Technicolored Strong Dynamics. Fermion masses ETC FCNC Walking Isospin Topcolor Other lurking challenges - Conclusions

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1 Technicolored Strong Dynamics Elizabeth H. Simmons Michigan State University Fermion masses ETC FCNC Walking Isospin Topcolor Other lurking challenges - Conclusions PASI (Buenos Aires) 7 March 2012

2 Last Time: QCD to Technicolor Chiral symmetry breaking in QCD inspired Technicolor: introduce new gauge force with symmetry SU(N)TC force carriers are technigluons, like QCD gluons add techniquarks carrying SU(N)TC charge: matter particles inspired by QCD quarks e.g. TL = (UL, DL) forms a weak doublet UR, DR are weak singlets Lagrangian has familiar global (chiral) symmetry SU(2)L x SU(2)R Susskind, Weinberg

3 From QCD to Technicolor If SU(N)TC force were stronger than QCD... then spontaneous symmetry breaking and pion formation would happen at a higher energy scale... e.g. gauge coupling becomes large at T L T R 250 GeV breaks electroweak symmetry `technipions Π TC become the WL, ZL Λ TC 1000 GeV W and Z boson masses are the size seen in experiment! So far, so good... but what about unitarization?

4 Challenges Affecting Model-Building We will consider how several key challenges have influenced EWSB models with new strong dynamics. 1. How can new strong dynamics generate fermion masses? Pure technicolor does not; an extension is needed (ETC). 2. How can the new dynamics generate fermion masses without large flavor-changing neutral currents (FCNC)? Changing the behavior of TC dynamics (walking) can help. 3. The dynamics splitting the top and bottom masses would tend to affect the rho-parameter. How to keep 0? Models with additional top strong interactions (topcolor) work. The important is the interplay between data and models, not the details of any one model...

5 Fermion Masses Extended Technicolor

6 Fermion Masses & ETC Interactions In extended technicolor, fermion masses arise when heavy ETC gauge bosons couple quarks and leptons to the condensing technifermions larger ETC gauge group subsumes TC ETC breaks to TC at scale M ETC > TC Dimopolous and Susskind Eichten and Lane

7 Fermion Masses & ETC Interactions 40 TeV 10 TeV 6TeV for m s for m c form b [g] Energy (GeV)

8 ETC Yields FCNC s ETC gauge boson exchange yields (after Fierzing) three classes of contact operators: vance: α ab QT a Q QT b Q 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 + PNGB masses fermion masses ( sγ 5 d)( sγ 5 d) Λ 2 ETC + ( µγ5 e)(ēγ 5 e) Λ 2 ETC +... FCNC

9 Flavor Changing Neutral Currents Bounds on FCNCs Too high to { account for strange and charm! (!) K 0 D 0 K0 D0 B 0 d B 0 d B 0 s B 0 s UFit Collaboration: JHEP 0803, 049 (2008)

10 Flavor-Changing Neutral Currents Walking Technicolor

11 Walking Technicolor If βtc 0, we expect γm 1, enhancing fermion masses. A realistic (E)TC model will not be like QCD! Holdom, Yamawaki et. al., Appelquist and Wijewardana

12 Walking Technicolor

13 A Model Builders Dream... Walking: γm large!? QCD-like γ small Figure: K. Holland XQCD 2008

14 How Big Does γm need to be? Region of interest for charm and strange! Gauge-NJL Models, top? current lattice studies * ETC ' 10 3 TeV Assuming no GIM-like FCNC suppression RSC and E. Simmons: arxiv [hep-lat]

15 Whence The Walking? (g TC ) 0 many technifermions - possibly colored (e.g. one-family model) - varied TC representations larger chiral symmetry than SU(2)L x SU(2)R) extra technipions beyond those needed for WL, ZL Prediction: Technipions ( TC ) visible at LHC Eichten, Lane, Womersley; Lane and Mrenna

16 LHC limits on Higgs Production Asymptotic 95% CL limit on σ/σ SM ATLAS + CMS Preliminary, L int = fb CMS-PAS-HIG , ATLAS-CONF /experiment s = 7 TeV Combined observed Combined expected H bb H ττ H γγ H H WW ZZ Higgs boson mass (GeV/c 2 )

17 LHC Technipion Sensitivity g g t t t P g g Q Q Q P b b P A(P! V 1 V 2 )=N TC A V1 V 2 g 1 g F P µ k µ 1 k Models with Colored Technifermions TC models PNGB and content v/f P A gg A l f FS one family (Farhi:1980) P p (3 L L Q 5 Q) 2 p3 4 3 p Variant one family (Casalbuoni:1998) P p (3Ē p 1 6 5E D 5 D) 1 p p 6 6 LR multiscale (Lane:1991) P p 2 ( L` 5 L` 2 Q p 2 5 Q) p TCSM low scale (Lane:1999) T p (3 L p L Q 5 Q) ND p p MR Isotriplet (Manohar:1990) P p (3 L L Q 5 Q) 4 p2 24 p 2y q 2 3

18 Technipion Properties 130 GeV One Variant Multiscale TCSM Isotriplet Decay Family one family low-scale SM Channel N TC N TC N TC N TC N TC N TC N TC N TC N TC N TC Higgs =2 =4 =2 =4 =2 =4 =2 =4 =2 =4 b b c c gg W + W GeV One Variant Multiscale TCSM Isotriplet Decay Family one family low-scale SM Channel N TC N TC N TC N TC N TC N TC N TC N TC N TC N TC Higgs =2 =4 =2 =4 =2 =4 =2 =4 =2 =4 b b c c gg W + W

19 Light Technipion Limits: γγ (σ x BR) P / (σ x BR) SM Variant One Family (Casalbuoni et al) ATLAS (4.9 fb -1 )+ CMS (4.76 fb -1 ) ATLAS (1.08 fb -1 ) + CMS (1.66 fb -1 ) N TC =4 N TC =3 N TC =2 γγ channel (σ x BR) P / (σ x BR) SM TCSM Low-Scale (Lane) ATLAS (4.9 fb -1 )+ CMS (4.76 fb -1 ) ATLAS (1.08 fb -1 ) + CMS (1.66 fb -1 ) N TC =4, N D =10 N TC =3, N D =8 N TC =2, N D =5 γγ channel 10-1 ATLAS/CMS Aug vs Dec 2011 Data M P [GeV] 10-1 ATLAS/CMS Aug vs Dec 2011 Data M P [GeV] LHC excludes orange region Isotriplet (Manohar-Randall) γγ channel Model curves are for NTC = 2, 3, 4 Minimum value is 2... (σ x BR) P / (σ x BR) SM ATLAS (4.9 fb -1 )+ CMS (4.76 fb -1 ) ATLAS (1.08 fb -1 ) + CMS (1.66 fb -1 ) N TC =4 N TC =3 N TC =2 Chivukula, Ittisamai, Ren, Simmons arxiv: [hep-ph] updated ATLAS/CMS Aug vs Dec 2011 Data M P [GeV]

20 Heavy Technipion Limits: ττ 10 3 One Family (Farhi-Susskind) ττ channel ε t = Multiscale (Lane-Ramana) ττ channel ε t =0.5 σ gg x BR(ττ) [pb] ATLAS (1.06 fb -1 ) N TC =4 N TC =3 N TC =2 Top-loop (N TC =2) σ gg x BR(ττ) [pb] ATLAS (1.06 fb -1 ) N TC =6 N TC =4 N TC =3 N TC =2 Top-loop (N TC =2) M P [GeV] M P [GeV] g g Q Q Q P +/- g g t t t P " t m t F P Chivukula, Ittisamai, Ren, Simmons arxiv: [hep-ph]

21 Precision Electroweak Corrections General amplitudes for on-shell 2-to-2 fermion scattering include deviations from the Standard Model: A NC = e 2 QQ Q 2 + (I 3 s 2 Q)(I 3 s 2 Q ) ( s2 ) c 2 e S 2 16π Q (1 αt ) + flavor 2G F S : size of electroweak symmetry breaking sector T : tendency of corrections to alter ratio MW/MZ data (e.g. from LEP II, SLC, FNAL) are sensitive to loop corrections, constraining αs, αt to be ~.001 QCD-like technicolor models predict larger S, T values S, T: Peskin & Takeuchi

22 Open Theoretical Questions Does γm=1 in a walking theory? Is it even large & positive? Can we calculate αs accurately? What is the spectrum (including PNGB masses)? What is the phase diagram (in the NF vs NC plane)? T QCD-like, ND=2 & NC=3 PDG2006: Erler and Langacker S Current Understanding from the Gap Equation in Rainbow Approximation

23 Questions for Lattice Gauge Theory NF IR free IR conformal (2) (3) Banks-Zaks Caswell (4) N c N * confinement χsb (1) Establish Phase Diagram (2) What is γm? Near 1? 2? ( !?) (3) What is S? The spectrum? Is there a 0 ++ (Higgs-like) state? (4) Other marginal/relevant operators? E.g. as suggested by Strong-ETC and Gauged-NJL models NC

24 Weak Isospin Violation New Strong Top- Quark Dynamics

25 Weak Isospin Violation T Text

26 Direct Contributions m t 175 GeV Text References

27 Indirect Contributions Text References Conclusion: t,b feel a new strong force not shared by other quarks or technifermions

28 Top Condensation and EWSB If the top quark feels a new strong interaction, a top-quark condensate can provide some or even all of electroweak symmetry breaking v 2 = f 2 TC + f 2 t some (topcolor*, topcolor-assisted technicolor*) in these models the top quark feels an additional gauge interaction that causes top condensation all (top mode^, top seesaw^^) sin! f t /v in top seesaw models, a heavy partner quark T forms the condensate; the top quark mass eigenstate that we observe is a seesaw mixture between T and the standard model s top quark gauge eigenstate * Hill ^Bardeen,Hill &Lindner; Yamawaki; Miranski; Nambu ^^Chivukula, Dobrescu, Georgi & Hill

29 Physical Realization: Topcolor One physical realization of a new interaction for top is a (spontaneously broken) extended color gauge group: topcolor M SU(3) h SU(3)`! SU(3) QCD where (t,b) feel SU(3)h and (u,c,d,s) feel SU(3)l Below the scale M, exchange of massive topgluons yields four-fermion interactions among top quarks 4 apple M 2 a 2 t µ 2 t Note: M >> 1TeV implies fine tuning

30 Topcolor-Assisted Technicolor (TC2) technicolor: provides most of EWSB and only fraction topcolor: provides most of mt hypercharge: keeps mb small t of mt C.T. Hill hep-ph/

31 Splitting Top and Bottom Masses κ α s cot 2 θ 3 κ α Y cot 2 θ 1 Text

32 Fermion Charge Assignments In any particular TC2 model, one must specify the fermion charge assignments in order to study the phenomenology. Consider a model where the topcolor sector treats the third generation fermions differently than than the lighter fermions. The weak and hypercharge groups treat all three generations identically, so the Z boson is flavor-universal. Braam, Flossdorf, Chivukula, DiChiara, Simmons arxiv:

33 Constraints on couplings There are theoretical and experimental limits on the effective four-fermion couplings due to exchange of heavy coloron or Z bosons: κ α s cot 2 θ 3 κ α Y cot 2 θ 1 constraints from gauged NJL gap equations Σ( p ) x x m o = x + + x < S 4 9 Y 4 3 S Y tt =0 bb =0 < 2 6 Y =0 NJL: Nambu & Jona-Lasinio,1961; gauged NJL: Bardeen, Leung, Love,1986 (PRL, Nucl.Phys.B.)

34 Theoretical Limits on Couplings Theoretical Limits on strong (K ) and hypercharge (K ) couplings in hypercharge-universal coloron models =0 Only top quark condenses inside triangle tt =0 bb =0 Text References

35 Precision Electroweak Corrections Deviations from Standard Model are defined from the amplitudes for on-shell 4-fermion scattering processes S T T S Peskin & Takeuchi Phys.Rev.Lett. 65: , 1990 and Phys.Rev.D46: , 1992 Barbieri, Pomarol, Rattazzi, Strumia hep-ph/ Chivukula, Simmons, He, Kurachi, Tanabashi hep-ph/

36 Change in Observables The change in observables due to new physics can be written in terms of the precision electroweak corrections Note: O 1 loop SM must be calculated for a reference Higgs mass. While TC2 has no Higgs, it has techni-resonances with mass ~ 1 TeV that unitarize WW scattering. A reasonable reference mass range is GeV. Finally, one calculates for Z-pole and LEPII observables (e.g. Z decay widths, scattering cross-sections) to compare model and data. ZFITTER: Bardin et al., hep-ph/ ; Arbuzov et al., SMATASY: Kirsch et al., hep-ph/

37 Limits on Z Mass and Coupling The Y-universal TC2 fit to the Z-pole and LEPII data with an 800 GeV Higgs reference mass yields: By comparison, a fit of the data to the SM with a 115 GeV Higgs mass gives: corresponding to a 3.7% probability, corresponding to a 3.5% probability. Putting the results in terms of the Z coupling and mass reveals that MZ > 2 TeV at 95% C.L., as shown by the allowed area inside the solid (dashed) curve for M H (ref) = 800 (1500) GeV: [10 3 ] References Allowed region is inside the curves.

38 Combining All Limits For such small K, we find that K ~1.9 (yellow region below). So the topgluon mass must be 18 TeV < M C < 25 TeV within this kind of model. =0 Only top quark condenses inside triangle tt =0 bb =0 References DATA

39 Variant TC2 Models Alternative fermion charge assignments define classic and flavor-universal TC2, each of which has a Z boson that distinguishes the third generation from the lighter fermions Quality of Fit Hill: hep-ph/ The fit with an 800 GeV Higgs reference mass gives corresponding to a 10-8 probability. Popovic, Simmons: hep-ph/ The non-universal Z boson of Classic and Flavor-Universal TC2 models is not consistent with precision EW data.

40 Limits on Topgluons / Colorons LHC dijet searches for flavor-universal colorons constrain MC > 3 TeV CERN-PH-EP CERN-PH-EP/ [pb] σ q* A Observed 95% CL upper limit Expected 95% CL upper limit 68% and 95% bands ATLAS L dt = 1.0 fb s = 7 TeV Mass [GeV] Cross Section B A (pb) CMS (1.0 fb ) s = 7 TeV η < 2.5, Δη < % CL Upper Limit Gluon-Gluon Quark-Gluon Quark-Quark String Resonance Excited Quark Axigluon/Coloron E 6 Diquark W Z RS Graviton Resonance Mass (GeV) Topgluons coupled preferentially to 3rd generation: FCNC bounds from B-meson mixing: M C > 6 TeV Fits of TC2 to precision electroweak data: M C ~ 18 TeV

41 Top Condensation? * Bardeen, Hill, Lindner 1990 Text Nambu 1988; Miransky, Tanabashi, Yamawakii 1989; Marciano 1989 & 1990; Miransky 1991

42 Challenges For Top Condensation The relationship between v, M, and mt when strong topcolor dynamics causes top condensation and EWSB Pagels-Stokar formula (1979) in NJL approximation 175

43 Top Seesaw 175 Dobrescu & Hill hep-ph/ ; Chivukula et al ; Collins, Grant, Georgi ; He, Hill, Tait

44 Other Lurking Challenges?

45 Bottom Quark Properties Those ETC dynamics (even if moderated by walking) would also affect R b (Z! b b)/ (Z! hadrons), shifting it relative to the SM by -5% RSC, EHS et al: hep-ph/ , ,

46 Final Data from LEPEWWG (2005) Basic ETC Addressing this theoretically could require modifying the top quark s weak interactions.

47 Constraints From Top-Pions % Burdman & Kominis hep-ph/ This and other b-flavor-related issues pose additional constraints on model-building... See also Buchalla et al. hep-ph/ ; Burdman et al ; Simmons ;

48 Conclusions

49 Conclusions Technicolor is a viable dynamical explanation of EWSB. Providing a dynamical explanation of flavor is challenging. We ve explored the model-experiment interface. Extended technicolor (ETC) yields fermion masses in principle... but would also inevitably cause FCNC. To avoid large FCNC, modify the TC gauge dynamics to walk between TC and ETC scales. Theoretical questions remain about the impact of walking upon the spectrum, S &T parameters, and phase diagram. Creating mt without large weak isospin violation points to new strong top dynamics. Rb still poses a challenge. LHC is joining FNAL and LEP as a source of data about states predicted by new strong dynamics models.

50