The Physics of Heavy Z-prime Gauge Bosons

Transcription

1 The Physics of Heavy Z-prime Gauge Bosons Tevatron LHC LHC LC LC 15fb fb -1 14TeV 1ab -1 14TeV 0.5TeV 1ab -1 P - =0.8 P + = TeV 1ab -1 P - =0.8 P + =0.6 χ ψ η LR SSM σ m Z' [TeV] Motivations Basics Models Experimental constraints and prospects Implications LHC/ILC, hep-ph/ Review: The Physics of Heavy Z-prime Gauge Bosons, [hep-ph]. Talk at:

2 Motivations Strings/GUTS Harder to break U(1) factors than non-abelian Supersymmetry: SU(2) U(1) and U(1) breaking scales both set by SUSY breaking scale (unless flat direction) µ problem Alternative electroweak breaking (TeV scale): DSB, Little Higgs Extra dimensions: Kaluza-Klein excitations (M R 1 2 TeV (10 17 cm/r))

3 Standard Model Neutral Current L SM NC = gj µ 3 W 3µ + g J µ Y B µ = ej µ em A µ + g 1 J µ 1 Z0 1µ A µ = sin θ W W 3µ + cos θ W B µ Z µ = cos θ W W 3µ sin θ W B µ θ W tan 1 (g /g) e = g sin θ W g 2 1 = g2 / cos 2 θ W J µ 1 = i f i γ µ [ɛ 1 L (i)p L + ɛ 1 R (i)p R]f i P L,R (1 γ5 ) 2 ɛ 1 L (i) = t 3i L sin 2 θ W q i ɛ 1 R (i) = sin2 θ W q i M 2 Z 0 = 1 4 g2 1 ν2 = M 2 W cos 2 θ W ν 246 GeV

4 Additional U(1) L NC = ej µ em A µ + n+1 α=1 g α J µ α Z0 αµ J µ α = i f i γ µ [ɛ α L (i)p L + ɛ α R (i)p R]f i ɛ α L,R (i) are U(1) α charges of the left and right handed components of fermion f i (chiral for ɛ α L (i) ɛα R (i)) g α V,A (i) = ɛα L (i) ± ɛα R (i) May specify left chiral charges for fermion f and antifermion f c ɛ α L (f) = Q αf ɛ α R (f) = Q αf c Q 1u = sin2 θ W and Q 1u c = sin2 θ W

5 Mass and Mixing Mass matrix for single Z M 2 Z Z = ( M 2 Z M 2 Z ) Eg., SU(2) singlet S; doublets φ u = ( φ 0 u φ u ), φ d = ( φ + d φ 0 d ) M 2 Z 0 = 1 4 g2 1 ( ν u 2 + ν d 2 ) 2 = 1 2 g 1g 2 (Q u ν u 2 Q d ν d 2 ) M 2 Z =g 2 2 (Q2 u ν u 2 + Q 2 d ν d 2 + Q 2 S s 2 ) ν u,d 2 φ 0 u,d, s = 2 S, ν 2 = ( ν u 2 + ν d 2 ) (246 GeV) 2

6 Eigenvalues M1,2 2, mixing angle θ tan 2 θ = M 2 Z 0 M 2 1 M 2 2 M 2 Z 0 For M Z (M Z 0, ) M 2 1 M 2 Z 0 4 M 2 Z M 2 2 M 2 2 M 2 Z θ 2 M 2 Z C g 2 g 1 M 2 1 M 2 2 [ Qu ν u 2 Q d ν d 2 ] with C = 2 ν u 2 + ν d 2

7 Kinetic Mixing General kinetic energy term allowed by gauge invariance L kin 1 4 F 0µν α F 0 αµν 1 4 F 0µν β F 0 βµν sin χ 2 F 0µν α F 0 βµν Negligible effect on masses for M 2 Z 0 M 2 Z, but L g 1 J µ 1 Z 1µ + (g 2 J µ 2 g 1χJ µ 1 )Z 2µ Usually absent initially but induced by loops in running couplings if heavy particles decouple (or by string-level loops) (usually small) f Z Z f

8 Anomalies and Exotics Must cancel triangle and mixed gravitational anomalies V 3 f V 1 V 2 No solution except Q 2 = 0 for family universal SM fermions Must introduce new fermions: SM singlets like ν c L (usually non-chiral under SM) D L + D R, ( E 0 E ) L + ( E 0 E ) or exotic SU(2) R Typeset by FoilTEX Supersymmetry: include Higgsinos and singlinos (partners of S)

9 The µ Problem In MSSM, introduce Higgsino mass parameter µ: W µ = µh u H d µ is supersymmetric. Natural scales: 0 or M P lanck GeV Phenomenologically, need µ SUSY breaking scale In Z models, U(1) may forbid elementary µ (if Q H u + Q Hd 0) If W µ = λ S SH u H d is allowed, then µ eff contributes to M Z λ S S, where S Can also forbid µ by discrete symmetries (NMSSM, nmssm, ), but simplest forms have domain wall problems U(1) is stringy version of NMSSM

10 Models Enormous number of models, distinguished by gauge coupling g 2, mass scale, charges Q 2, exotics, No simple general parametrization Will focus on TeV scale M Z with electroweak strength couplings

11 Sequential Z SM Same couplings to fermions as the SM Z boson Reference model Hard to obtain in gauge theory Kaluza-Klein excitations with TeV extra dimensions

12 Models based on T 3R and B L Motivated by minimal exotics (only νl c left-right SU(2) L SU(2) R U(1) BL needed), SO(10), and T BL 1 2 (B L), T 3R = Y T BL = 1 2 [u R, ν R ], 1 2 [d R, e R ] For non-abelian embedding and no kinetic mixing Q LR = 3 5 [ αt 3R 1 ] α T BL α = g R g BL = q (g R /g) 2 cot 2 θ W 1 g 2 = r 5 3 g tan θ W 0.46 More general: Q Y BL = ay + bt BL b(zy + T BL )

13 T 3R T BL Y QLR BL QY b Q 0 (z + 1) 6 6α u c L α α 3 z 1 6 d c L L L e + L 1 2 ν c L α α α 1 2 α α α 3 z 1 6 (z + 1) 2α z

14 The E 6 models Example of anomaly free charges and exotics, based on E 6 SO(10) U(1) ψ and SO(10) SU(5) U(1) χ 3 27: 3 S fields, 3 (D + D c ) pairs, 3 Higgs (or exotic lepton) pairs Supersymmetric version forbids µ term except χ model (SO(10)) SO(10) SU(5) 2 10Q χ 2 6Q ψ 2 15Q η (u, d, u c, e + ) (d c, ν, e ) ν c (D, H u ) (D c, H d ) S 0 4 5

15 General: Q 2 = cos θ E6 Q χ + sin θ E6 Q ψ (can add kinetic term ɛy ) g 2 = r 5 3 g tan θ W λ 1/2 g, λ g = O(1) SO(10) SU(5) 2Q I 2 10Q N 2 15Q S (u, d, u c, e + ) 0 1 1/2 5 (d c, ν, e ) ν c (D, H u ) (D c, H d ) 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 H u + H u

16 Minimal Gauge Unification Models Supersymmetric models with µ eff and MSSM-like gauge unification 3 ordinary families (with ν c ), one Higgs pair H u,d and n 55 pairs (D i + L i ) and (D c i + Lc i ) Q 55 Q ψ Q 55 Q ψ Q y 1/4 H u x 1/2 u c x y 1/4 H d 1 x 1/2 d c 1 + x y 1/4 S D 3/n 55 3/2 L 1 3y 1/4 D i z 3/4 e + x + 3y 1/4 Di c 3/n 55 z 3/4 ν c 1 x + 3y 1/4 S L 2/n n S 1 1 L 55 i + x + 3y + 3z/2 1/2 4n 55 L c i 2/n 55 Q Li 1/2

17 Other Models TeV scale dynamics (Little Higgs, un-unified, strong t t coupling, ) Kaluza-Klein excitations (large dimensions or Randall-Sundrum) Decoupled (leptophobic, fermiophobic, weak coupling, low scale, hidden sector, ) Secluded or intermediate scale SUSY (flat directions, Dirac m ν ) Family nonuniversal couplings (FCNC) String derived (may be T 3R, T BL, E 6 or random ) Stückelberg (no Higgs) Anomalous U(1) (string theories with large dimensions)

18 Experimental constraints and prospects Low energy weak neutral current: Z exchange and Z Z mixing L eff = 4G F 2 (ρ eff J wJ 1J 2 + yj 2 2 ) ρ eff =ρ 1 cos 2 θ + ρ 2 sin 2 θ w = g 2 cos θ sin θ(ρ 1 ρ 2 ) g 1 «2 g2 y = (ρ 1 sin 2 θ + ρ 2 cos 2 θ) ρ α M 2 W /(M 2 α cos2 θ W ) g 1 Z-pole (LEP, SLC): Z Z mixing (vertices; shift in M 1 ) V i = cos θg 1 V (i) + g 2 g 1 sin θg 2 V (i) A i = cos θg 1 A (i) + g 2 g 1 sin θg 2 A (i)

19 LEP2: four-fermi operator interfering with γ, Z Tevatron (CDF, D0): resonance in pp e + e, µ + µ, AB Z α in narrow width: dσ dy = 4π2 x 1 x 2 3M 3 α (f A q i (x 1 )f B q i (x 2 )+f Ā q i (x 1 )f B q i (x 2 ))Γ(Z α q i q i ) i Γ α f i Γ(Z α f i fi ) = g2 α C f i M α 24π ( ɛ α L (i)2 + ɛ α R (i)2) x 1,2 = (M α / s)e ±y C fi = color factor

20 M 2 [GeV] 2500 M 2 [GeV] 2500 Z χ Z ψ sin θ sin θ M 2 [GeV] M 2 [GeV] Z η Z LR sin θ sin θ

21 ρ 0 free ρ 0 = 1 sin θ (ρ 0 = 1) Tevatron LEP 2 χ ( ) ( ) ψ ( ) ( ) η ( ) ( ) LR ( ) ( ) sequential ( ) ( )

22 Future Prospects Tevatron and LHC: pp( pp) Z e + e, µ + µ, jj, tt, eµ, τ + τ Rates (total width) dependent on whether sparticle and exotic channels open (Γ Z /M Z for E 6 ) LHC discovery to 4 5 TeV ILC: 5σ intererence effects up to 5 TeV

23 Tevatron 15fb -1 LHC χ ψ η LR SSM 2σ 100fb -1 14TeV LHC LC 1ab -1 14TeV LC 0.5TeV 1ab -1 P - =0.8 P + = TeV 1ab -1 P - =0.8 P + = m Z' [TeV] LHC/ILC, hep-ph/

24 Diagnostics of Z Couplings LHC diagnostics to TeV Forward-backward asymmetries and rapidity distributions in l + l l FB A Forward backward asymmetry measurement 1.2 Z χ a) Z 1 LHC, s=14tev ψ M Z =1.5TeV y ll >0.8 Z η Z LR -1 Z η, L=100fb dn / dy Rapidity distribution -1 Z η, 100fb Z η : fit uu fit dd sum Z ψ 1.45 TeV<M ll <1.55 TeV b) [GeV] M ll Y ll LHC/ILC, hep-ph/

25 Other two body decays σ Z B l Γ Z = σ Z Γ l (total width cancels) τ polarization Associated production Z Z, Z W, Z γ Rare (but enhanced) decays Z W f 1 f 2 (radiated W ) Z W + W, Zh, or W ± H : longitudinal W, Z small mixing compensated by Γ(Z W + W ) = g2 1 θ2 M Z 192π MZ M Z «4 = g2 2 C2 M Z 192π Upgrade to hadronic polarization would be useful LHC/ILC diagnostics complementary

26 Implications of a TeV-scale U(1) Natural Solution to µ problem W hsh u H d µ eff = h S Extended Higgs sector Relaxed mass limits, couplings, parameters (e.g., tan β 1) Higgs singlets needed to break U(1) Doublet-singlet mixing highly non-standard collider signatures Extended neutralino sector Additional neutralinos, non-standard couplings, e.g., light singlino-dominated, extended cascades Enhanced cold dark matter, g µ 2 possibilities (even small tan β) Constraints on neutrino mass generation

27 Exotics (anomaly-cancellation) May decay by mixing; by diquark or leptoquark coupling; or be quasi-stable Z decays into sparticles/exotics 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 tan β) U(1) may couple to both ordinary and (quasi)-hidden sectors Z Z mass difference may communicate SUSY breaking Predictive spectrum with very heavy scalars, light SM gauginos Large A term and possible tree-level CP violation (no new EDM constraints) electroweak baryogenesis

28 Conclusions Heavy Z are extremely well motivated TeV scale likely, especially in supersymmetry and alternative EWSB Wide variety of models LHC discovery to 4-5 TeV, diagnostics to TeV Implications profound for particle physics and cosmology