A Pyramid Scheme for Particle Physics Jean-Fran cois Fortin New - PowerPoint PPT Presentation

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion A Pyramid Scheme for Particle Physics Jean-Fran¸ cois Fortin New High Energy Theory Center, Rutgers University Piscataway, NJ May 11-13, 2009 Phenomenology 2009 Symposium based on arXiv:0901.3578 [hep-th] Tom Banks, JFF

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Outline Motivation 1 Cosmological SUSY Breaking Metastable DSB Trinification and Pyramid scheme 2 Trinification and Pyramid scheme Discrete R-symmetry Phenomenology of Pyramid scheme 3 Spectrum Cosmology Conclusion 4 Features and problems

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Cosmological SUSY Breaking Cosmological constant an input parameter Banks LEFT Λ = 0 limit - Super-Poincar´ e symmetry - Discrete R -symmetry ⇒ Λ = 0 LEFT Λ � = 0 limit ⇒ R -breaking operators - UV/IR mixing effect - Metastable SUSY violating state with m 3 / 2 = K Λ 1 / 4 , K = O (10) - Constant term in superpotential such that c . c . = Λ - Tunneling probability of order O ( e − π ( RM P ) 2 ) ⇒ Constraints on LEFT

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Metastable DSB Metastable dynamical SUSY breaking - DSB ⇒ Natural hierarchy of scales M SUSY ≪ M P Witten - More generic than DSB in stable states Intriligator, Seiberg, Shih Direct gauge mediation and MSSM ⇒ G × SU (1 , 2 , 3) - No messenger sector - Solution of SUSY flavor problem - One loop gauge coupling unification SM gauge couplings in perturbative regime

b b b b Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Trinification and Pyramid scheme Trinification Glashow SU ( 3 ) P - SU (3) 3 ⋊ Z 3 - Gauge bosons in (8 , 1 , 1) ⊕ · · · 2 Higgs and 3 families in (3 , ¯ 3 , 1) ⊕ (¯ 3 , 1 , 3) ⊕ (1 , 3 , ¯ 3) T 3 , ¯ T 3 Pyramid scheme T 1 , ¯ T 2 , ¯ T 1 T 2 - Extra SU (3) P - Extra matter (trianons) T 1 + ¯ T 1 = (3 , 1 , 1 , ¯ 3) ⊕ (¯ 3 , 1 , 1 , 3) T 2 + ¯ T 2 = (1 , 3 , 1 , ¯ 3) ⊕ (1 , ¯ 3 , 1 , 3) SU ( 3 ) 3 T 3 + ¯ T 3 = (1 , 1 , 3 , ¯ 3) ⊕ (1 , 1 , ¯ 3 , 3) - One singlet S ⇒ µ -problem SU ( 3 ) 1 SU ( 3 ) 2 GUT SU (3) P × SU (3) 3 ⋊ Z 3 → LEFT SU (3) P × SU (1 , 2 , 3)

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Discrete R-symmetry Non-anomalous Yukawa terms, Higgs terms and trianon terms allowed Dimension 4 and 5 B and L violating terms forbidden (apart from neutrino seesaw operator) 3 � ( m i + y i S ) T i ¯ W = T i + GUT terms + g µ SH u H d i =1 E + λ ν M ( LH u ) 2 + W 0 + λ u H u Q ¯ U + λ d H d Q ¯ D + λ L H d L ¯

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion SU (3) P with N F = 9 flavors ⇒ IR free Without ISS mass terms - Free theory with SUSY - Forbidden by CSB ⇒ Dynamical metastable SUSY violating state with m 3 / 2 = K Λ 1 / 4 With ISS mass terms - Two heavy masses ⇒ Assumed SUSY and R -symmetry breaking metastable state Phenomenology suggests heavy m 1 , 3 > Λ 3 with m 2 ≈ Λ 3 Mass hierarchy Λ 3 ≈ m 2 � m 3 ≪ m 1

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Spectrum W = X (det M / Λ 3 − P ¯ P − Λ 2 3 ) + trianon terms + · · · Two kinds of messengers - N F = N C = 3 theory moduli M = Z a λ a , P = i Λ 3 e ( q + p ) / Λ 3 and ¯ P = i Λ 3 e ( q − p ) / Λ 3 - Heavy trianons SUSY breaking vacuum ⇒ � P � = � ¯ P � � = 0 R -symmetry breaking vacuum ⇒ � M � ∝ Id ⇒ V non − SUSY ≈ K − 1 M † M | m 2 Λ 3 | 2

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion M messengers m 2 Λ 3 = K Λ 1 / 4 m 3 / 2 = X g m P α i m i = 3 X i 4 π m 2 1 / 2 M field quartic scalar couplings of order O ( m 2 2 / Λ 2 3 ) ⇒ √ m 2 < 4 π Λ 3 Chargino mass bound of 160 GeV ⇒ X 2 m 2 TeV > 19 . 7 ⇒ Example: m 2 3 ≈ 1 - Assumption: m 2 = 1 . 7Λ 3 such that 2 4 π Λ 2 4 � - X 2 > 4 . 2 X g / K ⇒ Λ 3 = 5 . 1 TeV and m 2 = 8 . 6 TeV

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion T 1 , 3 messengers m 3 ≫ Λ 3 α ) 2 f ( M / m 3 , P / m 3 , ¯ d 2 θ ( W 3 � - Gluino effective couplings P / m 3 ) m 3 � Λ 3 due to gluino constraint - CW approximation breaks down - Chiral perturbation theory not suitable ⇒ Gluino/chargino and squark/slepton mass ratios suppressed compared to usual gauge mediation - No large contributions to Higgs potential ⇒ Good for little hierarchy problem

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Cosmology Gauge mediation ⇒ LSP gravitino thus no WIMP dark matter candidate Hidden baryon-like states as dark matter Banks, Mason, O’Neil Pyramid scheme ⇒ 3 accidental baryon number-like symmetries - 2 unbroken U B 1 , 3 ⇒ Observed DM density without asymmetry through non-thermal production with T reh < Λ 3 - 1 spontaneously broken U B 2

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Assumption: Negligible primordial asymmetries with low T reh U B 3 -charged particles as DM - QCD-like interactions with dynamical scale Λ 3 - Energy-independent annihilation cross section of order O (Λ − 2 3 ) - Annihilation to PNGB of spontaneously broken U B 2 with high multiplicity PNGB of spontaneously broken U B 2 (pyrmion) d 2 θ S (det T 2 ) / M GUT ⇒ � - Leading U B 2 breaking operator Light (MeV range) - Stellar cooling rates bound satisfied - Colorless constituents ⇒ Decay to e + e − , photons and neutrinos from operators like α 2 2 ∂ µ pJ µ / Λ 3 ∼ α 2 2 m e pe + e − / Λ 3 ⇒ Positron excess with DM annihilation cross section σ 0 = A / Λ 2 3

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion Features and problems Features Based on trinification ⇒ No Landau poles Heavy trianons needed for metastable SUSY violating state ⇒ colored sparticle mass suppression 2 unbroken baryon number-like symmetries ⇒ Non-thermal DM candidate compatible with experiments Pyrmion mass ⇒ Not produced in ordinary stars and positron excess compatible with experiments Problems Existence of metastable SUSY breaking state ⇒ Non-zero meson VEV