Echoes of supersymmetry: the relic Q-balls SUSY and Q-balls - PowerPoint PPT Presentation

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Echoes of supersymmetry: the relic Q-balls • SUSY and Q-balls • Inflation+SUSY ⇒ Q-balls • stable Q-balls as dark matter • interactions with matter, detection, constraints 1

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Echoes of supersymmetry: relic Q-balls Affleck−Dine condensate gravity waves baryonic Q−balls baryons stable unstable dark matter 2

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 SUSY and Q-balls nucleus Why would one suspect that SUSY SUSY ⇒ Q-balls? SUSY SUSY Bose−Einstein Q−ball 3

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Q-balls Let us consider a complex scalar field φ ( x, t ) in a potential that respects a U(1) symmetry: φ → e iθ φ . vacuum: φ = 0 � � φ † ↔ � conserved charge: Q = 1 d 3 x ∂ 0 φ 2 i Q � = 0 ⇒ φ � = 0 in some finite domain ⇒ Q-ball φ 2 = min , � Q-balls exist if U ( φ ) for φ = φ 0 > 0 Finite φ 0 : M ( Q ) ∝ Q Flat potential ( U ( φ ) ∼ φ p , p < 2 ); φ 0 = ∞ : ✓ ✏ M ( Q ) ∝ Q α , α < 1 ✒ ✑ 4

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Q-balls exist in (softly broken) SUSY because • the theory has scalar fields • the scalar fields carry conserved global charge (baryon and lepton numbers) • attractive scalar interactions (tri-linear terms, flat directions) force � φ 2 ) = min for non-vacuum values. ( U ( φ ) 5

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 MSSM, gauge mediated SUSY breaking Baryonic Q-balls (B-balls) are entirely stable if their mass per unit baryon charge is less than the proton mass. M ( Q ) = M S Q 3 / 4 ⇒ ∼ M S Q − 1 / 4 < 1GeV M ( Q B ) Q B � M S � 4 > ∼ 10 12 for Q B ≫ 1 TeV ✓ ✏ Such B-balls are entirely stable. ✒ ✑ 6

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Baryon asymmetry ✗ ✔ n B 6 . 1 +0 . 3 × 10 − 10 � � η ≡ n γ = − 0 . 2 ✖ ✕ 7

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 What happened right after the Big Bang? • Inflation probably took place • Baryogenesis – definitely after inflation Standard Model is not consistent with the observed baryon asymmetry (assuming inflation) 8

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Affleck–Dine baryogenesis • Natural if SUSY+Inflation • Can explain matter • Can explain dark matter • Predictions can be tested soon 9

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Inflation All matter is produced during reheating after inflation. SUSY ⇒ flat directions. During inflation, scalar fields are displaced from their minima. 10

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Affleck – Dine baryogenesis at the end of inflation a scalar condensate develops a large VEV along a flat direction CP violation is due to time-dependent background. Baryon asymmetry: φ = | φ | e iωt 11

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Affleck – Dine baryogenesis: an example Suppose the flat direction is lifted by a higher dimension operator W n = M n Φ n +3 . The expansion of the universe breaks SUSY and introduces mass 1 terms m 2 ∼ ± H 2 . The scalar potential: 1 V = − H 2 | Φ | 2 + M 2 n | Φ | 2 n +4 E ∼ 10 15 Assume the inflation scale GeV The Hubble constant H I ≈ E 2 /M p ≈ 10 12 GeV . T R ∼ 10 9 GeV 12

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 In this example, the final baryon asymmetry is n B ( ρ I /T R ) ∼ n B n B T R ρ Φ ∼ n γ n Φ m Φ ρ I � ( n − 1) � � ( n +1) T R M p � 10 − 10 ∼ 10 9 GeV m 3 / 2 Correct baryon asymmetry for n = 1 . (For n > 1 , too big.) [see, e.g., review by Dine, AK] 13

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 ✓ ✏ Fragmentation of the Affleck-Dine condensate ✒ ✑ [AK, Shaposhnikov] small inhomogeneities can grow unstable modes: ω 2 − U ′′ ( φ ) � 0 < k < k max = ⇒ Lumps of baryon condensate ⇒ Q-balls t x 14

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Numerical simulations of the fragmentation 40 40 40 40 30 30 30 30 20 20 20 20 10 10 10 10 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 (a) mt = 0 (b) mt = 75 (c) mt = 150 (d) mt = 375 40 40 40 40 30 30 30 30 20 20 20 20 10 10 10 10 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 (e) mt = 525 (f) mt = 675 (g) mt = 825 (h) mt = 900 15

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Three-dimensional charge density plots [Multamaki]. (i) mt = 900 (j) mt = 1050 (k) mt = 1200 (l) mt = 1350 16

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 ✓ ✏ Fragmentation of AD condensate can produce Q-balls ✒ ✑ SUSY Q-balls may be stable or unstable if stable ⇒ dark matter Affleck−Dine condensate baryonic Q−balls baryons stable unstable t x dark matter [AK, Shaposhnikov; Enqvist, McDonald] 17

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Interactions of SUSY Q-balls with matter Q−ball There is a Majorana mass term for quarks inside coming from quark the quark-squark-gluino vertex. Probability ∼ 1 for a quark to x reflect as an antiquark. Very fast! antiquark [AK, Loveridge, Shaposhnikov]. 18

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 A “candidate event” [Lattes, Fujimoto and Hasegawa, Phys.Rept. 65 , 151 (1980)] 19

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Stable Q-balls as dark matter Q-balls can accommodate baryon number at lower energy than a nucleon ⇒ B-Balls catalyze proton decay Signal: ✛ ✘ � � dE ρ GeV dl ∼ 100 1 g / cm 3 cm ✚ ✙ Heavy ⇒ low flux ⇒ experimental limits from Super-Kamiokande and other large detectors 20

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Present experimental limits [Arafune et al. ]; 21

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Ω B − ball / Ω matter ∼ 5 [Laine, Shaposhnikov] • Gauge-mediated SUSY breaking • Q B ∼ 10 26 ± 2 (in agreement with numerical simulations) More specifically, Ω B − ball / Ω matter ∼ 5 implies � − 1 / 2 η B ∼ 10 − 10 � M SUSY � � Q B 10 26 TeV 22

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Ω B − ball / Ω matter ∼ 5 23

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Ω B − ball / Ω matter ∼ 5 24

Alexander Kusenko (UCLA) Cosmic Frontier Snowmass ’13 Conclusion • SUSY + Inflation ⇒ Q-balls, some may be stable, can be dark matter • Typical size large ⇒ typical density small ⇒ need large detectors to search for relic Q-balls • Current bounds from Super-K. Future search using IceCube, HAWC possible. 25