MCT2 spectroscopy

Won Sang Cho (IPMU) In collaboration with Jihn E. Kim, Jihun Kim / M. Nojiri

Ref> arXiv:0912.2354KEK-PH 2010 Workshop

2010 2/19

for new particle mass measurement at the LHC

• BSM models with WIMP DMcandidate

Supersymmetry(R-parity)Universal Extra Dimension (KK-parity)Little Higgs(T-parity)

• Measurement of new particle masses is not an easy task.

Several missing particles ( N ≥ 2)Partonic CM frame ambiguityComplex event topologies

Dark matter production at the LHC

MissingWIMP

P P

01χ

∓

02χ

q

q

±

∓

MissingWIMP

Kinematic boundaries for mass measurement

• IF an event reconstruction is impossible, observing KINEMATIC BOUNDARY is a good way to measure new particle masses.

• Kinematic boundary of what ??(In general) Kinematic boundary = Surface of the

allowed phase space for our event process.

(*) Collider data analysis = Matching with (hypothetic) probability distribution function

2

( , , , ... : ) 1 | ( , , , ... : ) | ( ) ( , )i j

i j

P a b c d p

dx dx f f M ij a b c d k d k W k pφσ

= →∫

Phase space

Detector response

Dynamics for BG/New Physics

Practically, we use several 1-D observables which can be (mostly & only) sensitive to the change of physical parameters of our interest.

Good examples for mass parameter : 1) Invariant mass for single mother particle (Peak) 2) Transverse mass, MT (Endpoint)3) Invariant masses of visible particles in long

cascade decay chain (Endpoint)4) Stransverse mass, MT2 (Endpoint)

Useful for Non-reconstruct-able events !

• Precise measurement of these endpoints can provide us good information about the new physics particles !

Precise measurement of the endpoints

However, in general, identifying a meaningful endpoint is not a trivial task with many sources of systematic(model) uncertainties

- Various kinds of the signal distribution shape- Jet combinatorics with complex new event topololgy

(+hard ISR/FSR)- Hard to estimate the backgrounds, especially for jets.- In many cases, they are irreducible.

- Jet E resolution, Finite total decay widths effects.

• In the existence of large systematic uncertainty, extracting the mass parameter using global distribution fit would provide large uncertainty also.

Because of our ignorance about the exact model for signal and backgrounds, describing some distributions!

Global shape uncertainty in mass/endpoint estimation :

Ex) Gluino decay chain in SPS1a point, or in the other variational points.

The bulk distribution and endpoint structures changes a lot with feet or tails.

• Global fitting has large uncertainty..

• Local fitting near the region of threshold/endpoint ?

• Anyway, even with the bulk distribution with large uncertainty, one can always define the signal endpoint as a breakpoint(BP) in the distribution with proper resolution/width effect.

• Actually, there are many examples in which one tries to extract the endpoint by locally effective linear model functions near some breakpoints .

• Example of local endpoint measurement with simplified model function (1) – Invariant masses of visible particles in SUSY cascade decay chain – Gaussian smeared linear signal + backgrounds function fits well

with 1~10 GeV systematic uncertainty.

• Example of endpoint measurement with simplified model function (2) MT2

max (~qR~qR q~χ+ q~χ ) = RH squark mass w/ mχ known

ATLAS Technical Design Report 2009

MT2 endpoint measurement usually has O(1~10%) systematic uncertainty in fitting process (fitting function, cuts, range …)

• Can we reduce the systematic uncertainty in finding the meaningful signal endpoint(SBP) by local fitting?

What is the most reliable range for local fitting ??

• At least, it’s possible for MT2 endpoint measurement.

• The point is to transform the original distribution, by which the SBP is accentuated greatly!

• MT2 - An extension of the transverse mass, MT for the event with two missing particles [Lester,Summers,Barr, Stephens]

• For all events, MT &T2( mχ= mχ[true] ) ≤ mY[true]

1 22

2 1 2

(

min[max{ ( ), ( )}]over all possible WIMP transverse momenta

T T T

Y Y

M M Y M YMinimization

→

=⇒

1 1 1 1 2 2 2 2V (p ) + χ (k )) + (V (p ) + χ (k ))

MCT and MCT2

• The mass constraint from MT2 : p0 [Cho,Choi,Kim,Park]

0

2 2

= trial WIMP mass , Visible particle mass ~ 0

, the momentum of v & in the rest frame of Y2

Y

Y

xm mp

mχ−

=

0 0max 2 2T2

x

M (x) = p + p + x ,

1 2

22 1 2

2 2 2 2

2

2 2

(

m

= visible transverse momenta

in[max{ ( ), ( )}]

2 | | | | 2 ,T T T

T

T

Constransverse mass

p k

( ) for

p

p k

CT CT CT

CT V

T

V

C

Y Y

M M Y M

M m m

M

Y

m mχ χ

→

≡

≡ ++ + + + ⋅

1 1 1 1 2 2 2 2V (p ) + χ (k )) + (V (p ) + χ (k )

n

)

ii min&max over all possible invisible missing momentum T

[Cho, Kim, Kim / ArXiv:0912.2354]

k the LAB frame

i

max 2 2 2 2 2 2 2 22 ( ) 2 | | | | | | trial WIMP mass

00 0p p pCT V VM x m x m xx

= + + + + −

=

• Then, the endpoint behavior in trial WIMP mass, x, also provides the P0

• Condition for MCT2 endpoint : |PT ( Y1 + Y2 )| = 0

• IF mvis~ 0, MCT2 (x) projection can have significantly amplified endpoint structure (x = Trial missing ptl mass)

• Jmax(x) ⇒ ∞ as x⇒ 0

• One can control Jmax(x) by choosing proper value of x

Jmax(x=0.5p0)=106.

Jmax(x=p0)=19.

Jmax(x=2p0)=5.4

Jmax(x=5p0)=2.

Jmax(x=103p0)=1.

This features of MCT is also inherited by MCT2as long as δT≡|PT ( Y1 + Y2 )| = 0

• The endpoint amplfication of MCT is also inherited by MCT2 if

|PT ( Y1 + Y2 )| = 0

• A faint BP(e.g. signal endpoint) with small slope difference amplified by large Jacobian factor :

Δa ⇒ Δa` = Jmax2(x) Δa

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 !

• Example : LH or RH slepton pair production 2l + 2chi10

Parton level• 2 signal endpoints

with same signature (2 lepton+ MET)

• Precision of mass difference measurement can be significantly enhancedwith less systematic fitting errors

MCT2 = Mass difference resolver, hidden in complex inclusive signatures [work in progress with M. Nojiri]

• The mass differences can be described by several p0 values ⇒ From the accentuated BPs of inclusive MCT2

• P0 ≡ maximal absolute momentum of daughter particles in the rest frame of mother particles

• Ex) 2body decays : (Y ⇒ v+X) p0=(mY

2-mX2)/(2mY)

3body decays : (Y ⇒ v v+X) p0=(mY-mX)/2

• Then MCT2 amplification may resolve the several P0 scales, which can come from any identical mother particle pairs in inclusive signature.

Inclusive subsystem-MCT2 for hard 2N-jets + MET events [work in progress]

Simple Example : 0 01 1( ) ( ) ( ) ( )gg q q q q qq qqχ χ→ + + + → +

02 1Inclusive subsystem- ( 4 ~ 320 )TM p GeVχ =

012Inclusive subsystem- ( 4 ~ 320 )CTM p GeVχ =

• 2 mass differences to be resolved :

0 2 21

0 2 22

( ) / 2 =79 GeV

( ) / 2 311g q g

q q

p m m m

p m m m GeVχ

= −

= − = 0T2 1M Endpoint by 408.8 ??p GeV=

• 4 jets ⇒ 6 combinatoric jet pairs existfor Inclusive SS-MCT2

• Emergence of accentuated MCT2BPs might provide rich mass inform.

0T2 2M Endpoint by 757.5 ??p GeV=

0CT2 1M Endpoint by 376.3p GeV=

0CT2 2M Endpoint by 431p GeV=

• MCT2 distribution has very impressive endpoint structure enhancement with respect to varying trial WIMP mass,x

• Small slope discontinuities are amplified by J(x)2, accentuating the breakpoint structures clearly.

• It might give us a good chance to extract the various mass differences hidden in complex inclusive signatures withheavy systematic uncertainties with irreducibleheavy jet combinatoric backgrounds.

Conclusion