1. in mass measurements at the LHC Recent developments Yeong Gyun Kim
(KAIST)
YongPyong APCTP Workshop (Feb , 2008)

2. Contents SUSY at the LHC Edge method Mass relation method
MT2 kink method

3. LHC (the Large Hadron Collider) : 2008 ~
a proton + proton collider at 14 TeV c.m energy in the 26.6 km tunnel
1033 cm-2 s-1 ~ 10 fb-1/yr (low luminosity)
1034 cm-2 s-1 ~ 100 fb-1/yr (high luminosity)

4. 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

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

6. Characteristic signals of SUSY with Rp
Invisible LSPs
 Missing Transverse Energy
Decays of squarks and gluinos
 Large multiplicity of hadronic jets
and/or
Decays of sleptons and gauginos
 Isolated leptons

7. Effective mass
(Multi-jet plus missing ET signature is generic in most of R parity conserving models)
An excess of events with large Meff could be an initial discovery of “supersymmetry” (Model with new colored particles decaying into neutral stable particle)
A mSUGRA point with
m0=100 GeV, m1/2=300 GeV ,
A0=300 GeV, tanb=2.1
Signal (open circles)
SM background (histogram)
With 10 fb-1
(Hinchliffe etal. 1997)

8. LHC (5-sigma) Reach for mSUGRA
The LHC reach in
the jet plus MET channel
extends to squark and gluino
masses larger than 2 TeV
with 300 fb-1
~1.5 TeV with 1 fb-1
(one month at low luminosity)
~1 TeV with 100 pb-1
(a few days at low luminosity)

9. Measurement of SUSY masses
Precise measurement of SUSY particle masses
 Reconstruction of the SUSY theory
(SUSY breaking mechanism)
The mass measurement is not an easy task at LHC !
Final state momentum in beam direction
is unknown a priori
( parton center-of-mass energy is uncertain
at hadron colliders )
SUSY events always contain two invisible LSPs
 No masses can be reconstructed directly

10. 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

11. The Edge method Hinchliffe, Paige, etal. (1997) Basic idea
 Identify a particular long decay chain and measure
kinematic endpoints in distributions of invariant
masses of visible particles
 The endpoints are given by functions of SUSY
particle masses

12. When a long cascade decay chain can be identified,
various combinations of masses can be determined
in a model independent way
Five endpoint measurements
Four unknown masses

13. The SPS 1a benchmark point
A favourable scenario both for LHC and ILC
M_gluino = 595 GeV
M_qL= 534 GeV, M_uR = 522 GeV
M_N2 = 177 GeV, M_N1 = 96 GeV
M_eR = 143 GeV, M_eL= 202 GeV
(M_eR < M_N2)
[LHC/LC Study Group]

14. The Cut used to isolate the decay chain
[LHC/LC Study Group]
SM background is suppressed requiring
- two leptons and large MET (QCD processes)
- high hadronic activity and MET (Z/W+jets, ZZ/ZW/WW)
- subtraction of OSOF events (t tbar)

15. Dilepton invariant mass distribution after the cut
SUSY background mostly from uncorrelated chargino decays
Removed by Opposite-Sign Opposite Flavor (OSOF) subtraction
~ 77 GeV

16. Other invariant mass edges
[LHC/LC Study Group]
From five endpoint
measurements
Four invovled sparticle
masses can be obtained

17. Gluino mass measurement
Add a quark to an identified squark decay chain
Consider b squarks to reduce combinatorial background
(b-jet can be tagged)
[LHC/LC Study Group]
The momentum
near dilepton mass endpoint
can be approximated by
for SPS1a point

18. Gluino Mass vs. [LHC/LC Study Group] assuming nominal values
for neutralino masses

19. Mass relation method Consider the following cascade decay chain
Kawagoe, Nojiri, Polesello (2004)
Consider the following cascade decay chain
(4 two-body decays)
Completely solve the kinematics of the cascade decay
by using mass shell conditions of the sparticles

20. 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

21. Measurements of gluino and sbottom masses
(assuming that the masses of two neutralinos and
slepton are already known) in SPS 1a point
Kawagoe, Nojiri, Polesello (2004)
In this case, each event corresponds to
a different line in plane
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)
Gluino mass distribution with event pair analysis

22. What if we don’t have long enough decay chain
Both of 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

23. Cambridge mT2 variable (Stransverse Mass) Lester, Summers (1999)
Barr, Lester, Stephens (2003)

24. Cambridge mT2 (Lester and Summers, 1999)
Massive particles pair produced
Each decays to one visible
and one invisible particle.
For example,
For the decay, ( )

25. However, not knowing the form of the MET vector splitting, (
: 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

26. MT2 distribution for LHC point 5, with 30 fb-1,
The mother particle mass
can be determined by
endpoint measurement of
mT2 distribution
(Lester and Summers, 1999)
( with )

27. Yes ! The LSP mass is needed as an input for mT2 calculation
But it might not be known in advance
mT2 depends on a trial LSP mass
Maximum of mT2 as a function of the trial LSP mass
(Lester and Summers, 1999)
Can the correlation
be expressed by
an analytic formula
in terms of true
sparticle masses ?
Yes !

28. Right handed squark mass from the mT2
m_qR ~ 520 GeV, mLSP ~96 GeV
SPS1a point, with 30 fb-1
(LHC/ILC Study Group: hep-ph/ )

29. Unconstrained minimum of mT
We have global minimum of mT, which is given by
when
Trial LSP momentum

30. Solution of mT2 (the balanced solution)
(for no ISR)
with
Trial LSP momenta
mT2 : the minimum of mT(1) subject to the two constraints
mT(1) = mT(2) , and pTX(1) +pTX(2) = pTmiss

31. The balanced solution of squark mT2 in terms of visible momenta
(Lester and Barr )
with
(mq = 0 )

32. In order to get the expression for mT2max ,
We only have to consider the case where
two mother particles are at rest and all decay products
are on the transverse plane w.r.t proton beam direction,
for no ISR
(Cho, Choi, Kim and Park, 2007)
In the rest frame of squark, the quark momenta
if both quark momenta are along the direction of the transverse plane

33. The maximum of the squark mT2 (occurs at )
(Cho, Choi, Kim and Park, )
Well described by the above
Analytic expression with true
Squark mass and true LSP mass
Squark and LSP masses are
Not determined separately

34. Some remarks on the effect of squark boost
In general, squarks are produced with non-zero pT
The mT2 solution is invariant under
back-to-back transverse boost of mother squarks
(all visible momenta are on the transverse plane)

35. ‘Gluino’ mT2 variable W.S.Cho, K.Choi, C.B.Park In collaboration with
Ref) arXiv: , arXiv:

36. Gluino mT2 (stransverse mass)
A new observable, which is an application of mT2 variable to
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)

37. the following transverse mass can be constructed
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)

38. From the definition of the gluino mT2
Therefore, if the LSP mass is known, one can determine
the gluino mass from the endpoint measurement of the gluino
mT2 distribution.
However, the LSP mass might not be known in advance
and then, can be considered as a function of
the trial LSP mass , satisfying

39. Each mother particle
produces
one invisible LSP
and more than one
visible particles
Possible mqq values
for three body decays
of the gluino :

40. Consider simple cases where
two diquark invariant mass
are equal to each other
In the frame of gluinos at rest,
the momenta of diquark system
When two sets of decay products are parallel to each other ( ) on transverse plane
Gluino mT2

41. The gluino mT2 has a very interesting property( )
 The maximum of mT2 occurs when mqq= mqq (max)
 The maximum of mT2 occurs when mqq= 0
 mT2 = m_gluino for all mqq
This result implies that
( This conclusion holds also for more general cases where mqq1 is different from mqq2 )

43. mT2(max) = mqq(max) + mx For the red-line momentum configurations,
unbalanced solution of mT2 appears
In some momentum configuration ,
unconstrained minimum of one mT(2) is larger than
the corresponding other mT(1)
Then, mT2 is given by the unconstrained minimum of mT(2)
mT2(max) = mqq(max) + mx

44. If the function can be constructed from
experimental data, which identify the crossing point,
one will be able to determine the gluino mass and
the LSP mass simultaneously.
A numerical example
and a few TeV masses for sfermions

45. 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,
which corresponds to 300 fb-1 by PYTHIA
The generated events further processed with PGS detector simulation,
which approximates an ATLAS or CMS-like detector

46. Experimental selection cuts
At least 4 jets with
Missing transverse energy
Transverse sphericity
No b-jets and no-leptons
GeV

47. The four leading jets are divided into two groups of dijets by hemisphere method
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

48. The gluino mT2 distribution with the trial LSP mass mx = 90 GeV
Fitting with a linear function
with a linear background,
We get the endpoints
mT2 (max) =
The blue histogram :
SM background

49. as a function of the trial LSP mass for the benchmark point
Fitting the data points with the above
two theoretical curves, we obtain
GeV
The true values are
(No systematic error included)

50. Possible improvements of kink method
Barr, Gripaios and Lester (arXiv: [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)

51. Nojiri, Shimizu, Okada and Kawagoe (arXiv:0802.4008 [hep-ph])
proposed an inclusive study of mT2 variables using
a hemisphere method.
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 early
stage of the LHC experiment

52. Conclusion
Several approaches for determining SUSY particle masses at the LHC have been suggested for decade
The techniques are also applicable to any class of hadronic collider events with two missing particles
Determination of new particle masses using only kinematic information will be a crucial step to understand the nature of new physics model

53. BACKUP

54. SUSY at LHC

55. SUSY Mass Scale The peak of the Meff mass distribution provides
a good first estimate of the SUSY mass scale
mSUGRA models
Meff peak ~ 2 MSUSY
Typical measurement error
~ 20 % for mSUGRA model
for 10 fb-1
The spread might be larger
for a more general models
(Hinchliffe etal. 1997)

56. Cos(theta) distribution

57. Gluino mT2 distributions for AMSB bechmark point
True gluino mass = 780 GeV,
True LSP mass = 98 GeV

58. For ttbar events

59. Ross and Serna (arXiv:0712.0943 [hep-ph])
A Variant of ‘gluino’ mT2 with explicit constraint from
the endpoint of ‘diquark’ invariant mass (M2C)