LHC reach ATLAS sensitivity projections to LHC14: s = 14 TeV, 300fb - 1 s = 14 TeV, 3000fb - 1 1200 ( MS ) x ( MS or IT ) ( MS ) x ( MS or IT ) 800 1500 ( VBF h → bb ) x ( IT, r > 4cm ) ( VBF h → bb ) x ( IT, r > 4cm ) 2000 ( single lepton ) x ( IT, r > 50 μ m ) ( single lepton ) x ( IT, r > 50 μ m ) 1000 [ Folded SUSY ] [ Folded SUSY ] TLEP Br ( h → invisible ) [ Twin Higgs ] [ Twin Higgs ] 600 1500 800 1000 m T ( GeV ) 600 m T ( GeV ) m t ( GeV ) m t ( GeV ) 1000 400 500 400 500 200 200 20 30 40 50 60 20 30 40 50 60 m 0 ( GeV ) m 0 ( GeV ) Displaced searches probe TeV-scale uncolored top partners! DC, Verhaaren 1506.06141
LHC reach ATLAS 300fb -1 CMS 20 fb -1 � = �� ���� �� �� - � �������� �� % �� ��������� s = 14 TeV, 300fb - 1 1200 ( MS ) x ( MS or IT ) ��� 800 ( VBF h → bb ) x ( IT, r > 4cm ) ( single lepton ) x ( IT, r > 50 μ m ) 1000 [ Folded SUSY ] [ Twin Higgs ] ��� 600 � � [ ��� ] 800 m T ( GeV ) 600 m t ( GeV ) ��� 400 400 ��� 200 Twin Higgs 200 Folded Supersymmetry 20 30 40 50 60 �� �� �� �� �� �� �� m 0 ( GeV ) � π � [ ��� ] DC, Verhaaren 1506.06141 Csaki, Kuflik, Lombardo, Slone 1508.01522
LHC reach ATLAS 300fb -1 CMS 20 fb -1 � = �� ���� �� �� - � �������� �� % �� ��������� s = 14 TeV, 300fb - 1 1200 ( MS ) x ( MS or IT ) ��� 800 ( VBF h → bb ) x ( IT, r > 4cm ) ( single lepton ) x ( IT, r > 50 μ m ) 1000 [ Folded SUSY ] [ Twin Higgs ] ��� 600 � � [ ��� ] 800 m T ( GeV ) 600 m t ( GeV ) ��� 400 400 ��� 200 Twin Higgs 200 Folded Supersymmetry 20 30 40 50 60 �� �� �� �� �� �� �� m 0 ( GeV ) � π � [ ��� ] DC, Verhaaren 1506.06141 Csaki, Kuflik, Lombardo, Slone 1508.01522
LHC reach ATLAS 300fb -1 CMS 20 fb -1 � = �� ���� �� �� - � �������� �� % �� ��������� s = 14 TeV, 300fb - 1 1200 ( MS ) x ( MS or IT ) ��� 800 ( VBF h → bb ) x ( IT, r > 4cm ) ( single lepton ) x ( IT, r > 50 μ m ) 1000 Needs new searches: [ Folded SUSY ] [ Twin Higgs ] ��� 600 � � [ ��� ] 800 one DV + lepton m T ( GeV ) 600 one DV + VBF m t ( GeV ) ��� 400 close DV reconstruction 400 ��� 200 Twin Higgs 200 Folded Supersymmetry 20 30 40 50 60 �� �� �� �� �� �� �� m 0 ( GeV ) � π � [ ��� ] DC, Verhaaren 1506.06141 Csaki, Kuflik, Lombardo, Slone 1508.01522
Mirror Bottomonia In Fraternal Twin Higgs, Mirror Bottomonia can be at bottom of QCD’ spectrum - Higgs branching ratio to mirror bottoms is much larger than to mirror glue - lifetime of bottomonium 0++ state can be much shorter than for glueball - broadly same phenomenology, same decay modes Covered by ~ same search strategies!
Work in progress! Top partner direct production
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation to hard mirror gluons (PERTURBATIVE) SM Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production Great opportunity: - direct evidence of uncolored top partners. - might have comparable reach to exotic Higgs decays - could allow measurement of couplings and masses. - potentiall spectacular signatures: several DVs, or many bb, 𝝊𝝊 pairs Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation to hard mirror gluons (PERTURBATIVE) SM Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation perturbative to hard mirror gluons production (PERTURBATIVE) of TT system: OK SM Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation to hard mirror gluons de-excitation of the (PERTURBATIVE) bound state by photon/ glueball emission: SM OK..ish (for our needs) Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation to hard mirror gluons (PERTURBATIVE) annihilation of bound state into mirror glueballs and SM hidden/SM states: OK (c.f. stoponia etc) Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Top partner direct production emission of soft photons / glueballs Some glueballs will decay visbily in detector: EMERGING JETS* SM * see also 1502.05409 Schwaller, Stolarski, Weiler T pair production SM via DY or h* (s)quirkonium de-excitation slow Ts (PERTURBATIVE) T p p shower & hadronize into two DARK GLUEBALL JETS T T annihilation to hard mirror gluons hadronization of (PERTURBATIVE) mirror gluon jets into glueballs: SM hmmm….. Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Mirror Hadronization How do these mirror gluon jets evolve? Can convince yourself behavior is broadly QCD-like ⇒ form jets or mirror glueballs! How to estimate glueball multiplicity? How to estimate fraction of 0 ++ (i.e. potentially visible ) glueballs? Could just parameterize our ignorance by varying: ⌧ N 0 ++ � N avg ⌘ h N tot i r ≡ N tot But we know *a little bit* about how jets evolve… Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Mirror Hadronization Evolve dummy fragmentation functions with DGLAP equations! ⌧ N 0 ++ � N avg ⌘ h N tot i r ≡ N tot Average Glueball Multiplicity Normalized for 200 GeV Stops 2.5 2.0 m 0 = 15 N avg 〈 N 0 ++ 〉 m 0 = 30 m 0 = 50 1.5 1.0 500 1000 1500 2000 Light Stop Mass ( GeV ) Decouples ‘perturbative’ model parameter space (m T , m 0 , …) from non-perturbative 2D-parameterization of ignorance Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Compare to Higgs Decays Full exploration of signal in this factorized (theory) x (hadronization) parameter space is in progress… But first easy comparison to make: compare number of mirror glueballs produced in top partner production vs exotic Higgs decays! Normalized to ONE GLUEBALL at m T = 200 GeV (pessimistic!) R ≡ � ( pp → TT ) · Br( TT → g B g B ) · N avg ( m T ) � VBF ( pp → hjj ) · ✏ VBF · Br( h → g B g B ) r (fraction of 0 ++ ) VBF trigger efficiency ~ cancels out ~ 20% (optimistic) Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Compare to Higgs Decays ˜ ˜ ˜ ˜ 〈 N 0 ++ 〉 DGLAP σ DY ( pp → t 1 ) ⨯ Br ( t 1 → g B g B )/( σ VBF ( pp → h ) ⨯ Br ( h → g B g B ) ⨯ϵ VBF ) θ t = π / 2 1 t 1 t Blue Shading m b 1 m 0 = 30 1 ≤ m t ∼ ∼ 1000 0.001 Folded SUSY 800 t 1 = RH stop Stop Mass Splitting ( GeV ) 0.1 600 t 2 = LH stop 0.3 400 1 10 10 10 200 # glueballs from stop pair production 10 > # glueballs from exotic Higgs decays 1 0.1 0.3 0 500 1000 1500 2000 Light Stop Mass ( GeV ) β decay Chacko, DC, Verhaaren, 1512.XXXXX
Work in progress! Compare to Higgs Decays ˜ ˜ ˜ ˜ 〈 N 0 ++ 〉 DGLAP σ DY ( pp → t 1 ) ⨯ Br ( t 1 → g B g B )/( σ VBF ( pp → h ) ⨯ Br ( h → g B g B ) ⨯ϵ VBF ) θ t = π / 2 1 t 1 t Blue Shading m b 1 m 0 = 30 1 ≤ m t ∼ ∼ 1000 0.001 Even with this extremely Folded SUSY pessimistic signal yield 800 estimation, top partner direct t 1 = RH stop Stop Mass Splitting ( GeV ) 0.1 production can be the 600 t 2 = LH stop discovery channel! 0.3 400 1 10 10 10 200 # glueballs from stop pair production 10 > # glueballs from exotic Higgs decays 1 0.1 0.3 0 500 1000 1500 2000 Light Stop Mass ( GeV ) β decay Chacko, DC, Verhaaren, 1512.XXXXX
Probing Naturalness today: Experimental Upshot
Experimental Upshot Expand DV searches to include final states with just ONE displaced vertex Trigger/suppress background by requiring lepton or VBF jets Expand sensitivity to shorter lifetimes using tracker reconstruction. O(0.1 mm)? HXSWG report preview. PRELIMINARY!
Experimental Upshot signal toy model: H → XX → (bb’s and 𝜐𝜐 ’s) Cover these benchmark points and your searches will be sensitive to DV’s from Neutral Naturalness at the LHC HXSWG report preview. PRELIMINARY!
Experimental Upshot Simple Neutral Naturalness is the Show-Pony model for presenting results at each point in this (m 0 , m T ) plane, glueball lifetime is determined 10 hidden hadronization uncertainty: m T (top partner mass) don’t know this quantity, but should be few x 0.1 1 0.1 Show 𝞴 exclusions in (m 0 , m T ) space to assess improvement m 0 (0 ++ glueball mass) of searches and get rough idea of model exclusion HXSWG report preview. PRELIMINARY!
Summary Displaced signatures are a great LHC opportunity, and a “smoking gun” for most theories with EW top partners (e.g. FSUSY) and some singlet top partners (Fraternal Twin Higgs). DV’s can be produced in exotic Higgs decays or direct production of hidden sector states (top partners). LHC has TeV-scale reach for uncolored top partners if searches are slightly generalized! Many signatures still unexplored, e.g. Flavor, Indirect DM Detection…. Keep in mind: quasi-stable light hidden states are well motivated but not guaranteed in all theories of Neutral Naturalness. But we’ll still find these theories @ lepton collider/100TeV! DC, Saraswat 1509.04284 Thank you!
Backup Slides
Probing Naturalness exhaustively: A No-Lose Theorem for Generalized Top Partners.
Top Partners with SM Charge Start with TeV-scale top partners that carry SM charge. If QCD: produce plenty, discover at LHC or 100 TeV. If partners carry any EW charge, regardless of decay mode etc, will be detectable up to ~ 2+ TeV @ 100 TeV due to RG effects in DY spectrum measurements! Alves, Galloway, Rudermann, Walsh 1410.6810 TeV-scale SM-charged partners ARE DISCOVERABLE regardless of model details!
Neutral Top Partners We really only have one class of models for neutral top partners: Twin Higgs , which predicts Higgs coupling deviations ~ tuning at lepton colliders. Is this general? Would like to understand signatures of neutral top partners model-independently! Bottom-Up EFT/Simplified Model Approach! DC, Saraswat 1509.04284
Two distinct low-energy EFTs Fermion Partners Scalar Partners (Vector partners “same” as scalars)
Two distinct low-energy EFTs Fermion Partners Scalar Partners (Vector partners “same” as scalars) Only impose one condition on EFT: cancellation of quadratic divergence from top loop H t
Two distinct low-energy EFTs Fermion Partners Scalar Partners (Vector partners “same” as scalars) Relevant terms in the HEFT expansion: Condition to cancel one-loop quadratic divergence from top quark:
Two distinct low-energy EFTs Fermion Partners Scalar Partners (Vector partners “same” as scalars) Relevant terms in the HEFT expansion: Condition to cancel one-loop quadratic divergence from top quark: Non-renormalizable term limits what we can compute. Need partial UV completion for fermion partners!
Four possible Neutral Top Partner structures Fermion Partners Scalar Partners For fermion partners, have to distinguish how HHTT operator is generated. Strong Coupling Scalar Mediator Fermion Mediator
Four possible Neutral Top Partner structures Fermion Partners Scalar Partners For fermion partners, have to distinguish how HHTT operator is generated. Strong Coupling Scalar Mediator Fermion Mediator ? Twin Higgs Twin Higgs ? with composite/ with perturbative holographic UV UV completion completion
Four possible Neutral Top Partner structures Fermion Partners Scalar Partners For fermion partners, have to distinguish how HHTT operator is generated. Strong Coupling Scalar Mediator Fermion Mediator Much more general ? Twin Higgs Twin Higgs ? Twin Higgs! with composite/ with perturbative holographic UV UV completion completion than
Four possible Neutral Top Partner structures Fermion Partners Scalar Partners For fermion partners, have to distinguish how HHTT operator is generated. Strong Coupling Scalar Mediator Fermion Mediator For each scenario, analyze: Irreducible low-E signatures: - Zh cross section (lepton collider) - electroweak precision observables (lepton) - higgs cubic coupling (100 TeV) - top partner direct production (100 TeV)
Four possible Neutral Top Partner structures Fermion Partners Scalar Partners For fermion partners, have to distinguish how HHTT operator is generated. Strong Coupling Scalar Mediator Fermion Mediator For each scenario, analyze: Irreducible tunings { Δ i } of loop vs tree Irreducible low-E signatures: suffered by scenario ➾ Δ tot = f( Δ i ) - Zh cross section (lepton collider) These will relate to UV completion scale Λ UV . - electroweak precision observables (lepton) - higgs cubic coupling (100 TeV) Existing UV completions & symmetry arguments - top partner direct production (100 TeV) suggest SM-charged BSM states at this scale → Assume production at 100 TeV collider!
Strategy For each scenario: Find the LEAST TUNED probe with the theory can be while low-E experimentally escaping experimental inaccessible experimental Λ UV detection: probes parameter space: P min 10 TeV Δ tot = Max f( Δ i ) {P} or probe with 20 TeV direct production @ 100 TeV low-energy parameters m partner , X, Y,.... of the scenario This will allow us to determine how natural an “undiscoverable” theory could be....
Preview of Results
Preview of Results For each top partner structure…
Preview of Results For each top partner structure… .. we find the “tuning price” you have to pay to avoid any signatures @ 100 TeV or lepton colliders…
Preview of Results For each top partner structure… .. we find the “tuning price” you have to pay to avoid any signatures @ 100 TeV or lepton colliders… … as a function of the number of top partner dof…
Preview of Results … for different ways of For each top combining tunings and assumptions on UV reach. partner structure… .. we find the “tuning price” you have to pay to avoid any signatures ) n i m ( @ 100 TeV e v i t a v r e s n conventional (mult) o or lepton c colliders… … as a function of the number of top partner dof…
Preview of Results … for different ways of For each top combining tunings and assumptions on UV reach. partner structure… Very conservative: only top loop etc. Existing theories need UV completion at ~5 TeV .. we find the Even so…. “tuning price” you have to pay to avoid any signatures ) n i m ( @ 100 TeV e v i t a v r e s n conventional (mult) o or lepton c colliders… → need many partners to avoid … as a function of the discovery AND tuning! number of top partner dof…
How do we get there?
Neutral Naturalness Scenarios Fermion Partners Fermion Partners Fermion Partners Scalar Partners (strong coupling) (scalar mediator) (fermion mediator) Trickiest/most interesting case to analyze in complete generality...
Fermion Partner - Scalar Mediator ¯ T T This is the most complicated and important case. y ST T Contains Twin Higgs & Orbifold generalizations, S but is much more general. 1410.6808, 1411.7393 Craig, Knapen, Longhi µ HHS H † H Integrate out mediator(s) to match to natural IR theory: low-energy effective Lagrangian naturalness matching condition to cancel top loop
The Scalar Mediator Before we can proceed, we have to know: How heavy is the scalar mediator? Naive expectation: new scalars can’t be light, otherwise we have another hierarchy problem! ➾ m S should be significantly above weak scale! Naive counterargument: we know of many ways to solve the hierarchy problem! Dress up mediator sector with partners etc... Nope!
The Scalar Mediator Sacrificial Scalar Mechanism S unprotected H stabilized ¯ T T ¯ T ¯ t S H † H † S S H H ⇒ T t H unprotected S stabilized ¯ T T ¯ T t ¯ S S H † H † H † H H S S S S H ⇒ T t Consequences: 1. Mass of scalar is tied to UV completion scale! 2. m S >> m h makes it easy to compute experimental signals.
Higgs Mixing Take one scalar mediator S ¯ T T (generalizes simply) y ST T S µ HHS H † H
Higgs Mixing Take one scalar mediator S ¯ T T (generalizes simply) y ST T In the m S >> m h limit, mixing angle is simple: S µ HHS s θ ≈ − µ HHS H † H v m 2 X S
Computing Observables Take one scalar mediator S ¯ T T (generalizes simply) y ST T In the m S >> m h limit, mixing angle is simple: S µ HHS s θ ≈ − µ HHS H † H v m 2 S Naturalness condition: y 2 y 2 µ HHS y SST 3 s θ ≈ − 3 v t t = m 2 2 N f M T 2 N f y SST M T S Mediator mass drops out! Only depends on (M T , y SST )
Higgs Mixing in (m T , y STT ) Plane Lepton colliders have great sensitivity in much of parameter space.
Higgs Mixing in (m T , y STT ) Plane Lepton colliders have great sensitivity in much of parameter space. Twin Higgs models are subspaces (lines) in this more general parameter space.
Higgs Mixing in (m T , y STT ) Plane Lepton colliders have great sensitivity in much of parameter space. Twin Higgs models are But what if y STT is large?? subspaces (lines) in this more general parameter space.
Recall our main strategy: probe with low-E experimentally experimental inaccessible Λ UV probes parameter space: P 10 TeV or probe with 20 TeV direct production @ 100 TeV low-energy parameters m partner , X, Y,.... of the scenario
Recall our main strategy: We’ve determined the reach of low-energy observables (higgs mixing). probe with low-E experimentally experimental inaccessible Λ UV probes parameter space: P 10 TeV or probe with 20 TeV direct production @ 100 TeV low-energy parameters m partner , X, Y,.... of the scenario
Recall our main strategy: Now we exploit the 100 TeV collider’s ability to probe the UV scale. probe with low-E experimentally experimental inaccessible Λ UV probes parameter space: P 10 TeV or probe with 20 TeV direct production @ 100 TeV low-energy parameters m partner , X, Y,.... of the scenario
Recall our main strategy: Assuming 10 or 20 TeV can be probed, what unavoidable tuning are we stuck with? probe with low-E experimentally experimental inaccessible Λ UV probes parameter space: P 10 TeV or probe with 20 TeV direct production @ 100 TeV low-energy parameters m partner , X, Y,.... of the scenario
Tunings (1) Δ h(S) = log tuning of m h from mediator loops. (have to differentiate case where Higgs = PNGB from case without such symmetries....) Gets worse with large m S ! Can find conservative tuning estimate Δ S(T) = tuning from quadratic sensitivity of m S to T loops by maximizing (required by Sacrificial Scalar Mechanism!) over (unknown) mediator mass! Gets better with large m S ! ➾ Δ H,S = Max f( Δ h(S) , Δ S(T) ) m S
Tunings (1) Δ h(S) = log tuning of m h from mediator loops. (have to differentiate case where Higgs = PNGB from case without such symmetries....) Gets worse with large m S ! Can find conservative tuning estimate Δ S(T) = tuning from quadratic sensitivity of m S to T loops by maximizing (required by Sacrificial Scalar Mechanism!) over (unknown) mediator mass! Gets better with large m S ! ➾ Δ H,S = Max f( Δ h(S) , Δ S(T) ) m S Since we marginalize over m S , Δ H,S is uniquely defined in the (m T , y STT ) plane as the tuning from the mediator sector.
Tuning from Mediator in (m T , y STT ) Plane For Λ UV ≧ 20 TeV ( undetectable by 100 TeV ), high y STT is badly tuned!
Tunings (2) For Λ UV ≧ 20 TeV ( undetectable by 100 TeV ), top partners heavier than ~500 GeV give log-tuning to Higgs mass worse than 10% 0.20 Λ �� = �� ���� N f = 3 0.10 Δ h ( T ) N f = 24 Λ �� = �� ���� 0.05 N f = 3 N f = 24 0.02 200 500 1000 2000 m T ( GeV )
Log tuning from t vs T in (m T , y STT ) Plane For Λ UV ≧ 20 TeV ( undetectable by 100 TeV ), top partners heavier than ~500 GeV give log-tuning to Higgs mass worse than 10%
Log tuning from t vs T in (m T , y STT ) Plane For Λ UV ≧ 20 TeV ( undetectable by 100 TeV ), top partners heavier than ~500 GeV give log-tuning to Higgs mass worse than 10% No untuned parameter space left for N f ⨉ N S ~ O(SM)!
Fermion Partner - Scalar Mediator 0.500 0.100 Δ max 0.050 Λ �� = �� ��� �� ��� Δ � ˜ � Δ Fermion Partners 0.010 Scalar Mediator 0.005 1 5 10 50 100 500 1000 N f · N s A natural theory needs to have VERY MANY fermion partners/scalar mediators to possibly escape detection.
Need both colliders for full coverage! Large hidden sector coupling: Small hidden sector coupling: Higgs mixing is tiny, but need low Λ UV . theory can be healthy even for very large Λ UV , but Higgs mixing is large. No guaranteed signal at lepton collider, No guaranteed 100 TeV signals, but slam dunk at 100 TeV! but slam dunk at lepton colliders!
Need both colliders for full coverage! Large hidden sector coupling: Small hidden sector coupling: Higgs mixing is tiny, but need low Λ UV . theory can be healthy even for very large Λ UV , but Higgs mixing is large. No guaranteed signal at lepton collider, No guaranteed 100 TeV signals, but slam dunk at 100 TeV! but slam dunk at lepton colliders! Model building question: how to realize these non-Twin-Higgs possibilities?
… go through corresponding derivations for the other scenarios, with similar conclusions….
What’s the upshot?
1. Great discovery potential TODAY DC, Verhaaren 1506.06141 Chacko, DC, Verhaaren, 1512.XXXXX Long-lived hidden sector states (mirror glueballs, quarkonia) generate spectacular displaced signals that allow the LHC to probe TeV uncolored top partners 2. Implications for LHC searches Vertex searches with just one DV Displaced + VBF or lepton are required. Also, need sub-mm decay length reconstruction. HXSWG yellow report (soon!)
DC, Saraswat 1509.04284 3. No-Lose Theorem: Any theory of ~10% naturalness with O(SM) top partners will be discovered at a planned lepton collider and/or 100 TeV → Model-independent (bottom-up) and very conservative (only top loop etc) How to avoid this theorem? Could have top partner swarms, or neutral top partners without SM charges in UV completion. There might also be weird non-perturbative or stringy constructions that don’t need top partners?
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