Stop-lepton associated production at hadron colliders

Abstract

At hadron colliders, the search for R-parity violating supersymmetry can probe scalar masses beyond what is covered by pair production processes. We evaluate the next-to-leading order SUSY-QCD corrections to the associated stop or sbottom production with a lepton through R-parity violating interactions. We show that higher order corrections render the theoretical predictions more stable with respect to variations of the renormalization and factorization scales and that the total cross section is enhanced by a factor up to 70% at the Tevatron and 50% at the LHC. We investigate in detail how the heavy supersymmetric states decouple from the next-to-leading order process, which gives rise to a theory with an additional scalar leptoquark. In this scenario the inclusion of higher order QCD corrections increases the Tevatron reach on leptoquark masses by up to 40 GeV and the LHC reach by up to 200 GeV.

Full text

Page 1

arXiv:hep-ph/0211441v1 28 Nov 2002
MADPH-02-1309
CERN-TH/2002-344
IFT-P.093/2002
November 2002
Stop Lepton Associated Production at Hadron Colliders
Alexandre Alves1, Oscar´Eboli2,4and Tilman Plehn3,4
1Instituto de F´ ısica Te´ orica, IFT-UNESP, S˜ ao Paulo, Brazil
2Departamento de F´ ısica Matem´ atica, Universidade de S˜ ao Paulo, S˜ ao Paulo, Brazil
3Physics Department, University of Wisconsin, Madison, USA
4Theory Division, CERN, Geneva, Switzerland
Abstract
At hadron colliders, the search for R-parity violating supersymmetry can probe scalar
masses beyond what is covered by pair production processes. We evaluate the next-to-
leading order SUSY-QCD corrections to the associated stop or sbottom production with a
lepton through R-parity violating interactions. We show that higher order corrections ren-
der the theoretical predictions more stable with respect to variations of the renormalization
and factorization scales and that the total cross section is enhanced by a factor up to 70% at
the Tevatron and 50% at the LHC. We investigate in detail how the heavy supersymmetric
states decouple from the next-to-leading order process, which gives rise to a theory with an
additional scalar leptoquark. In this scenario the inclusion of higher order QCD corrections
increases the Tevatron reach on leptoquark masses by up to 40 GeV and the LHC reach by
up to 200 GeV.
I. INTRODUCTION
Supersymmetry is one of the most promising candidates for physics beyond the Standard Model, and
the search for supersymmetric particles is one of the most prominent tasks for current and future colliders.
Usually, searches for supersymmetric particles at colliders assume the conservation of R parity. However,
exact R parity is not in any way inherent to supersymmetric models, neither gauge invariance nor super-
symmetry actually require it [1,2]. R parity is imposed to bypass problems with flavor-changing neutral
currents, proton decay, atomic parity violation, and other experimental constraints. It is also crucial for
supersymmetric cold dark matter. R-parity conservation has a huge impact on searches for supersymmetric
particles at colliders: superpartners can only be produced in pairs and the final state has to include two sta-
ble LSPs. In the absence of R-parity conservation, single supersymmetric particles can be produced, which
can extend the reach of colliders [3–5]. It is interesting to notice that pair production of scalar top quarks
1

Page 2

(or sbottoms or scalar leptoquarks) in hadronic colliders is essentially model independent since the squark–
gluon interaction is fixed by SU(3) gauge invariance [6]. In contrast, single production takes place via an
unknown R-parity violating Yukawa interaction λ. Nevertheless, the available phase space for single stop
(sbottom/leptoquark) production is larger than the one for pair production, allowing the search to extend
considerably the bounds on these particles [7]. Moreover, the single production can also give information
on the Yukawa couplings λ.
In this letter, we assume that the superpotential exhibits a term λ′
for the lepton (quark) doublet superfield and Dcis the charge conjugates right handed quark superfield.
This way scalar tops (˜t1) and sbottoms (˜b1) couple to quark–lepton pairs just like a scalar leptoquark. The
production of single stops (sbottoms/leptoquarks) in association with a charged or neutral lepton proceeds
via [8]:
ijkǫabLa
iQb
jDc
kwhere L (Q) stands
p¯ p (pp) → qg → ℓ˜t1
(1)
We study this process taking into account the SUSY-QCD next-to-leading order corrections. We show how
higher order corrections not only enhance the total cross section, but also render the theoretical predictions
more stable with respect to variations of the renormalization and factorization scales.
All our results, of course, apply to models containing a single leptoquark in addition to the Standard
Model particles in the limit in which we decouple all supersymmetric states but the lightest stop or sbottom.
This way, we can obtain the QCD corrections to the single leptoquark production and analyze their impact
on the attainable Tevatron and LHC limits. In Section III we describe in detail the decoupling properties
of the heavy supersymmetric states including next-to-leading order effects in linking supersymmetric with
leptoquark-type observables.
Conventions: Throughout this paper we show consistent leading order or next-to-leading order cross
section predictions, including the respective one loop or two loop strong coupling constant and the corre-
sponding CTEQ5L or CTEQ5M1 parton densities [9]. We usually assume a scalar top (bottom/leptoquark)
mass of 200 GeV, a massless lepton, and we set the R-parity violating coupling λ′
more, we assume that the squark couple to a quark and a lepton without any additional suppression from
the squark mixing angle. Since the R-parity violating coupling as well as the mixing angle dependence
are universal factors, as far as QCD corrections are concerned, they can be trivially added. If not stated
otherwise, we scale the supersymmetric mass spectrum as m˜ g= m˜t1+ 100 GeV, m˜ q= m˜t1+ 200 GeV,
and m˜t2= m˜t1+ 300 GeV1.
SUSYto unity. Further-
II. NEXT-TO-LEADING ORDER CROSS SECTION
The leading order partonic cross section for the single stop (sbottom/leptoquark)production is given by:
dˆ σ
dˆt
= λ′2
SUSY
αs
24ˆ s2
?
−
ˆt
2ˆ s−
ˆtˆ u2
ˆ s(ˆ u − m2
˜t1)2+
ˆ uˆt
ˆ s(ˆ u − m2
˜t1)
?
(2)
Here ˆ s is the parton–parton center-of-mass energy,ˆt = (pq−p˜t1)2, and ˆ u = (pq−pℓ)2. From the definition
of λ′
SUSYin the Lagrangean we see that left handed stops are produced only in association with charged
1The FORTRAN code used in this letter is available from the authors: aalves@ift.unesp.br, tilman.plehn@cern.ch.
2

Page 3

10
-1
1
10
102
200 400600 8001000
σ[fb]: pp/pp
(all upper curves: NLO)
– → t
~µ−+X
m(t
~) [GeV]
pp
(1.8TeV)
–
pp
– (2.0TeV)
pp (14 TeV)
1.4
1.6
1.8
200400 6008001000
K: pp/pp
– → t
~µ−
m(t
~) [GeV]
pp
– (1.8 TeV)
pp
– (2.0 TeV)
pp (14 TeV)
10
-1
1
10
102
200 400 600 800 1000
σ[fb]: pp/pp
(all upper curves: NLO)
– → b
~µ++X
m(b
~) [GeV]
pp
(1.8TeV)
–
pp
– (2.0TeV)
pp (14 TeV)
1.4
1.6
200400 600800 1000
K: pp/pp
– → b
~µ+
m(b
~) [GeV]
pp
– (1.8 TeV)
pp
– (2.0 TeV)
pp (14 TeV)
Figure 1. The impact of the next-to-leading order corrections for the associated production of a top (upper row)
and bottom (lower row) squark as a function of the particle mass, shown for the leading order and next-to-leading
order cross sections (left) and the K factor (right). All scales are set to their central value, i.e. the squark mass. The
SUSY spectrum as a function of the stop (sbottom) mass is given in the text. The squark mixing angle, as well as the
R parity violating coupling λ′
SUSY, are set to unity.
leptons. In order to avoid strong bounds on λ′
example identify λ′
lepton is a muon. In the case of sbottoms, the Lagrangean allows their production in association either with
a charged lepton or with a neutrino. In that case we, for example, identify λ′
to an incoming up quark and again a muon in the final state. We emphasize that all higher order results are
the same for sbottom–leptonand sbottom–neutrinoproduction, since the SUSY-QCD corrections do not see
the charge of the lepton.
The complete set of O(λ′2
emission diagrams, as well as the (crossed) processes gg →˜t1ℓ¯ q, q¯ q →˜t1ℓ¯ q, and qq →˜t1ℓq. Several flavor
combinations of the incoming and outgoing quarks in these crossed processes are possible. The treatment
of heavy supersymmetric states is reviewed in Section III. We renormalize the couplings λ′
in the MS scheme, while the final state stop (sbottom/leptoquark) mass and the squark mixing angle are
renormalized using a generalized on–shell scheme, which includes a running mixing angle, evaluated with
the stop mass as the fixed renormalization scale. Using this scheme for the mixing angle [10] is known
to lead to problems for weak O(α) corrections [11], but it is certainly best suited for QCD corrections.
SUSYand have a clear and unsuppressed signal, we can for
231, which implies that the initial quark has down flavor and the associated
SUSY= λ′
SUSY= λ′
213, which corresponds
SUSYα2
s) corrections includes virtual gluon and gluino diagrams and real gluon
SUSYand αs
3

Page 4

The observable cross section in terms of a running mixing angle can, of course, be linked to the same
observable in any other renormalization scheme, and the numerical effect has been shown to be negligible
for a large set of renormalization schemes [10]. The purely gluon or quark induced subprocesses lead to
a double counting with pair production in the case of an intermediate on–shell stop (sbottom/leptoquark):
gg,q¯ q →˜t1˜t∗
production with a subsequent R-parity violatingdecay. The off–shell contributions, however, should be part
of the next-to-leading order corrections to the associated stop and lepton production. We, therefore, split the
contributions into these two parts, using the small width approximation, and explicitly subtract the on–shell
contribution coming from the squark pair production in the corresponding phase space points [12].
We display in Fig. 1 the effect of the next-to-leading order SUSY-QCD corrections to the associated
stop–lepton and sbottom–lepton productions. While the actual value of the cross sections depends on the
numerical value of the R-parity violating coupling λ′
drop out for the K factor, which is defined consistently as K = σNLO/σLO. As expected, there is hardly
any difference for the Tevatron Run I and Run II results. Because the limited energy of the Tevatron makes
it increasingly harder to radiate additional jets, we see that the next-to-leading order correction becomes
smaller for heavier squark masses. The K factor at the LHC looks qualitatively different. While the center-
of-mass energy is large compared to the squark mass, a sizeable fraction of the next-to-leading order cross
section comes from two initial state gluons. For small squark masses it is likely that the purely gluonic
initial state first produces an on-shell squark pair. This contribution we subtract, which automatically yields
a small K factor. For larger squark masses more of the intermediate stops will be off–shell and, thereby,
contribute to the K factor. On a very moderate level the difference between the K factors for the Tevatron
Run I and Run II already shows the same effect which we see very clearly at the LHC. We emphasize that
the smaller K factor for the LHC, as seen in Fig. 1 is entirely a function of the squark mass and not a feature
of the next-to-leading order corrections at the LHC.
In Fig. 1 we also observe a difference in the cross section and in the K factor between stop and sbottom
production. For the purely QCD corrections this is caused by the exchange of an incoming down quark
in the stop case by an incoming up quark in the sbottom case. The supersymmetric corrections involving
virtual gluinos require virtual quarks in the loops which match the flavor of the final state squark. Since
the top mass is essentially of the same order of the supersymmetric mass scale and the bottom mass is very
much smaller, this effect becomes visible. We note, however, that the behavior of the K factor as a function
of the squark mass at the Tevatron and at the LHC is the same for final state stops and sbottoms, as one
would expect from the arguments given above.
For production cross sections involving strongly interacting final states, the appropriate measure for
the theoretical uncertainty coming from higher order corrections is the renormalization and factorization
scale dependences. We show these scale dependences in Fig. 2. It is common to identify both of these
scales, however, this can lead to systematic cancellations in the variation of the cross section with this
common scale [13,5]. This, in turn, would yield a significant underestimate of the theoretical uncertainty.
The scale dependence for the associated stop–lepton production is shown for a stop mass of 200 GeV and
the corresponding SUSY spectrum. If one defines a theoretical error of the leading order cross section
corresponding to the variation Q = m˜t1/4···4m˜t1of the renormalization scale dependence, the theoretical
uncertainty at the Tevatron (LHC) is of the order of 20%. Notice that, in leading order, this uncertainty
comes from the variation of αs(QR). To next-to-leading order this error is reduced to 15% for the Tevatron,
and slightly less for the LHC.
In contrast, the factorization scale dependence of the leading order cross section is not identical for
1→˜t1(ℓ¯ q). The on–shell contributions of these processes are usually evaluated as stop pair
SUSYand on the squark mixing angle, both of them
4

Page 5

0.8
1
1.2
1.4
σ/σ0: pp/pp
– → t
~µ−+X
QR/m(t
~)
0.250.512
QF=m(t
~)=200 GeV
LO NLO
pp
pp (14 TeV)
– (2.0 TeV)
0.8
1
1.2
1.4
σ/σ0: pp/pp
– → t
~µ−+X
QF/m(t
~)
0.25 0.512
QR=m(t
~)=200 GeV
LONLO
pp
pp (14 TeV)
– (2.0 TeV)
Figure 2. Dependence of the total cross sections on the renormalization (left) and factorization (right) scales. The
other respective scale is fixed to the central scale. The stop mass is set to 200 GeV and fixes the central value for the
scales as well as the SUSY spectrum.
the Tevatron and the LHC. This is due to the fact that at the Tevatron the stops have to be produced
right at threshold while at the LHC they can be produced through partons with considerably lower par-
ton momentum fraction x. The leading order factorization scale dependence of this process at the LHC
is extraordinarily mild and, in comparison with other similar processes [12,5], artificially flat. This is
an effect of the choice of the renormalization scale and a cancellation involving a combination of logs
logQ2
of the slope from positiveto negativevalues when the stop mass increases from 100 to 500 GeV. Evaluating
the scale dependence of the total cross section at the LHC for a stop mass of 200 GeV is very close to the
turnover point, at which the factorization scale is actually flat.
Both leading order scale uncertainties add up to some 65% for the Tevatron and 40% for the LHC. The
next-to-leading order calculations reduce this uncertainty significantly to ∼ 25% for both colliders. Since
there is no cancellation in the cross section between the two scale variations at next-to-leading order, we
can obtain the same estimates by varying only the identified scale Q = QR = QF. These percentages
are, of course, only a rough theoretically motivated estimate. In particular, the leading order uncertainty
is more dependent on the powers of αsin the cross section than on the actual process [12] and, therefore,
has to be taken with a grain of salt. A comparison with the actual K factor given in Fig. 1 also shows that
the estimated leading order uncertainty for the LHC is indeed too small, while the leading order error band
covers the next-to-leading order curve well for the Tevatron. Furthermore, to next-to-leading order different
supersymmetric production processes give very consistent uncertainty estimates [5,6,12,13]. Since there is
no physics reason why the Tevatron and the LHC cross section should behave any differently as far as the
theoretical uncertainty is concerned, it is a good check to see that at the next-to-leading order level the scale
dependence is indeed similar for both experiments. Moreover, the next-to-leading error bands agrees well
with what one would expect from similar processes.
R/m2
˜t1×logQ2
F/m2
˜t1[13]. The leading order factorization scale dependence actually changes the sign
We present in Fig. 3 the effect of the next-to-leading order contributions on the lepton transverse mo-
mentum and rapidity distributions. We generally observe that the next-to-leading order corrections change
the shape of the lepton transverse momentum and rapidity distributions only at a negligible level. Looking
into the transverse momentum distributions in more detail, we see that, while for the Tevatron the lepton
5