Dark Forces at New Experimental Frontiers The Search for New States and Forces of Nature Conference, GGI, October 2009 Philip Schuster (SLAC Theory Group) with J.D. Bjorken, R. Essig, and N. Toro (0906.0580) R. Essig, and N. Toro (0903.3941) N. Toro and I. Yavin (0910.1602) D. Alves, S. Behbahani, and J. Wacker (0903.3945)
Dark Forces at New Experimental Frontiers • Theory of New Vector Bosons (and hints from dark matter) • e+e- Collider Searches (Babar, Belle, KLOE) • Fixed-Target Experiments (e.g. @ JLab)
New Forces? Known interactions: SU (3) SU (2) × U (1) ? × × (Strong) (Electro-weak) If ordinary matter is charged under a new force, we would have seen it (for masses ~TeV or less) What about forces we are not charged under?
Photon Mixing with New Vector Boson New vector bosons couple to the Standard Model by mixing with the photon δ L = ǫ F Y F A ′ γ A ′ GUT or Planck scale quantum corrections ǫ � eg D 16 π 2 ∼ 10 − 4 − 10 − 3 [Holdom ʻ 86] A ′ A ′ m 2 A ′ ∼ ǫ M 2 W (mass inherited from “electro-weak” scale) [Cheung, Ruderman, Wang, Yavin; Katz and Sundrum; Morrissey, Poland, Zurek]
Ordinary Matter is Milli-Charged Photon mixing with A’ is equivalent to electrically charged matter acquiring a milli-charge under the A’ A ′ A ′ × ǫ γ ∗ (equivalent) e × ǫ e e + e + e − e − What about the rest of the matter in the Universe?
Suppose Dark Matter is Charged Under a GeV-Scale Gauge Force Several Striking Consequences: • Annihilation enhanced at low velocities • Annihilation into light, not heavy states • Excited states split by O(MeV) • Scattering off matter: • rate similar to neutral current • scattering into excited state, enhanced modulation
Annihilation into Leptons Standard Model } A ′ DM Particles (m<m A’ /2) A ′ DM [Arkani-Hamed, Finkbeiner, Slatyer, Weiner; Cholis, Finkbeiner, Goodenough, Weiner; Pospelov & Ritz] [A. Strumia, Planck ’09] [Meade, Papucci, Strumia, Volansky
A’ Mediation of Inelastic DM-Nuclei Scattering Dark matter mass splitting: ~100 keV Large modulation amplitude, characteristics of recoil spectrum, and null results of other experiments explained by inelastic collisions [Tucker-Smith and Weiner; Arkani-Hamed, Finkbeiner, Slatyer, Weiner] arXiv:0804.2741, Bernabei et. al.
The Origin of a 100 keV Dark Sector Splitting Non-Abelian Higgsed Sector: Dark matter is a charged multiplet [Arkani-Hamed, Finkbeiner, Slatyer, Weiner] δ M DM ∼ α D δ M gauge ∼ α 2 D M gauge ∼ 100 keV (radiative splittings) (custodial symmetry breaking ) Non-Abelian Confined Sector: Dark matter is a dark heavy flavor meson [Alves, Behbahani, PS, Wacker] δ M DM ∼ Λ 2 Dark ∼ 100 keV → Λ Dark ∼ GeV M DM (hyperfine splittings) New particles at the GeV-scale are required
New Gauge Forces Are there new gauge forces? – an intriguing possibility Do new gauge forces explain astro/direct-detection data? Insight from laboratory experiments needed!
Production Mechanisms A ′ Fixed-Target: Electron or Proton collisions, E 1 x E 1 A’ decays to di-lepton, pions, multiple channels E 1 (1 − x ) (Jefferson Lab (Hall A, Hall B/CLAS), SLAC, MAMI (Mainz), ELSA (Bonn), XFEL (DESY), COMPASS (CERN), FNAL, ...) Colliding e+e-: On- or Off- shell A’, X=dark sector or leptons & pions (BELLE, BaBar, BES-III, KLOE, CLEO) High Energy Hadron Colliders: New heavy particles decaying into dark sector (lepton jets) (CDF & D0) (see talk by Itay Yavin)
See SLAC Dark Forces Workshop for Reference Organizers: R. Essig, M. Graham, M. Peskin, A. Roodman, P. Schuster, N. Toro, J. Wacker Workshop webpage: http://www-conf.slac.stanford.edu/darkforces2009/ All talks are posted at: http://indico.cern.ch/event/darkforces
Dark Forces at New Experimental Frontiers • Theory of New Vector Bosons (and hints from dark matter) • e+e- Collider Searches (Babar and Belle) • Fixed-Target Experiments (e.g. @ JLab)
Dark Sector Collider Production Off-Shell A ′ Radiative return σ ∝ ǫ 2 /s High-luminosity GeV-scale colliders
Normalizing Production Rates from DAMA/LIBRA e ε ∝ e ε g D g D q 2 = s = (10 . 58 GeV) 2 q 2 = µ 2 v 2 ≪ m 2 A ′ Can estimate production cross-section from DAMA/LIBRA scattering cross-section
DAMA-Normalized Production Rates Γ A' Pair Cross Section � Form � Factor iDM � � � 0.01 10 8 M DM � 1000 GeV, C Z decay sensitivity Cross � Section � fb � 10 5 � g � 2 � Μ constraint 100 Α D � 10 � 4 ~100 events in BaBar data 0.1 Α D �Α Σ � off � shell � � reference � Α D � 1 10 � 4 0.1 0.2 0.5 1.0 2.0 5.0 10.0 A' Mass � GeV � [see: Essig, PS, Toro]
GeV-Scale Colliders Figure of Merit is: L int /s BELLE BaBar KLOE CLEO-C BES III 725 fb − 1 430 fb − 1 2 . 5 fb − 1 ≈ 1 fb − 1 ?? fb − 1 (10 . 6 GeV) 2 (10 . 6 GeV) 2 (1 GeV) 2 (4 GeV) 2 (4 GeV) 2 No. of events for α D = α , ǫ = 10 − 2 (approx): 1,000 170,000 100,000 50,000 Missing from numerical comparison: – accessible mass range – kinematic acceptance & visibility of events Broad range of searches needed
Higgsed/Confined Dark Sector Signatures � + � − � − (a) (b) Higgsed: Confined: � + � + � − φ D η � � + D φ D � − !"#$%&'()*# γ q D &+*,'#-. +"!#*/01")0*/ W D e − e − e − e + e + e + A � ¯ q D W � D W D � + h D W � D W D � − φ D h D � + φ D � + W D φ D � + � − � − � − � + � − � + � − � − � − � + � + � + � − [see: Essig, PS, Toro; Batell, Pospelov, Ritz] Wide variety of multi-lepton final states
Final States (direct production) • “Generic”: - BaBar [via � -decay e + e − → γ l + l − search, H. Kim] � ? - Belle [Y. Kwon, J. Rorie] κ 2 - BES-III [H. Li, Y. Zheng] - KLOE [F. Bossi] • “Generic + higgs”: - not yet! α ′ κ 2 [interest from BaBar, Belle, BES-III, KLOE] • “Nonabelian”: e + e − → V ∗ → 4 l W 1 - BaBar [4l, M. Graham] � W 2 V Also: higher multiplicity (confining), 4l + E T , ... 8 From e+e- working group summary (DF workshop)
Search for narrow ǫ ∼ 10 − 4 Sensitivity to resonance pairs in e + e � � 4 lepton @ BaBar [M. Graham, arXiv:0908.2821] Matt Graham, SLAC September 25, 2009 Cross Section Upper Limits 2e2 � 4e Points: bin UL Lines: average UL 4 � (smaller line shows statistical error only) 23
Rare Meson Decays Existing data sets provide sensitivity to ǫ ∼ 10 − 3 [Reece & Wang ʼ 09] Good sensitivity in additional channels: ǫ � 10 − 3 (Babar, Belle, kTeV) Sensitivity to π → ee γ ǫ ∼ 10 − 4 − 10 − 3 (BES-III in 1 year) Sensitivity to J/ ψ → 6 l Searches ongoing...
Dark Forces at New Experimental Frontiers • Theory of New Vector Bosons (and hints from dark matter) • e+e- Collider Searches (Babar and Belle) • Fixed-Target Experiments (e.g. @ JLab)
Collider vs. Fixed-Target A ′ E 1 x E 1 E 1 (1 − x ) µ + Nucleus µ − σ ∼ α 3 Z 2 ǫ 2 σ ∼ α 2 ǫ 2 ∼ O (10 fb ) ∼ O (10 pb ) E 2 m 2 O(few) ab − 1 per decade O(few) ab − 1 per day
Unique Fixed-Target Kinematics [see: Bjorken, Essig, PS, Toro] ǫ 2 dx ∝ α 3 Kinematics very different d σ 1 from massless photon e · x + m 2 m 2 A (1 − x ) /x π bremsstrahlung x = E A E � 3 / 2 � m A l + ∼ (narrow) E e − ∼ m A A ′ E � 1 / 2 l − � m A Energy = E ∼ (wide) ...or other decays E e − Heavier product (here A’) E A ∼ E − m A takes most of beam energy E e ∼ m A
Lifetime A’ decays directly back to Standard Model: γ c τ ≈ 1 mm ( γ / 10) (10 − 4 / ǫ ) 2 (100MeV /m A ′ ) A’ decay to dark scalars: h D → l + l − l = e, µ, π γ c τ ≈ 2 × 10 8 cm ( γ / 10) ( α / α D ) × (10 − 3 / ǫ ) 4 ( m A ′ / GeV) 2 (GeV /m h D ) ...etc A’ production vs. decay product lifetime determine existing constraints and search strategies
Fixed-Target Territory [see: Bjorken, Essig, PS, Toro; BABAR Reece, Wang; Batell Pospelov, Ritz] ( g − 2) e ( g − 2) µ Υ (3 S ) → ( µ + µ − ) γ 0.01 0.1 1 0.01 0.01 di-lepton decay: 10 � 3 10 � 3 c τ ≈ 80 µm 10 � 4 10 � 4 c τ ≈ 1 cm 10 � 5 10 � 5 Ε 10 � 6 10 � 6 MegaWatt x Year 10 � 7 10 � 7 lower limit for seeing >10 events 10 � 8 10 � 8 10 � 9 10 � 9 0.01 0.1 1 mA' � GeV
Beam Dump Experiments shield decay volume (10 cm - 100 m) (50 cm - 100 m) e beam thick target tracking, calorimetry, ... SLAC E137: 10 20 e - (30 C) at 20 GeV, 200m shield SLAC E141: 10 16 e - at 9 GeV, 12 cm W target FNAL E774: 10 10 e - at 275 GeV, 20 cm W target
Past Beam Dump Limits (A’ di-lepton decay modes) 10 � 2 10 � 1 1 10 � 2 10 � 2 Production Mode: a e � � 3S � A ′ E774 a Μ E 1 x E 1 10 � 3 10 � 3 E 1 (1 − x ) 10 � 4 10 � 4 E141 Nucleus 10 � 5 10 � 5 E137 Ε 10 � 6 10 � 6 10 � 7 10 � 7 shield decay volume 10 � 8 10 � 8 (10 cm - 100 m) (50 cm - 100 m) SN 10 � 9 10 � 9 e beam 10 � 2 10 � 1 1 thick target tracking, calorimetry, ... m A ' � GeV � [see: Bjorken, Essig, PS, Toro]
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