New particle mass spectrometry at the LHC : Resolving combinatoric - PowerPoint PPT Presentation

New particle mass spectrometry at the LHC : Resolving combinatoric endpoints Won-Sang Cho (IPMU) 2010. 05. 10 PHENO 2010

Resolving every meaningful endpoints hidden in inclusive signature (1) Amplification of the endpoint structure Ref: arXiv0912.2354 [ W.Cho, J.E. Kim, J. Kim] (2) General combinatoric endpoints [Work in progress with M. M. Nojiri] � New particle mass spectrometry at the LHC

Amplification of M T2 endpoints • M CT2 ?? [ref) arXiv:0912.2354, Cho, Kim, Kim] for M 2 CT → V(p)+ χ (k) + V(p)+ χ (k) Y Y ≡ min[max{ ( ), ( )}] 2 M M Y M Y 2 1 2 CT CT CT ≡ + + + + + ⋅ 2 2 2 2 2 2 2 | p | | k | 2 p k , M m m m m χ χ T T T T CT V V i p = visible transverse momenta in the LAB frame T i min&max over a ll possi bl e invisible missing momentum k T

i Endpoint structures are amplified. i for accentuating Good several break points buried in several backgrounds. • Amplification factor is controlled by test mass

A ccentuating the buried break points in N -jet events � � → � � → χ χ i qq gq gq qqq qqq Endpoint from gluino decays Endpoint from squark decay → Systematic errors for physical constraints reduced by O(1/J ) in local fitting of break points. max J : Jacobian factor near the endpoint region max

This enhances our observability for several endpoints. (Previously) Impose hard cut, and remove the BG events near the endpoint. (Now) Well, moderate cut & irreducible BGs are okay, as long as there exist dim BPs from signal endpoints. We can magnify it ! Then, what endpoints are to be amplified by M CT2 projection ???

Complex new physics event topology at the LHC � δ : from ISR or Decays P P T A 1 α 1 B α β , =Visible or Invisible 1 β i j 1 A SM particles α i B i j β j A /B α A i j N B N β M =Intermediate new particles M Missing new physics particles � − δ × : System of interest with N M decay steps T

Decay chain crossing two particle endpoint functions as basic building blocks for mass reconstruction in N × M decay chains. Along the decay lines CM Energy is bounded above by decayed mother particles in a decay chain α α β β ≤ max ( , / , ) M M i j m k => M ,M ,M ,M .... A A A B B 1 α i j k m 1 B Crossing the decay lines 1 β 1 A CM Energy is not bounded in a event by event basis. α i B i α β max ( , ) (??)=> M ,M ,M ,M j β f i j A A B B i i+1 j j+1 j A ~ , , .... f M M M α N 2 2 B T CT CT N β M ~ i ( : i dot product ) P P Euclidean α β M i j Why two ? 1. Smallest combinatorics in NxM visibles = − 2. No internal combinatorics for f Combinatoric M 2 CT 3. Single massless SM particle in each decay chains => Simple and Good for endpoint amplification for C-M CT2

Combinatoric - M ( α - β ) [work in progress] CT2 i j Let's take a system of interest with transverse momentum, - δ . T → δ + α α α β β β pp ( ) ( ,... ... / ... ... /New physics missing PTLs) 1 i N 1 j N T → δ + α β / ( ) ( + (ass umed o t be) missing particles(E ')) i j T T (i=1..N, j=1..M) − α β ≡ 2 ( - ) min[m ax{ ( ), ( )}] C M M A M B 2 i j CT CT i CT j ≡ χ + χ + + ⋅ 2 2 2 2 | p | | k | 2 p k , M T T T T CT i p = visible transverse momenta T χ ≠ i = universal test mass for A & B ( in general M M ) i+1 j+ 1 A B i+1 j+1 α β = / i k ( ) + k ( ) = -( α + β ) - δ E ' T T iT jT T T i min&max over all possible invisible missing momentum k T

C-M CT2 ( α i - β j ) has well-defined (amplified) endpoint value for general non-zero δ T and univeral test mass, χ Universal test mass, χ = Controlling parameter of the amplification Utilizable for complex event topologies with additional missing particles Totally asymmetric system − − ≥ If ( 1)( 1) 3, all the masses can be measured M N only with C-M CT2 Totally symmetric case, N=M & intermediate particles with same masses. M ≥ If 2, all of the M+1 masses can be determined with C-M . CT2 The additional vertical constraints (M /M ) can be helpful, also. αα ββ

→ + + + → χ + χ � � � � � 0 � 0 Simple Example : ( ) ( ) ( ) ( ) gg q q q q qq qq 1 1 4jets � 6 possible pairs of jets / 3 Independent P P decay crossing pairs exist 1) α (1)- β (1) 2) α (1)- β (2)/ α (2)- β (1) α β 1 3) α (2)- β (2) 1 → χ + χ � � � 0 � 0 ( ) ( ) gq qq q 1 1 β α 3 jets � 3 pairs / 2 2 2 Independent decay crossing pairs exist Mass 2) α (1)- β (2)/ α (2)- β (1) scale 3) α (2)- β (2) MET : 2 WIMPs missing

Partonic level results : C-M T2 C-M Endpoint by DC pair-(1) T2 C-M Endpoint by DC pair-(2) T2 C-M Endpoint by DC pair-(3) T2 Combinatoric- M 2 T

Partonic level results : C-M CT2 C-M Endpoint by DC pair-(1) T2 C-M Endpoint by DC pair-(2) T2 C-M Endpoint by DC pair-(3) T2 Combinatoric- Combinatoric- M M 2 2 CT CT

Conclusion M CT2 : impressive endpoint structure • enhancement. Small slope discontinuities are amplified by J(x) 2 , • accentuating the breakpoint structures clearly. Extract the various constraints hidden in complex inclusive • signatures Combinatoric-M CT2 has well-defined endpoints and • power to accentuate them. With C-M CT2, ordinary combinatoric background is not only • background anymore. It provides mass information to be analyzed. Thus, C-M CT2 can be a useful tool for every new particle mass • measurement in generic complex event topologies.

Back up slides

• IF m vis ~ 0, M CT2 (x) projection can have significantly amplified endpoint structure (x = Trial missing ptl mass) • J max (x) ⇒ ∞ as x ⇒ 0 • One can control J max (x) by choosing proper value of x

A faint BP(e.g. signal endpoint) with small slope difference • amplified by large Jacobian factor : Δ a ⇒ Δ a` = J max 2 (x) Δ a With the accentuated BP structure, the fitting scheme (function/range) can be elaborated, and it can significantly reduces the systematic uncertainties in extracting the position of the BPs ! σ 2 δ 2 ~ Δ 2 BP a