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

1

Motivation Cosmological SUSY Breaking Metastable DSB

2

Trinification and Pyramid scheme Trinification and Pyramid scheme Discrete R-symmetry

3

Phenomenology of Pyramid scheme Spectrum Cosmology

4

Conclusion 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 m3/2 = KΛ1/4,

K = O(10)

• Constant term in superpotential such that c.c. = Λ
• Tunneling probability of order O(e−π(RMP)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 MSUSY ≪ MP

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

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

Trinification and Pyramid scheme

Trinification

Glashow

• SU(3)3 ⋊ Z3
• Gauge bosons in (8, 1, 1) ⊕ · · ·

2 Higgs and 3 families in

(3, ¯ 3, 1) ⊕ (¯ 3, 1, 3) ⊕ (1, 3, ¯ 3)

Pyramid scheme

• Extra SU(3)P
• Extra matter (trianons)

T1 + ¯ T1 = (3, 1, 1, ¯ 3) ⊕ (¯ 3, 1, 1, 3) T2 + ¯ T2 = (1, 3, 1, ¯ 3) ⊕ (1, ¯ 3, 1, 3) T3 + ¯ T3 = (1, 1, 3, ¯ 3) ⊕ (1, 1, ¯ 3, 3)

• One singlet S ⇒ µ-problem

SU(3)1 SU(3)2 SU(3)3 SU(3)P T1, ¯ T1 T2, ¯ T2 T3, ¯ T3

GUT SU(3)P × SU(3)3 ⋊ Z3 → 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) W =

3

• i=1

(mi + yiS)Ti ¯ Ti + GUT terms + gµSHuHd + λuHuQ ¯ U + λdHdQ ¯ D + λLHdL¯ E + λν M (LHu)2 + W0

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

SU(3)P with NF = 9 flavors ⇒ IR free Without ISS mass terms

• Free theory with SUSY
• Forbidden by CSB ⇒ Dynamical metastable SUSY violating

state with m3/2 = KΛ1/4

With ISS mass terms

• Two heavy masses ⇒ Assumed SUSY and R-symmetry

breaking metastable state

Phenomenology suggests heavy m1,3 > Λ3 with m2 ≈ Λ3 Mass hierarchy Λ3 ≈ m2 m3 ≪ m1

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

Spectrum

W = X(det M/Λ3 − P ¯ P − Λ2

3) + trianon terms + · · ·

Two kinds of messengers

• NF = NC = 3 theory moduli

M = Zaλa, P = iΛ3e(q+p)/Λ3 and ¯ P = iΛ3e(q−p)/Λ3

• Heavy trianons

SUSY breaking vacuum ⇒ P = ¯ P = 0 R-symmetry breaking vacuum ⇒ M ∝ Id ⇒ Vnon−SUSY ≈ K −1

M†M|m2Λ3|2

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

M messengers m3/2 = Xg m2Λ3 mP = KΛ1/4 mi

1/2

= 3Xi αi 4πm2 M field quartic scalar couplings of order O(m2

2/Λ2 3) ⇒

m2 < √ 4πΛ3 Chargino mass bound of 160 GeV ⇒ X2 m2

TeV > 19.7

⇒ Example:

• Assumption: m2 = 1.7Λ3 such that

m2

2

4πΛ2

3 ≈ 1

4

• X2 > 4.2
• Xg/K ⇒ Λ3 = 5.1 TeV and m2 = 8.6 TeV

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

T1,3 messengers m3 ≫ Λ3

• Gluino effective couplings
• d2θ (W 3

α)2f (M/m3, P/m3, ¯

P/m3)

m3 Λ3 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 UB1,3 ⇒ Observed DM density without asymmetry

through non-thermal production with Treh < Λ3

• 1 spontaneously broken UB2

Motivation Trinification and Pyramid scheme Phenomenology of Pyramid scheme Conclusion

Assumption: Negligible primordial asymmetries with low Treh UB3-charged particles as DM

• QCD-like interactions with dynamical scale Λ3
• Energy-independent annihilation cross section of order O(Λ−2

3 )

• Annihilation to PNGB of spontaneously broken UB2 with high

multiplicity

PNGB of spontaneously broken UB2 (pyrmion)

• Leading UB2 breaking operator
• d2θ S(det T2)/MGUT ⇒

Light (MeV range)

• Stellar cooling rates bound satisfied
• Colorless constituents

⇒ Decay to e+e−, photons and neutrinos from operators like α2

2∂µpJµ/Λ3 ∼ α2 2mepe+e−/Λ3

⇒ Positron excess with DM annihilation cross section σ0 = A/Λ2

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