1. Report on LHT at the LHC ～ Some results from simulation study ～ Shigeki Matsumoto (Univ. of Toyama) 1.What kinds of LHT signals are expected, and how accurately the LHC parameters are determined at the LHC? 2.Important to clarify the between the LHT study at the ILC and at the LHC. S. M., M. M. Nojiri, and D. Nomura, PRD75 (2007) S. M., T. Moroi and K. Tobe (arXiv:0806.3837, will be in PRD)

2. Little Higgs Model with T-parity New particles (will be) playing an important role are Heavy gauge bosons (γ H, Z H, W H ), Top partners (T ± ), Triplet Higgs! - - - - - - - - - -- - Triplet H H H T+T+ T–T– T-even T-odd except T + Masses of T-parity partners of quarks and leptons (q –, l – ) are assumed to be large! New physics parameters introduced in the LHC are Breaking Scale ( f ) and Top partner mass (λ 2 f) and m h ! (DM)

3. Proton New Colored Particles 7 TeV LHC is a “hadron” collider, so that colored new particles are copiously produced! Productions of top partners, in particular, T + & T – ! Littlest Higgs model with T-parity at the LHC Representative Points

4. ~ Signal Processes ~ Pair T + production, Single T + production, Pair T – production. Littlest Higgs model with T-parity at the LHC ~ Strategy to generate events ~ Event generation at the parton level including PDF effects: MadGraph/Event Fragmentation, initial and final state radiations, hadronization effects: PYTHIA Detector simulations including Jet reconstruction with cone algorithm, b and t jet tags, isolated leptons and photons identification, missing momentum from calorimater information: PDG4

5. T + pair production at the LHC SM BG: tt–production! (460 pb) - At the parton level Signal = bbqqlν - - Reconstruct Two T + -system: T + (lep) & T – (had) using the fact that the missing momentum p T is due to the neutrino emission and (p l + p ν ) 2 = m W 2. There are 6-fold ambiguity in the reconstruction of T + -system.  The combination to minimize ~ Output ~ Distribution of ~ Strategy to reduce BG ~

6. T + pair production at the LHC The distributions have distinguishable peaks at around the T + mass. SM BG are well below the signal.  From the distribution, we will be able to study the properties of T +. ~ Results ~ ~ Cut used in the analysis ~ ~ Discussion ~

7. T + pair production at the LHC We consider the bin Then, we calculate the # of events in the bin as a function of with being fixed. The peak of the distribution is determined by maximizing the # of events in the bin. We applied the procedure for ~ Results ~ ~ Conclusion ~ ~ Accuracy of the m T+ determination ~ The difference between the position of the peak and the input value of mT+ is, typically, 10-20 GeV!

8. T + single production at the LHC SM BG: tt & single t productions! - At the parton level Signal = bqlν Existence of very energetic jet (b from T + )! With the leading jet, reconstruct T + -system. There are 2-fold ambiguity to reconstruct neutrino momenta  & Reject events unless is small. Jet mass is also used to reduce the BG. ~ Output ~ Distribution of ~ Strategy to reduce BG ~

9. Single T + production occurs not through a QCD process but through a EW process (e.g. W-exchange). Distributions have distinguishable peaks at around the T + mass when sin 2 β is large enough!  From the cross section, we will be able to determine sinβ. ~ Results ~ ~ Cut used in the analysis ~ ~ Discussion ~ T + single production at the LHC

10. We use the side-band method to extract the # of the single production events, (L) (C) (R) after imposing the cuts. Then, cross section for the single T + production can be obtained from the # of events in the signal region. ~ Results (Point 2) ~ ~ Conclusion ~ ~ Accuracy of sinβ determination ~ The cross section, which is proportional to sin 2 β, will be determined with 10-20%. Parameter “sinβ”, which is given by a combination of f & λ 2, will be determined with 5-10% accuracy! T + single production at the LHC

11. T – pair production at the LHC SM BG: tt–production! (460 pb) - At the parton level Signal = (bqqA H )×2 1. Large missing momentum is expected in the signal event due to dark matter emissions. 2. Use the hemisphere analysis to reconstruct the top quark [S.M., Nojiri, Nomura (2007)]. 3. Since A H is undetectable, direct masurements of T – & A H are difficult.  M T2 variable! ~ Output ~ Distribution of M T2 ~ Strategy to reduce BG ~ T – decays into t + A H with 100 % branching ratio H1H1 H2H2

12. “MT2 variable” is a powerful tool to determine m T+ and m AH, which is defined by with being the postulated A H mass. Then, the end point of M T2 distribution is ~ Results (Point 2) ~ ~ Cut used in the analysis ~ ~ Discussion ~ T – pair production at the LHC 0100 200

13. End-point of the distribution of M T2 is determined by a combination of m T+, m AH, and the postulate mass. By looking at the position of the end-point with an appropriate value of, it is possible to get information of m AH & m T+ ! We have also checked that there is no contamination of the BG around End-point! ~ Results (Point 2) ~ ~ Conclusion ~ ~ Accuracy M T2 (max) determination ~ Using the distribution of the M T2 with, the upper end-point will be determined with 10-20 GeV accuracy (at Point 2)! T – pair production at the LHC With the use of quadratic function to estimate the end-point, using when. Theoretically, the end-point is 664 GeV.

14. ~ Results ~ ~ Observables ~ Testing the Model Case 1 (Conservative) Case 2 (Optimistic) (pink) T + pair (black) T + single (blue) T - pair (pink) T + pair (black) T + single (blue) T - pair

15. ~ Results ~ ~ Observables ~ Testing the Model Case 1 (Conservative) Case 2 (Optimistic) It is also possible to determine the cosmic abundance of the dark matter (AH) using the LHT data. However, it is also true that, when f is small enough, the determination has a large ambiguities.

16. Summary The top partners T + and T – play an essential role to discover the deviation from the SM at the LHC. It is possible to extract the LHT parameters from the data such as m T+, sinβ, M T2 (max), etc. It is also possible to test the model by looking at the non- trivial relation between the signal, though the method is rather model dependent. Discussion In the cosmological connection, it is important to get information about mass, spin, quantum numbers, interactions of the dark matter (A H ). At the LHC, it may be possible to extract the LHC parameters under the model dependent way, and estimate the cosmic abundance of the dark matter. However, it is very challenging to perform those under the model dependent way.