 15 TeV with 1 ab�1

of accumulated luminosity, which is well beyond the direct accessibility of any current operating collider.In the case of the warped/composite model, the sensitivity is larger for smaller values of g⇤, since in thislimit the couplings of Z’ to the leptons and to the bottom quark are larger. For g⇤ & 1� 2, only the ttfinal state contributes significantly, while the muon and bottom ones are subdominant.

We note that CLIC should also be able to study the signals for spin-2 Kaluza-Klein excitationsof extra-dimensional theories through g + Emiss

T [72]. Figure 1.18 shows the production cross section asa function of the fundamental gravity scale MD with the cut ET,g > 500 GeV. The SM background rate

28

CLIC, 1202.5940


• Benchmarks vs model independent studies of couplings(parametrization: Cvetic ea, 9501390, 9312329, 9303299)

• LHC/ILC (CLIC) diagnostics complementary

• Extensive references in

– The Hunt for New Physics at the Large Hadron Collider,1001.2693

– The Physics of Heavy Z′ Gauge Bosons, 0801.1345


Associated Collider Physics/Theoretical Issues

• Extended Higgs/neutralino sector (collider, dark matter)

• Quasi-chiral exotic fermions (anomaly cancellation)

(various decay possibilities)

• FCNC, tree-level B anomalies (non-universal charges)

• ν mass mechanisms

• Electroweak baryogenesis

• Z′ mediation of supersymmetry breaking


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

• ILC sensitivity (γ, Z, Z′ int.) to ∼ 5 (10) TeV at√s = 0.5(1) TeV

• CLIC: ∼ 30-40 TeV at√s = 3 TeV

• Further study: model independent joint analysis; tt

• Implications profound for particle physics and cosmology

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


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


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


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 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


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


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


• 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


non-standard gauge bosonspgl/talks/newgauge_pgl.pdf · 2013-02-19 · non-standard gauge bosons...

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