Table Of ContentUT-ICEPP 99-04
YITP–00–5
January 2000
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n Lepton Energy Asymmetry and Precision SUSY study
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J at Hadron Colliders
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1 Mihoko M. Nojiria, Daisuke Toyab and Tomio Kobayashib
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6 a YITP, Kyoto University, Kyoto, 606-8502, Japan
2 b ICEPP, Universiy of Tokyo, Hongo, Bunkyo, Tokyo, 113-0033, Japan
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p Abstract
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p
We study the distribution of lepton pairs from the second lightest
e
h neutralino decay χ˜0 → ˜ll followed by ˜l → χ˜0l. The distribution of
2 1
v: the ratio of lepton transverse momenta AT shows peak structure if
i m < mmax/2 is required. The peak position Apeak is described by
X ll ∼ ll T
a simple function of the ino and slepton masses in the m ∼ 0 limit.
r ll
a When a moderate m cut is applied, Apeak dependson the χ˜0 velocity
ll T 2
distribution, but the dependence would be corrected by studying the
peak
lepton P distribution. A and the edge of m distributions are
T T ll
used to determine the mass parameters involved in the decay for pa-
rameters of interest to LHC experiments. For some cases the ino and
slepton masses may be determined within 10% by the lepton distribu-
tion only independentof model assumptions. Correct combinations of
Apeak and medge would be identified even if different χ˜0 decay chains
T ll 2
areco-existing. TheanalysiscouldbeextendedtotheTevatronenergy
scale or other cascade decays.
1 Introduction
The Minimal Supersymmetric StandardModel(MSSM) [1]isoneof themost
promising extensions of the Standard Model. It offers a natural solution of
the hierarchy problem, amazing gauge coupling unification, and dark matter
candidates. If Nature chooses low energy supersymmetry (SUSY), sparticles
will be found for sure, as they will be copiously produced at future colliders
such as Large Hadron Collider (LHC) at CERN or TeV scale e+e− linear
colliders (LC) proposed by DESY, KEK, and SLAC. LHC would be a great
discovery machine. Squarks andgluinos with mass less thanafewTeV would
be found unless the decay patterns are non-canonical [2].
On the other hand, the MSSM suffers severe flavor changing neutral cur-
rent (FCNC) constraints if no mass relation is imposed on sfermion mass
parameters [3]. Various proposals have been made for the mechanism to in-
corporateSUSYbreaking in“oursector”, trying tooffernaturalexplanations
of such mass relations [4]. In short, it would be very surprising if sparticles
are found in future collider experiments — The discovery is not the final
goal, but it is the beginning of a new quest for “the mechanism” of SUSY
breaking.
Measurements of soft breaking masses would be an important aspect of
the study of SUSY, because different SUSY breaking mechanisms predict
different sparticle mass patterns. Studies at the Tevatron and LHC would
suffer from substantial uncertainties and backgrounds compared to an LC,
such as luminosity error, combinatorial backgrounds, and unknown initial
energy. While the discovery of sparticles is guaranteed at the LHC, detailed
studies there would be challenging. Therefore it is very interesting to see the
ultimate precision of supersymmetric studies at the LHC.
1
It is possible to determine masses of sparticles from the measurement of
end points of invariant mass distributions [2, 5, 6, 7]. For the minimal super-
gravity (MSUGRA) and gauge mediated (GM) models, there was substantial
success for the parameter points where the decay of the second lightest neu-
tralino to lepton pair χ˜0 → llχ˜0 is detected with substantial statistics. For
2 1
some case, one would be able to not only determine all MSUGRA parame-
ters, but also to measure the masses of some sparticles, using the edges and
end points of invariant mass distributions involving jets and leptons. The
systematic errors of such analyses may be controlled if the acceptance near
the end points and (jet) energy resolution are known.
Detailed studies in this direction have been performed, and we do not
repeat these here. In this paper, we instead study the ratio of lepton P
T
(lepton P asymmetry A ≡ Pl /Pl ; Pl < Pl ) for the decay χ˜0 → ˜ll →
T T T2 T1 T2 T1 2
llχ˜0. The information has been used in previous analyses [5, 8] in the context
1
of global fits of MSUGRA parameters. We show that it is possible to make
a direct connection between the peak structure of the asymmetry Apeak and
T
the ratio of the lepton energies in the neutralino rest frame A by using
E
events with m < mmax/2. We also point out that systematics due to the
ll ll
χ˜0 velocity distribution would be small and reduced further if one includes
2
the P distribution of the hardest lepton in the fit. Using the m end point
T ll
and the peak position of the A distribution, one can at least determine two
T
degrees of freedom of the three parameters involved in the χ˜0 decay, m ,
2 χ˜0
2
m and m . The measurements are based on lepton distributions only and
χ˜0 ˜l
1
free from uncertainty due to jet energy smearing.
The organization of this paper is as follows. In section 2, we analyze the
MSUGRApointswhichwerestudiedin[2,8],wheresquarkandgluinodecays
are the dominant sources of χ˜0. We concentrate on the case where χ˜0 → ˜ll is
2 2
2
open and followed by ˜l → lχ˜0. We find that the A distribution has a peak
1 T
if m < mmax/2 is required. In the limit where m ∼ 0, the peak necessarily
ll ∼ ll ll
agrees with the ratio of lepton energies A0 = E /E in the χ˜0 rest frame for
E l2 l1 2
any value of the χ˜0 velocity. A0 is a simple function of the ino and slepton
2 E
masses. We show that a small m cut promises smaller systematic errors
ll
by comparing distributions for different neutralino velocities. In section 3,
we show Monte Carlo simulations for the MSUGRA points. We find nearly
perfect quantitative agreement between the expectation and MC data for
wide parameter regions. In section 4, we show that systematics dues to
the χ˜0 velocity distribution could be corrected by the hardest lepton’s P
2 T
distribution. We also show expected errors on ino and slepton masses. For
the most optimistic cases where the end point of the lepton invariant mass
distributionofthethreebodydecaym3body isobservedinadditiontotheedge
ll
of the m distribution of the two body decay m2body, we can determine m ,
ll ll χ˜0
2
m and m from those (almost) purely kinematical information. At least
χ˜0 ˜l
1
two degrees of freedom of the three mass parameters would be determined
by our method if mmax ≫ 25 GeV. Section 5 is devoted to discussions.
ll
2 Distribution of lepton energy asymmetry
with m cut
ll
At hadron colliders, the second lightest neutralino χ˜0 would be produced in
2
q˜ and g˜ decays, or in χ˜±χ˜0 pair production. The decay χ˜0 → ˜ll could be a
1 2 2
dominant decay mode if it is open. Followed by ˜l → lχ˜0, the signal consists
1
of a same flavor and opposite sign lepton pair associated with some missing
momentum. Itis oneofthemost promising SUSYsignals athadroncolliders.
The decay process χ˜0 → ˜l±l∓ → χ˜0l±l∓ is described by two body kine-
2 1 1 1 2
matics and very simple. The m distribution of the lepton pair from the χ˜0
ll 2
3
cascade decay is
1 dΓ 1
= . (1)
Γdm2 (mmax)2
ll ll
where
(m2 −m2)(m2 −m2 )
mmax = χ˜02 ˜l ˜l χ˜01 . (2)
ll q m
˜l
The decay distribution is flat in m2. The only physical information we
ll
can get from the m distribution is therefore the value of the end point. It
ll
constrains one combination of the three masses involved in χ˜0 decay, as one
2
can see in Eq.(2).
In the rest frame of the second lightest neutralino, the energy of l is a
1
function of m and m , while E also depends on m and m :
χ˜02 ˜l l2 ll χ˜01
m2 −m2 m2 +m2 −m2
χ˜0 ˜l ll ˜l χ˜0
E = 2 , E = 1 (3)
l1 2m l2 2m
χ˜0 χ˜0
2 2
The angle θ between the two leptons in the χ˜0 rest frame is obtained by
ll 2
solving
m2 = 2E E (1−cosθ ) (4)
ll l1 l2 ll
θ = 0 for m = 0, while θ = π for m = mmax.
ll ll ll
In Eq.(3), we see that E is monochromatic in the χ˜0 rest frame. As
l1 2
a result, the energies of the two lepton are, asymmetric. The ratio of the
transverse momenta of the leptons, which we call the transverse momentum
asymmetry A = Pl /Pl (Pl > Pl ), provides another information on the
T T2 T1 T1 T2
decay kinematics.1 However, Pl and Pl depend on the parent neutralino
T1 T2
momentum, unlike the Lorentz invariant quantity m . The χ˜0 velocity dis-
ll 2
tribution in turn depends on m and m , although the χ˜0 decay distribution
q˜ g˜ 2
in the χ˜0 rest frame itself does not depend on them.
2
1One may also use lepton energy ratio E /E . In general, P distribution reflects
l1 l2 T
sparticle masses much better than energy distribution.
4
This distribution has been used in global fits of MSUGRA parameters;
A distribution “data” for one MSUGRA point generated by Monte Carlo
T
simulator are compared to those of different MSUGRA points[5, 8]. In this
model, all sparticle masses depend on a few universal soft breaking parame-
ters such asm , M, tanβ, etc. When we compare different MSUGRApoints,
0
we therefore change both the parameters of the χ˜0 decay, m , m and m ,
2 χ˜0 χ˜0 ˜l
2 1
and the parameters of χ˜0 momentum distributions m and m at the same
2 q˜ g˜
time. Therefore it was considered to be less important compared to invariant
mass distributions.
However it is possible to make a more direct connection with the first set
of mass parameters m , m and m if a moderate m cut is applied [9].
χ˜0 χ˜0 ˜l ll
2 1
When m is small compared to mmax, the lepton and anti-lepton nearly go
ll ll
in the same direction. Then the lepton momentum asymmetry becomes less
sensitive to the parent neutralino velocity. Even after the smearing due to
the boost of χ˜0, A0 ≡ E /E | still can be extracted from the peak of
2 E 1 2 mll=0
A = Pl /Pl 2;
T T2 T1
m2 −m2
Apeak(or 1/Apeak) ≃ A0 ≡ χ˜02 ˜l , (5)
T T E m2 −m2
˜l χ˜0
1
therefore Apeak constrains the mass parameters involved in χ˜0 decay, just as
T 2
mmax does. Note A0 has monotonous dependence on all parameters while
ll E
the m edge might be accidentally insensitive on m . 3
ll ˜l
In this paper, we study the power of the A distribution in the low m
T ll
region (m < mmax/2) to constrain the kinematics of the cascade decay
ll ll
χ˜0 → ˜ll → χ˜0ll. We chose the points shown in Table 1, but our method
2 1
can be applied in generic MSSM studies. Unlike the common approach to
2The lepton from χ˜0 decay and ˜l decay cannot be distinguished in the experiment. It
2
is understood that A0 means 1/A0 when A0 exceeds one.
E E E
3We thank to M. Drees for pointing out this.
5
m M m m m mmax A0
0 2 χ˜02 ˜lR χ˜01 ll E
IK[8] 100 150 135.5 120.7 65.2 51.8 0.368
point 5[2, 5] 100 300 233.0 157.2 121.5 109.1 0.336
point 5-2 115 300 233.2 167.1 121.6 111.6 0.496
point 5-3 120 300 233.3 170.6 121.6 111.6 0.565
point 5-4 125 300 233.3 174.2 121.6 111.1 0.646
Table 1: MassparametersandrelevantsparticlemassesinGeVforthe points studiedin
this paper. ISAJET[10]isusedto generatesparticlemasses. We alsoshowcorresponding
mmax and A0 in the table.
ll E
immediately gointofullMCsimulations, wefirststudythedecaydistribution
for fixed neutralino velocity (labeled by the boost factor γ and the pseudo-
χ˜0
2
rapidity η ) Γ(A (γ ,η )). 4
χ˜0 T χ˜0 χ˜0
2 2 2
The distribution we observe in experiments is expressed by convoluting
the distribution with the velocity distribution of χ˜0, F(γ,η), as follows;
2
dσ(A ) ≡ dγdη F(γ,η)Γ(A (γ,η)) (6)
T T
Z
the measured distribution is also affected by cuts on E/ , M , etc. However
T eff
it is still useful to know how Γ(A (γ ,η )) depends on the underlying mass
T χ˜0 χ˜0
2 2
parameters and the χ˜0 velocity.
2
In Fig. 1, we show the A distribution with/without invariant mass cuts
T
and Pl cuts. Here we take the IK point and γ = 1.9 , η = 0.2. The
T χ˜0 χ˜0
2 2
distribution is quite easily obtained by numerical integration.
The distribution without upper m cut has some structure around A =
ll T
0.3 (top solid histogram), but it is insignificant. (Here we took the events
with m > 12 GeV because large backgrounds from virtual photons are
ll
expected for m < 12 GeV [11]). With the cut Pl > 10 GeV and the same
ll T
χ˜0 velocity, events with A < 0.1 are hardly accepted, and the distribution
2 T
4The decay distribution Γ depends on γ and η through the Lorentz boost of all mo-
menta, which is implicitly shown as A (γ,η), or Pl(γ,η).
T T
6
Figure 1: A distributionfortheχ˜0 momentum(γ,η)=(1.9,1.2)withoutPl cut(solid),
T 2 T
and for Pl > 10 GeV (dashed). The upper histograms are without upper m cut while
T ll
the lower histograms are distributions with m <25 GeV.
ll
is roughly flat between 0.2 < A < 0.3 (top dashed histogram). When the
T
lepton energy in the χ˜0 rest frame is small, the acceptance efficiency of the
2
events strongly depends on the velocity of χ˜0, because of the Pl cut. The
2 T
A distribution would depend on the cuts and the distribution of χ˜0 velocity
T 2
introducing systematical errors to the analysis.
On the other hand, once a moderate m cut is applied, the decay distri-
ll
bution becomes nearly independent of Pl cuts (bottom histograms). Here
T
we integrate the region between 12 GeV< m < 25 GeV ∼ mmax/2. The
ll ll
distribution has a peak at A ∼ A0 = 0.368. The peak is outside the small
T E
A region affected by the Pl cut. It is also clear from the plot that the shoul-
T T
der of the distribution without m cut comes from the events with m < 25
ll ll
GeV. Note that cosθ = 0.86(0.44) for m = 12(25) GeV in the χ˜0 rest
ll ll 2
frame, therefore the angle between the lepton and the anti-lepton in the pair
7
is rather small with the m cut.
ll
To put it differently, events above mmax/2 are merely backgrounds to the
ll
A0 measurement. This is easily understood when we consider the lepton
E
configuration near the m end point. The two leptons go in exactly opposite
ll
directions and the asymmetry is modified maximally when one of the leptons
goes to the direction of χ˜0 momentum, A ≡ Elab/Elab = A | × 1±β,
2 1 2 E mll=mmllax 1∓β
where A = 0.29 and β = 0.855 for Fig. 1. The lepton energy asymmetry in
E
the laboratory frame can range from nearly 0 to 1 due to the boost.
Figure 2: A distribution under different m cuts. (γ,η)= (1.4, 0.2), and Pl >10 GeV
T ll T
for solid and dotted histogram, while the dashed histogram is for γ =2.3 and η =0.2.
It is worth noting that the A distribution peaks at smaller value of A
T T
as one increases the m cut. In Fig. 2, we show distributions with different
ll
m cuts, 0 GeV< m < 10 GeV (solid narrow), 10 GeV < m < 20 GeV
ll ll ll
(dashed), 20 GeV< m <28.3 GeV (solid wide), for γ = 1.4 and η = 0.2.
ll χ˜0 χ˜0
2 2
The distribution has a sharp peak at a position consistent with A0 for the
E
sample with m < 10 GeV.Apeak = 0.323 for the same neutralino velocity for
ll T
8
10 GeV < m < 20 GeV (dashed histogram). This shift cannot be explained
ll
by A deviation from A0(A = 0.363(0.354)) for m = 10(20)GeV, but it
E E E ll
comes from the smearing of A distribution for finite lepton angle.
T
The dotted histogram shows a distribution for a higher neutralino veloc-
ity γ = 2.3 and η = 0.2 with 10 GeV < m < 20 GeV. The peak position
ll
is shifted very little, Apeak ∼ 0.321, therefore it may still be used to deter-
T
mine the decay kinematics5. On the other hand, the distribution off the peak
depends more on the neutralino velocity. Using the whole distribution intro-
duces a dependence on the χ˜0 momentum distribution, and the fit would be
2
more assumption dependent.
The distribution is more and more smeared out and peaks at a lower A
T
for larger m cuts. The dependence on the χ˜0 momentum is also bigger for
ll 2
the large m sample; Apeak = 0.26 (0.24) for γ = 1.4 (2.3) and 20 GeV <
ll T
m < 28.3GeV.(Onlythedistributionfortheformerisshowninthefugure.)
ll
The distribution is shifted to smaller A reducing the acceptance of the
T
Pl > 10 GeV cut. Some information on the neutralino velocity distribution
T
is therefore necessary to deduce the neutralino decay kinematics from the A
T
distribution while increasing them cut inorder toincrease thestatistics and
ll
removevirtualphotonbackgrounds. Thiswillbediscussed indetailinsection
4.
Note that mmax ∼ 50GeV for IK, therefore requiring m < 25 GeV re-
ll ll
duces thenumber ofevents inthesampleby1/4. Therewardisadistribution
which is less sensitive to Pl cuts and to the χ˜0 velocity distribution, and a
T 2
simple correspondence to the quantity in the χ˜0 rest frame.
2
Finally we demonstrate sensitivity of the A distribution to the slepton
T
5Peaksaredetermined by fitting the distributionnear the peak to a polynomialfitting
function.
9
