Exotic Dark Matter as Spin-off of Proton Stability Kaustubh Agashe (University of Maryland)
Outline and Summary Warped extra dimensions address Planckweak and flavor hierarchies: new (KK) particles at a few TeV (precision tests) GUT: Proton Stability Dark Matter (+ precision gauge coupling unification) Exotic DM at colliders: Z 3 (warped) vs. Z 2 Double (vs. single) endpoints in decay of single DM partner (for off-shell intermediate particles) cusp in two visible particle invariant mass (vs. not) for on-shell
WARPED EXTRA DIMENSION
Basics of extra dimensions 4D extra... Particle in 5D: SM ( x µ,y) Fourier expand y (a la 1D box) m 4D Lightest mode (SM) + heavier (Kaluza-Klein: KK) with profiles wavefunction 1 0.5-0.5 0.2 0.4 0.6 0.8 1 5m 4m 3m 2m m KK s -1 y
Motivations for warped... Planck-weak and flavor hierarchy (without severe flavor problem) Weakly-coupled tool for 4D strong dynamics: dual to 4D composite Higgs (AdS/CFT) GUT s: (i) dark matter from proton stablity (KA, Servant); (ii) gauge coupling unification with precision SUSY (KA, Contino, Sundrum)
Gravity and Higgs (Randall, Sundrum) kr log (M Pl /TeV) /π 10
SM in bulk (Davoudiasl, Hewett, Rizzo; Pomarol; Grossman, Neubert; Chang, Hisano, Nakano, Okada,Yamaguchi; Gherghetta, Pomarol)
Couplings from overlap of profiles Flavor hierarchy (fermion-higgs) without hierarchy in 5D parameters (5D Yukawa, 5D mass M): fermion profile e kπrm......related to Planck-weak hierarchy Couplings to KK large (small) for top, Higgs, other KK s (electron)
NO PARITY, PRECISION TESTS NEW PARTICLES FEW TEV
Summary (rough) no parity SM SM SM tree-level contributions to flavor and EW precision tests s s e + v v m s m d md v m s KK gluon m s m d md v m s g 2 /g KK Z (n) or W (n) g gkk Z (0) or W (0) d d e lower limit on KK mass scale: O(3) TeV (built-in mechanism + model-building) ~
GUT
Problem: rapid proton decay ( d c l ) ( q u c ) X, Y 5 of SU(5) 10 of SU(5) KK modes of X,Y TeV + couplings not enough... Yukawa
Solution: Orbifold GUT s (GUT breaking on boundary: Kawamura; Hall, Nomura... ) x µ x µ SM gauge symmetry 5D GUT gauge symmetry Planck brane TeV brane Planck brane Dirichlet y =0 y TeV brane SM gauge (++) zero-mode X, Y...( +) no zero-mode Neumann y = πr
Split fermion multiplets zero-mode ( q(++) ) ( q ( +) ) no zero-mode l ( +) X,Y l(++) quark and lepton zero-modes from different multiplets X, Y do not couple SM quark to SM lepton
Hypercharge still quantized No quark-lepton unification, but... GUT representation SM quark and SM lepton
DM : SPIN-OFF OF PROTON STABILITY
Exotic stable GUT partners (KA, Servant) higher-order (e.g., 5D cut-off) effects can undo spiltting gauge U(1) B : assign multiplets baryon-number of zero-mode (cannot do it without split multiplets) exotics ( q (n 0) ) ( q (0) ) l (0) B=0 SM l (n 0) B=1/3 Extra particles (no zero-modes) are exotic ( wrong combination of B and color: SM have right...)
Z 3 symmetry Φ Φ e 2πi [ B (α ᾱ) 3 number of color indices ] SM not charged, GUT partners are... lightest Z 3 -charged particle (LZP) stable
Who s LZP? Can it be DM?
GUT partners of t R light heavy top + constraint from shift in Zb b t R (not t L : partner of b L ) near TeV brane GUT partners (no zero-modes) of gauge KK ( 3 TeV) t R < light ( 1 TeV) vs.
Exotic partner of t R as WIMP dark matter: I ν R ν R t R X S ν R t R Annihilation: 10 2 10 annihilation is dominated by heavy KK gauge boson exchange! h 2 annihilation is dominated by Z " 0 exchange #" # 1 10-1 10-2 10-3!h 2 = 0.110! 0.01 M KK =6 TeV M KK =3 TeV 10-4 10 10 2 10 3 m LZP (GeV)
Exotic partner of as WIMP dark matter: II ν R t R Direct detection (small coupling to Z): 10-5 3 TeV ν R v v! n-lzp (pb) (spin-independent) 10-6 10-7 4 TeV 6 TeV 10 TeV Z (n) Z (0) 10-8 ν R 10-9 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 g 10
UNIFICATION OF GAUGE COUPLINGS
LO: magic of β-function: SM 2t R H (KA, Contino, Sundrum) 40 Α 1 1 Α 2 1 30 20 Α 1 1 Α 3 1 10 0 4 6 8 10 12 14 16 Log 10 Μ GeV
COLLIDER SIGNALS FOR WARPED DM
Decay of DM ``partners into SM (visible) + DM (invisible) pair produce DM partners... DM SM (e or p) DM partner SM state
...like any other DM model (SUSY, UED, Little Higgs with T-parity)?
...NO... Z 3 VS. Z 2! [KA, Kim,Toharia, Walker (in progress); see also Walker]
Z 3 : decay into 1 and 2 DM and Z 2 : 1 DM...3 allowed by symmetry, but requires quartic vertex with different particles (nonrenormalizable, except purely scalar)...vs. cubic (easily renormalizable) to obtain 2 DM in Z 3
Off-shell intermediate... Endpoint in invariant mass of (massless) visible/ SM particles = M mother N DM M DM M mother M DM single endpoint for Z 2 vs. two M mother 2 M DM and M mother M DM for Z 3
Pure kinematics/phase space 0.010 0.008 d 1 dm ab GeV 1 0.006 0.004 M mother = 800 GeV M DM = 300 GeV BR: 50%, 50% 0.002 0.000 0 100 200 300 400 500 m...depends on BR s ab GeV of 1 vs. 2 DM; gap between endpoints (=DM mass!)... 0.004 0.004 0.003 0.003 dm ab 0.002 d 1 dm ab GeV 1 0.002 0.001 0.001 0.000 0 100 200 300 400 500 600 m ab GeV 0.000 0 100 200 300 400 500 M mother = 700 GeV;M DM = 100 GeV; BR: 50%, 50% M mother = 800 GeV;M DM = 300 GeV; BR: 75%, 25% m ab GeV
On-shell intermediate: number of endpoints cannot distinguish... endpoints depend on intermediate particle mass multiple endpoints in Z 2 same final state, e.g. in SUSY: from different intermediate for l + l χ 0 2 χ 0 1 l L or l R
New ``topology in Z 3...... due to Z 3...absent in Z 2
Cusp in invariant mass of 2 visible particles c DM a...... D C B A 1 2 Γ 0 Γ 0 u v = θ(1 u)θ(u)θ(1 v)θ(v) u 1 cos θ(c) cb 2 v 1 cos θ(b) ca 2 θ integrate over 1 combination of u, v -function of one variable determines range of, distribution: other generates derivative discontinuity (cusp) within this range (see Han, Kim, Song for related Z 2 M ca M ca -even decay...)
No cusp for Z 2 topology... c a... D C A 1 Γ 0 Γ 0 v = θ(1 v)θ(v) single θ -function determines range of M ca
Only two visible particles Z 3 Z 2 Invariant mass has cusp for, not for Z 3 Z 2
Pure kinematics/phase space 0.004 7. 10 6 6. 10 6 0.003 5. 10 6 d 1 dm ab 0.002 d 1 dm ab 2 4. 10 6 3. 10 6 0.001 2. 10 6 1. 10 6 0.000 0 100 200 300 400 500 m ab massless 0 0 50 000 100 000 150 000 200 000 250 000 m ab 2 100 massless 700 500 300 100
Inclusion of matrix element (spins) 4 body decay: Inv. mass distribution of f1 s1 cusp cusp 4 body decay: Inv. mass distribution of f1 s1 Events per 45 2 GeV 2 Bin 1000 800 600 400 200 m f1 100 GeV m s1 100 GeV Events per 45 2 GeV 2 Bin 1000 800 600 400 200 m f1 100 GeV m s1 100 GeV 0 100 2 150 2 200 2 250 2 300 2 350 2 400 2 m 2 f1s1 in GeV 2 0 100 2 150 2 200 2 250 2 300 2 350 2 400 2 m 2 f1s1 in GeV 2 f 1 100 GeV f 2 100 GeV f 3 100 GeV F 1 V 1 F 2 s 1 600 GeV 400 GeV 250 GeV 100 GeV Most cases cusp survives (not in a few cases)
Other cases... more than two visible particles: cusp in for resolve by other invariant masses (e.g., M cba or M cb...) c b a M ca Z 2...... D C B A multiple mother, e.g., χ 0 4, 3, 2 l + l χ 0 1 in SUSY (need degenerate for comparable cross-section?) experimental errors...
Conclusions DM symmetry does not have to be Z 2 Z 3 Z 2 DM partner decays: distinguished from by number of endpoints in invariant mass of SM/visible (for off-shell intermediate) and cusps (for on-shell)
BACK-UP SLIDES
Running of Gauge Coupling (Pomarol; Randall, Schwartz; Goldberger, Rothstein; KA, Delgado, Sundrum; Choi, Kim; Contino, Creminelli, Trincherini) Subtle: gauge bosons flat loops span extra dimension, sensitive to Planck and TeV cut-off scales (AdS/CFT more intuitive) Gauge boson loops: non-universal; effectively cut-off at high scale (a la SM) Fermion loops non-universal (unlike SM): & H (near TeV brane) loop cut-off at (warped-down) TeV; other fermion (near UV brane) loops cut-off at high scale 2 nd t R t R : running due to light GUT partners
Unification in CFT picture Global unified symmetry for CFT LO running of SM gauge couplings from CFT loops universal Composite t R and H above TeV, replace running due to t R and H by CFT Add external fermions to make composite GUT partners of t R heavy SM - t R SM (anti-)gut partners of UV cutoff unified global symmetry t R TeV t R H + + GUT partners
Assumptions Bulk unified gauge symmetry global unified symmetry CFT has t R Localization parameter (bulk mass) of : unification improved relative to SM in entire range (preferred by precision data); precision unification for sizable range
NLO precision SUSY 1 Α U 35. 31. 27. 23. 19. 15. 11. 6.7 δ 3 = ( ) α theory 3 α exp 3 /α exp 3 0.1 in SUSY (α 3 at M Z ) 3 0.3 0.2 0.1 0 0.1 0.2 0.3 1 2 3 4 5 6 7 8 b strong (size of 4D strong sector) Landau pole below GUT scale
Signals Complete GUT multiplets at few TeV scale (KK gauge bosons and fermions) light GUT partners of unification t R for precision
Unbroken subgroup of U(1) B break U(1) B to avoid massless gauge boson break on Planck brane: ( q 3 l ) /M 2 Pl Unsplitting if B =1/3: ( q(++) ) ( q c ( ) ) ( q ( +) ) l ( +) B=1/3 l c (+ ) B= 1/3 l(++) B=0 mix on Planck brane To suppress proton decay, break, e.g. preserves Z 3 B = integer