Discovering Technicolor

Transcription

1 Discovering Technicolor Stefano Di Chiara Origin of Mass 2011, Odense

2 Outline Standard Model (Extended) Technicolor Minimal Walking Technicolor Beyond MWT Outlook and Conclusions 2

3 Main References Discovering Technicolor, Andersen et al. 11 Dynamical Stabilization of the Fermi Scale, Sannino 08 Strong Dynamics, Hill & Simmons 03 Lectures on Technicolor, Chivukula 00 Dynamical EW Symmetry Breaking, King 95 3

4 Elementary Particle Spectrum Experimentally detected elementary particles: Gauge symmetry: SU(3) C SU(2) L U(1) Y fermion and gauge boson kinetic Lagrangians: L k f = q Li D µ γ µ q Li + l Li D µ γ µ l Li + ū Ri D µ γ µ u Ri + d Ri D µ γ µ d Ri + ē Ri D µ γ µ e Ri, L k g = 1 F bµν G 4 F Gµν b + F aµν W F Wµν a + F µν B F Bµν. M Z,M W ± = 0, Goldstone s theorem: there is one massless Nambu Goldstone Boson (NGB) for each broken generator 3 broken generators. 4

5 Standard Model Standard model Higgs scalar: 0 φ 0 = 1 0,Q= T 3 + Y = 2 v ,Q ij 0 φ 0 j =0 SU(2) L U(1) Y U(1) EM. The EW symmetry breaking is triggered by the potential of the Higgs Lagrangian: L H = (D µ φ) D µ φ V (φ), V (φ) = µ 2 φ φ λ φ φ 2,µ 2 < 0. Yukawa couplings allow to give mass also to fermions: L Y = q Li Y uij φu Rj q Li Y dij φdrj L Li Y eij φe Rj + hc. 5

6 Puzzles No collider experimental result gives deviation from SM prediction greater than 3σ (until lately, but there are 100s). Still, there are open problems: Fine tuning Dark matter and energy Neutrino masses Matter-antimatter asymmetry Gauge Couplings Unification... 6

7 SM Higgs mass at one loop: SM Fine Tuning M 2 H = M 2 H = M 0 H 2 + M 2 H, M 0 H 2 = λv 2 2, 3Λ2 M 2 8π 2 v 2 H 4m 2 t +2MW 2 + MZ 2 +O log Λ2 v 2 = H f H W, Z, H W, Z, H + + f If Λ = GeV (Planck scale) M H : λ has to be MH 2 determined up to the 32nd digit to miraculously cancel the quantum correction... 7

8 Supersymmetry One possible solution is Supersymmetry: add new 19 particles, a few more parameters,... u u d d Or one can look at QCD for inspiration... 8

9 Dynamical EWSB In QCD at a Λ QCD the interaction becomes strong and the quarks form a bound state with non-zero vev: 0 ū L u R + d L d R 0 =0,T 3 L+Y L = Y R = Q SU(2) L U(1) Y U(1) EM Redefine fields in terms of composite peudo-scalars and plug in L k f q =(u, d),j µ 5a = qγµ γ 5 τ a 2 q = f π µ π a L k f g 2 f π +W + µ µ π + + g 2 f π W µ µ π + g 2 f π 0W 0 µ µ π 0 + g 2 f π 0B+ µ µ π 0 9

10 QCD W ± W ± W ± π ± = + + = 1 p p 2 (gf π ±/2)2 1 p = 1 p 2 (gf π ±/2) 2 The EW bosons have acquired masses: M QCD W = gf π ±/2, ρ = M QCD W M QCD Z cos 1 (θ W )=1, Given the experimental value for the pion decay constant f π = 93 MeV M QCD W = 29 MeV! 10

11 Technicolor The effective Lagrangian expansion breaks down at Λ QCD 4πf π =1.2 GeV Λ TC 4πv =3TeV,v= 246 GeV. A Technicolor (TC) model able to give the right masses to the EW gauge bosons is simply scaled up QCD: SU(N) TC SU(3) C SU(2) L U(1) Y. To generate the fermion masses an Extended Technicolor (ETC) interaction is necessary. 11

12 Extended Technicolor If the ETC gauge group gets broken at some large scale Λ ETC Λ TC, the massive ETC gauge bosons can be integrated out. Four fermion interactions, technifermion condensate SM mass terms Q L ψ L G µ ETC ψ R Q R g2 ETC M 2 ETC ( Q L Q R )( ψ R ψ L ) m ψ g2 ETC M 2 ETC QQ. The lowest ETC scale is determined by the heaviest mass: m t = 173 GeV Λ3 TC Λ 2 ETC Λ ETC 10 TeV 12

13 pngb Masses Without specifying an ETC one can write down the most general ETC sector: L ETC = α ab QL T a Q R QR T b Q L Λ 2 ETC +β ab QL T a Q R ψr T b ψ L Λ 2 ETC +γ ab ψl T a ψ R ψr T b ψ L Λ 2 ETC The first terms generate masses for the uneaten NGB. These can be estimated by: Q R Q L Λ 3 TCΣ, Σ exp(iπ c T c /F T ), T GETC (M cd PNGB) 2 α abλ 6 TC Λ 2 ETC F 2 T Tr([ T c,t a ][T b, T d ]) M PNGB = O Λ 2 TC Λ ETC 13

14 FCNC s G ETC d s D d D D G ETC G ETC d G ETC d d D s The second terms generate masses for the SM fermions, while the third terms are responsible for Flavor Changing Neutral Currents (FCNC): L S=2 = γ sd ( sγ 5 d)( sγ 5 d) Λ 2 ETC + hc, γ sd sin 2 θ c Measured value of the neutral kaon mass splitting determines tight bound on ETC scale: m 2 m 2 K γ sd f 2 K m2 K Λ 2 ETC Λ ETC 10 3 TeV. 14

15 Fermion Mass Renormalization The limits on Λ ETC from the large value of m t and the FCNC experimental data seem to be incompatible, but that was without taking into account renormalization: γ m = d log m d log µ,m3 QQ QQ ETC = QQ TC exp Σ(p 2 )=3C 2 (R) p [ ] 1 Σ(p) p γ m(µ),p γ m(µ) 2 ; γ m (µ) =1 = d 4 k α((k p) 2 ) Σ(k 2 ) (2π) 4 (k p) 2 Z(k 2 )k 2 + Σ 2 (k 2 ) k 1 α TC(µ) α C ΛETC dµ Λ TC µ γ m(µ) From the Schwinger-Dyson equations in the rainbow (=one gluon exchange) approximation:, α C π 3C 2 (R).

16 Running vs Walking TC α α µ µ β for Λ ETC >µ>λ TC : α Running TC: α(µ) 1 ln µ, QQ ETC QQ TC Walking TC: β(α )=0 QQ ETC QQ TC ΛETC Λ TC γm (α ) A Walking TC obtains a big boost to both fermion and pngb masses, while FCNC are unaffected. 16

17 Walking TC Look for Walking TC (β(α )=0) in theory space (Representation (R), Number of colors (N), Number of flavors (N f )) by studying β(g) = β 0 α 2 4π β 1 α 3 (4π) 2, α = 4π β 0 β 1, β 0 = 11 3 C 2(G) 4 3 T (R), β 1 = 34 3 C 2 2 (G) 20 3 C 2(G)T (R) 4C 2 (R)T (R). The conformal window is defined by requiring asymptotic freedom, existence of a Banks-Zaks fixed point, and conformality to arise before chiral symmetry breaking: β 0 > 0 N f > 11 4 d(g)c 2 (G) d(r)c 2 (R), β 1 < 0 N f < d(g)c 2(G) d(r)c 2 (R) α < α c N f > d(g)c 2(G) d(r)c 2 (R) 17C 2 (G) 10C 2 (G) + 6C 2 (R) 17C 2 (G) + 66C 2 (R) 10C 2 (G) + 30C 2 (R). 17

18 Walking in the SU(N) Phase diagram for theories with fermions in the: fundamental representation (grey) two-index antisymmetric (blue) two-index symmetric (red) adjoint representation (green) The S parameter for a TC model is estimated by: S th = 1 N f 6π 2 d(r), 12π S ex 95%

19 TC Models Walking Technicolor candidate models: Fundamental: 12πS(N =3,N f = 12) = 36, 12πS(N =2,N f = 8) = 16 Adjoint: 12πS(N =2,N f = 2) = 6, 12πS(N =3,N f = 2) = 16 2 I. Symmetric: 12πS(N =2,N f = 2) = 6, 12πS(N =3,N f = 2) = 12 2 I. Antisymmetric: 12πS(N =3,N f = 12) = 36 Alternatives to reduce S: Custodial TC (S =0) Partially Gauged TC Split TC The best (fully gauged) Walking TC candidates are: Adj,N =2,N f =2 2-IS, N =3,N f =2 19

20 Ideal Walking A strong ETC sector increases the value of the fermion mass anomalous dimension. In gauged Nambu-Jona-Lasinio (gnjl): 1 λ ααc 2 L gnjl = L TC + 16π2 λ d[r]n f Λ 2 ETC γ m (λ) =1 ω +2ω λ λ c, ω ψ L ψ R ψr ψ L 1 α α c 1 4 λ c = 1 4 Sym. SχSB α α c Assuming λ = λ c =0.75 one gets γ m (λ = λ c )=1+ω =1.73 By using dimensional analysis m t = 172 GeV for Λ ETC 10 7 TeV! An accurate estimate of Λ TC and TT TC is needed to determine Λ ETC. 20

21 Phase Diagram with 4F Interaction Phase diagram for SU(N) representations with chiral symmetry breaking (dashed) line determined for λ c = N f N

22 Minimal Walking TC TC-fermions in the SU(2) TC adjoint rep.: a =1, 2, 3; Q a U a L = L DL a,ur,d a R a Heavy leptons to cancel Witten anomaly NL L L =,N R,E R E L N extra neutrino E extra electron Gauge anomalies cancel for hypercharge assignment Y (Q L )= y y +1 2, Y(U R,D R )= 2, y 1, 2 Y (L L )= 3 y 3y +1 2, Y(N R,E R )=, 3y U TC-up D TC-down G TC-gluon 22 U(1) Y SU(2) L SU(3) C SU(2) TC

23 MWT Lagrangian For y = 1 3 TC-fields have SM-like hypercharges, for y =1 D R corresponds to a techni-gaugino. L MWT = L SM L H + L TC, L TC = 1 4 F a µνf aµν + i Q L γ µ D µ Q L + iūrγ µ D µ U R + i D R γ µ D µ D R +i L L γ µ D µ L L + iērγ µ D µ E R + i N R γ µ D µ N R, with the covariant derivatives defined by the fields quantum numbers. The techniquarks condense and break EW: Q α i Q β j αβe ij = 2 U R U L +D R D L,Q= U L D L iσ 2 U R iσ 2 D R 0,E= I I 0 SU(2) L U(1) Y U(1) EM 23

24 S-T Parameters The ellipses give the S and T 90% CL region for M H = 117 GeV (blue), 300 GeV (yellow), 1 TeV (red). MWT s S and T region (green) calculated for y = 1 3 (left panel), y =1(right panel) and M Z m E,N 10 M Z. 24

25 Low Energy Lagrangian Low energy Lagrangian: L Higgs = 1 2 Tr D µ MD µ M V(M)+L ETC, where the potential reads V(M) = m2 M 2 Tr[MM ]+ λ 4 Tr MM 2 + λ Tr 2λ Det(M)+Det(M ), MM MM M ij Q i Q j with i, j =1...4, M = v 2 E. M transforms under the full SU(4) group according to M umu T, with u SU(4). Global SU(4) SO(4) 6 uneaten NGB 25

26 ETC Scalar Sector In order to give masses to the 6 uneaten Goldstone bosons we add the following term which is generated in the ETC sector: L ETC m2 ETC 4 Tr MBM B + MM, M 2 pngb = m 2 ETC. 26

27 Composite Vector Bosons Composite vector bosons of a theory with a global SU(4) symmetry described by the four-dimensional traceless Hermitian matrix: A µ = A aµ T a, where T a are the SU(4) generators. Under an arbitrary SU(4) transformation, A µ transforms like A µ ua µ u, where u SU(4). The techniquark content is expressed by the bilinears: A µ,j i Q α i σ µ α β Q β,j 1 4 δj i Qα k σµ α β Q β,k. 27

28 MWT Gauge Sector The minimal kinetic Lagrangian is: L kinetic = 1 2 Tr Wµν W µν 1 4 B µνb µν 1 F 2 Tr µν F µν +m 2 Tr C µ C µ, where W µν and B µν are the EW elementary field strength tensors, and F µν = µ A ν ν A µ i g [A µ,a ν ]. The vector field C µ is defined by C µ A µ g g G µ, with G µ given by G µ = gw a µ L a + g B µ Y. 28

29 MWT Phenomenology Invariant mass distribution M for pp R 1,2 + signal and background processes given by g =2(left), g =3(right) and M A =0.5 TeV (purple), 1 TeV (red), 1.5 TeV (green). R 1 (R 2 ) is the lighter (heavier) vector meson. Number of events/20 10 fb M ll (GeV) Number of events/20 10 fb M ll (GeV) 29

30 Vector Resonance Signals Transverse mass distribution M T 3 for pp R± 1,2 ZW± ν signal and background processes, calculated with g =2(left), 4 (right), and M A =0.5 TeV (green), 1 TeV (red). The R 1,2 coupling to W ±,Z is enhanced for large values of g, balancing the suppression coming from the quark-r 1,2 couplings. Number of events/20 10 fb M T 3l(GeV) Number of events/20 10 fb M T 3l(GeV)

31 Composite Higgs Production The cross section for pp WH production at 7 TeV versus M A for S =0.3, s =(+1, 0, 1) and g =3(left) and g =6(right). The dotted line at the bottom indicates the SM cross section level. The resonant production of heavy vectors can enhance HW and ZH production by a factor 10. (pp WH)(pb) 1 M H =200 GeV, S=0.3, g ~ =3 sm s=-1 s=0 s=+1 (pp WH)(pb) 1 M H =200 GeV, S=0.3, g ~ =6 sm s=-1 s=0 s= M A (GeV) M A (GeV)

32 Unification in MWT Unification ingredients for MWT: Make g TC run at scale X by embedding SU(2) Adj in SU(3) F Delay unification (M GUT v) to avoid the experimental bounds on the proton decay by adding a wino and a bino Unification of g Y,g L,g s in umwt (left) and MSSM (right) log 10! [log 10 (GeV)] log 10! [log 10 (GeV)]

33 umwt Gauge Unification Unification of gauge couplings in the umwt: TC,Adj -1 TC,fund -1 X log 10! [log 10 (GeV)] 33

34 Bosonic Technicolor f R f L H U L U R y f y U M 2 H (ŪLU R )( f R f L ) m f y f y U M 2 H Λ 3 TC By supersymmetrizing the theory and taking the limit of scalars much heavier than their fermion superpartners, one finds that the theory is not fine tuned: m f m f m 2 f y 16π 2 m2 f 1 log m 2 f µ 2 M 2 H M 2 H In the same limit the FCNC generated by scalars are suppressed. = O(1) 34

35 From MWT to N=4 SUSY MWT Minimal S-partners N=1 Multiplets N=4 G µ G µ V D R DR V Φ 3 Ū R Ū R Ū R Φ 3 Φ 1 U L D L U L D L Ũ L D L Φ 1 Φ 2 Φ 2 Superpotential for SU(N) N =4Super Yang-Mills (4SYM): f(φ) = g 3 2 ijkf abc Φ a i Φ b jφ c k,i=1, 2, 3; a =1,,N2 1; 35

36 Minimal Super Conformal TC Superfield SU(2) TC SU(3) c SU(2) L U(1) Y Φ L Adj 1 1/2 N =4 Φ 3 Adj V Adj th Lepton Family Λ L 1 1-3/2 N E H 1 1 1/2 H 1 1-1/2 36

37 MSCT Superpotential Spectrum: 4SYM + lepton 4th superfamily + MSSM Gauge group: SU(2) TC SU(3) C SU(2) L U(1) Y f(φ) TC = g TC 3 2 ijk abc Φ a i Φ b jφ c k + y U ij3 Φ a i H j Φ a 3 + y N ij3 Λ i H j N + y E ij3 Λ i H je + y R Φ a 3Φ a 3E. MSCT represents a possible UV completion of MWT. 37

38 Dark Matter TIMP = Technicolor Interacting Massive Particle, complex technibaryon scalar, singlet under the SM interactions, stable at low energies (because of U(1) TC B symmetry). TIMP naturally explains the observed ratio between dark matter and baryonic matter, as well as the measured excesses in e ± cosmic rays. 38

39 Neutrino Masses N R can be used to give mass to neutrinos by see-saw mechanism, which allows very small masses to be produced for natural values of the Yukawa couplings. 39

40 Inflation It is possible to obtain successful inflation via non-minimal coupling of a composite scalar to gravity, with the underlying dynamics preferred to be near conformal, and the inflation scale of the order of M GUT. 40

41 Conclusions Technicolor solves fine tuning Walking dynamics allow to satisfy experimental constraints MWT viable model with interesting LHC phenomenology TIMP viable dark matter candidate Unification, ν masses, inflation, explained within TC framework 41

42 Backup Slides 42

43 Puzzles No collider experimental result gives deviation from SM prediction greater than 3σ (until lately, but there are 100s). Still, there are open problems: Fine tuning: the first 32 digits of the tree level and one loop contributions to M H must cancel to give M H 100 GeV Dark matter and energy: the SM describes only 4% of the Universe s particle content Neutrino masses: the SM assumes the neutrino massless; allowed Yukawa interactions would be un-naturally small Matter-antimatter asymmetry: the relative abundance of matter cannot be generated by SM physics Unification: a common origin of the observed forces would reduce the theory arbitrariness; unification is ruled out in the SM... 43

44 One Family ETC A toy ETC model: each entire family belongs to a single ETC fermion. SU(N ETC ) SU(3) C SU(2) W U(1) Y : Q L =(N ETC, 3, 2) 1/6 L L =(N ETC, 1, 2) 1/2 U R =(N ETC, 3, 1) 2/3 E R =(N ETC, 1, 1) 1 D R =(N ETC, 3, 1) 1/3 N R =(N ETC, 1, 1) 0 The lowest ETC scale is determined by the heaviest mass: m t = 173GeV Λ ETC 10 TeV Because of global symmetry breaking there are also massless NGB SU(N TC + 3) Λ 1 m 1 Λ3 TC Λ 2 1 SU(N TC + 2) Λ 2 m 2 Λ3 TC Λ 2 2 SU(N TC + 1) Λ 3 m 3 Λ3 TC Λ 2 3 SU(8) L SU(8) R SU(8) V 60 NGB SU(N TC ) 44

45 Vector-Scalar Couplings The C µ fields couple with M via gauge invariant operator: L M C = g 2 r 1 Tr + i g r 3 2 Tr C µ + g 2 s Tr [C µ C µ ]Tr C µ C µ MM + g 2 r 2 Tr C µ MC µt M M(D µ M) (D µ M)M MM. The dimensionless parameters r 1, r 2, r 3, s express interaction strength in units of g, and are therefore expected to be of order one. The fermions are coupled to the low energy effective Higgs through effective SM Yukawa interactions. 45

46 Weinberg Sum Rules The free parameters of the low energy spectrum are: r 1,r 2,r 3,s,M A,M H, g, with A referring to the axial-vector meson. Three of these parameters can in principle be eliminated by using the constraints from the S parameter and the Weinberg Sum Rules (WSR). The 1st and 2nd WSR are obtained from the vector and axial-vector two-point correlation functions, by assuming partial conservation of the axial current and they read F 2 V F 2 A = F 2 π,f 2 V M 2 V F 2 AM 2 A = a 8π2 d(r) F 4 π, where a is expected to be positive and O(1) for a walking theory and 0 for a running one. 46

47 Vector Resonance Signals pp R 1,2 +. Signal and background cross sections for g = 2, 3, 4, and required luminosity for 3σ and 5σ signals. g M A M R1,2 σ S (fb) σ B (fb) L (fb 1 ) for 3σ L (fb 1 ) for 5σ M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 = M 1 = M 2 =

48 Vector Resonance Signals pp R ± 1,2 ZW± ν. Signal and background cross sections for g =2, 3, 4 and required luminosity for 3σ and 5σ signals. M R1,2 are the physical masses (GeV). g M A M R1 M R2 σ B (fb) σ S (fb) L (fb 1 ) for 3σ L (fb 1 ) for 5σ