Simple and direct communication of dynamical supersymmetry breaking - PowerPoint PPT Presentation

Simple and direct communication of dynamical supersymmetry breaking Andrea Romanino SISSA with Francesco Caracciolo arXiv:1207 .5376 also based on earler work with Nardecchia, Ziegler, Monaco, Spinrath, Pierini

Supersymmetry Leads to Gauge coupling unification Plausible dark matter candidate (with R P , independently motivated) Calculable theory, can be extrapolated up to M Pl Needs to be broken, hopefully spontaneously Effective description in terms of O(100) parameters Most of the parameter space not viable q j ˆ ij ˆ q j ˆ i ˆ l j ˆ h d + µ ˆ h u ˆ W = λ U u c h u + λ D d c h d + λ E e c ij ˆ i ˆ i ˆ ij ˆ h d FCNC and CPV: useful constraint on supersymmetry breaking ij ˜ i ˜ − L soft = A U u c q j h u + A D d c q j h d + A E e c l j h d + m 2 ij ˜ i ˜ i ˜ ij ˜ ud h u h d + h.c. LHC, unavoidable FT (depending on messenger scale) i ) † ˜ d c ) ij ( ˜ l ) ij ˜ i ˜ q † l † u c u c d c d c m 2 m 2 i ) † ˜ m 2 m 2 + ( ˜ q ) ij ˜ i ˜ q j + ( ˜ u c ) ij (˜ j + ( ˜ j + ( ˜ l j h d h † m 2 e c i ) † ˜ e c j + m 2 h u h † u h u + m 2 M 3 > 1.2 TeV + ( ˜ e c ) ij (˜ d h d + M 3 g A + M 2 W a + M 1 W a ˜ ˜ B ˜ ˜ LHC, avoidable FT 2 ˜ g A ˜ B + h.c. 2 2 m sq > 1.4 TeV (but m 1,2 ≠ m 3 ) m H ≈ 125 GeV? (but NMSSM, λ SUSY)

Origin of supersymmetry breaking

A wide class of models of supersymmetry breaking ? [Polchinski Susskind, Dine Fischler, Dimopoulos Raby, Barbieri Ferrara Nanopoulos] ? SUSY breaking MSSM Hidden Observable sector sector Z chiral superfield <Z> = F θ 2 M Q chiral superfield F » (M Z ) 2 SM singlet d 4 θ Z † Z Q † Q m = F � → m 2 ˜ Q † ˜ Q, M 2 M

A wide class of models of supersymmetry breaking ? SUSY breaking MSSM Hidden Observable sector sector

A useful guideline: the supertrace constraint Str M 2 ≡ ∑ bosons m 2 - ∑ fermions m 2 (weighted by # of dofs) Str M 2 = 0 Ren. Kähler + tree level + Tr(T a ) = 0: Holds separately for each set of conserved quantum numbers MSSM: incompatible with (Str M 2 ) f,MSSM = ∑ sfermions m 2 - ∑ fermions m 2 > 0 d − 1 m 2 lightest d -sfermion ≤ m 2 G = G SM : incompatible with 3 g � D Y ˜ (if D Y < 0, consider up sfermions)

Addressing the supertrace constraint Ren. Kähler + tree level + Tr(T a ) = 0 → Str M 2 = 0 Supergravity: non-renormalizable Kähler: Str ≠ 0 FCNC ? FCNC OK “Loop” gauge-mediation: loop-induced: Str ≠ 0 �� � Anomalous U(1)’ s: Tr(T a ) ≠ 0: Str ≠ 0 � � � � � � FCNC OK Tree-level gauge mediation: Str = 0 � � � � � � FCNC OK

Tree - level gauge mediation Z † Q † d 4 θ Z † Z Q † Q � M 2 V Z Q ↑ massive vector of a spontaneously broken U(1) G ⊃ G SM x U(1) ⇒ Z, Q charged under U(1) F 2 M ≈ M V scale of U(1) breaking m 2 Q = q Q q Z ˜ M 2 V /g 2

⇒ Need of extra heavy (through U(1) breaking) fields SU(5)xU(1) ⊆ G, flavour universal charges, q Z > 0 for definitess - (l, d c ) = 5: �� � q 5 > 0 � (m 25 > 0, tree level) (q, u c , e c ) = 10: � q 10 > 0 � � (m 210 > 0, tree level) SU(5) 2 xU(1) anomaly cancellation: �� � � 0 = 3(q 5 + 3q 10 ) + extra > 0 < 0 (guaranteed if SU(5)xU(1) is embedded in SO(10)) M from U(1) breaking Masses 2 (before EWSB) _ - � � � � � 5 + 10 � � � � � extra = Φ + Φ � fermions � � 0 � � � � � � M 2 STr = 0 � scalars � � 0 + m 2 � � � � M 2 - m 2

The extra heavy fields as chiral messengers U(1) breaking: � � � <Y> = M SUSY breaking: � � <Z> = F θ 2 � In concrete models: q Z = q Y _ h Y Φ Φ � → M Φ = hM � Z k Φ _ Φ k F M g ∼ α k Z Φ Φ � → �� � � � 4 π h M V light V light Φ Φ X h M

A wide class of models of supersymmetry breaking ? SUSY breaking MSSM Hidden Observable sector sector

Phenomenologically viable supersymmetric models not always are theoretically complete Theoretically complete models of susy breaking not always are phenomenologically viable Phenomenologically viable and theoretically complete models not always are extremely simple

Reminder Non-renormalization: � W cl = W all orders in PT � � � “Classical” breaking W = W cl + W NP “Dynamical” M SUSY ≈ M 0 e -(2 π / α b) breaking

The (problematic) role of the R-symmetry An exact R-symmetry prevents (Majorana) gaugino masses Nelson-Seiberg: R-symmetry needed in a susy-breaking model where i) the susy-breaking minimum is stable and ii) the superpotential is generic Non vanishing gaugino masses then require non generic superpotential (R-breaking) � or metastable susy-breaking minima � � � or spontaneous R-breaking � � � � � � or Dirac gaugino masses

as if it that were not enough.. Spontaneous R-breaking in generalized O’R models needs R ≠ 0,2 (e.g. ISS flows to R = 0,2) Shih, hep-th/0703196 Curtin Komargodski Shih Tsai, 1202.5331 Even if R ≠ 0,2: the stability (everywhere) of the pseudoflat direction along which the R-symmetry is spontaneously broken forces M g = 0 at 1-loop Komargodski Shih, 0902.0030 More gaugino screening takes place (semi-direct) Arkani-Hamed Giudice Luty Rattazzi, hep-ph/9803290 Argurio Bertolini Ferretti Mariotti, 0912.0743

A simple, viable, dynamical model: 3-2 + messenger/observable fields [N=1 global, canonical K, no FI]

Reminder: 3-2 model [Affleck Dine Seiberg] SU(3) strong at Λ 3 where SU(2) weak Λ 7 SU(3) SU(2) G ⊇ G SM 3 W cl = h QD c L W NP = det Q ˜ 3 2 1 Q Q 3 1 1 U c ✓ D c ◆ 3 1 1 D c V NP ˜ Q = 1 2 1 L U c V cl h « 1: calculability SU(3) x SU(2) broken at M = Λ 3 /h 1/7 » Λ 3 SUSY broken at F = h M 2 « M 2 <L 2 > = 0.3 M + 1.3 F θ 2 � � <L 1 > = 0

Details   a 0 a ≈ 1.164 √ Q = ˜  M � a 2 − b 2 � Q = b 0 L = M 0  b ≈ 1.131 0 0 p 0 1 a 2 − b 2 − 1 / ( a 3 b 2 ) a 0 A F � 0 a 2 � F Q = F ˜ Q = − 1 / ( a 2 b 3 ) 0 F L = F @ 0 0

Coupling to observable fields: semi-direct GM [Seiberg, Volansky, Wecht] Messengers SU(2) Messengers G SM MSSM +MSSM SUSY non trivial, M g = 0 SU(3)

Our model [Caracciolo, R] SU(3) SU(2) G ⊇ G SM L † , Q † Φ † 3 2 1 Q U c 3 1 1 D c 3 1 1 1 2 1 L V 3 1 2 Φ i R SM L, Q Φ 1 1 φ i R SM F 2 Φ = � g 2 T 3 m 2 m 2 m 2 ˜ = ⌥ ˜ ˜ φ = 0 M 2 V ✓ φ i ◆ , φ i Φ i = f i [no explicit mass term] W = L Φ i φ i → M φ i φ i + F θ 2 φ i φ i M 2 m 2 f = MSSM fields M f = 0 f = + ˜ ˜ m 2 − ˜ φ ± = M 2 ± F 2 M 2 M φ , φ = M φ i , φ i = messengers of MGM ˜ 2 gaugino masses

More details L † , Q † f † c = 2 a 8 b 8 + 2 a 2 + 4 a 4 b 4 √ m 2 = c F 2 a 2 − b 2 − 2 b 2 ˜ ≈ 1 . 48 M 2 3 a 8 b 6 − a 6 b 8 L, Q f L k φ φ a 2 F α i M 3 (TeV) ≈ 0 . 35 ˜ m M i = 12 √ 4 π M a 2 − b 2 V i V i φ φ X M > 10 11 GeV

Yukawa interactions and Higgs Yukawa interactions SM fermions have T 3 = -1/2 → Higgs doublets have T 3 = 1 (triplets) W Y = λ uij Φ i Φ j H u + λ dij Φ i Φ j H d The Higgs sector Is model dependent Two additional Higgs pairs not coupled to the SM fermions The Higgs pair interacting with fermions has negative soft masses

A-terms h L 2 i φ φ X φ Do arise from δ K = W = y L Φ φ = yL 2 φφ + yL 1 f φ f † f L 1 Because of the embedding of the messenger U(1) in a larger group (SU(2), SO(10)) A t ≈ − α y Numerically: (no A-m 2 problem) M 3 6 α 3

In order to get a 125 GeV Higgs tan b = 10 tan b = 50 8.0 8.0 7.5 7.5 7.0 7.0 6.5 6.5 y t y t 6.0 6.0 5.5 5.5 5.0 5.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 é é m t 1 H GeV L m t 1 H GeV L

2-loop corrections to sfermion masses “Minimal” gauge mediation: �� O(1%) �� flavour-blind Matter-messenger couplings: � O(3%) � � flavour-safe

More details ! ✓ F L f y T f y T ◆ 2 y ∗ y ∗ g 2 T f f 2(4 π ) 2 − 2 c r r m 2 δ ˜ f = 2 (4 π ) 2 + f (4 π ) 2 (4 π ) 2 M L q + 3 y u c y † u c + 3 y d c y † d c + 2 y l y † l + y n c y † n c + y e c y † 6 y q y † � � T = Tr e c 8 Tr( y ∗ y T ) + y ∗ y T �⇤ D y ∗ y T � ⇥ 12 < 1 . 5 8 Tr( y ∗ y T ) + y ∗ y T �⇤ D y ∗ y T � 13 < 0 . 5 · 10 2 ⇥ 8 Tr( y ∗ y T ) + y ∗ y T �⇤ D y ∗ y T � 23 < 1 . 5 · 10 2 ⇥ 8 Tr( y ∗ y T ) + y ∗ y T �⇤ U y ∗ y T � ⇥ 12 < 6 .

Summary Supersymmetry breaking remains the key of phenomenologically and theoretically successful supersymmetry models Phenomenological issues/guidelines: FCNC, fine-tuning Theoretical issues/guidelines: Str, R-symmetry A simple, theoretically complete, and phenomenologically viable option Susy breaking is communicated by extra, SB gauge interactions Messenger and observable fields are charged under the hidden sector gauge group Positive sfermion masses arise at the tree level, in a dynamical realization of TGM, but are not hierarchically larger than gaugino’ s A-terms are generated, and are possibly sizeable