Naturalizing SUSY with the relaxion and the inflaton

Transcription

1 Naturalizing SUSY with the relaxion and the inflaton Tony Gherghetta KEK Theory Meeting on Particle Physics Phenomenology, (KEK-PH 2018) KEK, Japan, February 15, 2018 [Jason Evans, TG, Natsumi Nagata, Zach Thomas, arxiv: ] [Jason Evans, TG, Natsumi Nagata, Marco Peloso, arxiv: ] 1 KEK-PH February 2018

2 LHC Run 2: SUSY remains elusive... [GeV] 1 χ 0 m ~ tt, ~ t t χ 0 pp Moriond 2017 CMS Preliminary miss SUS , 0-lep (H T ) SUS , 0-lep (M T2 ) SUS , 0-lep stop SUS , 1-lep stop SUS , 2-lep stop Comb. 0-, 1- and 2-lep stop fb (13 TeV) Expected Observed m t ~ = m t 0 χ 1 + m m~ t [GeV] m g & 1900 GeV m t & 1050 GeV 2 KEK-PH February 2018

3 [Giudice, Strumia ] SUSY breaking scale GeV 3 KEK-PH February 2018

4 Higgs mass in minimal SUSY [Pardo Vega, Villadoro ] Requires large stop masses or large A-terms Increases tuning in supersymmetric models 4 KEK-PH February 2018

5 Why is m t & TeV and not near electroweak scale? There is no low-energy supersymmetry SUSY top partners are uncolored e.g. Folded SUSY Neutral Naturalness Anthropic - we live in a multiverse YOU ARE HERE Is there an alternative possibility? Yes! 5 KEK-PH February 2018

6 Special point in parameter space: m 2 H =0 not related to symmetry e.g. supersymmetry m 2 H ' Instead, m 2 H ' 0 related to early-universe dynamics! e.g. self-organized criticality Dynamical evolution sets the SUSY scale! explains why m t v! This talk Hidden Naturalness 6 KEK-PH February 2018

7 Relaxion mechanism [Graham, Kaplan, Rajendran ] Introduce scalar field (relaxion): V (,h)=g 3 2 (1 V ( ) breaks shift symmetry:! + c g ) H 2 + h H cv cos f back reaction from strong dynamics Slope controls where relaxion stops! barrier 3 cv f g. 30 g 3 3 cv f 1000 TeV However: Relaxion = QCD axion large QCD! Alternatively, non-qcd dynamics requires new fermions near electroweak scale coincidence? 7 KEK-PH February 2018

8 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 ( new term g ) H 2 + h H 4 + A(,,H) cos f where A(,,H)= 4 + c g 3 c g H 2 new term -- cancels large potential barrier! [Assuming no H 2 coupling and 2 4 cos 2 terms] f 8 KEK-PH February 2018

9 Obtain: [Espinosa et al ] Cosmological Evolution Stages: I. trapped, rolls II. A = 0; both and, roll III. EWSB barrier appears IV. stops, continues to roll GeV for g =0.1g ' But M P, so still require a UV completion... Instead, apply to SUSY little hierarchy! 9 KEK-PH February 2018

10 Supersymmetric two-field relaxion mechanism [Evans, TG, Nagata, Thomas ] Embed, into chiral superfields S, T 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 10 KEK-PH February 2018

11 Break shift symmetry to generate potential for, Superpotential: W S,T = 1 2 m SS m T T 2 m S,m T = 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 11 KEK-PH February 2018

12 Scanning of soft mass parameters [Batell, Giudice, McCullough ] Assume large initial, field value and,f f,m T m S m m m S F S F T m S SUSY is broken by relaxion! Z Soft terms: 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! 12 KEK-PH February 2018

13 Electroweak symmetry breaking Obtain: [assuming m T m S (F T F S )] + 3 M L cos f assume subdominant. v 2 Order parameter: decreases until D( ) < 0 EWSB Critical value: D( )=0 occurs when µ 0 m S f m SUSY For: m S 10 7 GeV msusy f GeV 10 5 GeV 10 5 GeV µ m SUSY, m 2 H u m 2 H d Bµ m 2 SUSY Solves little hierarchy problem! 13 KEK-PH February 2018

14 The Inflaton-Relaxion model [Evans, TG, Nagata, Peloso ] Identify amplitudon as the inflaton! D-term inflation F-I where ± charged under U(1) } U(1) gauge coupling } term } Local minimum: ± =0 c = g apple p 2 generates periodic potential vacuum energy CMB epoch relaxion epoch 14 KEK-PH February 2018

15 Scalar potential Slow-roll parameters: i.e. 15 KEK-PH February 2018

16 Inflation check list Spectral tilt 39 n s 1 ' 2 = N CMB H I GeV Low-scale inflation! Density perturbations Cosmic strings U(1) broken during inflation via dynamical D-terms Reheating Energy stored in + requires cancellation of large h + i: 16 KEK-PH February 2018

17 Constraints Inflaton, relaxion slow roll m S H I Stability of relaxion minimum Classical rolling d dt H 1 I >H I Sufficient number of e-folds N e ' H I d dt & 2 H2 I m S 2 = HI 10 7 GeV GeV m S 2 Loop corrections to inflaton mass <m T 17 KEK-PH February 2018

18 [Evans, TG, Nagata, Peloso, ] Phenomenologically interesting region! = 10 8,r TS = KEK-PH February 2018

19 Mass [GeV] Generic particle spectrum: Âq, Â l, Ê H u,d, s Âg, Á W, Ê B } Split-SUSY like 10 0 t, h, Z, W relaxion Features: i) No SUSY flavor problem ii) Preserves gauge coupling unification iii) Relaxino/Gravitino dark matter iv) Collider signal long-lived NLSP decay v) Higgs-relaxion mixing,, Â 10 9 ÊG = Â relaxino/gravitino 19 KEK-PH February 2018

20 Long-lived Particles [in preparation] Higgs can mix with the relaxion-inflation sector Higgs-scalar: Higgsino-relaxino: relaxion waterfall field Direct axion-like coupling: Possible signal at MATHUSLA experiment! 20 KEK-PH February 2018

21 Summary Inflaton-relaxion dynamics can explain SUSY scale up to 10 9 GeV --- preserves QCD axion solution to strong CP problem --- naturalizes supersymmetry Predicts split-susy-like + invisible spectrum --- relaxino/gravitino = dark matter --- invisible spectrum = sign of dynamical relaxation! UV completion possible with multi-axion/ clockwork fields 21 KEK-PH February 2018

22 Questions/Future Work What fixes the scale of the explicit breaking? --- PeV scale: GeV. m S GeV Alternate ways to generate periodic potential? Other ways to incorporate inflation? e.g. F-term inflation Cosmological constant --- how to reconcile large number of vacua? --- requires non-anthropic solution? Ways to search for invisible sector --- beam dump experiments, superradiance, pulsar timing array, MATHUSLA. 22 KEK-PH February 2018

23 Extra slides 23 KEK-PH February 2018

24 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 (eliminates f G 0 µ G 0µ ) V period = A(,,H u H d ) 3 N cos f where g S,g T real m N = e ective mass 24 KEK-PH February 2018

25 } } } ' 0 } Supergravity effects For super-planckian field excursions m 2 T 2 m2 T 4 Requires no-scale SUSY breaking with field X M 2 P 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! 25 KEK-PH February 2018

26 UV completion [Based on Kaplan, Rattazzi: ] 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: relaxion 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! 26 KEK-PH February 2018