View
9
Download
0
Category
Preview:
Citation preview
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)
[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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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 ′
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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?
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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?)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
-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%
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
[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]
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
*)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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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
�
�
– Typeset by FoilTEX – 1
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• Gauge unification requires additional non-chiral Hu +H∗u
• Can add kinetic term −εY (Qχ − εY ⇒ QY BL)
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
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%
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
• 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
ATLAS Exotic Dilepton/Lepton+MET (3/16) Paul Langacker (IAS, Princeton)
Recommended