Transverse Mass Kink

Yeong Gyun Kim(KAIST)

In collaboration withW.S.Cho, K.Choi, C.B.Park

Introduction

Cambridge mT2 variable

‘Gluino’ mT2 variable

Conclusion

Contents

Started on 10th September 2008. Initial beam commissioning progressed well.

LHC Commissioning with beam

An incident : a helium leak into the LHC tunnel. The LHC is able to restart in 2009.

We are entering exciting period in particle physics.

The LHC is about to explore for the first timethe TeV energy scale.

The origin of EWSB ?The nature of dark matter ?Supersymmetry ?Extra dimensions ?

General features for SUSY at the LHC SUSY production is dominated by gluinos and squarks, unless they are too heavy

Squark and gluino production rates

-determined by strong interaction, and the squark and gluino masses,

-do not depend on the details of model

(Baer etal. 1995) ~50 pb for m_gluino~500 GeV~ 1 pb for m_gluino~1000 GeV

The gluinos and squarks cascade down, generally in several steps, to the final states including multi-jets (and/or leptons) and two invisible LSPs

Characteristic signals of SUSY with Rp

Invisible LSPs

Large Missing Transverse Energy

Decays of squarks and gluinos

Large multiplicity of hadronic jets

and/or Decays of sleptons and gauginos

Isolated leptons

LHC focus weekTokyo 24/6/2008

T. LariINFN Milano

Supersymmetry searches

Discovery potential

5 evidence after 1 fb-1 (including systematics) expected if squarks lighter than 1300 GeV 0-lepton and 1-lepton best modes for mSUGRANo attempt to combine channels yet

~~

preliminary

(Taken from T.Lari’s talk in LHC focus week at IPMU)

Discovery of Supersymmetry

Mass measurements

Measurements of spin, couplings

Precise measurement of SUSY masses

Reconstruction of SUSY theory (SUSY breaking sector)

Weighing Dark Matter with collider

M1: M2: M3 = 1 : 2 : 6 mSUGRA pattern 3.3 : 1 : 9 AMSB pattern etc.

Distinguishing SUSY from other models

The rate of KK-gluon vs. gluino(Datta, Kane,Toharia 2007)

Mass (GeV)

SUSY events always contain two invisible LSPs

No masses can be reconstructed directly

Final state momentum in beam direction is unknown a priori, due to our ignorance of initial partonic center of mass frame

The Mass measurement is Not an easy task at the LHC !

Several approaches (and variants) of mass measurements proposed

Invariant mass Edge method Hinchliffe, Paige, Shapiro, Soderqvist, Yao ; Allanach, Lester, Parker, Webber

… Mass relation method Kawagoe, Nojiri, Polesello ; Cheng, Gunion, Han, Marandellea, McElrath

Transverse mass (MT2 ) kink method Cho, Choi, YGK, Park ; Barr, Lester, Gripaios ; Ross, Serna; Nojiri, Shimizu, Okada, Kawagoe

Basic idea

Identify a particular long decay chain and measure kinematic endpoints of various invariant mass distributions of visible particles

The endpoints are given by functions of SUSY particle masses

Invariant mass edge method

Hinchliffe, Paige, etal.(1997)

If a long enough decay chain is identified, It would be possible to measure sparticle masses in a model independent way

3 step two-body decays

Invariant mass edges

In total, five endpoint measurements

Four invovled sparticle masses can be obtained

for SPS1a point

Mass relation method

Consider the following cascade decay chain (4 step two-body decays)

Kawagoe, Nojiri, Polesello (2004)

Completely solve the kinematics of the cascade decay by using mass shell conditions of the sparticles

One can write five mass shell conditions

which contain 4 unknown d.o.f of LSP momentum

Each event describes a 4-dim. hypersurface in 5-dim. mass space, and the hypersurfcae differs event by event

Many events determine a solution for masses through intersections of hypersurfaces

Measurements of gluino and sbottom masses (assuming that the masses of two neutralinos and slepton are already known) in SPS 1a point

In this case, each event corresponds to a different line in plane

Gluino mass distribution with event pair analysis

Two events are enough to solve the gluino and sbottom masses altogether

Build all possible event pairs (with some conditions)

m_gluino ~ 592 GeV

(300 fb-1)

Kawagoe, Nojiri, Polesello (2004)

Both the Edge method and the Mass relation method rely on a long decay chain to determine sparticle masses

What if we don’t have long enough decay chain but only short one ?

In such case, MT2 variable would be useful to get information on sparticle masses

(Stransverse Mass)Cambridge mT2 variable

Lester, Summers (1999)Barr, Lester, Stephens (2003)

Cambridge mT2(Lester and Summers, 1999)

Massive particles pair produced

Each decays to one visible and one invisible particle.

For example,

For the decay,

( )

( : total MET vector in the event )

However, not knowing the form of the MET vector splitting,the best we can say is that :

with minimization over all possible trial LSP momenta

MT2 distribution for

LHC point 5, with 30 fb-1,

(Lester and Summers, 1999)Endpoint measurement of mT2 distribution determinesthe mother particle mass

( with )

The LSP mass is needed as an input for mT2 calculation.However, it might not be known in advance.

Introduce a trial LSP mass for MT2 calculation.

Now mT2 depends not only on visible momenta but also on the trial LSP mass.

The maximum of mT2 can be considered as a function of the trial LSP mass.

Varying “” …

mT2()

mB mA

Does not just translate …

Shape may also change … more on this later.

(Taken from Lester’s talk in the LHC focus week at IPMU)

Maximum of mT2 as a function of the trial LSP mass

(Lester and Summers, 1999)

The correlation from a numerical calculationcan be expressed by an analytic formulain terms of truesparticle masses

Well described by the above Analytic expression with trueSquark mass and true LSP mass

The maximum of the squark mT2 as a function of

(Cho, Choi, YGK and Park, 2007)

Squark mass and LSP mass are Not determined separately

‘Gluino’ mT2 variable

W.S.Cho, K.Choi, Y.G.Kim, C.B.Park

Ref) PRL 100 (2008) 171801 [arXiv:0709.0288], JHEP 02 (2008) 035 [arXiv:0711.4526].

Gluino mT2 (stransverse mass)

A new observable, which is an application of mT2 variable tothe process

Gluinos are pair produced in proton-proton collision

Each gluino decays into two quarks and one LSP through three body decay (off-shell squark)

or two body cascade decay (on-shell squark)

For each gluino decay, the following transverse mass can be constructed

: Mass and transverse momentum of qq system

: Trial mass and transverse momentum of the LSP

With two such gluino decays in each event, the gluino mT2 is defined as

(minimization over all possible trial LSP momenta)

mqq value for three body gluino decay

Each mother particleproducesone invisible LSPand more than one visible particle

MT2 maximum as a function of trial LSP mass depends on di-quark invariant mass (mqq)

mqq=minimum

mqq=mqq

mqq=maximum

Trial LSP mass

MT2maximum

(Assume mqq (1) = mqq (2), for simplicity )

If the function can be constructed from experimental data, which identify the KINK, one will be able to determine the gluino mass and the LSP mass simultaneously.

A numerical example

and a few TeV masses for sfermions

Experimental feasibility

An example (a point in mAMSB)

with a few TeV sfermion masses (gluino undergoes three body decay)

Wino LSP

We have generated a MC sample of SUSY events by PYTHIA, which corresponds to 300 fb-1

The generated events further processed with PGS detector simulation,which approximates an ATLAS or CMS-like detector

Event selection cuts

At least 4 jets with

Missing transverse energy

Transverse sphericity

No b-jets and no-leptons

GeV

The four leading jets are divided into two groups of dijets by hemisphere analysis

Seeding : The leading jet and the other jet which has the largest with respect to the leading jet are chosen as two ‘seed’ jets for the division

Association : Each of the remaining jets is associated to the seed jet making a smaller opening angle

If this procedure fail to choose two groups of jet pairs, We discarded the event

The gluino mT2 distributionwith the trial LSP mass mx = 90 GeV

Fitting with a linear functionwith a linear background,We get the endpoints

mT2 (max) =

The blue histogram :SM background

as a function of the trial LSP mass for a benchmark point

Fitting the data points with the abovetwo theoretical curves, we obtain

The true values are GeV

The above results DO NOT include systematic uncertainties associated with, for example, fit function, fit range and binning of the histogram etc. to determine the endpoint of mT2 distribution.

SM backgrounds are generated by PYTHIA. It may underestimate the SM backgrounds.

Some Remarks

For case of two body cascade decay

m2qq

max =

Therefore,

,

For three body decayFor two body cascade decay

Barr, Gripaios and Lester (arXiv:0711.4008 [hep-ph])

Instead of jet-paring with hemisphere analysis, we may calculate mT2 for all possible divisions of a given event into two sets, and then minimize mT2

MTGen vs. Hemisphere analysis

M2C (A Variant of ‘gluino’ mT2)

Ross and Serna (arXiv:0712.0943 [hep-ph])

A Variant of ‘gluino’ mT2 with explicit constraint from the endpoint of ‘diquark’ invariant mass (M2C)

Nojiri, Shimizu, Okada and Kawagoe (arXiv:0802.2412)

Even without specifying the decay channel, mT2 variable still shows a kink structure in some cases.

This might help to determine the sparticle masses at the earlystage of the LHC experiment

Inclusive mT2

(Cho,Choi, YGK, Park, arXiv:0804.2185)

Standard Candle for MT2 study

Top quark mT2 distribution with m_nu = 0

With 10 fb-1 ,2 b jets, 2 leptons,Large missing ET

for input mt=170.9 GeVWithout systematic uncertainty

Standard Candle for MT2 study

mT2 max vs. trial neutrino mass Shape of mT2 distribution

The di-leptonic channel will provide a good playground for mT2 excercise

Is there any other usefulness of MT2, after determining new particle masses ?

Yes! M.A.O.S (MT2-Assissted On-Shell)reconstruction of WIMP momentum. PT MT2 solution

PZ On-Shell condition

See W.S.Cho’s TalkThis lunch time !

Conclusion

Maximum of gluino MT2 as a function of trial LSP mass shows a kink structure at true LSP mass from which gluino mass and LSP mass can be determined altogether.

Top-quark MT2 provides an independent way of measuring the top-quark mass and can serve as a Standard Candle for general MT2 analysis.

MAOS reconstruction of WIMP momentum may open a new window for investigating New physics structures

See W.S.Cho’ Talk Today !

The Horror of the Heights

Arther Conan Doyle

(1913)

The Horror of the Heights(2008-)

Nothing new in the TeV scale….

“ There are jungles of the upper air, and there are worse things than tigers which inhabit them. I believe in time they will map these jungles accurately out “

- Armstrong in ‘the Horror of the Height’

The Hope of the Heights (2008-)

SUSY jungle (sps1a)