Pseudo stransverse mass shining on buried new particles

Won Sang Cho (Seoul National University) In collaboration with Jihn E. Kim and Jihun Kim

2009. 11. 11. IPMU Focus Week “QCD in connection with BSM study at LHC”

Contents

• Motivation• Pseudo transverse mass, MπT and pseudo stransverse mass,

MπT2 endpoint• Measuring meaningful endpoints

Amplification of the breakpoint structure and reduction of systematic uncertainties.

• Experimental examplesMulti MπT2 endpoints buried in same signature (2l or 2jet + MET)Measuring mass constraint in heavy jet combinatoric backgrounds.

• Conclusion

Motivation• Pair-produced new particle Y decaying into visible particles, V plus

invisible WIMPs, χ .

• Measuring new particle masses is not easy.

Partonic CM frame ambiguitySeveral missing particlesComplex event topologies

• When the event reconstruction is impossible, measuring kinematic boundaries is a good way to determine new particle masses.

Transverse mass of W-boson / Invariant mass methods / MT2-kink methods .. Observing the endpoints (kinematic boundaries) of the variables is important.

1 2 1 1 2 2+ +P P Y Y etc V V etcχ χ+ → + + → + +

• However, in general, identifying a meaningful endpoint is not a trivial task with many sources of systematic uncertainties.

- Various kinds of the signal endpoint shape- Hard to estimate the backgrounds, especially for jets.

- Jet combinatorics with hard ISR- In many cases, they are irreducible.

- Jet E resolution, Finite total decay widths effects.- …

• Example of endpoint measurement (1) Invariant masses of visible particles in SUSY cascade decay chain Gaussian smeared linear signal + backgrounds function fits wellwith 1~10 GeV systematic uncertainty.

• Example of endpoint measurement (2)

MT2max (~qR~qR q~χ+ q~χ )= RH squark mass, mx known

ATLAS Technical Design Report 2009

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

• In the existence of large systematic uncertainty, extracting the mass parameter using template least chi-square methods or global fit would provide large uncertainty also.

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

• Can we reduce the systematic uncertainty in finding the signal endpoint ?

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

• MT2 - An extension of the transverse mass, MT for the event with two missing particles

• For all events, MT &T2(mχ=mχtrue) ≤ mY

true

2 2 2 2 2 2 2 2 | | | | 2

Independent of the longditudinal momenta.One may use an arbitrary trial WIMP mass to define

(True WIMP mass = )

T V V T T

T

true

M m m m m

m M

m

χ χ

χ

χ

→

= + + + + − ⋅

⇒⇒

T Tp k p k

of Transve Y V(p)rse ma + χ(k)ss

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 2Str of V (p ) + χ (k )) + ansverse ma (V (p ) + χ (k )ss )

MπT and MπT2

• The mass constraint from MT2 : p0[Cho,Choi,Kim,Park : arXiv-0709.0288/arXiv-0711.4526]

0

2 2

= trial WIMP mass , Visible particle mass ~ 0

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

,0 0max 2 2T2M (x) = p + p + x

Y

Y

xm mp

mχ−

= x

• It’s an interesting result of MT2 kinematics because each of the two mother particles is not at rest in LAB frame!

1 2

It is only valid when total transverse momentum of 2 mother particle system is zero. ( ( ) ( ) 0)(!)

T Tp Y p Y+ =

Mπ and MπT

2 2 2 2 2 2 2 2

Defined in with fixed endp

2 |

oint,

| | 2

| T T

any frame

p k p kT V V T TM m m m m M

M

Mχ χ

⇒

→

= + + + + − ⋅ ≤

T

πT π

Transverse mass(M ) & invariant mass(M)

Pseudo

of Y V(p) + χ(

transverse mass(M ) & pseudo invariant mass(M

k

)

)

2 2 2 2 2 2 20 0 0 0

2 2 2 2 2 2 2 00 0 0

2 | | | | 2 ( )

( 2 | | | | 2 ( )

# R( ) is the rotation in transverse plain by anlge, # rapidity difference between t

T T T T

T T T T

p p (R( )p ) p

p p (R( )p ) p

T V V

V V

m m m m

M m m m m Cosh

π χ χ

π χ χ

π

η π

π πη

= + + + + − ⋅ −

≤ = + + + + Δ − ⋅ −

Δ = Defined in with fixed endpoint,

he visible and invisible particle

Endpoint useful only for

s

a T

the rest frame of Y mother particle with P = 0

TM Mπ π⇒

⇒

(*) The way of combininig momenta constituents for MπT is exactly same with the collider variable, MCT [Tovey, arXiv:0802.2879]

If it is possible, then the pseudo transverse mass endpoint will also provide us the P0

How about the new mother particle pair, each with nonzero PT ?

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

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

π = + + + + −

=

• MπT endpoint can be realized using MπT2 (pseudo-stransverse mass) variable defined in the LAB framefor the pair of mother particles with total PT=0 !

1 2

22 1 2

2 2 2 2 2 2

2

(

# s' are v

min[max{ ( ), ( )}]

2 | | | | 2 ,

isible transvT T T T

T

Pseudo - stransverse mass ( ) for

p

k (R( )

p ) k

p

T T T

T V V

T

Y Y

M M Y M Y

M m m m m

M

π π π

π χ

π

χ π

→

≡

≡ + + + + − ⋅

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

erse momenta # min&max over all possible invisible momentum Tk

in the LAB frame

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

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

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

π = + + + + −

=

• Condition for PST endpoint : δT≡|PT ( Y1 + Y2 )| = 0

( )2 ( ) 22

22 (1) ( 2 ) 2

(1) 2 ( 2 ) 2

(1) ( 2 ) (1) ( 2 )

( s ing le visib le particle in each decay chain )

( , , )

4[1 ][ ( ) ](2 )

i v iv T TT

T v vT v v

v v v vT T T T T

F or

M m P A

A m mA m m

A E E P P

π χ χ

χ

= −

+ + −− −

= + ⋅

π TT 2M so lu tion for an even t w ith δ = 0

• Properties of MπT2 (x) distribution

- If mvis~ 0, MπT2 (x) projection of events has amplified endpoint structure with proper value of trial WIMP mass, x originated from Jacobianfactor between MT and MπT

1 1

2

0

max

min

m ax region, J , w hen is sm allmin region, J 1

~ ( ( ), ( ))( ) ( )

( )J= ( )( )

T TT T

x o

x

T

T

d dJ M x M xdM x dM x

M x E PM x

M xM

E P

π ππ

π

σ σσ σ− −

+−

⎧→

→ ∞→⎨

⎩

• In result of very different compression rate, most of the large MT2 events are accumulated in narrow MπT2 endpoint region

Stra

nsve

rse

mas

s, M

T2

• A faint breakpoint(e.g. signal endpoint) with small slope difference, Δa Δa` = J2 Δa by the amplification in MπT2 projection.

With the salient breakpoint structure, the fitting scheme(function/range) can be elaborated, and it reduces the sysmematicuncertainties in extracting the position of the breakpoint.

i

i

2 2 22 2

2 4 2 2

( )

i i

(2

Statistical error fo

statistical error of the i-th bin

(using Least Square me

Error analysis with histogra

thods)r breakpoint

1~ ~

1( )

m : (x ,y )

)

~

(BP

BP BP

stat statBP T BP

Ja J a J

MJπ

σ

σ σδ δ

δ δ

σ

Δ Δ

±=

→

∴

0 0

)2

0

( ) ( )2 2

( )

However, the error propagation factor ~ J for getting p , ( ) ~ ( ) : No advantage for statistical errors.

T

stat statT Tp p

M

M Mπδ δ

i i 2 2

2 22 4 2 4

2 2

(x ,y ) Find the BP with maximal "Coefficient of Explanation"

' 1~

Systematic

~

( ' ~ , similar square sum of residuals

error for BP using Segmented Linear Regression

a

:

fter

BP BPa J a Jε εδ δ

ε ε

→

∑ ∑→

Δ Δ∑ ∑

0 0

( ) ( )2 22

( ) ( )2 2

maximization elaborated fitting functions)

1( ) ~ ( )

Taking into account the error propagation factor, 1( ) ~ ( ) : O(1/J) reduction is expected!

sys sysBP T BP T

sys sysT Tp p

with

M MJ

M MJ

π

π

δ δ

δ δ

∴

• Shining on buried new particle endpoints (1)- 2 signal endpoints from same signature (2lepton+ MET)- 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 δT<20GeV

cuts

LSP

LH/RH squark mass = 722, 618 GeVm (chi10)=400 GeV , with sizable bino and wino components

• Shining on buried new particle endpoints (2)- Amplifying & identifying the correct 2 jet signal endpoint from squark decays to gluino.(~q~q j1 ~g j2 ~g j1 j3j5 χ + j2 j4j6χ ) using >6 jets events.- SUSY spectrum

1036.6 GeVqm =

649.4 GeVgm =

01

98.6 GeVmχ

=

( ) 0.5 pb, ( ) ~ ( ) 3 pbqq gq ggσ σ σ= =

The spectrum is properly separated so that the jets from squark decay and gluino decay are hard to be distinguished by any cuts.

We want to get the mass constraint, p0

2 20p

2q g

q

m mm−

=

by construction of subsystem MπT2 using j1, j2with gluino pair as effective missing particles.

j1, j2

• Event and jet selection scheme for subsystem MπT2

- No particular 2-jet selection scheme.- For signal processes, there exist 15 jet-paring combinations.- Also there exists many background processes with gluino+squark / gluino+gluino production with hard ISR jets / …- We just consider all the hardest 6 jets and constructed all possible subsystem MπT2

(n=1..15) as follows

Effective MET corresponding as if gluino PT sum

Total METSum of the PT of 4 jets, not

selected as 2 squark jet candidate

Sum of the PT of hardest 6 jets

PT of 6jet system

Trial gluino mass

• Histogram of all the subsystem MπT2 and MT2

• Expecting the correct tagged values (<1/15) consistently contribute to a slight slope discontinuity in MT2

• Then, see the breakpoint enhancement in MπT2 projection!

• Trial gluino mass = 1.24 p0 = 389.7GeV J =12.2• Expected endpoint : MπT2 =519.5, MT2 =814.8 GeV• Bin size in selected as best one among 10×(1,2,2.5) GeV• Model fitting function : Gaussian smeared step func / G. S. linear functions• Mean values of measured endpoint & Systematic uncertainty in fitting

(varying ranges, widths, while keeping χ2/n < 2. )

MπT2 exp=519.4±0.2 GeV, MT2

exp=797±20 GeV δMπT2 / δMπT2 ~ 1/J2

/

• Simulation : PYTHIA(~q~q, ~g~g, ~q~g production)(fully showered and hadronized)

PGS 4.0- ΔE/E = 0.6/E in hadronic calorimeter- Jets were reconstructed using cone algorithm, ΔR = 0.5

- We ignored the jet invariant masses in constructing MT2 and MπT2 (It was effective for reducing the jet energy res. effects in identifying the endpoint at the expected position.)

• MπT2 distribution has very impressive endpoint structure enhancement with respect to varying trial WIMP mass,x

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

• It might give us a chance to measure the mass constraints with reduced systematic uncertainties, even in the case with irreducible heavy jet combinatoric backgrounds.

Conclusion