INDUCED EWSB GGI, Florence September 21, 2015 Jamison Galloway - PowerPoint PPT Presentation

INDUCED EWSB GGI, Florence September 21, 2015 Jamison Galloway Based on work with: A. Azatov, S. Chang, M. Luty, E. Salvioni, Y. Tsai, Y. Zhao

outline o Introduction/Motivation o Modeling, take one: realization with strong dynamics o Modeling, take two: realization with perturbative dynamics o Implications: phenomenology at the LHC o A conclusion or two

introduction h mass: Examples: o v / f in comp. H (MCHM4) h couplings: o ‘non-alignment’ in type-1 2HDM (tree-level) at large tan β o Higgs mixing with singlet *ref: M. Pieri @ LHCP 2015

introduction h mass: Examples: h couplings: δκ V . 0 . 08 o type-1 2HDM (tree-level) at variable tan β δκ F . 0 . 16 *ref: M. Pieri @ LHCP 2015

introduction h mass: Examples: h couplings: o light top partners δκ γ ,g . 0 . 14 (loop-level) o charged Higgses *ref: M. Pieri @ LHCP 2015

takeaway (and assumptions going forward) o h confirmed at 125 GeV o Tree-level couplings are already at ~SM ± 10% o Loop-level at ~SM ± 15%, consistent with… o …null results from partner searches up to ~600 GeV

takeaway (and assumptions going forward) o h confirmed at 125 GeV **~ SUSYish** o Tree-level couplings are already at ~SM ± 10% **composite H tuned at least at 10%** o Loop-level at ~SM ± 15%, consistent with… **~inconclusive** o …null results from partner searches up to ~600 GeV **still room for (somewhat) natural elementary H ** I’ll take this circumstantial evidence for an elementary Higgs seriously; assume SUSY stabilization and focus on the question of mass

SUSY Higgs and its mass λ ≤ 1 8( g 2 + g 0 2 ) m 2 h = 2 λ v 2 m h ≤ m Z SUS’ic relation for H quartic is too small by a factor of 2… ⇒ need an order one breaking! Can be done with spectrum, but not very naturally results from SUSY HD m SUSY (GeV) tan β 160 tan b = 50 tan b = 4 3 × 10 7 1 150 tan b = 2 tan b = 1 140 2 10 6 m h 130 4 35 × 10 3 m h = 125 GeV 120 50 10 4 M 1 = M 2 = M 3 = m = 1 TeV 110 4 6 8 10 12 14 16 18 problem: δ m 2 H ∝ m 2 log 10 m SUSY @ GeV D SUSY *ref: Vega, Villadoro (JHEP 2015) High SUSY scale (and thus pressure on naturalness) boils down to very special role of quartic (and very ‘special’ smallness of it) unavoidable consequence of V(H) with negative quadratic

induced EWSB: a strong model [ turn that frown upside down ] V ( H ) ∼ + (125) 2 | H | 2 + λ | H | 4 what if… o EW intact { o massless W, Z, fermions naively: o physical mass approximately independent of quartic o EW broken by QCD { less naively: o W, Z acquire mass ∼ gf π / 2 ∼ 50 MeV h ∼ 10 − 5 eV o electron mass m e ∼ y e y q × 4 π f 3 π /m 2 4 strong NO votes (consensus may well be misguided; ~1.5 yes votes cf. Trump leading GOP)

induced EWSB: a strong model Higgs ‘VEV’ in previous example fixed by QCD… …consider instead a TC-like sector } y u Λ 3 λ Λ 3 Λ TC = TeV QCD TC “ v ” ∼ → 16 π 2 m 2 16 π 2 m 2 “ v ” → λ × TeV h h H | H | 2 − ( λ H ψψ 0 + h . c . ); ψ = ( ⇤ , 2) 0 , ψ 0 = ( ⇤ , 1) � 1 / 2 ∆ V UV = m 2 ✓ λ Λ 3 ◆ *contrast H | H | 2 − c 1 ∆ V ( µ < TeV) = m 2 TC 16 π 2 H + h . c . e.g. SILH

induced EWSB: a strong model Higgs ‘VEV’ in previous example fixed by QCD… …consider instead a TC-like sector } y u Λ 3 λ Λ 3 Λ TC = TeV QCD TC “ v ” ∼ → 16 π 2 m 2 16 π 2 m 2 “ v ” → λ × TeV h h H | H | 2 − ( λ H ψψ 0 + h . c . ); ψ = ( ⇤ , 2) 0 , ψ 0 = ( ⇤ , 1) � 1 / 2 ∆ V UV = m 2 ✓ λ Λ 3 ◆ H | H | 2 − c 1 ∆ V ( µ < TeV) = m 2 TC 16 π 2 H + h . c . Upshot: o Confining dynamics induces . h H i 6 = 0 o Elementary Higgs VEV naturally right size. * o Elementary Higgs mass is independent of quartic. o New isotriplet (minimally) of scalars exists below ~TeV. * Corrections from quartic < 20%

induced EWSB: a strong model EFT coupling H to TeV scale strong sector (w/ nonlinear sigma field) *ref: Azatov, Galloway, Luty (PRL 2012) ∆ L = f 2 + 1 kinetic: ( D µ Σ ) † ( D µ Σ ) ( D µ H ) † ( D µ H ) TC ⇥ ⇤ ⇥ ⇤ tr 2 tr 4 W = g 2 ⇒ m 2 4 ( f 2 TC + v 2 h ) “bipartisan EWSB” Λ 4 − n interaction: X � n H † λ Σ � ∆ L = 16 π 2 tr c n n ≥ 1 ✏ ⌘ � v h controlled expansion parameter ⌧ 1 Λ ✏ . 0 . 1 with v h = 230 GeV , λ = 0 . 5 constraint from Higgs @ LHC: δ g V V H p . 0 . 08 (2 − δ ) δ ≈ 95 GeV f < v × ⇒ g (SM) V V H

induced EWSB: a strong model Recap: an ‘induced’ VEV for the elementary field Λ 2 λ × f v h ∼ m 2 4 π h [sensible for λ = O (1) , Λ ∼ TeV] …(recklessly) reimagine as a linear sigma model m 2 λ σ TC × f σ TC v h ∼ m 2 4 π h [ i.e. treat ] Λ ∼ 4 π f → m σ → v 2 m 2 ⇒ ✏ ≡ � v h h h f 2 m 2 Λ σ

induced EWSB: a strong model Recap: Λ 2 λ Criteria for generalized induced EWSB × f v h ∼ m 2 4 π h o H in isolation does NOT break EW [sensible for λ = O (1) , Λ ∼ TeV] o EW broken appreciably by heavy fields |{z} |{z} ( f ∼ v h ) ( m σ � m h ) …(recklessly) reimagine o i.e. EW nonlinearly realized at scales > 125 m 2 λ σ TC × f σ TC o coupling H to heavy EWSB source induces <H> v h ∼ m 2 4 π h o can be realized in 2HDM (with weaker couplings)… [ i.e. treat ] Λ ∼ 4 π f → m σ → v 2 m 2 ⇒ ✏ ≡ � v h h h f 2 m 2 Λ σ

induced EWSB: a perturbative model [ considering a single H doublet ] V = m 2 H | H | 2 − m 2 Σ | Σ | 2 − κ 2 ( H † Σ + h . c . ) + λ Σ | Σ | 4 ‘auxiliary Higgs’ λ Σ � λ H small mixing ) h Σ i = f / | m Σ | σ / λ Σ f 2 � m 2 , m 2 p λ Σ h H h 2 − κ 2 fh + O ( κ 4 ) ⇒ v h ∝ κ 2 f V e ff ( h ) = 1 2 m 2 → , m 2 H *ref: Galloway, Luty, Tsai, Zhao (PRD 2014); Alves, Fox, Weiner (PRD 2015) TREE - LEVEL TUNING H Simplified Model L 3.0 Higgs mass corrected Contours : FT - 1 via coupling to Σ : 2.5 H see text L decoupling 10 % 30 % 50 % 65 % 2.0 λ l S ⇒ δ m 2 16 π 2 m 2 σ ( × mixing angles) 1.5 h ∝ 1.0 LIGHT HIGGS VACUUM COUPLINGS (reminiscent of corrections from stops STABILITY H 95 % CL L 0.5 with important distinction that σ needn’t m h < 125 GeV m S ` m h 120 140 160 180 200 220 240 be pushed to >>TeV scales) f @ GeV D

phenomenology: TC-like model ( H u , H d , Σ ) ⇒ 8 physical scalars: } π (1 , 2 , 3) H ±   2 , A 0 TC 2 1 , H ± H 0 1 , A 0 {   1 MSSM    h    G ± , G 0 ∆ L ⊃ � ( v h + H ) 0 ⇒ m 2 π ∼ ( � u v u + � d v d ) × Λ ≡ ( ✏ u + ✏ d ) × Λ 2 ≈ (500 GeV) 2 Heavy Higgses (pions) produced by, decay to, SM via mixing or through auxiliary fields’ SU(2) couplings UNIQUE signals: compare with MSSM ( H couples to f ), NMSSM (“ S ” inherits *all* quantum numbers from mixing),

phenomenology: TC-like model [ examples, exclusions ] o Decouple second H (to simplify) o sub-TeV pseudoscalar remains from TC sector o couples to fermions only through mixing: Zh persists even at m>350 o A > Zh to cover most space @ LHC o powerful exclusion for strong model due to small ff couplings *ref: Chang, Galloway, Luty, Salvioni, Tsai (JHEP 2015)

phenomenology: 2HDM-like model [ illustrating possibility of reduced trilinear ] o direct searches exclude up to m ~ 400 o 50% reduction in H trilinear remains possible (!) o even at large tan β significant reduction persists (~30%) for large ‘auxiliary’ self-interactions

conclusions o h @ LHC still allows ~1/3 of W mass to be generated elsewhere o If excitations of this other EWSB source are heavy and couple to H , the Higgs EFT contains a tadpole o non-zero Higgs VEV may not require negative quadratic; H may not break EW at all *in isolation* o Higgs quartic is consequently untethered from mass > may provide breathing room in SUSY theories especially > can generate large deviations in Higgs self-couplings o appearance of light stops will require explanation of Higgs mass; physical mass is essentially free parameter in induced EWSB o rich spectrum contains sub-TeV scalars with unique (i.e. non-MSSM) footprints o Nonstandard Higgs and add’l scalars still in play… …any surprise is welcome; many nicely motivated, *and* still viable!

BACKUP

coincidence issue The active participants: plus two sterile flavors: SU (2) TC SU (2) L SU (2) R b = N ψ ⇤ ⇤ 1 IR fixed point ⇒ = ψ 0 ⇤ 1 ⇤ o Strongly coupled o Self-dual 1 ⇤ ⇤ H with potential ∆ W = λ H ψψ 0 o Phase transition induced by g TC SUSY breaking o STRONG fixed point above (RG induced by soft masses) sets without Λ TC ∼ m h m 0 conspiracy g ∗ b ≥ 5 o As in the QCD toy case: 3 N b = N is *free*, independent of m h µ quartic at leading order m ( ψ ) ∼ TeV 0

EWPT and strong model S Parameter: ✓ Λ 2 ✓ Λ 2 ◆ ◆ 1 1 ∆ S (IR) ∆ S (IR) vs. 12 π log 12 π log TC ' Ind . ' m 2 m 2 h π | {z } | {z } ∼ 4 π ∼ 16 π 2 T Parameter: λ u v u = λ d v d ⇒ custodial limit → T corresponds to a variable parameter of the theory , 0.4 120 m ref = 120 GeV 0.3 350 ↵ T = ( ✏ u − ✏ d ) 2 H’less 0.2 0.1 T [ Notice that increasing T tends 0 to decrease S above] - 0.1 - 0.2 - 0.3 - 0.3 - 0.2 - 0.1 0.0 0.1 0.2 0.3 0.4 S