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Resonant signature of the Littlest Higgs model with T-parity at Linear Colliders

Resonant signature of the Littlest Higgs model with T-parity at Linear Colliders. Shigeki Matsumoto (KEK, Theory). Collider signatures of the Little Higgs model with T-parity, with focusing on the production of the T - quark at ILC.

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Resonant signature of the Littlest Higgs model with T-parity at Linear Colliders

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  1. Resonant signature of the Littlest Higgs model with T-parity at Linear Colliders Shigeki Matsumoto (KEK, Theory) Collider signatures of the Little Higgs model with T-parity, with focusing on the production of the T- quark at ILC. Collaborated with M.Asano, S.M., N.Okada, M. Nojiri and K. Fujii • The Littlest Higgs model with T-parity: p.2 – p.9 • ( Please skip these pages if you know the model ) • 2. The T- quark production at the ILC: p.10 – p.17 1

  2. Many people expect that the SM will be extended at a high scale L > EW scale. On the other hand, the scale L should be larger than 5-10 TeV. This constraint is obtained by the electroweak precision measurements. [R.Barbieri & A.Strumia, (1998)] Little hierarchy problem This fact leads to the fine-tuning problem, which comes from quadratic divergent corrections to the Higgs mass. mh2 = h + h m02 (bare mass) L2 corrections We need about 0.1 % fine-tuning for mh ~ 100 GeV. This problem is called “Little hierarchy problem”. 2

  3. Little Higgs mechanism has been proposed to solve the Little hierarchy problem. Little Higgs mechanism Basic idea of the mechanism is 1. Higgs boson is regarded as a pseudo NG boson associated with a symmetry breaking at a high scale. 2. The pattern of the breaking is arranged to cancel quadratic divergent corrections to the Higgs mass at one-loop level (collective symmetry breaking). New particles are necessarily introduced and the divergences are cancelled at one-loop level due to these particles’ contributions. As a result, the new physics scale L can be taken to be 10 TeV without the little hierarchy problem!! 3

  4. The Littlest Higgs model (LH) The simplest model using this mechanism is called the Littlest Higgs model, which is described based on the non-linear sigma model under SU(5)/SO(5) breaking. [Arkani-Hamed, Cohen, Katz and Nelson (2002)] f ~ O(1) TeV SO(5)⊃SU(2)×U(1) (SM gauge) SU(5)⊃[SU(2)×U(1)]2 (gauged) f ~ L /4p is the vacuum expectation value of the braking. The subgroup [SU(2)×U(1)]2 in SU(5) is gauged, and broken into the SM gauge group under SU(5)/SO(5) breaking. Due to the existence of gauge interactions, the global SU(5) symmetry is not exact, and the Higgs acquires a mass term. 4

  5. Lagrangian (Kinetic term) Directions of the breaking Gauge-Higgs sector in the LH NB boson fields SM gauges : A, W±, Z Heavy gauges : AH, WH±, ZH SM Higgs : h Triplet Higgs : Φ 4 gauge bosons: B1, W1 , B2, W2 Σ= (24 – 10) pions : After SU(5)/SO(5) and EW breakings 10 & 30 are eaten by heavy gauge bosons (AH, WH, and ZH) 21/2 is nothing but the Higgs, while 3 is the triplet Higgs. 5

  6. Top sector in the LH Top Yukawa interaction In addition to the top quark, the heavy top (vector-like & SU(2)L-singlet) is introduced to cancel the quadratic divergent correction to the Higgs mass. SM top quark : t , Heavy top : T = (U, UR)T 6

  7. The Littlest Higgs model with T-parity (LHT) Original LH is still suffered from severe constraints by EWPM 1. Tree-level corrections from the exchange of a heavy gauge boson. 2. Non-vanishing vacuum expectation value of the triplet Higgs. L must be larger than 100 TeV !!  fine-tuning again We impose T – parity:( B1(W1) ⇔ B2(W2), P ⇔ –WPW) where W= diag.(1,1,–1,1,1)  no heavy gauge boson exchanges, no triplet VEV In the top sector, two additional top-like quarks are introduced, which are ”T-parity” partners for top and heavy top (T) quarks. We use the notation, t- and T- for these quarks. Under the T-parity Lightest T-odd Particle (LTP) (AH in this model) is stable, and could be a dark matter !! (A, W±, Z, h, t, T ) are T-even (AH, WH±, ZH, F, t-, T- ) are T-odd 7

  8. Cancellation of the quadratic divergent corrections Since the Higgs is a pseudo NG boson, its potential is induced from gauge boson and top quark loops (Colman-Weinberg potential). V(φ) = －μ2φ2 + λφ4 Quadratic divergent corrections to m2 are cancelled due to new particles' contributions at 1-loop level. Thus, 1-loop logarithmic and 2-loop quadratic corrections contribute to m2. Induced from logarithmic divergent corrections at 1-loop. W,Z WH,ZH Cancellation!! + h h t t T h + h + h t T 8

  9. Parameters in the LHT and WMAP Constraint Undetermined parameters in LHT are f, mh, l1, l2 II. LHT has a dark matter candidate. Thus, we impose the WMAP constraint for the relic abundance of dark matter Wh2. In LHT, dark matter annihilates into weak gauge bosons through the diagram, where each vertices are determined by SM gauge couplings. Therefore, the mass of the dark matter is determined by f, thus Wh2 depends on f and mh. I. The mass of the SM top is given by mt = l1l2v/(l12 + l22), v = 246 GeV. With fixed mt, R = l1/l2 is usually taken to be a free parameter. Wh2 of dark matter WMAP Due to the reason I and II, free parameters in LHT is f and R. Higgs mass is determined by f 9

  10. Physics on the top sector of the LHT Particles in the top sector have a important role for the Little Higgs mechanism. Thus, it is interesting to see if there is any chance to detect these particles. In particular, the discovery of the T- quark will suggest the existence of the Little Higgs mechanism with T-parity !! Properties of the T- quark I. Mass The mass of the T- quark is given by mT- =l2 f. Since the range of f is limited due to the WMAP constraint, the mass is expected to be several hundred GeV – a few TeV. ( Please see p.12 for more details. ) 10

  11. II. Interactions Since the T- quark is SU(2)L singlet, its interactions are In addition to these, there are other interactions with F. T- T- T- A, Z = B AH, ZH = BH G t, T T- T- III. Decay Because mT > mT- and mF > mT-, the T- quark decays into the SM top and dark matter (AH). Its width is a few GeV. Excluded (can’t predict the correct mt) 11

  12. Constraint on mT- from electroweak precision measurements The mass of the T- quark (mT-) is constrained from electroweak precision measurements (EWPM). Essential reason is that the contribution from additional Top quarks to the r-parameter (mass ratio between mZ and mW) becomes large for smaller mT-. Allowed region from EWPM in (f, mT-) plane is shown below. mT- should be larger than 480 GeV. 5s mh is about 120 GeV. In other regions, mh is much heavier. Allowed 12

  13. The T- quark production at the LHC Since the mass of the T- quark is not so large, many T- will be pair-produced at the LHC. Main production mode for these quarks is a gluon fusion, while final state is t tbar + missing energy. [J.Hubisz and P.Meade (2004)] There are many other modes which produce the same final state, e.g. from tt, tT, t-t-, TT productions. Thus, it is easy to find the deviation from the SM, while difficult to make sure the existence of the T-. Production s [pb] Events/ 300 [fb-1] mT- [GeV] 13

  14. Production of the T- pair in linear colliders When the Higgs is not heavy (mh ~ 120 GeV), the mass of the T- quark is about 500 GeV. Thus, it must be produced at the threshold region in the 1TeV linear collider. • Is the production cross section is suppressed? • No! Because the T- quark has the color, the cross section will be enhanced at the threshold region due to the resonance composed of the T- quark pair. • We can distinguish the signal from the SM B.G. AH e+ T- t g, Z t e- T- AH 14

  15. Production cross section for the T- pair Below, we show the cross section as a function of s1/2. We use the sample point (f = 590 GeV and mT- = 490 GeV). The dark matter mass (mAH) is 83 GeV in this case. This point satisfies both WMAP and EWPM constraints. The cross section achieves 100 fb at s1/2 ~ 1 TeV!! 15

  16. The SM background for the T- pair production The top and anti-top quarks with ~ 270 GeV energy will be detected as a signal of the T- pair production when mT- ~ 500 GeV. On the other hand, main background comes from the SM process, e+e- t tbar + n nbar, its differential s is about 10-3 fb/GeV (see below). 1.5 dsBG/dE (10-3fb/GeV) In 200 fb-1 luminosity, event #s with the cut 250 GeV < Et,Etbar <300 GeV are Signal: 104 B.G.: 10 1 0.5 s1/2 = 980 GeV ( top ) ( anti-top ) 0 (GeV) 250 270 290 16

  17. Summary • Littlest Higgs model with T-parity is the attractive scenario for physics beyond the SM. • The model solve the “Little hierarchy problem” and provide a good candidate for non-baryonic dark matter. • In this model, there are many top-like quarks. Especially the search for the T- quark is important, since its discovery means the existence of the Little Higgs mechanism with Z2 symmetry (T-parity). • If the Higgs mass is around 120 GeV, the T- quark can be lighter ~ 500 GeV, and it is easy to find the signal at the ILC with 1 TeV center of mass energy. Future directions • Production of other top partners such as T, t- quarks. • Investigation about how accurately parameters related to the Little Higgs mechanism are measured. 17

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