The existence of M ΔT2 endpoint s and shining buried new particles

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1 he existence of M Δ2 endpoint s and shining buried new particles Won Sang Cho (SNU) KIAS-KAIS-YIP Joint Workshop on DM, LHC and Cosmology

2 Contents Introduction ransverse mass and pseudo transverse mass, M Δ he existence of pseudo stransverse mass (M Δ2 ) endpoint Properties and experimental feasibility Measuring M Δ2 endpoints Observing multi M Δ2 endpoints buried in same signature (2l or 2jet + ME) Conclusion

3 Event topology Pair-produced new particle Y decaying into visible particles, V plus an invisible WIMP, χ : PI ( ) + PJ ( ) Y+ Y V+ χ + V+ χ

4 Measuring the new particle masses is not easy. Partonic CM frame ambiguity (at HC) Missing information from several missing particles (at least, 2 in several NP models with DM) Complex event topologies Several methods Using Invariant mass edges, On-shell relations, M 2 - endpoints Hybrids with states of art will be the best. Using the M 2 - endpoint has strong power for mass measurement with short decay chains

5 Possibility of mass measurement in various new event topology 2 (Unknown new masses) -1 (Constraint) = 1 (more need) What is the constraint by measuring M 2 -endpoints?? ( = number of visible particles in each decay chain ) Kong,Park, Machev 09

6 M 2 - the extension of the transverse mass, M for the event with two missing particles ransve rse ma ss of Y V(p) + χ(k) M = m + m + 2 m + p m + k 2p k V χ V χ Independent of the longditudinal momenta. One may use an arbitrary trial WIMP mass m to define M true (rue WIMP mass = m ) χ χ Stransverse ma ss of Y Y ( V (p )+ χ (k )) + (V (p ) + χ (k )) 1 2 M = min[max{ M ( Y ), M ( Y )}] Minimization over all possible WIMP transverse momenta For all events, M &2 (m χ =m χ true ) m Y true

7 In the n=1 case, the constraint from M 2 - endpoint is p 0 [C.C.K.P.] 0 0 M (x) = p + p + x x p = trial WIMP mass 0 max = m 2 2 Y x 2m m Y,, the momentum of v & χ in the rest frame of Y It s an interesting result of M 2 kinematics because each of the two mother particles is not at rest in LAB frame! #Caution It is only when total transverse momentum of 2 mother particle system is zero. ( p( Y1) + p( Y2) = 0) It is known that if (Y1Y2) system has non zero P, then one can also get the boosted momenta as nontrivial constraints [B.Gripaios, A.Barr,C.Lester], providing the possibility to get the 2 unknown masses even with most simple 2-body kinematics (Practically hard to observe as lack of statistics of the event with a fixed 'highest boost'.)

8 M 2 max for n=1, m x known ALAS echnical Design Report 2009 M 2 -endpoint measurement usually has O(1~10%) systematic error from fitting process (fitting function, cuts, range ).

9 hen P 0 from other observable?

10 M and M Δ (p) ransverse mass(m ) & invariant mass(m) of Y V(p)+ χ( k) M = m + m + 2 m + p m + k 2p k M V χ V χ Defined in any frame with fixed M endpoint, M. Pseudo transverse mass ( M Δ ) & pseudo invariant mass( M M = m + m + 2 m + p m + p 2 (R(Δ)p ) ( ) p Δ V χ V χ M ( = m + m + 2 m + p m + p CoshΔ 2 (R(Δ)p ) ( ) p Δ V χ V χ η # R( Δ) is the rotation in transverse plain by anlge, Δ, # Δ η = rapidity difference between the visible and invisible particles Defined in the rest frame of Y with fixed M endpoint, M Endpoint useful only for a mother particle with P = 0 Δ Δ ) Δ

11 If it is possible, then the pseudo-transverse mass endpoint measurement will also provide us the P 0. M Δ ( x) = m + x + 2 m + p x + p + CosΔ p max V V x = trial WIMP mass How about the new mother particle pair, each with nonzero P?

12 M Δ endpoint can be visible using M Δ2 (pseudostransverse mass) variable defined in the LAB frame, for the pair of mother particles with total P =0! Def > Pseudo - stransverse mass ( M Y Y 1 2 Δ 2 ) for ( V(p )+χ (k )) + (V (p ) + χ (k )) M min[max{ M ( Y ), M ( Y )}] 2 Δ 2 Δ 1 Δ 2 M m + m + 2 m + p m + k 2 (R(Δ)p ) k, Δ V χ V χ # p s' are visible transverse momenta in the LAB frame # min&max over all possible invisible momentum k

13 hen, the endpoint behavior in trial WIMP mass, x, also provides the P 0 M Δ 2 ( x) = m + x + 2 m + p x + p + CosΔ p x = trial WIMP mass max V V his realization results from the same reason of M 2 max (x) being described by p 0, as if each of the two mothers is transversely at rest in LAB frame. Condition for PS endpoint : δ P ( Y 1 + Y 2 ) = 0

14 Disadvantage of using PS (or P) endpoint - Weak for nonzero δ (from ISR..) effect even with correct WIMP mass input. ( always need δ upper bound cut ) - he nonzero δ effect on the endpoint : he shifted endpoint of M max max 1 π π 2 π ( x) by δ ΔM ( x)/ M ( x) ~ f ( xˆ ) α cos φ, (small α) π 1 cos φα ( xˆ 1) 2, 0 ( xˆ 1) where xˆ = x/ po, α= δ / MY, and φ = azimuthal angle of visible particle in the mother particle's rest frame. However, even with nonzero delta, the multi peak differences can be preserved within the more suppressed shift!!

15 Advantage of using PS endpoint -If Δ=π and m vis ~ 0, then M π2 (x) projection of the events has extremely enhanced endpoint structure with proper value of trial WIMP mass(x), originated from Jacobian factor between M and M π 1 dσ 1 dσ σ ~ J ( M π ( x), M π ( x)) σ dm π ( x) dm ( x) hen, M π ( x) 2 E x + Po 2 M max region, ( ) ( ) ~ finite M ( x) E x P0 J, M π ( x) M min region, 0 ( small x ) M ( x) such that J max / J min for small x ignoring the visible mass.

16 Stransverse mass, M 2 In result of very different compression rate, most of the large M 2 events are accumulated in narrow M π2 endpoint region

17 his sharp endpoint (effective triangular fit) can be rather free from the systematic errors of fitting ranges, cuts, and functions, as it shrink the higher range of M 2 distribution into very narrow region (depending on x) he ranges of M 2 and M π2 distribution in varying trial WIMP mass M 2 (M WIMP ) - M WIMP M π2 (M WIMP ) - M WIMP rial M WIMP

18 Uprise of buried new particle endpoints - May be possible, depending on the mother particles production rate and branching ratio, giving same signature (2lepton/jet + ME) - Measurement of mass differences precisely with small systematic fit errors - Example (1) LH or RH slepton pair production 2l + 2chi10 Parton level Detector level with δ <20GeV cuts

19 Example (2) LH/RH squark mass measurement using 2 jet + ME signature LH/RH squark mass = 722, 618 GeV m (chi10)=400 GeV, with sizable bino and wino components LSP Uprise of buried endpoint

20 CUs used : 1) Njet 2 2) No b-jets, No leptons 3) δ = P (Y 1 )+P (Y 2 ) < 20 GeV 4) P of 2 nd hardest jet > 80 GeV

21 Conclusion Pseudo-stransverse mass(ps) distribution has very impressive endpoint structure enhancement with respect to varying trial WIMP mass. It might give us a chance to measure the p 0 constraint with reduced systematic uncertainties from endpoint fitting. In addition, the several buried endpoints can be uprised in the PS projection, enabling us to measure the mass differences between the different mother particles, buried in same signature (2l(2jet) + ME) (he multi PS endpoint differences are rather free from the δ effect) Optimal value of trial WIMP mass with good resolution power, should be studied.