Life beyond the minimal supersymmetry

Transcription

1 Life beyond the minimal supersymmetry Wojciech Kotlarski Technische Universität Dresden April 27, 2017, Dresden, Germany

2 Intro: SUSY is not hip anymore more conservative approach - move from speculation (SUSY, extra dimensions) to more tangible things - dark matter and study of the Higgs and the top quark great for experimentalists though may make a lot of theorists unemployed m a i n p r o b l e m : w e (theorists) overpromised and didn t deliver on the promise (MSSM) picture from A. Belyaev talk at the HEP2016 (Valparaiso, Chile) 1

3 Plan of the talk How to construct a SUSY model? Why we believe(d) in the Minimal Supersymmetric Standard Model (MSSM)? The alternatives - Minimal R-symmetric Supersymmetric Standard Model as an example Side-by-side comparison: Higgs boson mass strongly interacting sector at the LHC dark matter Conclusions 2

4 How to construct a SUSY theory? SUSY is the only non-trivial extension of the Poincare algebra. For simplest (N=1) SUSY we get {Q,Q } = { Q, Q } =0, [Q,P µ ]=[ Q,P µ ]=0 {Q, Q } =2 µ P µ, [M µ,q ]=ı( µ ) Q, [M µ, Q ]=ı( µ ) Q, under SUSY transformation particles will transform into each other group particles into irreducible representations (we call them supermultiplets) p =(E,0, 0,E) {Q 2,Q {Q 1,Q 2 } =0 1 } =4E Q Q 1st state i = Q 1 E, Q 1 i =0 0 i 2nd state Q 1 i The only remaining point is how to assign SM fields to supermultiplet. Note that SUSY commutes with internal (i.e. gauge) symmetries so every multiplet must have definite gauge charges. 3

5 Landscape of supersymmetric models MSSM 4

6 Landscape of supersymmetric models singlet extended SSM SUSY with R-parity violation additional U(1) s R-symmetry MSSM models with Dirac gauginos triplet extended SSM and many others. 4

7 The MSSM A model consists of the field content and interactions We define interactions using an object called superpotential W = µĥuĥd Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu Final touch - add SUSY breaking terms B µ - term soft scalar masses Majorana gaugino masses A - terms 5

8 R-symmetry additional symmetry of the SUSY algebra allowed by the Haag - Łopuszański - Sohnius theorem for N=1 it is a global UR(1) symmetry under which the SUSY generators are charged implies that the spinorial coordinates are also charged Q R ( ) =1,! e ı Superpotential example L 3 Z d 2 W Superpotential is polynomial in fields. For W to transform homogeneously superfields must have definite R-charges e ı Q R e ı (Q R 1) e ı Q R = (y) + p 2 (y) + F (y) Similarly one can work out other parts of the Lagrangian 6

9 R-symmetry additional symmetry of the SUSY algebra allowed by the Haag - Łopuszański - Sohnius theorem for N=1 it is a global UR(1) symmetry under which the SUSY generators are charged implies that the spinorial coordinates are also charged Q R ( ) =1,! e ı Superpotential example (we want it to be) R-invariant L 3 Z d 2 W Superpotential is polynomial in fields. For W to transform homogeneously superfields must have definite R-charges e ı Q R e ı (Q R 1) e ı Q R = (y) + p 2 (y) + F (y) Similarly one can work out other parts of the Lagrangian 6

10 R-symmetry additional symmetry of the SUSY algebra allowed by the Haag - Łopuszański - Sohnius theorem for N=1 it is a global UR(1) symmetry under which the SUSY generators are charged implies that the spinorial coordinates are also charged Q R ( ) =1,! e ı Superpotential example transforms as e 2ı (we want it to be) R-invariant L 3 Z d 2 W Superpotential is polynomial in fields. For W to transform homogeneously superfields must have definite R-charges e ı Q R e ı (Q R 1) e ı Q R = (y) + p 2 (y) + F (y) Similarly one can work out other parts of the Lagrangian 6

11 R-symmetry additional symmetry of the SUSY algebra allowed by the Haag - Łopuszański - Sohnius theorem for N=1 it is a global UR(1) symmetry under which the SUSY generators are charged implies that the spinorial coordinates are also charged Q R ( ) =1,! e ı Superpotential example transforms as e 2ı (we want it to be) R-invariant L 3 Z d 2 W transforms as e 2ı Superpotential is polynomial in fields. For W to transform homogeneously superfields must have definite R-charges e ı Q R e ı (Q R 1) e ı Q R = (y) + p 2 (y) + F (y) Similarly one can work out other parts of the Lagrangian 6

12 Low-energy R-symmetry realization Different possible models that one can construct Natural choice leptons and quarks Good: no barion and lepton number violating terms e ı Q R e ı (Q R 1) e ı Q R p = (y) + 2 (y) + F (y) Q R =1 Q R =1 Q R =0 Higgs Q R =0 Q R =0 Q R = 1 Bad: No Majorana masses for higgsinos and gauginos W =µ d ˆRd Ĥ d + µ u ˆRu Ĥ u + d ˆRd ˆT Ĥ d + u ˆRu ˆT Ĥ u + d Ŝ ˆR d Ĥ d + u Ŝ ˆR u Ĥ u Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu 7

13 MSSM vs. MRSSM superpotencial µĥuĥd Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu soft-susy breaking terms superpotencial µ d ˆRd Ĥ d + µ u ˆRu Ĥ u Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu d ˆRd ˆT Ĥ d + u ˆRu ˆT Ĥ u + d Ŝ ˆR d Ĥ d + u Ŝ ˆR u Ĥ u soft-susy breaking terms B µ - term B µ -term soft scalar masses soft scalar masses Majorana gaugino masses A - terms Dirac gaugino masses no A-terms Kribs, Popitz, Weiter (2008) 8

14 MSSM vs. MRSSM superpotencial µĥuĥd Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu soft-susy breaking terms superpotencial µ d ˆRd Ĥ d + µ u ˆRu Ĥ u Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu d ˆRd ˆT Ĥ d + u ˆRu ˆT Ĥ u + d Ŝ ˆR d Ĥ d + u Ŝ ˆR u Ĥ u soft-susy breaking terms B µ - term B µ -term soft scalar masses soft scalar masses Majorana gaugino masses A - terms Dirac gaugino masses no A-terms Kribs, Popitz, Weiter (2008) 2

15 MSSM vs. MRSSM superpotencial µĥuĥd Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu soft-susy breaking terms superpotencial µ d ˆRd Ĥ d + µ u ˆRu Ĥ u Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu d ˆRd ˆT Ĥ d + u ˆRu ˆT Ĥ u + d Ŝ ˆR d Ĥ d + u Ŝ ˆR u Ĥ u soft-susy breaking terms B µ - term B µ -term soft scalar masses soft scalar masses Majorana gaugino masses A - terms Dirac gaugino masses no A-terms Kribs, Popitz, Weiter (2008) 8

16 MSSM vs. MRSSM superpotencial µĥuĥd Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu soft-susy breaking terms superpotencial µ d ˆRd Ĥ d + µ u ˆRu Ĥ u Y d ˆd ˆq Ĥ d Y e ê ˆl Ĥd + Y u û ˆq Ĥu d ˆRd ˆT Ĥ d + u ˆRu ˆT Ĥ u + d Ŝ ˆR d Ĥ d + u Ŝ ˆR u Ĥ u soft-susy breaking terms B µ - term B µ -term soft scalar masses soft scalar masses Majorana gaugino masses A - terms Dirac gaugino masses no A-terms Kribs, Popitz, Weiter (2008) 8

17 Particle content summary: MSSM vs. MRSSM different number of physical states Higgs completely new states R-Higgs CP-even CP-odd charged charginos neutral charged sgluon MSSM MRSSM neutralino gluino MSSM 4 1 MRSSM 4 1 Majorana fermions Dirac fermions 9

18 Particles content summary: MSSM vs. MRSSM different number of physical states Higgs completely new states R-Higgs CP-even CP-odd charged charginos neutral charged sgluon MSSM MRSSM neutralino gluino MSSM 4 1 MRSSM 4 1 Majorana fermions Dirac fermions most important difference from the point of view of direct searches of supersymmetry at the LHC 9

19 Exemplary mass spectrum 3600 Mass / GeV H 4 H ± 2 A 3 H ± 3 O S q 2000 H 3 A g D H A 2 1 H ± 1 R 2 R 1 H 1 c 4 c r ± 2 c ± r ± 2 c 1 ± 1 t, b O A ñ, l ± 10

20 What we do know there is a Higgs boson with mass of 125 GeV it s standard model like realistic SUSY models must accommodate this Moriond

21 Higgs boson mass in the MSSM in the MSSM (h d,h u ) mix giving two physical states h and H h is Standard Model like, with tree-level mass mh < mz leading 1-loop correction to mh m 2 h = m 2 Z cos m4 t 4 2 v 2 ln M 2 S m 2 t + x 2 t 1 x 2 t 12 M S p m t 1 m t 2 x t X t /M S Dependence on the stop mixing parameter xt xt = 0 5 TeV xt = 6 1 TeV why do we care especially about the stops? 12

22 NMSSM solution to the Higgs mass problem Next-to-Minimal Supersymmetric Standard Model MSSM + gauge single superfield W NMSSM = SH u H d + f(s) in simples version f(s) =apple Ŝ3 /3 Ŝ In the basis: ĥ = H d cos + H u sin, Ĥ = H d cos H u sin, ŝ = S m 2 hh = m 2 Z cos v 2 sin

23 Lightest Higgs boson mass in the MRSSM measured Higgs mass mixture of hd,hu,s,t tree-level result 1-loop quantum correction leading 2- loop corrections one of dimensionless parameters of the model +5 GeV at 2-loop 14

24 SUSY status at the beginning of Run II ATLAS SUSY Searches* - 95% CL Lower Limits Status: August 2016 Model e,µ,τ,γ Jets E miss T ATLAS Preliminary s =7,8,13TeV L dt[fb 1 ] Mass limit s =7,8TeV s =13TeV Reference Inclusive Searches 3 rd gen. g med. 3 rd gen. squarks direct production EW direct Long-lived particles RPV Other MSUGRA/CMSSM 0-3 e,µ/1-2 τ 2-10 jets/3 b Yes 20.3 q, g 1.85 TeV m( q)=m( g) q q, q q χ jets Yes 13.3 q 1.35 TeV m( χ 0 1)<200 GeV, m(1 st gen. q )=m(2 nd gen. q ) ATLAS-CONF q q, q q χ 0 1 (compressed) mono-jet 1-3 jets Yes 3.2 q 608 GeV m( q)-m( χ 0 1)<5GeV g g, g q q χ jets Yes 13.3 g 1.86 TeV m( χ 0 1)=0GeV ATLAS-CONF g g, g qq χ ± 1 qqw ± χ jets Yes 13.3 g 1.83 TeV m( χ 0 1)<400 GeV, m( χ ± )=0.5(m( χ 0 1)+m( g)) ATLAS-CONF g g, g qq(ll/νν) χ 0 3 e,µ 4jets g 1.7 TeV m( χ 0 1)<400 GeV ATLAS-CONF g g, g qqwz χ e,µ(ss) 0-3 jets Yes 13.2 g 1.6 TeV m( χ 0 1) <500 GeV ATLAS-CONF GMSB ( l NLSP) 1-2 τ +0-1l 0-2 jets Yes 3.2 g 2.0 TeV GGM (bino NLSP) 2 γ - Yes 3.2 g 1.65 TeV cτ(nlsp)<0.1 mm GGM (higgsino-bino NLSP) γ 1 b Yes 20.3 g 1.37 TeV m( χ 0 1)<950 GeV, cτ(nlsp)<0.1 mm, µ< GGM (higgsino-bino NLSP) γ 2jets Yes 13.3 g 1.8 TeV m( χ 0 1)>680 GeV, cτ(nlsp)<0.1 mm, µ>0 ATLAS-CONF GGM (higgsino NLSP) 2 e,µ(z) 2jets Yes 20.3 g 900 GeV m(nlsp)>430 GeV Gravitino LSP 0 mono-jet Yes 20.3 F 1/2 scale 865 GeV m( G)> ev, m( g)=m( q)=1.5 TeV g g, g b b χ b Yes 14.8 g 1.89 TeV m( χ 0 1)=0GeV ATLAS-CONF g g, g t t χ e,µ 1 3 b Yes 14.8 g 1.89 TeV m( χ 0 1)=0GeV ATLAS-CONF g g, g b t χ e,µ 3 b Yes 20.1 g 1.37 TeV m( χ 0 1)<300 GeV b 1 b 1, b 1 b χ b Yes 3.2 b m( χ GeV 1)<100 GeV b 1 b 1, b 1 t χ ± 1 2 e,µ(ss) 1 b Yes 13.2 b m( χ 0 1)<150 GeV, m( χ ± 1 )= m( χ GeV 1)+100 GeV ATLAS-CONF t 1 t 1, t 1 b χ ± e,µ 1-2 b Yes 4.7/ t m( χ ± 1 )=2m( χ 0 1), m( χ 0 1 GeV GeV 1)=55 GeV , ATLAS-CONF t 1 t 1, t 1 Wb χ 0 1 or t χ e,µ 0-2 jets/1-2 b 1 Yes 4.7/13.3 t m( χ GeV GeV 1)=1 GeV , ATLAS-CONF t 1 t 1, t 1 c χ mono-jet Yes 3.2 t m( t 1 )-m( χ GeV 1)=5GeV t 1 t 1 (natural GMSB) 2 e,µ(z) 1 b Yes 20.3 t m( χ GeV 1)>150 GeV t 2 t 2, t 2 t 1 + Z 3 e,µ(z) 1 b Yes 13.3 t m( χ GeV 1)<300 GeV ATLAS-CONF t 2 t 2, t 2 t 1 + h 1 e,µ 6jets+2b Yes 20.3 t m( χ GeV 1)=0GeV l L,R l L,R, l l χ e,µ 0 Yes 20.3 l GeV m( χ 0 1)=0 GeV χ + 1 χ 1, χ + 1 lν(l ν) 2 e,µ 0 Yes 20.3 χ ± GeV m( χ 0 1)=0 GeV, m( l, ν)=0.5(m( χ ± 1 )+m( χ 0 1 1)) χ + 1 χ 1, χ + 1 τν(τ ν) 2 τ - Yes 20.3 χ ± 355 GeV m( χ 0 1)=0 GeV, m( τ, ν)=0.5(m( χ ± 1 )+m( χ 0 1 1)) χ ± 1 χ0 2 l L ν l L l( νν),l ν l L l( νν) 3 e,µ 0 Yes 20.3 χ ± 715 GeV m( χ ± 1 )=m( χ 0 2), m( χ 0 1)=0, m( l, ν)=0.5(m( χ ± 1 )+m( χ 0 1)) , χ 0 2 χ ± 1 χ0 2 W χ 0 1Z χ e,µ 0-2 jets 1 Yes 20.3 χ ± 425 GeV m( χ ± 1 )=m( χ 0 2), m( χ 0 1)=0, l decoupled , , χ 0 2 χ ± 1 χ0 2 W χ 0 1h χ 0 1, h b b/ww/ττ/γγ e,µ,γ 0-2 b Yes 20.3 χ ± 270 GeV m( χ ± 1 )=m( χ 0 2), m( χ 0 1)=0, l decoupled , χ 0 2 χ 0 2 χ0 3, χ 0 2,3 l R l 4 e,µ 0 Yes 20.3 χ GeV m( χ 0 2)=m( χ 0 3), m( χ 0 1)=0, m( l, ν)=0.5(m( χ 0 2)+m( χ 0 2,3 1)) GGM (wino NLSP) weak prod. 1 e,µ+ γ - Yes 20.3 W GeV cτ<1mm GGM (bino NLSP) weak prod. 2 γ - Yes 20.3 W 590 GeV cτ<1mm Direct χ + 1 χ 1 prod., long-lived χ ± 1 Disapp. trk 1 jet Yes 20.3 χ ± m( χ ± 1 )-m( χ 0 1) 160 MeV, τ( χ ± GeV 1 )=0.2 ns Direct χ + 1 χ 1 prod., long-lived χ ± 1 de/dx trk - Yes 18.4 χ ± m( χ ± 1 )-m( χ 0 1) 160 MeV, τ( χ ± GeV 1 )<15 ns Stable, stopped g R-hadron jets Yes 27.9 g 850 GeV m( χ 0 1)=100 GeV, 10 µs<τ( g)<1000 s Stable g R-hadron trk g 1.58 TeV Metastable g R-hadron de/dx trk g 1.57 TeV m( χ 0 1)=100 GeV, τ>10 ns GMSB, stable τ, χ 0 1 τ(ẽ, µ)+τ(e,µ) 1-2 µ χ GeV 10<tanβ< GMSB, χ 0 1 γ G, long-lived χ 0 2 γ - 1 Yes 20.3 χ GeV 1<τ( χ 0 1)<3 ns,sps8model g g, χ 0 1 eeν/eµν/µµν displ. ee/eµ/µµ χ TeV 7 <cτ( χ 0 1)< 740 mm, m( g)=1.3 TeV GGM g g, χ 0 1 Z G displ. vtx + jets χ TeV 6 <cτ( χ 0 1)< 480 mm, m( g)=1.1 TeV LFV pp ν τ + X, ν τ eµ/eτ/µτ eµ,eτ,µτ ν τ 1.9 TeV λ 311 =0.11, λ 132/133/233= Bilinear RPV CMSSM 2 e,µ(ss) 0-3 b Yes 20.3 q, g 1.45 TeV m( q)=m( g), cτ LS P <1mm χ + 1 χ 1, χ + 1 W χ 0 1, χ 0 1 eeν, eµν, µµν 4 e,µ - Yes 13.3 χ ± m( χ TeV 1)>400GeV, λ 12k 0(k = 1, 2) ATLAS-CONF χ + 1 χ 1, χ + 1 W χ 0 1, χ 0 1 ττν e, eτν τ 3 e,µ+ τ - Yes 20.3 χ ± m( χ 0 1)>0.2 m( χ ± GeV 1 ), λ g g, g qqq large-r jets g 1.08 TeV BR(t)=BR(b)=BR(c)=0% ATLAS-CONF g g, g qq χ 0 1, χ 0 1 qqq g g, g t 1 t, t 1 bs large-r jets g 1.55 TeV m( χ 0 1)=800 GeV ATLAS-CONF e,µ(ss) 0-3 b Yes 13.2 g 1.3 TeV m( t 1 )<750 GeV ATLAS-CONF t 1 t 1, t 1 bs 0 2jets+2b t GeV GeV ATLAS-CONF , ATLAS-CONF t 1 t 1, t 1 bl 2 e,µ 2 b t TeV BR( t 1 be/µ)>20% ATLAS-CONF Scalar charm, c c χ c Yes 20.3 c 510 GeV m( χ 0 1)<200 GeV *Only a selection of the available mass limits on new states or phenomena is shown Mass scale [TeV] 15

25 Fine print: MSSM status at the beginning of Run II 16

26 Fine print: MSSM status at the beginning of Run II MSUGRA/CMSSM 16

27 Fine print: MSSM status at the beginning of Run II MSUGRA/CMSSM those limits are model dependent and can be much weaker 16

28 MRSSM signatures at the LHC sgluon pair production pp! OO complex fields O split by D-term contribution into scalar (S) and pseudoscalar (A) parts m 2 O A = m 2 O m 2 O S = m 2 O + 4(MO D ) 2 naturally heavy, might decay into quarks through loop-induced coupling O S Coupling proportional to m. q. If O A is lighter than other SUSY particles but m OA > 2m t decays exclusively to top quarks O A O A same sign squark pair production diagram present in the MRSSM O A gd gd q q q pp! q L q R O A gd gd q MSSM diagram with Majorana mass insertion doesn t exist q q Dirac gluino g D pair production, with cross section roughly twice as large as in the MSSM 17

29 Leading order analysis 18

30 Leading order analysis while the red lines are the same squark anti-squark pair production becomes subdominant 18

31 NLO K-factors 19

32 Dirac dark matter candidate Dirac neutralino mass matrix m 0 = 0 MB D g 1 1v d 2 g 1v u 0 MW D 1 2 g 1 2v d 2 g 2v u 2 dv d µ d + p2 d v S + dv T 2 0 p1 1 2 dv d p1 1 2 uv u p2 2 uv u 0 µ u + u v S u v T 2 1 C A neutralinos stable by R-symmetry (not R-parity) they annihilate through right-handed stau- or Z-exchange in general: modification of an annihilation cross section 20

33 Dark matter direct detection Spin-independent cross section for Dirac neutralino is driven by Z and squark exchange (with destructive interference between them) no quark spin flip required in squark exchange Dirac dark matter couples to a Z boson through a vector current leading to a spin independent interaction P-value derived from the log likelihood for the direct detection by LUX L (m, {f N } N) = (µ + b)n e (µ+b) N! where N and b are observed and expected numbers of event by the LUX experiment, respectively, and μ is the expected number of signal events for given wimp mass and effective couplings 21

34 2 component dark matter consider scenarios where the lightest particle with R=1 is neutralino or sneutrino with mass m LSP1 if m R 0 1 < 2 m LSP1, lightest neutral R- Higgs is also stable two SUSY dark matter candidates with relic densities Ω1 and Ω2 requirements Ωtotalh 2 (Ω1 + Ω2)h substantial fraction Ω2/Ωtotal 22

35 Summary The SUSY in not a concrete theory It is a set of principles allowing to constructed different models of BSM physics Because something is excluded in the MSSM doesn't mean it s excluded in the SUSY There are aspects of SUSY (especially Dirac gauginos) which are not being searched for by the experimental collaborations If there are any experimentalists in the room looking for a new project - we encourage you to give it a shoot 23

36 Summary The SUSY in not a concrete theory It is a set of principles allowing to constructed different models of BSM physics Because something is excluded in the MSSM doesn't mean it s excluded in the SUSY There are aspects of SUSY (especially Dirac gauginos) which are not being searched for by the experimental collaborations If there are any experimentalists in the room looking for a project - we encourage you to give it a shoot Thank you! 21