beyond the standard model @ the tev scale nathaniel craig uc santa barbara 2017 ICTP Summer School on Particle Physics
The Hierarchy Problem Quantum gravity cutoff Higgs sector cutoff Uninteresting flow to IR, possibly w/ new mass thresholds Standard Model (~unique vacuum) ⇒ hierarchy problem energy m H is not technically natural
Adding a symmetry …and breaking it softly we assumed the symmetry protecting the weak scale was continuous. are their other options? ⇒ “neutral naturalness”
̃ Discrete symmetries Discrete Symmetry-based approaches to symmetry hierarchy problem employ continuous symmetries. Leads to partner states w/ SM quantum numbers. Discrete symmetry Neutral partners m Discrete symmetries can also serve to protect the Higgs. } ≲ 4 π /G Leads to partner states w/ non- SM quantum numbers. “Neutral naturalness” Higgs m h
[Chacko, Goh, Harnik ’05] The Twin Higgs Consider a scalar H transforming as a fundamental under a global SU(4) symmetry: V ( H ) = − m 2 | H | 2 + λ | H | 4 Potential leads to spontaneous symmetry breaking, | ⇥ H ⇤ | 2 = m 2 2 λ � f 2 SU (4) → SU (3) yields seven goldstone bosons. 5
The Twin Higgs ✓ H A ◆ Now gauge SU(2) A x SU(2) B ⊂ SU(4), w/ H = H B Us Twins Then 6 goldstones are eaten, leaving one behind. Explicitly breaks the SU(4); expect radiative corrections. 9 9 A Λ 2 | H A | 2 + g 2 | H A | 2 + | H B | 2 � 64 π 2 g 2 Λ 2 � g 2 B Λ 2 | H B | 2 � � V ( H ) ⊃ V ( H ) ⊃ 64 π 2 But these become SU(4) symmetric if g A =g B from a Z 2 Quadratic potential has accidental SU(4) symmetry . 6
The Twin Higgs Full theory: extend Z 2 to all SM matter and couplings. SM A x SM B x Z 2 ?? Λ 2 ✓ ◆ � t + 9 4 g 2 + . . . | H A | 2 + | H B | 2 � − 6 y 2 V ( H ) ⊃ 16 π 2 | h H A i | 2 + | h H B i | 2 = f 2 SM B ~f (h B ,t B ,W B ,Z B …) Breaks “quadratic” SU(4), higgses EWK A & EWK B Gives a radial mode, a goldstone mode, and eaten goldstones. SM A ~v v ≪ f for SM-like Higgs to be the goldstone (h A ,t A ,W A ,Z A …) Primary coupling between SM A and SM B is via Higgs portal
twin higgs & the hierarchy problem Q A 3 The top partner acts as expected − 6 y 2 from global symmetry protection, but 16 π 2 Λ 2 t is not charged under QCD. t A L ⊃ − y t t A † 3 − y t t B † R ˜ H A Q A R ˜ H B Q B R 3 m T f − h 2 x 2 f + . . . h + . . . + 6 y 2 t B Q B 16 π 2 Λ 2 t R 3 No direct limit on top partner. 8
“Neutral” naturalness Simplest theory: exact mirror copy of SM 5 TeV [Chacko, Goh, Harnik ’05] But this is more than you need, and mirror 1st, 2nd gens lead to cosmological problems t’ L t’ R b’ L Many more options where symmetry is approximate, e.g. a w’,z’ good symmetry for heaviest SM particles. h [NC, Knapen, Longhi ’14; Geller, Telem ’14; NC, Katz, Strassler, Sundrum ’15; Barbieri, Greco, g’ Rattazzi, Wulzer ’15; Low, Tesi, Wang ’15, NC, Knapen, Longhi, Strassler ‘16] 9
Finding a mirror h Higgs still a PNGB, tuning as in Limit v 2 /f 2 < 0.1 other global symmetries → Δ ~10 (10% tuning) Unlikely to improve much in Run 2 Partner states are SM neutral, couple only • 95% Exclusion to the Higgs. Lighter than m h /2: modest VBF invisible Higgs decays. 4 ggH 3 t ¯ tH | c φ | Heavier than m h /2: • 2 produce through an off-shell Higgs. 1 √ s = 14 TeV 100 150 200 250 300 350 400 450 Hard but very interesting; directly m φ ( GeV ) probe naturalness [NC, Lou, McCullough, Thalapillil ‘14] 10
[NC, Katz, Strassler, Sundrum ’15; Curtin, Verhaaren ’15; Chacko, Curtin, Verhaaren ‘16 ] Exotic Higgs Decays SM • Twin sector must have twin QCD, confines around QCD h* scale 0 ++ • Higgs boson couples to h bound states of twin QCD 0 ++ h* • Various possibilities. Glueballs most interesting; have same quantum # as Higgs SM c t H 0 ++ L@ log 10 H m LD L ⊃ − α 0 v h 0 a 0 µ ν 3 - 6 f G µ ν G - 3 a f 6 π 1400 6 Produce in rare Higgs decays (BR~10 -3 -10 -4 ) 0 1200 gg → h → 0 ++ + 0 ++ + . . . f @ GeV D Decay back to SM via Higgs 1000 0 ++ → h ∗ → f ¯ f 800 3 Long-lived, decay length is macroscopic; length scale ~ LHC detectors 0 20 40 60 80 100 11 m 0 @ GeV D
Searching for mirrors Signal: displaced decays of SM Higgs • with BR >10 -3 ( σ .Br~20fb @ Run 1). ATLAS: HCAL/ECAL & muon chamber • [Csaki, Kuflik, Lombardo, Slone ’15] searches powerful, sensitive to �� % �� ����� ����� �� σ⨯ �� / σ �� displaced Higgs decay . � CMS s = 8 TeV ( recast ) CMS: use inner tracker, see vertex • on short decay lengths. trigger �� - � thresholds too high. 40 GeV 10 GeV 50 GeV 25 GeV more room for innovation in the • �� - � ATLAS 60 GeV 40 GeV s = 8 TeV displaced decay search program… � �� � �� � �� � �� � �� � 12 π ν ������ �������� ( � τ ) [ �� ]
Selecting a vacuum we assumed that we ended up in the vacuum with the observed weak scale due to some anthropic pressure. can we instead do so dynamically? ⇒ “relaxion”
Dynamical selection What if the weak scale is selected by dynamics, not symmetries? Old idea: couple Higgs to field whose minimum sets m H =0 Old problem: How to make m H =0 a special point of potential? New solution: what turns on when m H2 goes negative? V ( φ ) Vev gives quark masses which give axion potential! You are here. “Relaxion” [Graham, Kaplan, Rajendran ‘15] φ But: immense energy stored in evolving field, need dissipation.
[Graham, Kaplan, Rajendran ‘15] Ex.1: QCD/QCD’ relaxion First thought: use an axion coupled to QCD. V ( φ ) 1 φ ( − M 2 + g φ ) | H | 2 + V ( g φ ) + ˜ G µ ν G µ ν 32 π 2 You are here. f ( − M 2 + g φ ) | H | 2 + V ( g φ ) + Λ 4 cos( φ /f ) ⇒ φ φ + 3 H ˙ ¨ dissipation: inflation! φ + V 0 ( φ ) = 0 requirements: (1) φ scan over entirety of its range ∆ φ = ( gM 2 /H 2 i ) N & M 2 /g ⇒ N & H 2 i /g 2 (2) vacuum energy (3) barriers form during inflation H i > M 2 that are H i < Λ QCD exceeds change in sufficient to M P l vacuum energy stop scanning due to scanning
QCD relaxion (4) classical rolling beats quantum fluctuations i → H i < ( gM 2 ) 1 / 3 φ /H 2 H i < V 0 Additional substantial concerns: • non-compact shift symmetry? • cosmological constant? Just need Higgs + non-compact axion + inflation w/ • Very low Hubble scale ( ≪ Λ QCD ) • 10 Giga-years of inflation Care required to avoid transferring fine-tuning to inflationary sector. In vacuum, φ is the axion, stops well away from θ = 0 → gives O(1) contribution to θ QCD
[Graham, Kaplan, Rajendran ‘15] QCD’ Relaxion Fix: make it someone else’s QCD + axion Field SU (3) N SU (3) C SU (2) L U (1) Y I.e. axion of a L − 1 / 2 ⇤ ⇤ different SU(3); − L c +1 / 2 ⇤ ⇤ need to tie in − N 0 ⇤ Higgs vev − − N c 0 ⇤ − − 1. New quarks must get most of mass from Higgs: L ⊃ m L LL c + m N NN c + yHLN c + y 0 H † L c N 2. Must confine, but with light flavor Λ 4 ' 4 π f 3 π 0 m N Decouple from tev scale? 17
QCD’ Relaxion (smallest see-saw mass from m N ≥ yy 0 v 2 /m L Now EWSB if L heavy) yy 0 m N ≥ 16 π 2 m L log( M/m L ) (Radiative Dirac mass) { But also (Higgs wiggles biggest) m N ≥ yy 0 f 2 π 0 /m L 4 π v f π 0 < v and m L < These bounds imply p log( M/m L ) New confining physics near weak scale! Couples to Higgs, electroweak bosons; hidden valley signatures. Various possibilities (N f =1, pions not light) To my knowledge, no systematic study to date. 18
[Hook, Marques-Tavares ‘16] Ex. 2: Interactive relaxion Alternative possibility: keep bumps across entire potential, turn on dissipation at a special point of potential. another source of dissipation: particle production L ⊃ − φ consider axion-like couplings 4 f F ˜ F to massive gauge field: ! A ± k ˙ φ e.0.m. for transverse k 2 + m 2 ¨ A ± + A ± = 0 polarizations: f A ± k ˙ φ ± = k 2 + m 2 ˙ A ± ( k ) ∝ e i ω ± t for ω 2 φ ≈ constant f ± < 0 ⇒ | ˙ ω 2 φ | & 2 fm A exponentially growing solution for ̇ growing mode drains energy from φ
⇒ Ex. 2: Interactive relaxion apply to relaxion: use electroweak gauge fields Instead of Use coupling to EWK gauge bosons: φ B ) + Λ 4 cos φ φ f ( g 2 W ˜ W − g 0 2 B ˜ f G ˜ G f 0 Exponential production of EWK gauge bosons + inflation around h~v slows evolution Important subtlety: can’t couple to pairs of photons! For dissipation to become efficient at h~v , can only couple to bosons acquiring mass from EWSB. L ⊃ − 1 1 R + φ (Not a tuning, can be made natural f ( W L ˜ W L − W R ˜ W 2 W 2 W R ) L − with symmetries, e.g., SU(2) L x SU(2) R ) 4 g 2 4 g 2 L R ⇒ L ∝ ( θ L + θ R ) F ˜ F φ → φ + α θ L → θ L − α θ R → θ R + α
Lowering the cutoff …in diverse dimensions usually assume low cutoff is due to e.g. geometry of an extra dimension, giving uniform prediction for new resonances & strong limits. can we do the same thing with order instead of disorder? ⇒ “gravitational anderson localization”
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