Perturbative Unitarity Constraints on a SUSY Higgs portal Sonia El Hedri with Kassahun Betre, Devin Walker ERC Workshop, Schloss Waldthausen November 12, 2014 arXiv:1407.0395 arXiv:1410.1534 1 / 40
Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Unitarity and Perturbativity Unitarity and the NMSSM parameters Relic density constraints Parameter scan and results 2 / 40
Finding New Energy Scales Application to the NMSSM Parameter scan and results 3 / 40
GeV 10 21 GeV GeV 10 18 GeV 10 Planck scale 10 15 GeV 10 GeV 10 12 GeV New scales? GeV 10 9 GeV 10 GeV 10 6 GeV 10 EW GeV 10 3 GeV 10 ? } EW scale H W H W , Z J Heavy pions 0 1 GeV 10 QCD 4 / 40
Finding new energy scales How to look for the next energy scale? I Break down of the theory? ∆ SM perturbative up to the GUT scale ∆ Electroweak vacuum metastable Degrassi, Di Vita, Elias-Miró, Espinosa, Giudice, Isidori, Strumia, [arXiv:1205.6497] I New observations ∆ Evidence for Dark Matter, neutrino masses, . . . ∆ Unknown/too high energy scale I Naturalness arguments ∆ Upper bounds depend on the fine-tuning I Other possibilities?? 5 / 40
Finding new energy scales How to look for the next energy scale? I Break down of the theory? ∆ SM perturbative up to the GUT scale ∆ Electroweak vacuum metastable Degrassi, Di Vita, Elias-Miró, Espinosa, Giudice, Isidori, Strumia, [arXiv:1205.6497] I Look for new phenomena ∆ Evidence for Dark Matter, neutrino masses, . . . ∆ Unknown/too high energy scales I Naturalness arguments ∆ Avoid fine-tuning of the Higgs mass ∆ Upper bounds depend on the tolerated fine-tuning I Perturbative Unitarity 6 / 40
Unitarity in the Standard Model I Breaking of perturbative unitarity is a sign for new physics I Light pion e ff ective theory : unitarity violated around 1 . 2 GeV ∆ Axial and vector resonances at 800 MeV I Fermi theory : Unitarity violated around 350 GeV ∆ W boson at 80 GeV I Electroweak theory : unitarity violated around 1 TeV ∆ Higgs boson at 125 GeV 7 / 40
E ff ects of unitarity on couplings ReT ii < 1 2 Dimensionless Unitarity Dimensionful Unitarity A κ φ 1 1 φ 2 2 A 2 A 2 123 A λ ∝ g A ~ λ 2 2 φ 3 s − m φ 2 3 1 φ 2 A κ φ 1 2 A 2 Bounds on quartic couplings Bounds on mass ratios Lee, Quigg, Thacker [Phys. Rev. D 16, Schuessler, Zeppenfeld [arXiv:0710.5175] 1519 (1977)] 8 / 40
Anchoring the spectrum: Low Energy Observables I Unitarity constrains BSM theories ∆ Upper bounds on dimensionless couplings ∆ Upper bounds on ratios of scales I Does not prevent decoupling What if new phenomena are observed? I Couple unitarity to low energy observables 9 / 40
Unitarity and Dark Matter I Dark Matter is one of the only evidences of new physics beyond the SM I Unknown mass, known relic density I Only gravitational couplings observed Thermal Dark Matter I Dark Matter relic density is obtained through annihilation to lighter particles I Dark Matter cannot decouple from the light sector I Relic Density known as a function of DM couplings 10 / 40
Thermal Dark Matter Heavy dark matter requires large couplings ∆ Unitarity violation at large mass g 2 ˜ χ 0 SM 123 φ 1 . λ 2 ∝ g χ 0 SM g 2 ˜ 123 φ 1 s − m ∝ g SM 2 GeV Ge 3 I Existing Unitarity Bound : 120 TeV for λ = 4 π Griest and Kamionkowski, 1990 I Much tighter bounds for specific theories! 11 / 40
A recipe for constraining new models I Applies to I Models predicting a Dark Matter candidate I Known production and annihilation mechanisms I Dimensionful unitarity : upper bounds on the mass ratios I Contracted spectrum I Dimensionless unitarity : upper bounds on dimensionless couplings I Tension with Relic Abundance constraints for heavy Dark Matter Unitarity and Relic Abundance set an upper bound on the masses of the new particles! I Unitarity constraints on the Higgs portal ∆ 10 TeV bounds Walker [arXiv:1310.1083] 12 / 40
Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results 13 / 40
Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results 14 / 40
The NMSSM Higgs sector I Focus on NMSSM Higgs Sector H d + 1 W NMSSM = ≠ λ ˆ S ˆ H u . ˆ 3 κ ˆ S 3 H d H † V soft = m 2 d H d + m 2 H u H † u H u + m 2 S S † S λ A λ SH u H d ≠ 1 3 4 3 κ A κ S 3 + h . c . ≠ I Winos, Binos and Sfermions decoupled I Six parameters after EWSB λ , κ , tan β , µ, A λ , A κ 15 / 40
NMSSM spectrum: Decoupling limit I One light Higgs, m h = 125 GeV I Heavy Higgs masses depending on µ 2 , A λ µ and A κ µ I Higgsino/Singlino Dark Matter m DM ≥ µ I DM annihilation governed by λ and/or κ 16 / 40
Upper Bounds on the NMSSM I Tree-level study Z cos 2 2 β + λ v 2 sin 2 2 β Ø ( 125 GeV ) 2 m 2 λ Ø 0 . 7 I Using unitarity + Relic abundance measurements I We want to obtain ∆ Upper bounds on λ , κ ∆ Upper bounds on A λ , κ /µ ∆ Upper bound on µ 17 / 40
Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Unitarity and Perturbativity Unitarity and the NMSSM parameters Relic density constraints Parameter scan and results 18 / 40
NMSSM and Unitarity S S S S µ + κ 2 A 2 λ κ 2 S κ µ + ∝ g s − m 2 S S S S S I Lee-Quigg-Thacker type bounds on λ and κ If s ≥ 5 m 2 S A κ 2 A κ B A Ã κ 2 + O µ I All heavy particle masses are of order µ or less 19 / 40
Perturbative Unitarity Constrains a given scattering matrix S = 1 + iT Optical theorem S † S = I ∆ 1 2 ( T ≠ T † ) = | T 2 ii | Use Partial Wave Decomposition ⁄ 1 ij = λ 1 / 4 λ 1 / 4 ˜ T J i f T ij P J ( cos θ ) d cos θ 32 π s − 1 We find T ii | < 1 T ii | 2 ∆ | Re ˜ Im ˜ T ii = | ˜ 2 20 / 40
Perturbative Unitarity: a Geometric view d y =Im ˜ T J ii Argand diagram Exact Matrix Element 1 / 2 ( cle (called A r x =Re ˜ T J SM 1 SM 1 ii - or the Born ap 2 2 Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)] 21 / 40
Perturbative Unitarity: a Geometric view d y =Im ˜ T J ii Argand diagram nth-loop 1 / 2 ( cle (called A r x =Re ˜ T J Tree Level ii or the Born ap Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)] 22 / 40
Perturbativity breakdown d y =Im ˜ T J 2 | | ii − Argand diagram TL a � = d min | x TL | | − EW 1 / 2 ( d min ? } cle (called A r x =Re ˜ T J min x TL ii or the Born ap Schuessler and Zeppenfeld [arXiv:07105175, Schuessler’s thesis (2005)] 23 / 40
Perturbativity breakdown I Conservative estimate of loop corrections 0.5 41% 0.4 0.3 a' 1/2 0.2 0.1 0.0 0.0 0.2 0.4 0.6 0.8 Tree T ii Schuessler and Zeppenfeld [arXiv:07105175, Schuessler thesis (2005)] 24 / 40
Large s study: Quartic Couplings Constraints on dimensionless couplings 3.0 For large s , only quartic 2.5 couplings remain 2.0 1.5 T ii | < 1 Κ lim s →∞ | Re ˜ 2 1.0 0.5 λ , κ . 3 0.0 0 1 2 3 4 Λ 25 / 40
Unitarity and SUSY breaking scales �� I m H , m A , m χ depend on A λ , , µ, A λ , A κ A κ , µ I Trilinear couplings ∆ vanish at high energy I Energy-dependent scattering amplitudes electroweak ∆ Scan over s scale 26 / 40
General Optimal s 2.5 � b � 2.0 � Max Eigenvalue � 1.5 1.0 0.5 0.0 0 20 40 60 80 100 120 s � TeV � 5 m h 27 / 40
Unitarity: Summary I Upper bounds on λ and κ λ , κ . 3 I Optimal bounds for s ≥ 5 m 2 H I Upper bounds on ratios of scales A λ µ and A κ µ ≥ O ( 1 ) I µ is the only scale left unconstrained ∆ Need to constrain the DM mass! 28 / 40
Finding New Energy Scales Application to the NMSSM Overview Unitarity bounds Relic density constraints Parameter scan and results 29 / 40
Relic density Relic density anchors the heavy spectrum h , H , A , SM ˜ χ ∝ λ , κ h , H 12 , A 12 ˜ χ h , H , A , SM I λ and κ increase with the DM mass I Maximal mass when λ or κ hits the unitarity bound 30 / 40
Loopholes in Fine-Tuned Regions I Higgs funnels: s-channel resonances when | 2 m χ ≠ m H i | R = min i . 0 . 1 m H i I t-channel resonances: not in our model but can exist if m χ 0 ≥ m W + m χ ± I Sommerfeld enhanced regions: for low Higgsino-Chargino splitting H 0 ˜ H ± ˜ − − S S . . . . . . W ± W ± H 0 H 0 H 0 ˜ H ± ˜ 31 / 40
Finding New Energy Scales Application to the NMSSM Parameter scan and results 32 / 40
Finding upper bounds: procedure I Uniform scan over 6 parameters with the 125 GeV Higgs mass constraint λ , | κ | < 4, | A i | , | µ | < 40 TeV I Apply vacuum constraints Kanehata, Kobayashi, Konishi, Seto, Shimomura [arXiv:1103.5109] I Unitarity: allow for at most 40% loop corrections to tree-level amplitudes | Re T ij | Æ 1 2 I Compute relic density using MicrOmegas and NMSSMTools Ω h 2 < 0 . 1199 + 0 . 0081 (Planck measurement) 33 / 40
Results: Dark Matter | 2 m DM ≠ m H i | I Fine Tuning Factor R = min i m H i 34 / 40
Results: Higgs sector 35 / 40
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