Naturalizing Supersymmetry with the Relaxion

Transcription

1 Naturalizing Supersymmetry with the Relaxion Tony Gherghetta University of Minnesota Beyond the Standard Model OIST Workshop, Okinawa, Japan, March 4, 2016 Jason Evans, TG, Natsumi Nagata, Zach Thomas [ ] 1

2 SUPERSYMMETRY is a theoretically appealing framework for Beyond the Standard Model Stabilizes Planck/weak scale hierarchy Dark matter Gauge coupling unification Low-energy limit of string theory BUT where are the superpartners?!? [notwithstanding the 750 GeV resonance...] 2

3 LHC Limits: The Missing Superpartners Problem m g & 1700 GeV m t & 750 GeV 3

4 Higgs mass in MSSM [Pardo Vega, Villadoro ] Requires large stop masses or large A-terms 4

5 EWSB V (h) = µ 2 h H 2 + h H 4 (m A m Z, tan 1) µ 2 h ' µ 2 3y 2 t 4 2 m2 t log mess m t (tan 1) Increases tuning in supersymmetric models BUT why is m t ~10 TeV and not near electroweak scale? There is no low-energy supersymmetry Anthropic - we live in a multiverse YOU ARE HERE Dynamical relaxation sets the SUSY scale! This talk 5

6 Relaxion mechanism Relaxion field V (,h)=g 3 2 (1 V ( ) shift symmetrybreaking parameter [Graham, Kaplan, Rajendran ] scans Higgs-mass squared parameter: g ) H 2 + h H cv cos f back reaction from strong dynamics Slope controls where relaxion stops! g 3 3 cv f barrier 3 cv f TeV However: Relaxion = QCD axion large QCD! Alternatively, non-qcd dynamics requires new fermions near electroweak scale coincidence? 6

7 In general: V (,h)=g (1 g ) H 2 + h H c n v n cos f n =1 Requires new source of EWSB e.g. QCD n =2 2 c H 2 cos f Gauge invariant - new source not required! However, quantum corrections generate: 4 c cos f, 3 cg cos f Large potential barriers! Introduce second field, [Espinosa et al ] V (,,h)=g 3 + g ( g ) H 2 + [see C. Grojean talk] h H 4 + A(,,H) cos f where A(,,H)= 4 + c g 3 c g H 2 cancels large potential barrier! 7

8 Obtain: [Espinosa et al ] GeV for g =0.1g ' Assumes no But M P H 2 coupling and 2 4 cos 2 terms f apply to little hierarchy, instead! 8

9 Supersymmetric two-field relaxion mechanism Embed, into chiral superfields S,T [Evans, TG, Nagata, Thomas ] relaxion amplitudon Shift symmetries: = NG boson = NG boson where Q i = MSSM matter superfields, f,f = decay constants H u,h d = MSSM Higgs superfields 9

10 Break shift symmetry to generate potential for, Superpotential: W S,T = 1 2 m SS m T T 2 where m S,m T are mass parameters V (, )= 1 2 m S m T 2 2 Kahler potential: K = K(S + S,T + T ) shift invariant no renormalisable coupling of to H u,h d! But can couple to MSSM Higgs fields via U(S + S,T + T )e q H S f H u H d mu-term: W µ = µ 0 e q H S f H u H d 10

11 Scanning of soft mass parameters Assume large initial, field value V = F ~ K 1 F ~ and,f f,m T m S [Batell, Giudice, McCullough ] m m m S F S F T m S Soft terms: SUSY is broken by relaxion! Z d 4 1 M 2 [(S + S ) 2 +(T + T ) 2 ] m B A ijk m S M Z d 2 c as 16 2 f TrW aw a only S shift symmetry induces chiral anomaly f M M a a 4 m S M varies as relaxion evolves! 11

12 Electroweak symmetry breaking Assume m T m S [avoids SUSY-breaking coupling to Higgs] Order parameter decreases until D( ) < 0 EWSB Critical value: D( )=0 occurs when µ 0 m S f m SUSY µ m SUSY, m 2 H u m 2 H d Bµ m 2 SUSY Solves little hierarchy problem! Field value: may be super- Planckian! 12

13 Generation of periodic potential Assume SU(N) gauge theory with singlet superfields N, N Fermion condensate: h N N i' 3 N N = confinement scale N N! e i f N N V period = A(,,H u H d ) 3 N cos f where g S,g T real m N = e ective mass 13

14 Cosmological Evolution, evolution determined by where A(,,H u H d )= m N g S p 2 + g T p 2 + ML H u H d ( m N,g S > 0,g T < 0) Initially:, f } H u = H d =0 fixed, free to roll When A =0, decreases, tracking evolution ( m T < m S ) Finally: m S 2. 3 N f A(,, v2 ( ) 4 sin 2 ) 0 H u = v u,h d = v d EW symmetry broken! 14

15 Constraints Assume de-sitter phase with Hubble parameter H I Inflaton dominates vacuum energy, slow roll m S H I Classical rolling Sufficient number of e-folds N e & H2 I m S 2 = 1012 HI 100 GeV GeV m S 2 Inflaton SUSY-breaking subdominant Can be ameliorated with D-term inflation [in preparation] 15

16 [Evans, TG, Nagata, Thomas ] Phenomenologically interesting region! = 10 2,r TS =0.1,r =0.1,r SUSY =

17 } } } ' 0 } Supergravity effects For super-planckian field excursions m 2 T 2 m2 T 4 M 2 P Requires no-scale SUSY breaking with field X W X ' 0 Gravitino sub-planckian super-planckian F = F S F>F S relaxino eaten by gravitino relaxino, no longer Goldstino, remains light } Can be dark matter! 17

18 TeV 100 m, h 10 s, 1 M a gauginos Generic particle spectrum: sfermions, Higgsinos relaxion [due to large amplitude of periodic potential] } Split-SUSY like 0.1 h 10 6 m 3/2, Higgs relaxino/gravitino Features: i) Relaxino/Gravitino dark matter ii) No SUSY flavor problem iii) Preserves gauge coupling unification iv) Collider signal long-lived NLSP decay 18

19 UV completion [Based on Rattazzi, Kaplan: ] Consider set of chiral superfields i, i,s i (i =0,...N) } spontaneous breaking } explicitly breaks U(1) N+1 to U(1) Massless mode: Identify remnant U(1) as shift symmetry S S y coupling f f 0 V V 0 / cos f y 0 N N N coupling Similarly: V N / 4 N cos 2 N f ' 4 N 1 4 N N f = m S 2! = g S! 19

20 Conclusion Dynamical relaxation with two fields can explain heavy superpartner scale up to 10 9 GeV --- preserves QCD axion solution to strong CP problem --- naturalizes supersymmetry Sparticle spectrum is split-susy like Relaxino/gravitino = dark matter UV completion possible with multi-axion like fields 20