UCRHEP-T428
MSUHEP-061208
Resummation E�e
ts in the Sear
h of SM Higgs Boson
at Hadron Colliders
Qing-Hong Cao
Department of Physi
s and Astronomy,
University of California at Riverside, Riverside, CA 92521
Chuan-Ren Chen
Department of Physi
s and Astronomy,
Mi
higan State University, E. Lansing, MI 48824
Abstra
t
We examine the soft-gluon resummation e�e
ts, in
luding the exa
t spin 
orrelations among
the �nal state parti
les, in the sear
h of the Standard Model Higgs boson, via the pro
ess
gg → H → WW/ZZ → 4 leptons, at the Tevatron and the LHC. A 
omparison between the
resummation and the Next-to-Leading order (NLO) 
al
ulation is performed after imposing various
kinemati
s 
uts suggested in the literature for the Higgs boson sear
h. For the H → ZZ mode, the
resummation e�e
ts in
rease the a

eptan
e of the signal events by about 25%, as 
ompared to the
NLO predi
tion, and dramati
ally alter various kinemati
s distributions of the �nal state leptons.
For the H → WW mode, the a

eptan
e rates of the signal events predi
ted by the resummation
and NLO 
al
ulations are almost the same, but some of the predi
ted kinemati
al distributions are
quite di�erent. Thus, to pre
isely determine the properties of the Higgs boson at hadron 
olliders,
the soft-gluon resummation e�e
ts have to be taken into a

ount.
Ele
troni
 address: q
ao�u
r.edu
Ele
troni
 address: 
r
hen�pa.msu.edu
http://arxiv.org/abs/0704.1344v2
mailto:qcao@ucr.edu
mailto:crchen@pa.msu.edu
I. INTRODUCTION
Although Standard Model (SM) explains su

essfully all 
urrent high energy physi
s
experimental data, the me
hanism of ele
toweak spontaneous symmetry breaking, arising
from the Higgs me
hanism, has not yet been tested dire
tly. Therefore, sear
hing for the
Higgs boson (H) is one of the most important tasks at the 
urrent and future high energy
physi
s experiments. The negative result of dire
t sear
h at the LEP2, via the Higgsstrahlung
pro
ess e+e− → ZH , poses a lower bound of 114.1GeV on the SM Higgs boson mass
(MH) [1℄. On the other hand, global �ts to ele
troweak observables prefer MH . 200GeV at
the 95% 
on�den
e level [2℄, while the triviality arguments put an upper bound ∼ 1TeV [3℄.
There is 
urrently an a
tive experimental program at the Tevatron to dire
tly sear
h for
the Higgs boson. The Large Hadron Collider (LHC) at CERN, s
heduled to operate in late
2007, is expe
ted to establish the existen
e of Higgs boson if the SM is truly realized in
Nature. At the LHC, the SM Higgs boson is mainly produ
ed through gluon-gluon fusion
pro
ess indu
ed by a heavy (top) quark loop. On
e being produ
ed, it will de
ay into a
fermion pair or ve
tor boson pair. The strategy of sear
hing for the Higgs boson depends
on how it de
ays and how large the de
ay bran
hing ratio is. If the Higgs boson is lighter
than 130GeV, it mainly de
ays into a bottom quark pair (bb̄). Unfortunately, it is very
di�
ult to sear
h for the Higgs boson in this mode due to the extremely large Quantum
Chromodynami
s (QCD) ba
kground at the LHC. However, the H → γγ mode 
an be used
to dete
t a Higgs boson with the mass below 150 GeV [4, 5℄ though the de
ay bran
hing
ratio of this mode is quite small, ∼ O(10−3). If the Higgs boson mass (MH) is in the region
of 130GeV to 2MZ (MZ being the mass of Z boson), the H → ZZ∗ mode is very useful
be
ause of its 
lean 
ollider signature of four isolated 
harged leptons. The H → WW (∗)
mode is also important in this mass region be
ause of its large de
ay bran
hing ratio. When
MH > 2MZ , the de
ay mode H → ZZ → ℓ+ℓ−ℓ′+ℓ′− is 
onsidered as the �gold-plated� mode
whi
h is the most reliable way to dete
t the Higgs boson up to MH ∼ 600GeV be
ause the
ba
kgrounds are known rather pre
isely and the two on-shell Z bosons 
ould be re
onstru
ted
experimentally. For MH > 600GeV, one 
an dete
t the H → ZZ → ℓ+ℓ−νν̄ de
ay 
hannel
in whi
h the signal appears as a Ja
obian peak in the missing transverse energy spe
trum.
The dis
overy of the Higgs boson relies on how well we understand the signals and its
ba
kgrounds, be
ause one needs to impose optimal kinemati
s 
uts to suppress the huge
ba
kgrounds and enhan
e the signal to ba
kground ratio (S/B). Many works have been
done in the literature to 
al
ulate the higher order QCD 
orre
tions to the dominant pro-
du
tion pro
ess of the Higgs boson gg → H [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18℄. In
addition to determine the in
lusive produ
tion rate of the Higgs boson, an a

urate predi
-
tion of kinemati
s of the Higgs boson is very essential for the Higgs boson sear
h. However,
a �x order 
al
ulation 
annot reliably predi
t the transverse momentum (QT ) distribution
of Higgs boson for the low QT region where the bulk events a

umulate. This is be
ause
of large 
orre
tions of the form ln(Q2/Q2T ) due to non-
omplete 
an
ellations of soft and

ollinear singularities between virtual and real 
ontributions, where Q is the invariant mass
of the Higgs boson. Therefore, one needs to take into a

ount the e�e
ts of the initial state
multiple soft-gluon emissions in order to make a reliable predi
tion on the kinemati
 distri-
butions of the Higgs boson. One approa
h to a
hieve this is to in
lude parton showering [19℄
whi
h resums the universal leading logs in Monte Carlo event generators, e.g. HERWIG [20℄
and PYTHIA [21℄, whi
h are 
ommonly used by experimentalists. The showering pro
ess
just depends on the initial state parton and the s
ale of the hard pro
ess being 
onsidered.
The advantage is that it 
ould be in
orporated into various physi
s pro
esses. Re
ently,
an approa
h to mat
h NLO matrix element 
al
ulation and parton showing Monte Carlo
generators, MC�NLO [22, 23℄, has been proposed. Another approa
h is to in
lude 
orre
tly
the soft-gluon e�e
ts is to 
al
ulate an analyti
al result by using the Collins-Soper-Sterman
(CSS) resummation formalism [24, 25, 26, 27℄ to resum these large logarithmi
 
orre
tions to
all order in αs. However, in pra
ti
e the power of logarithms in
luded in Sudakov exponent
depends on whi
h level the �xed order 
al
ulation has been performed [28, 29, 30, 31, 32℄.
It is very interesting to 
ompare the predi
tions between parton showering and resumma-
tion 
al
ulation and detailed 
omparisons have been presented in Ref. [28, 33, 34, 35, 36℄
whi
h 
on
luded that all of the distributions are basi
ally 
onsistent with ea
h other, ex
ept
PYTHIA in the small QT region and HERWIG in the large QT region.
In addition, the spin 
orrelation among the Higgs de
ay produ
ts has been proved to
be 
ru
ial to suppress the ba
kgrounds [37, 38℄. Hen
e, an a

urate theoreti
al predi
tion,
whi
h in
orporates the initial state soft-gluon resummation e�e
ts and the spin 
orrelations
among the Higgs de
ay produ
ts, is needed. In this paper, we present su
h a 
al
ulation
and study the soft-gluon resummation (RES) e�e
ts on various kinemati
s distributions
of �nal state parti
les. Furthermore, we examine the impa
t of the RES e�e
ts on the
Figure 1: Tree level Feynman diagram of pro
ess gg → H → V1(→ ℓ1ℓ̄2)V2(→ ℓ3ℓ̄4).
a

eptan
e rate of the signal events with various kinemati
s 
uts (whi
h were suggested in
the literature [37, 39℄ for Higgs sear
h) and 
ompare them with the leading order (LO) and
NLO predi
tions
The paper is organized as follows. In Se
. II, we present our analyti
al formalism of
the CSS resummation. In Se
. III, we present the in
lusive 
ross se
tion of the signal
pro
ess for several ben
hmark masses of the Higgs boson. In Se
. IV, we study the pro
ess
gg → H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ for MH = 140GeV at the Fermilab Tevatron and for MH =
170GeV at the LHC. In Se
. V, we examine the pro
ess gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− for
MH = 140GeV and 200GeV, respe
tively, and the pro
ess gg → H → ZZ → ℓ+ℓ−νν̄ for
MH = 600GeV, at the LHC. Our 
on
lusions are given in Se
. VI.
II. TRANSVERSE MOMENTUM RESUMMATION FORMALISM
At the hadron 
olliders, the SM Higgs boson is mainly produ
ed via gluon-gluon fusion
pro
ess through a heavy quark triangle loop diagram, 
f. Fig 1, in whi
h the e�e
t of the
triangle loop is repla
ed by the e�e
tive ggH 
oupling (denoted as the bold dot). Taking
advantage of the narrow width of the Higgs boson, we 
an fa
torize the Higgs boson pro-
du
tion from its sequential de
ay. The resummation formula was already presented in Ref.
The NLO Quantum Ele
trodynami
s (QED) and ele
troweak (EW) 
orre
tions to the Higgs de
ay pro
ess
H → WW/ZZ → 4ℓ were 
al
ulated in Ref. [40℄ and Ref. [41℄, respe
tively. Re
ently, the NLO QCD

orre
tion to the Higgs boson de
ays H → WW/ZZ → 4q with hadroni
 four-fermion �nal states was

al
ulated in Ref. [42℄. Sin
e the higher order 
orre
tions for Higgs produ
tion are dominated by the
initial state soft-gluon resummation e�e
ts, we fo
us our attention on the RES e�e
ts in this work. It is
worth mentioning that the NLO QED 
orre
tions to the Higgs boson de
ay H → WW/ZZ → 4ℓ have
been implemented in ResBos [43℄ program, and the phenomenologi
al study of the 
ombined RES e�e
ts
and the QED 
orre
tion will be presented elsewhere.
[28℄. Here, we list some of the relevant formulas as follows, for 
ompleteness:
dσ(h1h2 → H(→ V V → ℓ1ℓ2ℓ3ℓ4)X)
dQ2dQ2TdydφHdΠ4
= σ0(gg → H)
Q2ΓH/mH
(Q2 −m2H)2 + (Q2ΓH/mH)2
M(H → V1V2 → ℓ1ℓ2ℓ3ℓ4)
(2π)2
d2b eiQT ·bW̃gg(b∗, Q, x1, x2, C1,2,3)W̃
gg (b, Q, x1, x2) + Y (QT , Q, x1, x2, C4)
where Q, QT , y, and φH are the invariant mass, transverse momentum, rapidity, and az-
imuthal angle of the Higgs boson, respe
tively, de�ned in the lab frame, and dΠ4 represents
the four-body phase spa
e of the Higgs boson de
ay, de�ned in the Collin-Soper frame [44℄.
In Eq. (1), |M(· · · )|2 denotes the matrix element square of the Higgs boson de
ay and reads
M(H → V1V2 → ℓ1ℓ2ℓ3ℓ4)
2G3Fm
(q21 −m2V )2 +m2V Γ2V
(q22 −m2V )2 +m2V Γ2V
C+(p1 · p3)(p2 · p4) + C−(p1 · p4)(p2 · p3)
where mV is the ve
tor boson mass, qi(pi) denotes the momentum
of the ve
tor boson Vi
(the lepton ℓi), and GF is the Fermi 
oupling 
onstant. Here,
a212 + b
a234 + b
± 4a12b12a34b34,
where a12 and b12 respe
tively denote the ve
tor and axial ve
tor 
omponents of the V ℓ1ℓ2

oupling, while a34 and b34 are the ones for V ℓ3ℓ4. For the W boson, mV = mW , and
a = b =
while for the Z boson, mV = mZ , and
a = 4 sin θ2W − 1, b = −1 for Z → ℓ+ℓ−,
a = 1, b = 1 for Z → νν̄,
The dire
tion of momentum pi is de�ned to be outgoing from the mother parti
le.
where θW is the weak mixing angle. In Eq. (1), the fun
tion W̃gg sums over the soft gluon

ontributions that grow as Q−2T × [1 or ln(Q2T/Q2)] to all order in αS, whi
h 
ontains the
singular part as QT → 0. The 
ontribution whi
h is less singular than those in
luded in W̃gg
is 
al
ulated order-by-order in αS and is in
luded in the Y term. Therefore, we 
an obtain
the NLO results by expending the above resummation formula, i.e. Eq. (1), to the α3S order.
More details 
an be found in Ref. [43℄. In our 
al
ulation, σ0 in
ludes the 
omplete LO

ontribution with �nite quark mass e�e
ts [45, 46, 47, 48℄. It has been shown [9℄ that this
pres
ription approximates well the exa
t NLO in
lusive Higgs produ
tion rate.
For the numeri
al evaluation, we 
hose the following set of SM input parameters [49℄:
GF = 1.16637× 10−5GeV−2, α = 1/137.0359895,
mZ = 91.1875GeV, αs(mZ) = 0.1186,
me = 0.5109997MeV, mµ = 0.105658389GeV.
Following Ref. [50℄, we derive the W boson mass as mW = 80.385GeV. Thus, the square
of the weak gauge 
oupling is g2 = 4
2m2WGF . In
luding the O(αs) QCD 
orre
tions to
W → qq̄′, we obtain the W boson width as ΓW = 2.093GeV and the de
ay bran
hing
ratio of Br(W → ℓν) = 0.108 [51℄. In order to in
lude the e�e
ts of the higher order
ele
troweak 
orre
tions, we also adapt the e�e
tive Born approximation in the 
al
ulation of
the H → ZZ → 4 leptons mode by repla
ing the sin2 θW in the Zℓℓ 
oupling by the e�e
tive
sin2 θ
W = 0.2314, 
al
ulated at the mZ s
ale.
III. INCLUSIVE CROSS SECTIONS
For the mass of the Higgs boson being within the intermediate mass range, it will prin
i-
pally de
ay into two ve
tor bosons whi
h sequentially de
ay into either lepton or quark pairs.
Leptons are the obje
ts whi
h 
an be easily identi�ed in the �nal state, so the di-lepton de
ay
mode is regarded as the �golden 
hannel� due to its 
lean signature and well-known ba
k-
ground. The drawba
k is that the di-lepton mode su�ers from the small de
ay bran
hing
ratio for the ve
tor boson de
ay (V → ℓℓ̄). For example, the bran
hing ratio of Z → ℓ+ℓ−
is only about 3.4%. Due to the huge QCD ba
kgrounds, the purely hadroni
 de
ay modes
are not as useful for dete
ting the Higgs boson.
In this paper, we fo
us on the purely leptoni
 de
ays of the ve
tor bosons in the H →
Table I: In
lusive 
ross se
tions of gg → H → V V → 4ℓ at the Tevatron Run 2 and the LHC in
the unit of fb, i.e. σ(gg → H)×Br(H → V V )×Br(V → ℓ1ℓ2)×Br(V → ℓ3ℓ4) for various Higgs
boson masses. Here, ℓ and ℓ′ denote either e or µ.
WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− ZZ → ℓ+ℓ−νν̄(=
i=e,µ,τ
νiν̄i)
MH 140GeV 170GeV 140GeV 200GeV 600GeV
Tevatron LHC LHC LHC LHC
RES 13.1 891.1 11.0 17.7 6.3
NLO 11.5 848.9 10.5 16.4 5.6
LO 4.0 405.3 5.1 8.0 2.4
WW (∗) and H → ZZ(∗) modes. To 
over the intermediate mass range, we 
onsider the
following ben
hmark 
ases: (i) H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ (ℓ, ℓ′ = e or µ) for MH = 140GeV
at the Femilab Tevatron Run 2 (a 1.96 TeV pp̄ 
ollider), and for MH = 170GeV at the LHC
(a 14 TeV pp 
ollider); (ii) H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− (ℓ, ℓ′ = e or µ) for MH = 140 and
200GeV at the LHC; (iii) H → ZZ → ℓ+ℓ−νν̄ for MH = 600GeV at the LHC, where ℓ = e
or µ, and ν = νe, νµ or ντ . All the numeri
al results are 
al
ulated by using ResBos [43℄. We
adapt CTEQ6.1L parton distribution fun
tion in the LO 
al
ulation and CTEQ6.1M parton
distribution fun
tion [52℄ in the NLO and RES 
al
ulations. The renormalization s
ale (µR)
and fa
torization s
ale (µF ) are 
hosen to be the Higgs boson mass in our 
al
ulations, i.e.
µR = µF = MH .
The in
lusive 
ross se
tions for those ben
hmark masses of the Higgs boson are sum-
marized in Table I where di�erent sear
hing 
hannels are 
onsidered. For 
omparison, we
show the QT distributions 
al
ulated by using the RES and NLO 
al
ulations in Fig. 3(a).
The RES 
al
ulation is similar to that presented in Ref. [28, 29℄ with the known A and
B [53, 54, 55, 56, 57℄, but with A
g in
luded, where [58℄
A(3)g =
CACFNf
(ζ(3)−
+ C3A(
11ζ(3)
+C2ANf(−
7ζ(3)
) , (2)
where CA = 3, CF = 4/3, Nf = 5 and the Riemann 
onstant ζ(3) = 1.202... . We also
use the modi�ed parton momentum fra
tions x1 and x2 to take into a

ount the kinemati

orre
tions due to the emitted soft gluons [28℄, with x1 = mT e
S and x2 = mT e
0 50 100 150 200
 (GeV)
 = 140 GeV
 = 170 GeV
 = 200 GeV
 = 600 GeV
Figure 2: Normalized distributions of transverse momentum of Higgs boson predi
ted by RES

al
ulation at the LHC.
where mT =
Q2T +Q
S is the 
enter-of-mass energy of the hadron 
ollider. We
also adopt the mat
hing pro
edure des
ribed in the Ref. [43℄ and the non-perturbation 
on-
tribution W̃NP of BLNY form in the Ref. [59℄. In Fig. 2, we show the transverse momentum
distributions of Higgs boson predi
ted by RES 
al
ulation at the LHC. As we see that the
peak position is shifted to larger QT region and the shape be
omes broader when the mass
of Higgs be
omes heavier.
It is 
lear that the predi
tion of NLO 
al
ulation blows up in the QT → 0 region and the
RES e�e
ts have to be in
luded to make a reliable predi
tion on event shape distributions.
In the NLO 
al
ulation, it is ambiguous to treat the singularity of the QT distribution near
QT = 0, see the dashed 
urve in Fig. 3(a). Before presenting our numeri
al results, we
shall explain how we deal with the singularity in the NLO 
al
ulation when QT ∼ 0. In
ResBos, we divide the QT phase spa
e with a separation s
ale Q
T . We 
al
ulate the QT
singular part of real emission and virtual 
orre
tion diagrams analyti
ally and integrate the
sum of these two parts up to Q
T . By this pro
edure, it yields a �nite NLO 
ross se
tion,
for integrating QT from 0 up to Q
T , whi
h is put into the QT = 0 bin of the NLO QT
distribution (for bin width larger than Q
T ). Sin
e the separation s
ale Q
T is introdu
ed
in the theoreti
al 
al
ulation for te
hni
al reasons only and is not a physi
al observable, the
sum of both 
ontributions from QT > Q
T and QT < Q
T should not depend on Q
T . As
shown in Fig. 3(b), the NLO total 
ross se
tion indeed does not depend on the 
hoi
e of
0 50 100 150 200
  (GeV)
0 2 4 6 8
 (GeV)
σ ( Q
total
σ ( Q
 )(a) (b)
Figure 3: (a) Distribution of transverse momentum of Higgs boson, and (b) NLO total produ
tion

ross se
tion of Higgs boson via gluon gluon fusion as MH = 170GeV at the LHC.
T as long as it is not too large. We refer the readers to the Se
. 3 and the Appendix
of Ref. [43℄ for more details. In this study, we 
hoose Q
T = 0.96GeV in our numeri
al

al
ulations.
As mentioned in the Introdu
tion, MC�NLO, whi
h mat
hes NLO 
al
ulations and par-
ton showering Monte Carlo event generators, not only predi
ts a reliable QT of the Higgs
boson but also in
ludes spin 
orrelations among the Higgs de
ay produ
ts. Therefore it is in-
teresting to 
ompare the QT predi
tions between MC�NLO and RES 
al
ulations. In order
to 
ompare the di�eren
es in shape more pre
isely, we show the QT distributions predi
ted
by MC�NLO and ResBos in Fig. 4 for MH = 140( 170, 200, 600)GeV. All distributions
are normalized by the total 
ross se
tions for the 
orresponding Higgs boson masses. The
bottom part of ea
h QT distribution plot presents the ratio between MC�NLO and ResBos.
We note that for a light Higgs boson the distributions are 
onsistent in the peak region
[34, 36℄, where the di�eren
e is about 10%, but they are quite di�erent in the large QT
region, say QT & 100GeV. For a heavy Higgs boson, e.g. MH = 600GeV, these two dis-
tributions are very di�erent in the small QT region, and MC�NLO tends to populate more
events in the small QT region, as 
ompared to ResBos. Sin
e the Higgs boson is a s
alar, the
distributions of Higgs boson de
ay produ
ts just depend upon the Higgs boson's kinemati
s.
Therefore, the di�eren
e in the QT distribution predi
tions between MC�NLO and ResBos
may prove to be 
ru
ial for the pre
ision measurements of the Higgs boson's properties. A
further detailed study of the impa
t of the QT di�eren
e on the Higgs boson sear
h is in
MC@NLO
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
 = 140 GeV
 = 200 GeV
 = 170 GeV
 = 600 GeV
(a) (b)
(c) (d)
MC@NLO / RES
Figure 4: Comparison of the QT distributions between ResBos and MC�NLO.
order and will be presented elsewhere.
IV. PHENOMENOLOGICAL STUDY OF THE H → WW MODE
In the sear
h for SM-like Higgs boson via H → WW (∗) mode, two s
enarios of W boson
de
ay were 
onsidered in the literature [60, 61, 62℄: one is that both W bosons de
ay
leptoni
ally, another is that one W boson de
ays leptoni
ally and another W boson de
ays
hadroni
ally. Throughout this paper, we only 
on
entrate on the di-lepton de
ay mode, i.e.
H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ , at the Tevatron and the LHC. The 
ollider signature, therefore,
is two isolated opposite-sign 
harged leptons plus large missing transverse energy ( 6ET ) whi
h
originates from the two neutrinos. In this se
tion, we �rst examine the RES e�e
ts on various
kinemati
s distributions, and then show the RES e�e
ts on the Higgs mass measurement.
Finally, we study the RES e�e
ts on the a

eptan
es of the kinemati
s 
uts suggested in the
literature for Higgs sear
h.
(a) (b) (c)
Figure 5: Kinemati
 
on�gurations of Higgs de
ay (H → WW → ℓ+ℓ−νν̄) in the rest frame of H:
(a) H → W++W
+ , (b) H → W
− and (
) H → W
0 . Here, +(−, 0) denotes the right-handed
(left-handed, longitudinal) polarization state of the W boson. The long arrows denote the moving
dire
tions of the �nal-state leptons. The short bold arrows denote the parti
les' spin dire
tions.
A. Basi
 kinemati
s distributions
For a heavy Higgs boson, the two ve
tor bosons, whi
h are generated from the spin-0 Higgs
boson de
ay, are predominantly longitudinally polarized, while the longitudinal and trans-
verse polarization states are demo
rati
ally populated when the Higgs boson mass is near the
threshold for de
aying into the ve
tor boson pair [63, 64℄. When 140GeV ≤ MH ≤ 170GeV,
the transverse polarization modes 
ontribute largely. The two 
harged leptons in the �nal
state have di�erent kinemati
s be
ause of the 
onservation of angular momentum, 
f. Fig.
5, therefore, one 
harged lepton is largely boosted and its momentum be
omes harder while
another be
omes softer. Making use of these di�eren
es, one 
an impose asymmetri
 trans-
verse momentum (pT ) 
uts on the two 
harged leptons to suppress the ba
kground. On the
event-by-event basis, we arrange the two 
harged leptons in the order of transverse momen-
tum: pLmaxT denotes the larger pT between the two 
harged leptons while p
T is the smaller
one. Fig. 6 shows the distributions of pLmaxT , p
T and missing energy (6ET ) for MH = 140GeV
at the Tevatron (�rst row) and for MH = 170GeV at the LHC (se
ond row). Furthermore,
in Fig. 7 we show the distributions of cos θLL, φLL and ∆YLL without imposing any kinemat-
i
s 
ut, where cos θLL is the 
osine of the opening angle between the two 
harged leptons,
φLL is the azimuthal angle di�eren
e between the two 
harged leptons on the transverse
plane, and ∆YLL is the rapidity di�eren
e of two 
harged leptons in the lab frame. Sin
e
we are mainly interested in the shapes of the kinemati
s distributions, the 
urves shown in
the �gures are all normalized by the 
orresponding total 
ross se
tions. The solid 
urves
present the distributions in
luding the RES e�e
ts, the dashed and dotted 
urves present
0 20 40 60 80 100
max (GeV)
0 20 40 60 80
 (GeV)
0 20 40 60 80 100
/ET (GeV)
0 20 40 60 80 100
max (GeV)
0 50 100
 (GeV)
0 50 100 150 200
/ET (GeV)
(a) (b) (c)
(d) (e) (f)
Figure 6: Normalized distributions of the leading transverse momentum pLmax
, softer transverse
momentum pLT of the leptons, and the missing energy 6ET in gg → H → WW → ℓ+ℓ′−νℓν̄ℓ′ . The
panels (a) to (
) are for MH = 140GeV at the Tevatron, and (d) to (f) are for MH = 170GeV at
the LHC.
the distributions 
al
ulated at the NLO and LO, respe
tively.
We note that the pT distributions of the 
harged leptons and the missing energy distri-
butions are modi�ed largely by the RES e�e
ts. This 
an be understood as follows. The
two 
harged leptons prefer to move in the same dire
tion due to the spin 
orrelation among
the de
ay produ
ts of the Higgs boson, 
f. the distributions of cos θLL in Figs. 7(a) and (d).
Hen
e, one 
an approximately treat the Higgs boson de
ay as �two-body� de
ay, i.e. de
ay-
ing into two 
lusters as H → (ℓ+ℓ′−) (νℓν̄ℓ′). This is in analogy to the W boson produ
tion
and de
ay in the Drell-Yan pro
ess, ud̄ → W+ → ℓ+ν, whi
h has been shown in Ref. [51℄
that the transverse momentum of lepton (pℓT ) is very sensitive to the transverse momentum
of the W boson. The same sensitivity also applies to 6ET . As shown in Figs. 6(
) and (f), the

lear Ja
obian peak of the 6ET distribution around MH/2 in the LO 
al
ulation is smeared
in the NLO and RES 
al
ulations. Furthermore, the 6ET distribution in the NLO and RES

al
ulations has a long tail due to the non-zero transverse momentum of the Higgs boson.
Sin
e the RES 
al
ulation in
ludes the e�e
ts from multiple soft-gluon radiation, the 6ET
-1 -0.5 0 0.5 1
0 1 2 3
-4 -2 0 2 4
-1 -0.5 0 0.5 1
0 1 2 3
-4 -2 0 2 4
(a) (b) (c)
(d) (e) (f)
Figure 7: Normalized distributions of cos θLL, φLL and ∆YLL in gg → H → WW → ℓ+ℓ′−νℓν̄ℓ′ :
The panels (a) to (
) are for MH = 140GeV at the Tevatron and (d) to (f) are for MH = 170GeV
at the LHC.
distribution near the Ja
obian peak is further smeared in the RES 
al
ulation as 
ompared
to the NLO 
al
ulation. When MH = 140GeV, only one W boson is on-shell and the two

harged leptons do not move as 
lose as they do in the 
ase of MH = 170GeV (in whi
h

ase, both W bosons are on-shell). However the parallel 
on�guration is still preferred.
The dominant ba
kgrounds of the H → WW (∗) mode are from the W boson pair pro-
du
tion and top quark pair produ
tion. The latter, as the redu
ible ba
kground, 
an be
suppressed with suitable 
uts su
h as jet-veto, but the former, as the irredu
ible ba
k-
ground, still remains even after imposing the basi
 kinemati
 
uts. In order to redu
e this
intrinsi
 ba
kground, one needs to take advantage of the 
hara
teristi
 spin 
orrelations of
the 
harged leptons in the H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ de
ay. For example, the distribution of
the di�eren
e in azimuthal angles of the 
harged leptons peaks at smaller value (
f. Figs. 7(b)
and (e)) for the signal than that for the WW 
ontinuum produ
tion ba
kground [60, 62℄.
We note that the RES e�e
ts do not a�e
t the cos θLL and φLL distributions very mu
h, as
shown in Figs. 7(a), (b), (d) and (e).
To 
losely examine the di�eren
e in their predi
tions, we also present the ratio of the RES
10 20 30 40 50 60
max (GeV)
RES/NLO
RES/LO
0 10 20 30 40
 (GeV)
0 10 20 30 40 50 60 70
/ET (GeV)
10 20 30 40 50 60
max (GeV)
0 10 20 30 40 50
 (GeV)
0 20 40 60 80
/ET (GeV)
(a) (b) (c)
(d) (e) (f)
Figure 8: Ratio of the Resummation 
ontribution to NLO and LO 
ontributions in gg → H →
WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ . The panels (a) to (
) are for MH = 140GeV at the Tevatron while (d) to (f)
are for MH = 170GeV at the LHC.

ontribution to the NLO and LO 
ontributions in Fig. 8. We note that the ratio is about one
below the peak regions of pLmaxT , p
T and 6ET , and be
omes larger than one above the peak
region, where both the LO and NLO 
ontributions drop faster than the RES 
ontribution
does, whi
h is 
onsistent with the results shown in Fig. 6. This uneven behavior indi
ates
that one 
annot simply use the leading order kinemati
s with the 
onstant K-fa
tor in
luded
to mimi
 the higher order quantum 
orre
tions. We should stress that even though the NLO
and RES 
al
ulations in
lude the same 
ontributions of the hard gluon radiation from initial
states, the e�e
ts of the multiple soft-gluon radiation 
ould 
ause more than 25% di�eren
e
between RES and NLO predi
tions in the large pT and 6ET region.
B. Higgs mass measurement
In order to identify the signal events 
learly, it is 
ru
ial to re
onstru
t the invariant mass
of the Higgs boson. Unfortunately, one 
annot dire
tly re
onstru
t the MH distribution in
the H → WW mode due to the two neutrinos in the �nal state. Instead, both the transverse
mass MT and the 
luster transverse mass MC [65℄, de�ned as
2pLLT 6ET (1− cos∆φ(pLLT , 6ET )),
LL+ 6ET , (3)
yield a broad peak near MH . In Eq. (3), p
T (mLL) denotes the transverse momentum
(invariant mass) of the two 
harged lepton system, and ∆φ(pLLT , 6ET ) is the di�eren
e in
azimuthal angles between pLLT and 6ET on the transverse plane. We note that the upper
endpoint of MT distribution 
an 
learly re�e
t the mass of Higgs boson, 
f. Figs. 9(a) and
(
). MT is insensitive to QT be
ause it depends on QT in the se
ond order, 
f. Eq. (3).
Therefore, the position of the endpoint is only subje
t to MH and ΓH . The latter e�e
ts 
an
be safely ignored be
ause ΓH is very small (less than about 1.5GeV), for the Higgs boson
mass less than 200GeV. The 
luster transverse mass MC also exhibits a 
lear Ja
obian peak
with a 
lear edge at MH , 
f. Figs. 9(b) and (d). But both the line shape and the Ja
obian
peak of MC distribution are modi�ed by the RES e�e
ts be
ause MC is dire
tly related to
6ET whi
h depends on QT in the �rst order. We suggest that one should use MT to extra
t
the mass of Higgs in H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ mode be
ause the upper endpoint of the
MT distribution is insensitive to high order 
orre
tions.
C. A

eptan
e study
In order to separate the signal from its 
opious ba
kgrounds, one needs to impose optimal

uts to suppress ba
kgrounds and enhan
e the signal to ba
kground ratio (S/B ) simulta-
neously. The sele
tion of the optimal 
uts highly depends on how well we understand the
kinemati
s of the signal and ba
kground pro
esses. As shown above, the RES e�e
ts modify
the distributions of transverse momentum of the 
harged leptons and the missing energy
largely, therefore, it is important to study the RES e�e
ts on the a

eptan
es of the kine-
mati
s 
uts. Here, we impose a set of kinemati
s 
uts used by experimental 
olleagues in
Refs. [37, 39℄. The 
orresponding a

eptan
es are summarized in Table II.
• For the sear
h for a 140 GeV Higgs boson at the Tevatron, we impose the following
basi
 
uts:
pLmaxT > 15GeV , p
T > 10GeV,
|YL| < 2.0 , 6ET > 20GeV, (4)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
(a) (b)
(c) (d)
Figure 9: Normalized distributions of the transverse mass MT and the 
luster mass MC in gg →
H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ : (a) and (b) are for MH = 140GeV at the Fermilab Tevatron while (
)
and (d) are for MH = 170GeV at the LHC.
and the optimal 
uts as follows:
mLL <
< MT < MH − 10GeV
φLL < 2.0 rad ,
+ 20GeV < HT < MH (5)
where YL denotes the rapidity of 
harged lepton, and HT denotes the s
alar sum of
the transverse momenta of �nal state parti
les, i.e. HT ≡ |peT | + |p
T | + | 6ET |. The
overall e�
ien
y of the 
uts is about 68% , 69% and 70% after imposing the basi
 
uts
(Eq. (4)) for RES, NLO and LO 
al
ulations, respe
tively, and about 44% for both
RES and NLO 
al
ulations and 46% for LO 
al
ulation after imposing the optimal

uts (Eq. (5)).
• For the sear
h of a 170 GeV Higgs boson at the LHC, we require the following basi

uts:
pLmaxT > 20GeV , p
T > 10GeV,
|YL| < 2.5 , 6ET > 40GeV, (6)
Table II: A

eptan
e of gg → H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ events after imposing the basi
 
uts and
the optimal 
uts for MH = 140GeV at the Tevatron and MH = 170GeV at the LHC.
MH = 140GeV MH = 170GeV
basi
 (Eq. (4)) optimal (Eq. (5)) basi
 (Eq. (6)) optimal (Eq. (7))
RES 0.68 0.44 0.61 0.19
NLO 0.69 0.44 0.61 0.19
LO 0.70 0.46 0.63 0.20
and the optimal 
uts:
mLL < 80.0GeV , MH − 30.0GeV < MT < MH ,
φLL < 1.0 rad , θLL < 0.9 rad , |∆YLL| < 1.5 , (7)
The 
ut e�
ien
y is about 61% for both RES and NLO 
al
ulations, but about 63%
for LO 
ontribution after imposing the basi
 
ut (Eq. (6)). After imposing the optimal

uts (Eq. (7)), the a

eptan
es of RES and NLO are about 19%, while LO is 20%.
V. PHENOMENOLOGICAL STUDY OF THE H → ZZ MODE
In the sear
h for the SM Higgs boson, the H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− is an important
dis
overy 
hannel for a wide range of Higgs boson mass. The appearan
e of four 
harged
leptons with large transverse momenta is an attra
tive experimental signature. This so-

alled �gold-plated� mode provides not only a 
lean signature to verify the existen
e of the
Higgs boson but also an ex
ellent pro
ess to explore its spin and CP properties [66℄. In
this se
tion, we study three mass values of MH (140, 200 and 600GeV) at the LHC. For
MH = 140GeV and 200GeV, we require the two Z bosons both de
ay into 
harged leptons;
for MH = 600GeV, we require one Z boson de
ays into a 
harged lepton pair and another Z
boson de
ays into a neutrino pair, i.e. ℓ+ℓ−νν̄. In this se
tion we �rst study the RES e�e
ts
on various kinemati
s distributions and then examine the RES e�e
ts on the a

eptan
es of
the kinemati
s 
uts.
0 20 40 60 80 100
max (GeV)
0 20 40 60 80
 (GeV)
0 50 100 150
max (GeV)
0 20 40 60 80 100
 (GeV)
(a) (b)
(c) (d)
Figure 10: Normalized distributions of pLmax
and pLT in gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′−: (a) and (b)
are for MH = 140GeV; (
) and (d) are for MH = 200GeV at the LHC.
A. gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′−
Similar to the H → WW (∗) mode, we also arrange the four 
harged leptons of the
H → ZZ(∗) mode in the order of transverse momentum. We denote pLmaxT as the largest
pT of the four 
harged leptons while p
T the se
ond leading pT . In Fig. 10, we show the
distributions of pLmaxT and p
T for MH = 140 and 200GeV, respe
tively. Due to the similar
kinemati
s dis
ussed in the H → WW (∗) mode, the shapes of the distributions of pLmaxT
and pLT are 
hanged signi�
antly by the RES e�e
ts. The typi
al feature is that the RES
e�e
ts shift the pT of the 
harged lepton to the larger pT region and, therefore, in
rease the
a

eptan
es of the kinemati
s 
uts. The numeri
al results will be shown later.
Although one 
an measure the Higgs boson mass by re
onstru
ting the invariant mass of
the four 
harged leptons, one still needs to re
onstru
t the Z bosons in order to suppress
the ba
kgrounds. The re
onstru
tion of the Z boson depends on the lepton �avors in the
�nal state. In this study, we 
onsider two s
enarios: di�erent �avor 
harged lepton pairs,
i.e. H → 2e2µ, and four same �avor 
harged leptons, i.e. H → 4e( or 4µ). Hen
e, we have
two methods for re
onstru
ting the Z bosons:
1. Di�erent �avor 
harged lepton pairs (2e2µ):
In this 
ase, it is easy to re
onstru
t the Z bosons be
ause both ele
tron and muon
lepton �avors 
an be tagged. Using the �avor information, the Z bosons 
an be
re
onstru
ted by summing over the same �avor opposite-sign leptons in the �nal state.
2. Four same �avor 
harged leptons (4e/4µ):
If the �avors of four leptons are all the same, one needs to pursue some algorithms
to re
onstru
t the Z boson mass. In our analysis, we �rst pair up the leptons with
opposite 
harge. We require the pair whose invariant mass is 
losest to MZ to be
the one generated from the on-shell Z boson, and the other pair is the one generated
from another Z boson, whi
h 
ould be on-sell or o�-shell. We name it as the minimal
deviation algorithm (MDA) in this paper.
In Fig. 11, we show the pT distributions of the re
onstru
ted Z boson for 140 and 200GeV,
respe
tively. When the �nal state lepton �avors are di�erent, one 
an re
onstru
ted the Z
boson perfe
tly by mat
hing the lepton �avor. For the same �avor leptons, the re
onstru
ted
Z boson distributions in the MDA are shown as the solid, dashed and dot-dashed 
urves for
RES, NLO and LO, respe
tively. Some points are worthy to point out as follow:
• We note that the MDA 
an perfe
tly re
onstru
t the distributions of true Z bosons,
irregardless whether these two Z bosons are both on-shell or only one of them is
on-shell.
• When MH = 200GeV, both Z bosons are produ
ed on-shell and boosted. The peak
position of the transverse of momentum pZT is around
(MH/2)
2 −m2Z ∼ 41GeV. For
all the 
ases, the RES e�e
ts 
hange the shape of pZT largely and shift the p
T to the
larger value region.
It has been shown in Ref. [67℄ that angular 
orrelation between the two Z bosons from
the Higgs de
ay 
an be used to suppress the intrinsi
 ba
kground from ZZ pair produ
tion
e�
iently. One of the useful angular variables is the polar angle (θ∗Z) of the (ba
k-to-ba
k)
Z boson momenta in the rest frame of the Higgs boson [67℄. As shown in Fig. 12, in the rest
frame of Higgs boson, the ba
k-to-ba
k Z bosons like to lie in the dire
tion perpendi
ular to
the z−axis, whi
h is the moving dire
tion of the Higgs boson in the lab frame. After being
0 20 40 60 80 100
 (GeV)
0 20 40 60 80 100
 (GeV)
0 20 40 60 80 100
 (GeV)
(a) (b) (c)
Figure 11: Normalized transverse momentum of Z boson in gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− at the
LHC: (a) is the pT distributions of o�-shell Z boson for MH = 140GeV, (b) is the pT distributions
of on-shell Z boson for MH = 140GeV and (
) is the pT distributions of on-shell Z boson for
MH = 200GeV.
0 0.5 1 1.5
0 0.5 1 1.5
(a) (b)M
 = 140 GeV M
 = 200 GeV
Figure 12: Normalized polar angle of the (ba
k-to-ba
k) Z boson momenta distributions in the rest
frame of the Higgs boson in gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− at the LHC: (a) is for MH = 140GeV
, (b) is for MH = 200GeV.
boosted to the lab frame, two Z bosons will move 
lose to ea
h other, 
.f. Fig. 13(b), where
θZZ is the opening angle between the two Z bosons in the lab frame. Another interesting
angular variable is the angle between the two on-shell Z boson de
ay planes (φDP ) in the rest
frame of the Higgs boson, whi
h is shown in Fig. 13(a). The two Z bosons are re
onstru
ted
as explained above. Sin
e the angle θ∗Z and φDP are de�ned in the rest frame of the Higgs
boson, the non-zero transverse momentum of the Higgs boson does not a�e
t these two
variables. Therefore, as 
learly shown in the �gures, all the distributions of the angular
variables mentioned above are the same for the RES, NLO and LO 
al
ulations.
-1 -0.5 0 0.5 1
cos φ
-1 -0.5 0 0.5 1
cos θ
(a) (b)
Figure 13: Normalized distributions of cosφDP and cos θZZ in the rest frame of the Higgs boson
with mass 200GeV in gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′− at the LHC.
B. gg → H → ZZ → ℓ+ℓ−νν̄
Although the �gold-plated� mode, H → ZZ → ℓ+ℓ−ℓ′+ℓ′−, is 
onsidered to be the most
e�e
tive 
hannel for the SM Higgs boson dis
overy at the LHC, it su�ers from the small
de
ay bran
hing of Z → ℓ+ℓ−. Moreover, the larger the Higgs mass be
omes, the smaller
the produ
tion rate is. When the Higgs boson mass is larger than 600 GeV, the H →
ZZ → ℓ+ℓ−νν̄ 
hannel may be
ome important be
ause the de
ay bran
hing ratio (Br) of
H → ZZ → ℓ+ℓ−νν̄ is six times of the Br of H → ZZ → ℓ+ℓ−ℓ′+ℓ′−. The drawba
k is that
one 
annot re
onstru
t the Higgs mass from the �nal state parti
les due to the presen
e of
two neutrinos. In this dis
overy 
hannel, the missing transverse energy ( 6ET ) is 
ru
ial to
suppress the ba
kground [37℄. The 6ET distribution is shown in Fig. 14(a) whi
h exhibits a
Ja
obian peak around MH/2, and the soft-gluon resummation e�e
ts smear the Ja
obian
peak and shift more events to the larger 6ET region. Similar to the H → WW mode, the
kinemati
s of this 
hannel is similar to the W boson produ
tion and de
ay in the Drell-Yan
pro
ess, therefore the shape of 6ET distribution 
hange signi�
antly by the RES 
ontributions.
The Higgs boson mass 
an be measured from the peaks of the distributions of the transverse
mass MT and the 
luster mass MC , 
f. Eq. (3), as shown in Fig. 14(b) and (
). Although
the upper endpoint of MT is insensitive to high order 
orre
tions as we mentioned in the
study of H → WW (∗) mode, the Ja
obian peak is smeared out by the width (ΓH) e�e
ts
of the Higgs boson. For MH = 600GeV, the total de
ay width of the Higgs boson is about
0 100 200 300 400 500
/ET (GeV)
0 200 400 600 800
 (GeV)
0 200 400 600 800
 (GeV)
(a) (b) (c)
Figure 14: Normalized distributions of 6ET , MT and MC in gg → H → ZZ → ℓ+ℓ−νν 
hannel with
MH = 600GeV at the LHC.
Table III: A

eptan
e of the pro
ess gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′− for MH = 140 (200)GeV and
the pro
ess gg → H → ZZ → ℓ+ℓ−νν̄ for MH = 600GeV after imposing 
uts.
MH = 140GeV MH = 200GeV MH = 600GeV
basi
 (Eq. 8) optimal (Eq. 9) basi
 (Eq. 8) optimal (Eq. 9) basi
 (Eq. 10)
RES 0.53 0.15 0.67 0.14 0.55
NLO 0.54 0.12 0.67 0.11 0.56
LO 0.53 0 0.67 0 0.58
120 GeV, whi
h is quite sizable and generates a noti
eable smearing e�e
t on the Ja
obian
peak.
C. A

eptan
e study
The dis
overy potential of the H → ZZ → ℓ+ℓ−ℓ′+ℓ′− and H → ZZ → ℓ+ℓ−νν̄ modes
has been studied in Ref. [37℄ after imposing the following 
uts:
• For MH = 140GeV and 200GeV, the intermediate mass range, we impose the basi

uts:
pET > 7.0GeV, |YL| < 2.5, pLT > 20GeV, (8)
and the optimal 
uts:
, (9)
where pET and YL are the transverse momentum and rapidity of ea
h 
harged lepton,
respe
tively, and p
T is the pT of the harder Z boson.
• For MH = 600GeV, we require:
pLT > 40GeV, |YL| < 2.5 ,
pLLT > 200GeV, 6ET > 150GeV, (10)
where pLLT is the transverse momentum of the two 
harged lepton system. The numeri-

al results of the a

eptan
es of the various 
uts are summarized in Table III. For the
H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− mode, the RES and NLO 
ontributions have almost the same
a

eptan
es after imposing the basi
 
uts. However, after imposing the optimal 
uts the
a

eptan
e of the RES 
ontribution is larger than the one of the NLO 
ontribution by 25%,
and the LO 
ontribution is largely suppressed. For the H → ZZ → ℓ+ℓ−νν̄ mode, the
a

eptan
es of the RES and NLO 
al
ulations are similar to ea
h other.
VI. CONCLUSION
The sear
h for the SM Higgs boson is one of the major goals of the high energy physi
s
experiments at the LHC, and the ve
tor boson de
ay modes, H → WW (∗) or H → ZZ(∗),
provide powerful and reliable dis
overy 
hannels. The LHC has a great potential to dis-

over the Higgs boson even with low luminosity (∼ 30 fb−1) during the early years of run-
ning [37, 38, 68℄. In order to extra
t the signal from huge ba
kground events, we should
have better theoreti
al predi
tions of the signal events as well as ba
kground events. In
this paper, we examine the soft gluon resummation e�e
ts on the sear
h of SM Higgs boson
via the dominant produ
tion pro
ess gg → H at the LHC and dis
uss the impa
ts of the
resummation e�e
ts on various kinemati
s variables whi
h are relevant to the Higgs sear
h.
A 
omparison between the resummation e�e
ts and the NLO 
al
ulation is also presented.
For H → WW (∗) → ℓ+ℓ−νν̄ mode, we study MH = 140GeV at the Tevatron and
MH = 170GeV at the LHC. Due to the spin 
orrelations between the �nal state parti
les,
this pro
ess is similar to the W boson produ
tion and de
ay in the Drell-Yan pro
ess.
The shapes of the kinemati
s distributions are modi�ed signi�
antly by RES e�e
ts. For
example, the e�e
ts 
ould 
ause ∼ 50% di�eren
e 
ompared to NLO 
al
ulation in the
transverse momentum distribution of the leading lepton (p
T ), when MH = 170GeV. The
Higgs boson mass 
annot be re
onstru
ted dire
tly from the �nal state parti
les be
ause of
two neutrinos. Therefore, the upper endpoint in the transverse mass distribution 
an be
used to determine the mass of the Higgs boson, and we found that it is insensitive to the
RES e�e
ts. After imposing various kinemati
s 
uts, the LO, NLO and RES 
al
ulations
yield similar a

eptan
e of the signal events.
For the H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− mode, the so-
alled �gold-plated� mode, we study
MH = 140GeV and MH = 200GeV at the LHC in this paper. We pursue an algorithm,

alled minimal deviation algorithm in this paper, to re
onstru
t the two Z bosons when the
four 
harged leptons in the �nal state have the same �avors. The RES e�e
ts 
hange the
shapes of kinemati
s signi�
antly, e.g. pLmaxT and p
T distributions. However, the variables
φDP and θ
Z , de�ned in the Higgs rest frame, are insensitive to RES e�e
ts. After imposing
the optimal kinemati
s 
uts, the RES e�e
ts 
ould in
rease the a

eptan
e by 25% 
ompared
to that of NLO 
al
ulation while the LO 
ontribution is largely suppressed. When the Higgs
boson is heavy (600GeV), we 
onsider the H → ZZ → ℓ+ℓ−νν̄ mode be
ause of its larger
de
ay bran
hing ratio, as 
ompared to the H → ZZ → ℓ+ℓ−ℓ′+ℓ′− mode. The shape of 6ET
distribution, whi
h is 
ru
ial to suppress the ba
kgrounds, is largely modi�ed be
ause it is
sensitive to the transverse momentum of the Higgs boson.
In summary, we have presented a study of initial state soft-gluon resummation e�e
ts
on the sear
h for the SM Higgs boson via gluon-gluon fusion at the LHC. The e�e
ts not
only signi�
antly modify some of the kinemati
 distributions of the �nal state parti
les, as

ompared to the NLO and LO predi
tions, but also enhan
e the a

eptan
e of the signal
events after imposing the kinemati
 
uts to suppress the large ba
kground events. Therefore,
we 
on
lude that the initial state soft-gluon resummation e�e
ts should be taken into a

ount
as sear
hing for the Higgs boson at the LHC. In addition, we note that the spin 
orrelations
among the �nal state leptons 
ould be modi�ed by the ele
troweak 
orre
tions to the Higgs
boson de
ay. Therefore, we have implemented the NLO QED 
orre
tion in the ResBos 
ode,
and the phenomenologi
al study will be presented in the forth
oming paper.
A
knowledgments
We thank Professor C.-P. Yuan for a 
riti
al reading and useful suggestions. We also
thank Dr. Kazuhiro Tobe for useful dis
ussions. Q.-H. Cao is supported in part by the U.S.
Department of Energy under grant No. DE-FG03-94ER40837. C.-R. Chen is supported in
part by the U.S. National S
ien
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	introduction
	Transverse momentum resummation formalism
	Inclusive cross sections
	Phenomenological study of the HWW mode
	Basic kinematics distributions
	Higgs mass measurement
	Acceptance study
	Phenomenological study of the HZZ mode
	ggHZZ(*)+-+-
	ggHZZ+-
	Acceptance study
	Conclusion
	Acknowledgments
	References

  We examine the soft-gluon resummation effects, including the exact spin
correlations among the final state particles, in the search of the Standard
Model Higgs boson, via the process $gg\to H\to WW/ZZ \to 4 leptons, at the
Tevatron and the LHC. A comparison between the resummation and the
Next-to-Leading order (NLO) calculation is performed after imposing various
kinematics cuts suggested in the literature for the Higgs boson search. For the
$H\to ZZ$ mode, the resummation effects increase the acceptance of the signal
events by about 25%, as compared to the NLO prediction, and dramatically alter
various kinematics distributions of the final state leptons. For the $H\to WW$
mode, the acceptance rates of the signal events predicted by the resummation
and NLO calculations are almost the same, but some of the predicted kinematical
distributions are quite different. Thus, to precisely determine the properties
of the Higgs boson at hadron colliders, the soft-gluon resummation effects have
to be taken into account.

UCRHEP-T428
MSUHEP-061208
Resummation E�e
ts in the Sear
h of SM Higgs Boson
at Hadron Colliders
Qing-Hong Cao
Department of Physi
s and Astronomy,
University of California at Riverside, Riverside, CA 92521
Chuan-Ren Chen
Department of Physi
s and Astronomy,
Mi
higan State University, E. Lansing, MI 48824
Abstra
t
We examine the soft-gluon resummation e�e
ts, in
luding the exa
t spin 
orrelations among
the �nal state parti
les, in the sear
h of the Standard Model Higgs boson, via the pro
ess
gg → H → WW/ZZ → 4 leptons, at the Tevatron and the LHC. A 
omparison between the
resummation and the Next-to-Leading order (NLO) 
al
ulation is performed after imposing various
kinemati
s 
uts suggested in the literature for the Higgs boson sear
h. For the H → ZZ mode, the
resummation e�e
ts in
rease the a

eptan
e of the signal events by about 25%, as 
ompared to the
NLO predi
tion, and dramati
ally alter various kinemati
s distributions of the �nal state leptons.
For the H → WW mode, the a

eptan
e rates of the signal events predi
ted by the resummation
and NLO 
al
ulations are almost the same, but some of the predi
ted kinemati
al distributions are
quite di�erent. Thus, to pre
isely determine the properties of the Higgs boson at hadron 
olliders,
the soft-gluon resummation e�e
ts have to be taken into a

ount.
Ele
troni
 address: q
ao�u
r.edu
Ele
troni
 address: 
r
hen�pa.msu.edu
http://arxiv.org/abs/0704.1344v2
mailto:qcao@ucr.edu
mailto:crchen@pa.msu.edu
I. INTRODUCTION
Although Standard Model (SM) explains su

essfully all 
urrent high energy physi
s
experimental data, the me
hanism of ele
toweak spontaneous symmetry breaking, arising
from the Higgs me
hanism, has not yet been tested dire
tly. Therefore, sear
hing for the
Higgs boson (H) is one of the most important tasks at the 
urrent and future high energy
physi
s experiments. The negative result of dire
t sear
h at the LEP2, via the Higgsstrahlung
pro
ess e+e− → ZH , poses a lower bound of 114.1GeV on the SM Higgs boson mass
(MH) [1℄. On the other hand, global �ts to ele
troweak observables prefer MH . 200GeV at
the 95% 
on�den
e level [2℄, while the triviality arguments put an upper bound ∼ 1TeV [3℄.
There is 
urrently an a
tive experimental program at the Tevatron to dire
tly sear
h for
the Higgs boson. The Large Hadron Collider (LHC) at CERN, s
heduled to operate in late
2007, is expe
ted to establish the existen
e of Higgs boson if the SM is truly realized in
Nature. At the LHC, the SM Higgs boson is mainly produ
ed through gluon-gluon fusion
pro
ess indu
ed by a heavy (top) quark loop. On
e being produ
ed, it will de
ay into a
fermion pair or ve
tor boson pair. The strategy of sear
hing for the Higgs boson depends
on how it de
ays and how large the de
ay bran
hing ratio is. If the Higgs boson is lighter
than 130GeV, it mainly de
ays into a bottom quark pair (bb̄). Unfortunately, it is very
di�
ult to sear
h for the Higgs boson in this mode due to the extremely large Quantum
Chromodynami
s (QCD) ba
kground at the LHC. However, the H → γγ mode 
an be used
to dete
t a Higgs boson with the mass below 150 GeV [4, 5℄ though the de
ay bran
hing
ratio of this mode is quite small, ∼ O(10−3). If the Higgs boson mass (MH) is in the region
of 130GeV to 2MZ (MZ being the mass of Z boson), the H → ZZ∗ mode is very useful
be
ause of its 
lean 
ollider signature of four isolated 
harged leptons. The H → WW (∗)
mode is also important in this mass region be
ause of its large de
ay bran
hing ratio. When
MH > 2MZ , the de
ay mode H → ZZ → ℓ+ℓ−ℓ′+ℓ′− is 
onsidered as the �gold-plated� mode
whi
h is the most reliable way to dete
t the Higgs boson up to MH ∼ 600GeV be
ause the
ba
kgrounds are known rather pre
isely and the two on-shell Z bosons 
ould be re
onstru
ted
experimentally. For MH > 600GeV, one 
an dete
t the H → ZZ → ℓ+ℓ−νν̄ de
ay 
hannel
in whi
h the signal appears as a Ja
obian peak in the missing transverse energy spe
trum.
The dis
overy of the Higgs boson relies on how well we understand the signals and its
ba
kgrounds, be
ause one needs to impose optimal kinemati
s 
uts to suppress the huge
ba
kgrounds and enhan
e the signal to ba
kground ratio (S/B). Many works have been
done in the literature to 
al
ulate the higher order QCD 
orre
tions to the dominant pro-
du
tion pro
ess of the Higgs boson gg → H [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18℄. In
addition to determine the in
lusive produ
tion rate of the Higgs boson, an a

urate predi
-
tion of kinemati
s of the Higgs boson is very essential for the Higgs boson sear
h. However,
a �x order 
al
ulation 
annot reliably predi
t the transverse momentum (QT ) distribution
of Higgs boson for the low QT region where the bulk events a

umulate. This is be
ause
of large 
orre
tions of the form ln(Q2/Q2T ) due to non-
omplete 
an
ellations of soft and

ollinear singularities between virtual and real 
ontributions, where Q is the invariant mass
of the Higgs boson. Therefore, one needs to take into a

ount the e�e
ts of the initial state
multiple soft-gluon emissions in order to make a reliable predi
tion on the kinemati
 distri-
butions of the Higgs boson. One approa
h to a
hieve this is to in
lude parton showering [19℄
whi
h resums the universal leading logs in Monte Carlo event generators, e.g. HERWIG [20℄
and PYTHIA [21℄, whi
h are 
ommonly used by experimentalists. The showering pro
ess
just depends on the initial state parton and the s
ale of the hard pro
ess being 
onsidered.
The advantage is that it 
ould be in
orporated into various physi
s pro
esses. Re
ently,
an approa
h to mat
h NLO matrix element 
al
ulation and parton showing Monte Carlo
generators, MC�NLO [22, 23℄, has been proposed. Another approa
h is to in
lude 
orre
tly
the soft-gluon e�e
ts is to 
al
ulate an analyti
al result by using the Collins-Soper-Sterman
(CSS) resummation formalism [24, 25, 26, 27℄ to resum these large logarithmi
 
orre
tions to
all order in αs. However, in pra
ti
e the power of logarithms in
luded in Sudakov exponent
depends on whi
h level the �xed order 
al
ulation has been performed [28, 29, 30, 31, 32℄.
It is very interesting to 
ompare the predi
tions between parton showering and resumma-
tion 
al
ulation and detailed 
omparisons have been presented in Ref. [28, 33, 34, 35, 36℄
whi
h 
on
luded that all of the distributions are basi
ally 
onsistent with ea
h other, ex
ept
PYTHIA in the small QT region and HERWIG in the large QT region.
In addition, the spin 
orrelation among the Higgs de
ay produ
ts has been proved to
be 
ru
ial to suppress the ba
kgrounds [37, 38℄. Hen
e, an a

urate theoreti
al predi
tion,
whi
h in
orporates the initial state soft-gluon resummation e�e
ts and the spin 
orrelations
among the Higgs de
ay produ
ts, is needed. In this paper, we present su
h a 
al
ulation
and study the soft-gluon resummation (RES) e�e
ts on various kinemati
s distributions
of �nal state parti
les. Furthermore, we examine the impa
t of the RES e�e
ts on the
Figure 1: Tree level Feynman diagram of pro
ess gg → H → V1(→ ℓ1ℓ̄2)V2(→ ℓ3ℓ̄4).
a

eptan
e rate of the signal events with various kinemati
s 
uts (whi
h were suggested in
the literature [37, 39℄ for Higgs sear
h) and 
ompare them with the leading order (LO) and
NLO predi
tions
The paper is organized as follows. In Se
. II, we present our analyti
al formalism of
the CSS resummation. In Se
. III, we present the in
lusive 
ross se
tion of the signal
pro
ess for several ben
hmark masses of the Higgs boson. In Se
. IV, we study the pro
ess
gg → H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ for MH = 140GeV at the Fermilab Tevatron and for MH =
170GeV at the LHC. In Se
. V, we examine the pro
ess gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− for
MH = 140GeV and 200GeV, respe
tively, and the pro
ess gg → H → ZZ → ℓ+ℓ−νν̄ for
MH = 600GeV, at the LHC. Our 
on
lusions are given in Se
. VI.
II. TRANSVERSE MOMENTUM RESUMMATION FORMALISM
At the hadron 
olliders, the SM Higgs boson is mainly produ
ed via gluon-gluon fusion
pro
ess through a heavy quark triangle loop diagram, 
f. Fig 1, in whi
h the e�e
t of the
triangle loop is repla
ed by the e�e
tive ggH 
oupling (denoted as the bold dot). Taking
advantage of the narrow width of the Higgs boson, we 
an fa
torize the Higgs boson pro-
du
tion from its sequential de
ay. The resummation formula was already presented in Ref.
The NLO Quantum Ele
trodynami
s (QED) and ele
troweak (EW) 
orre
tions to the Higgs de
ay pro
ess
H → WW/ZZ → 4ℓ were 
al
ulated in Ref. [40℄ and Ref. [41℄, respe
tively. Re
ently, the NLO QCD

orre
tion to the Higgs boson de
ays H → WW/ZZ → 4q with hadroni
 four-fermion �nal states was

al
ulated in Ref. [42℄. Sin
e the higher order 
orre
tions for Higgs produ
tion are dominated by the
initial state soft-gluon resummation e�e
ts, we fo
us our attention on the RES e�e
ts in this work. It is
worth mentioning that the NLO QED 
orre
tions to the Higgs boson de
ay H → WW/ZZ → 4ℓ have
been implemented in ResBos [43℄ program, and the phenomenologi
al study of the 
ombined RES e�e
ts
and the QED 
orre
tion will be presented elsewhere.
[28℄. Here, we list some of the relevant formulas as follows, for 
ompleteness:
dσ(h1h2 → H(→ V V → ℓ1ℓ2ℓ3ℓ4)X)
dQ2dQ2TdydφHdΠ4
= σ0(gg → H)
Q2ΓH/mH
(Q2 −m2H)2 + (Q2ΓH/mH)2
M(H → V1V2 → ℓ1ℓ2ℓ3ℓ4)
(2π)2
d2b eiQT ·bW̃gg(b∗, Q, x1, x2, C1,2,3)W̃
gg (b, Q, x1, x2) + Y (QT , Q, x1, x2, C4)
where Q, QT , y, and φH are the invariant mass, transverse momentum, rapidity, and az-
imuthal angle of the Higgs boson, respe
tively, de�ned in the lab frame, and dΠ4 represents
the four-body phase spa
e of the Higgs boson de
ay, de�ned in the Collin-Soper frame [44℄.
In Eq. (1), |M(· · · )|2 denotes the matrix element square of the Higgs boson de
ay and reads
M(H → V1V2 → ℓ1ℓ2ℓ3ℓ4)
2G3Fm
(q21 −m2V )2 +m2V Γ2V
(q22 −m2V )2 +m2V Γ2V
C+(p1 · p3)(p2 · p4) + C−(p1 · p4)(p2 · p3)
where mV is the ve
tor boson mass, qi(pi) denotes the momentum
of the ve
tor boson Vi
(the lepton ℓi), and GF is the Fermi 
oupling 
onstant. Here,
a212 + b
a234 + b
± 4a12b12a34b34,
where a12 and b12 respe
tively denote the ve
tor and axial ve
tor 
omponents of the V ℓ1ℓ2

oupling, while a34 and b34 are the ones for V ℓ3ℓ4. For the W boson, mV = mW , and
a = b =
while for the Z boson, mV = mZ , and
a = 4 sin θ2W − 1, b = −1 for Z → ℓ+ℓ−,
a = 1, b = 1 for Z → νν̄,
The dire
tion of momentum pi is de�ned to be outgoing from the mother parti
le.
where θW is the weak mixing angle. In Eq. (1), the fun
tion W̃gg sums over the soft gluon

ontributions that grow as Q−2T × [1 or ln(Q2T/Q2)] to all order in αS, whi
h 
ontains the
singular part as QT → 0. The 
ontribution whi
h is less singular than those in
luded in W̃gg
is 
al
ulated order-by-order in αS and is in
luded in the Y term. Therefore, we 
an obtain
the NLO results by expending the above resummation formula, i.e. Eq. (1), to the α3S order.
More details 
an be found in Ref. [43℄. In our 
al
ulation, σ0 in
ludes the 
omplete LO

ontribution with �nite quark mass e�e
ts [45, 46, 47, 48℄. It has been shown [9℄ that this
pres
ription approximates well the exa
t NLO in
lusive Higgs produ
tion rate.
For the numeri
al evaluation, we 
hose the following set of SM input parameters [49℄:
GF = 1.16637× 10−5GeV−2, α = 1/137.0359895,
mZ = 91.1875GeV, αs(mZ) = 0.1186,
me = 0.5109997MeV, mµ = 0.105658389GeV.
Following Ref. [50℄, we derive the W boson mass as mW = 80.385GeV. Thus, the square
of the weak gauge 
oupling is g2 = 4
2m2WGF . In
luding the O(αs) QCD 
orre
tions to
W → qq̄′, we obtain the W boson width as ΓW = 2.093GeV and the de
ay bran
hing
ratio of Br(W → ℓν) = 0.108 [51℄. In order to in
lude the e�e
ts of the higher order
ele
troweak 
orre
tions, we also adapt the e�e
tive Born approximation in the 
al
ulation of
the H → ZZ → 4 leptons mode by repla
ing the sin2 θW in the Zℓℓ 
oupling by the e�e
tive
sin2 θ
W = 0.2314, 
al
ulated at the mZ s
ale.
III. INCLUSIVE CROSS SECTIONS
For the mass of the Higgs boson being within the intermediate mass range, it will prin
i-
pally de
ay into two ve
tor bosons whi
h sequentially de
ay into either lepton or quark pairs.
Leptons are the obje
ts whi
h 
an be easily identi�ed in the �nal state, so the di-lepton de
ay
mode is regarded as the �golden 
hannel� due to its 
lean signature and well-known ba
k-
ground. The drawba
k is that the di-lepton mode su�ers from the small de
ay bran
hing
ratio for the ve
tor boson de
ay (V → ℓℓ̄). For example, the bran
hing ratio of Z → ℓ+ℓ−
is only about 3.4%. Due to the huge QCD ba
kgrounds, the purely hadroni
 de
ay modes
are not as useful for dete
ting the Higgs boson.
In this paper, we fo
us on the purely leptoni
 de
ays of the ve
tor bosons in the H →
Table I: In
lusive 
ross se
tions of gg → H → V V → 4ℓ at the Tevatron Run 2 and the LHC in
the unit of fb, i.e. σ(gg → H)×Br(H → V V )×Br(V → ℓ1ℓ2)×Br(V → ℓ3ℓ4) for various Higgs
boson masses. Here, ℓ and ℓ′ denote either e or µ.
WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− ZZ → ℓ+ℓ−νν̄(=
i=e,µ,τ
νiν̄i)
MH 140GeV 170GeV 140GeV 200GeV 600GeV
Tevatron LHC LHC LHC LHC
RES 13.1 891.1 11.0 17.7 6.3
NLO 11.5 848.9 10.5 16.4 5.6
LO 4.0 405.3 5.1 8.0 2.4
WW (∗) and H → ZZ(∗) modes. To 
over the intermediate mass range, we 
onsider the
following ben
hmark 
ases: (i) H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ (ℓ, ℓ′ = e or µ) for MH = 140GeV
at the Femilab Tevatron Run 2 (a 1.96 TeV pp̄ 
ollider), and for MH = 170GeV at the LHC
(a 14 TeV pp 
ollider); (ii) H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− (ℓ, ℓ′ = e or µ) for MH = 140 and
200GeV at the LHC; (iii) H → ZZ → ℓ+ℓ−νν̄ for MH = 600GeV at the LHC, where ℓ = e
or µ, and ν = νe, νµ or ντ . All the numeri
al results are 
al
ulated by using ResBos [43℄. We
adapt CTEQ6.1L parton distribution fun
tion in the LO 
al
ulation and CTEQ6.1M parton
distribution fun
tion [52℄ in the NLO and RES 
al
ulations. The renormalization s
ale (µR)
and fa
torization s
ale (µF ) are 
hosen to be the Higgs boson mass in our 
al
ulations, i.e.
µR = µF = MH .
The in
lusive 
ross se
tions for those ben
hmark masses of the Higgs boson are sum-
marized in Table I where di�erent sear
hing 
hannels are 
onsidered. For 
omparison, we
show the QT distributions 
al
ulated by using the RES and NLO 
al
ulations in Fig. 3(a).
The RES 
al
ulation is similar to that presented in Ref. [28, 29℄ with the known A and
B [53, 54, 55, 56, 57℄, but with A
g in
luded, where [58℄
A(3)g =
CACFNf
(ζ(3)−
+ C3A(
11ζ(3)
+C2ANf(−
7ζ(3)
) , (2)
where CA = 3, CF = 4/3, Nf = 5 and the Riemann 
onstant ζ(3) = 1.202... . We also
use the modi�ed parton momentum fra
tions x1 and x2 to take into a

ount the kinemati

orre
tions due to the emitted soft gluons [28℄, with x1 = mT e
S and x2 = mT e
0 50 100 150 200
 (GeV)
 = 140 GeV
 = 170 GeV
 = 200 GeV
 = 600 GeV
Figure 2: Normalized distributions of transverse momentum of Higgs boson predi
ted by RES

al
ulation at the LHC.
where mT =
Q2T +Q
S is the 
enter-of-mass energy of the hadron 
ollider. We
also adopt the mat
hing pro
edure des
ribed in the Ref. [43℄ and the non-perturbation 
on-
tribution W̃NP of BLNY form in the Ref. [59℄. In Fig. 2, we show the transverse momentum
distributions of Higgs boson predi
ted by RES 
al
ulation at the LHC. As we see that the
peak position is shifted to larger QT region and the shape be
omes broader when the mass
of Higgs be
omes heavier.
It is 
lear that the predi
tion of NLO 
al
ulation blows up in the QT → 0 region and the
RES e�e
ts have to be in
luded to make a reliable predi
tion on event shape distributions.
In the NLO 
al
ulation, it is ambiguous to treat the singularity of the QT distribution near
QT = 0, see the dashed 
urve in Fig. 3(a). Before presenting our numeri
al results, we
shall explain how we deal with the singularity in the NLO 
al
ulation when QT ∼ 0. In
ResBos, we divide the QT phase spa
e with a separation s
ale Q
T . We 
al
ulate the QT
singular part of real emission and virtual 
orre
tion diagrams analyti
ally and integrate the
sum of these two parts up to Q
T . By this pro
edure, it yields a �nite NLO 
ross se
tion,
for integrating QT from 0 up to Q
T , whi
h is put into the QT = 0 bin of the NLO QT
distribution (for bin width larger than Q
T ). Sin
e the separation s
ale Q
T is introdu
ed
in the theoreti
al 
al
ulation for te
hni
al reasons only and is not a physi
al observable, the
sum of both 
ontributions from QT > Q
T and QT < Q
T should not depend on Q
T . As
shown in Fig. 3(b), the NLO total 
ross se
tion indeed does not depend on the 
hoi
e of
0 50 100 150 200
  (GeV)
0 2 4 6 8
 (GeV)
σ ( Q
total
σ ( Q
 )(a) (b)
Figure 3: (a) Distribution of transverse momentum of Higgs boson, and (b) NLO total produ
tion

ross se
tion of Higgs boson via gluon gluon fusion as MH = 170GeV at the LHC.
T as long as it is not too large. We refer the readers to the Se
. 3 and the Appendix
of Ref. [43℄ for more details. In this study, we 
hoose Q
T = 0.96GeV in our numeri
al

al
ulations.
As mentioned in the Introdu
tion, MC�NLO, whi
h mat
hes NLO 
al
ulations and par-
ton showering Monte Carlo event generators, not only predi
ts a reliable QT of the Higgs
boson but also in
ludes spin 
orrelations among the Higgs de
ay produ
ts. Therefore it is in-
teresting to 
ompare the QT predi
tions between MC�NLO and RES 
al
ulations. In order
to 
ompare the di�eren
es in shape more pre
isely, we show the QT distributions predi
ted
by MC�NLO and ResBos in Fig. 4 for MH = 140( 170, 200, 600)GeV. All distributions
are normalized by the total 
ross se
tions for the 
orresponding Higgs boson masses. The
bottom part of ea
h QT distribution plot presents the ratio between MC�NLO and ResBos.
We note that for a light Higgs boson the distributions are 
onsistent in the peak region
[34, 36℄, where the di�eren
e is about 10%, but they are quite di�erent in the large QT
region, say QT & 100GeV. For a heavy Higgs boson, e.g. MH = 600GeV, these two dis-
tributions are very di�erent in the small QT region, and MC�NLO tends to populate more
events in the small QT region, as 
ompared to ResBos. Sin
e the Higgs boson is a s
alar, the
distributions of Higgs boson de
ay produ
ts just depend upon the Higgs boson's kinemati
s.
Therefore, the di�eren
e in the QT distribution predi
tions between MC�NLO and ResBos
may prove to be 
ru
ial for the pre
ision measurements of the Higgs boson's properties. A
further detailed study of the impa
t of the QT di�eren
e on the Higgs boson sear
h is in
MC@NLO
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
 = 140 GeV
 = 200 GeV
 = 170 GeV
 = 600 GeV
(a) (b)
(c) (d)
MC@NLO / RES
Figure 4: Comparison of the QT distributions between ResBos and MC�NLO.
order and will be presented elsewhere.
IV. PHENOMENOLOGICAL STUDY OF THE H → WW MODE
In the sear
h for SM-like Higgs boson via H → WW (∗) mode, two s
enarios of W boson
de
ay were 
onsidered in the literature [60, 61, 62℄: one is that both W bosons de
ay
leptoni
ally, another is that one W boson de
ays leptoni
ally and another W boson de
ays
hadroni
ally. Throughout this paper, we only 
on
entrate on the di-lepton de
ay mode, i.e.
H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ , at the Tevatron and the LHC. The 
ollider signature, therefore,
is two isolated opposite-sign 
harged leptons plus large missing transverse energy ( 6ET ) whi
h
originates from the two neutrinos. In this se
tion, we �rst examine the RES e�e
ts on various
kinemati
s distributions, and then show the RES e�e
ts on the Higgs mass measurement.
Finally, we study the RES e�e
ts on the a

eptan
es of the kinemati
s 
uts suggested in the
literature for Higgs sear
h.
(a) (b) (c)
Figure 5: Kinemati
 
on�gurations of Higgs de
ay (H → WW → ℓ+ℓ−νν̄) in the rest frame of H:
(a) H → W++W
+ , (b) H → W
− and (
) H → W
0 . Here, +(−, 0) denotes the right-handed
(left-handed, longitudinal) polarization state of the W boson. The long arrows denote the moving
dire
tions of the �nal-state leptons. The short bold arrows denote the parti
les' spin dire
tions.
A. Basi
 kinemati
s distributions
For a heavy Higgs boson, the two ve
tor bosons, whi
h are generated from the spin-0 Higgs
boson de
ay, are predominantly longitudinally polarized, while the longitudinal and trans-
verse polarization states are demo
rati
ally populated when the Higgs boson mass is near the
threshold for de
aying into the ve
tor boson pair [63, 64℄. When 140GeV ≤ MH ≤ 170GeV,
the transverse polarization modes 
ontribute largely. The two 
harged leptons in the �nal
state have di�erent kinemati
s be
ause of the 
onservation of angular momentum, 
f. Fig.
5, therefore, one 
harged lepton is largely boosted and its momentum be
omes harder while
another be
omes softer. Making use of these di�eren
es, one 
an impose asymmetri
 trans-
verse momentum (pT ) 
uts on the two 
harged leptons to suppress the ba
kground. On the
event-by-event basis, we arrange the two 
harged leptons in the order of transverse momen-
tum: pLmaxT denotes the larger pT between the two 
harged leptons while p
T is the smaller
one. Fig. 6 shows the distributions of pLmaxT , p
T and missing energy (6ET ) for MH = 140GeV
at the Tevatron (�rst row) and for MH = 170GeV at the LHC (se
ond row). Furthermore,
in Fig. 7 we show the distributions of cos θLL, φLL and ∆YLL without imposing any kinemat-
i
s 
ut, where cos θLL is the 
osine of the opening angle between the two 
harged leptons,
φLL is the azimuthal angle di�eren
e between the two 
harged leptons on the transverse
plane, and ∆YLL is the rapidity di�eren
e of two 
harged leptons in the lab frame. Sin
e
we are mainly interested in the shapes of the kinemati
s distributions, the 
urves shown in
the �gures are all normalized by the 
orresponding total 
ross se
tions. The solid 
urves
present the distributions in
luding the RES e�e
ts, the dashed and dotted 
urves present
0 20 40 60 80 100
max (GeV)
0 20 40 60 80
 (GeV)
0 20 40 60 80 100
/ET (GeV)
0 20 40 60 80 100
max (GeV)
0 50 100
 (GeV)
0 50 100 150 200
/ET (GeV)
(a) (b) (c)
(d) (e) (f)
Figure 6: Normalized distributions of the leading transverse momentum pLmax
, softer transverse
momentum pLT of the leptons, and the missing energy 6ET in gg → H → WW → ℓ+ℓ′−νℓν̄ℓ′ . The
panels (a) to (
) are for MH = 140GeV at the Tevatron, and (d) to (f) are for MH = 170GeV at
the LHC.
the distributions 
al
ulated at the NLO and LO, respe
tively.
We note that the pT distributions of the 
harged leptons and the missing energy distri-
butions are modi�ed largely by the RES e�e
ts. This 
an be understood as follows. The
two 
harged leptons prefer to move in the same dire
tion due to the spin 
orrelation among
the de
ay produ
ts of the Higgs boson, 
f. the distributions of cos θLL in Figs. 7(a) and (d).
Hen
e, one 
an approximately treat the Higgs boson de
ay as �two-body� de
ay, i.e. de
ay-
ing into two 
lusters as H → (ℓ+ℓ′−) (νℓν̄ℓ′). This is in analogy to the W boson produ
tion
and de
ay in the Drell-Yan pro
ess, ud̄ → W+ → ℓ+ν, whi
h has been shown in Ref. [51℄
that the transverse momentum of lepton (pℓT ) is very sensitive to the transverse momentum
of the W boson. The same sensitivity also applies to 6ET . As shown in Figs. 6(
) and (f), the

lear Ja
obian peak of the 6ET distribution around MH/2 in the LO 
al
ulation is smeared
in the NLO and RES 
al
ulations. Furthermore, the 6ET distribution in the NLO and RES

al
ulations has a long tail due to the non-zero transverse momentum of the Higgs boson.
Sin
e the RES 
al
ulation in
ludes the e�e
ts from multiple soft-gluon radiation, the 6ET
-1 -0.5 0 0.5 1
0 1 2 3
-4 -2 0 2 4
-1 -0.5 0 0.5 1
0 1 2 3
-4 -2 0 2 4
(a) (b) (c)
(d) (e) (f)
Figure 7: Normalized distributions of cos θLL, φLL and ∆YLL in gg → H → WW → ℓ+ℓ′−νℓν̄ℓ′ :
The panels (a) to (
) are for MH = 140GeV at the Tevatron and (d) to (f) are for MH = 170GeV
at the LHC.
distribution near the Ja
obian peak is further smeared in the RES 
al
ulation as 
ompared
to the NLO 
al
ulation. When MH = 140GeV, only one W boson is on-shell and the two

harged leptons do not move as 
lose as they do in the 
ase of MH = 170GeV (in whi
h

ase, both W bosons are on-shell). However the parallel 
on�guration is still preferred.
The dominant ba
kgrounds of the H → WW (∗) mode are from the W boson pair pro-
du
tion and top quark pair produ
tion. The latter, as the redu
ible ba
kground, 
an be
suppressed with suitable 
uts su
h as jet-veto, but the former, as the irredu
ible ba
k-
ground, still remains even after imposing the basi
 kinemati
 
uts. In order to redu
e this
intrinsi
 ba
kground, one needs to take advantage of the 
hara
teristi
 spin 
orrelations of
the 
harged leptons in the H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ de
ay. For example, the distribution of
the di�eren
e in azimuthal angles of the 
harged leptons peaks at smaller value (
f. Figs. 7(b)
and (e)) for the signal than that for the WW 
ontinuum produ
tion ba
kground [60, 62℄.
We note that the RES e�e
ts do not a�e
t the cos θLL and φLL distributions very mu
h, as
shown in Figs. 7(a), (b), (d) and (e).
To 
losely examine the di�eren
e in their predi
tions, we also present the ratio of the RES
10 20 30 40 50 60
max (GeV)
RES/NLO
RES/LO
0 10 20 30 40
 (GeV)
0 10 20 30 40 50 60 70
/ET (GeV)
10 20 30 40 50 60
max (GeV)
0 10 20 30 40 50
 (GeV)
0 20 40 60 80
/ET (GeV)
(a) (b) (c)
(d) (e) (f)
Figure 8: Ratio of the Resummation 
ontribution to NLO and LO 
ontributions in gg → H →
WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ . The panels (a) to (
) are for MH = 140GeV at the Tevatron while (d) to (f)
are for MH = 170GeV at the LHC.

ontribution to the NLO and LO 
ontributions in Fig. 8. We note that the ratio is about one
below the peak regions of pLmaxT , p
T and 6ET , and be
omes larger than one above the peak
region, where both the LO and NLO 
ontributions drop faster than the RES 
ontribution
does, whi
h is 
onsistent with the results shown in Fig. 6. This uneven behavior indi
ates
that one 
annot simply use the leading order kinemati
s with the 
onstant K-fa
tor in
luded
to mimi
 the higher order quantum 
orre
tions. We should stress that even though the NLO
and RES 
al
ulations in
lude the same 
ontributions of the hard gluon radiation from initial
states, the e�e
ts of the multiple soft-gluon radiation 
ould 
ause more than 25% di�eren
e
between RES and NLO predi
tions in the large pT and 6ET region.
B. Higgs mass measurement
In order to identify the signal events 
learly, it is 
ru
ial to re
onstru
t the invariant mass
of the Higgs boson. Unfortunately, one 
annot dire
tly re
onstru
t the MH distribution in
the H → WW mode due to the two neutrinos in the �nal state. Instead, both the transverse
mass MT and the 
luster transverse mass MC [65℄, de�ned as
2pLLT 6ET (1− cos∆φ(pLLT , 6ET )),
LL+ 6ET , (3)
yield a broad peak near MH . In Eq. (3), p
T (mLL) denotes the transverse momentum
(invariant mass) of the two 
harged lepton system, and ∆φ(pLLT , 6ET ) is the di�eren
e in
azimuthal angles between pLLT and 6ET on the transverse plane. We note that the upper
endpoint of MT distribution 
an 
learly re�e
t the mass of Higgs boson, 
f. Figs. 9(a) and
(
). MT is insensitive to QT be
ause it depends on QT in the se
ond order, 
f. Eq. (3).
Therefore, the position of the endpoint is only subje
t to MH and ΓH . The latter e�e
ts 
an
be safely ignored be
ause ΓH is very small (less than about 1.5GeV), for the Higgs boson
mass less than 200GeV. The 
luster transverse mass MC also exhibits a 
lear Ja
obian peak
with a 
lear edge at MH , 
f. Figs. 9(b) and (d). But both the line shape and the Ja
obian
peak of MC distribution are modi�ed by the RES e�e
ts be
ause MC is dire
tly related to
6ET whi
h depends on QT in the �rst order. We suggest that one should use MT to extra
t
the mass of Higgs in H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ mode be
ause the upper endpoint of the
MT distribution is insensitive to high order 
orre
tions.
C. A

eptan
e study
In order to separate the signal from its 
opious ba
kgrounds, one needs to impose optimal

uts to suppress ba
kgrounds and enhan
e the signal to ba
kground ratio (S/B ) simulta-
neously. The sele
tion of the optimal 
uts highly depends on how well we understand the
kinemati
s of the signal and ba
kground pro
esses. As shown above, the RES e�e
ts modify
the distributions of transverse momentum of the 
harged leptons and the missing energy
largely, therefore, it is important to study the RES e�e
ts on the a

eptan
es of the kine-
mati
s 
uts. Here, we impose a set of kinemati
s 
uts used by experimental 
olleagues in
Refs. [37, 39℄. The 
orresponding a

eptan
es are summarized in Table II.
• For the sear
h for a 140 GeV Higgs boson at the Tevatron, we impose the following
basi
 
uts:
pLmaxT > 15GeV , p
T > 10GeV,
|YL| < 2.0 , 6ET > 20GeV, (4)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
0 50 100 150 200
 (GeV)
(a) (b)
(c) (d)
Figure 9: Normalized distributions of the transverse mass MT and the 
luster mass MC in gg →
H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ : (a) and (b) are for MH = 140GeV at the Fermilab Tevatron while (
)
and (d) are for MH = 170GeV at the LHC.
and the optimal 
uts as follows:
mLL <
< MT < MH − 10GeV
φLL < 2.0 rad ,
+ 20GeV < HT < MH (5)
where YL denotes the rapidity of 
harged lepton, and HT denotes the s
alar sum of
the transverse momenta of �nal state parti
les, i.e. HT ≡ |peT | + |p
T | + | 6ET |. The
overall e�
ien
y of the 
uts is about 68% , 69% and 70% after imposing the basi
 
uts
(Eq. (4)) for RES, NLO and LO 
al
ulations, respe
tively, and about 44% for both
RES and NLO 
al
ulations and 46% for LO 
al
ulation after imposing the optimal

uts (Eq. (5)).
• For the sear
h of a 170 GeV Higgs boson at the LHC, we require the following basi

uts:
pLmaxT > 20GeV , p
T > 10GeV,
|YL| < 2.5 , 6ET > 40GeV, (6)
Table II: A

eptan
e of gg → H → WW (∗) → ℓ+ℓ′−νℓν̄ℓ′ events after imposing the basi
 
uts and
the optimal 
uts for MH = 140GeV at the Tevatron and MH = 170GeV at the LHC.
MH = 140GeV MH = 170GeV
basi
 (Eq. (4)) optimal (Eq. (5)) basi
 (Eq. (6)) optimal (Eq. (7))
RES 0.68 0.44 0.61 0.19
NLO 0.69 0.44 0.61 0.19
LO 0.70 0.46 0.63 0.20
and the optimal 
uts:
mLL < 80.0GeV , MH − 30.0GeV < MT < MH ,
φLL < 1.0 rad , θLL < 0.9 rad , |∆YLL| < 1.5 , (7)
The 
ut e�
ien
y is about 61% for both RES and NLO 
al
ulations, but about 63%
for LO 
ontribution after imposing the basi
 
ut (Eq. (6)). After imposing the optimal

uts (Eq. (7)), the a

eptan
es of RES and NLO are about 19%, while LO is 20%.
V. PHENOMENOLOGICAL STUDY OF THE H → ZZ MODE
In the sear
h for the SM Higgs boson, the H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− is an important
dis
overy 
hannel for a wide range of Higgs boson mass. The appearan
e of four 
harged
leptons with large transverse momenta is an attra
tive experimental signature. This so-

alled �gold-plated� mode provides not only a 
lean signature to verify the existen
e of the
Higgs boson but also an ex
ellent pro
ess to explore its spin and CP properties [66℄. In
this se
tion, we study three mass values of MH (140, 200 and 600GeV) at the LHC. For
MH = 140GeV and 200GeV, we require the two Z bosons both de
ay into 
harged leptons;
for MH = 600GeV, we require one Z boson de
ays into a 
harged lepton pair and another Z
boson de
ays into a neutrino pair, i.e. ℓ+ℓ−νν̄. In this se
tion we �rst study the RES e�e
ts
on various kinemati
s distributions and then examine the RES e�e
ts on the a

eptan
es of
the kinemati
s 
uts.
0 20 40 60 80 100
max (GeV)
0 20 40 60 80
 (GeV)
0 50 100 150
max (GeV)
0 20 40 60 80 100
 (GeV)
(a) (b)
(c) (d)
Figure 10: Normalized distributions of pLmax
and pLT in gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′−: (a) and (b)
are for MH = 140GeV; (
) and (d) are for MH = 200GeV at the LHC.
A. gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′−
Similar to the H → WW (∗) mode, we also arrange the four 
harged leptons of the
H → ZZ(∗) mode in the order of transverse momentum. We denote pLmaxT as the largest
pT of the four 
harged leptons while p
T the se
ond leading pT . In Fig. 10, we show the
distributions of pLmaxT and p
T for MH = 140 and 200GeV, respe
tively. Due to the similar
kinemati
s dis
ussed in the H → WW (∗) mode, the shapes of the distributions of pLmaxT
and pLT are 
hanged signi�
antly by the RES e�e
ts. The typi
al feature is that the RES
e�e
ts shift the pT of the 
harged lepton to the larger pT region and, therefore, in
rease the
a

eptan
es of the kinemati
s 
uts. The numeri
al results will be shown later.
Although one 
an measure the Higgs boson mass by re
onstru
ting the invariant mass of
the four 
harged leptons, one still needs to re
onstru
t the Z bosons in order to suppress
the ba
kgrounds. The re
onstru
tion of the Z boson depends on the lepton �avors in the
�nal state. In this study, we 
onsider two s
enarios: di�erent �avor 
harged lepton pairs,
i.e. H → 2e2µ, and four same �avor 
harged leptons, i.e. H → 4e( or 4µ). Hen
e, we have
two methods for re
onstru
ting the Z bosons:
1. Di�erent �avor 
harged lepton pairs (2e2µ):
In this 
ase, it is easy to re
onstru
t the Z bosons be
ause both ele
tron and muon
lepton �avors 
an be tagged. Using the �avor information, the Z bosons 
an be
re
onstru
ted by summing over the same �avor opposite-sign leptons in the �nal state.
2. Four same �avor 
harged leptons (4e/4µ):
If the �avors of four leptons are all the same, one needs to pursue some algorithms
to re
onstru
t the Z boson mass. In our analysis, we �rst pair up the leptons with
opposite 
harge. We require the pair whose invariant mass is 
losest to MZ to be
the one generated from the on-shell Z boson, and the other pair is the one generated
from another Z boson, whi
h 
ould be on-sell or o�-shell. We name it as the minimal
deviation algorithm (MDA) in this paper.
In Fig. 11, we show the pT distributions of the re
onstru
ted Z boson for 140 and 200GeV,
respe
tively. When the �nal state lepton �avors are di�erent, one 
an re
onstru
ted the Z
boson perfe
tly by mat
hing the lepton �avor. For the same �avor leptons, the re
onstru
ted
Z boson distributions in the MDA are shown as the solid, dashed and dot-dashed 
urves for
RES, NLO and LO, respe
tively. Some points are worthy to point out as follow:
• We note that the MDA 
an perfe
tly re
onstru
t the distributions of true Z bosons,
irregardless whether these two Z bosons are both on-shell or only one of them is
on-shell.
• When MH = 200GeV, both Z bosons are produ
ed on-shell and boosted. The peak
position of the transverse of momentum pZT is around
(MH/2)
2 −m2Z ∼ 41GeV. For
all the 
ases, the RES e�e
ts 
hange the shape of pZT largely and shift the p
T to the
larger value region.
It has been shown in Ref. [67℄ that angular 
orrelation between the two Z bosons from
the Higgs de
ay 
an be used to suppress the intrinsi
 ba
kground from ZZ pair produ
tion
e�
iently. One of the useful angular variables is the polar angle (θ∗Z) of the (ba
k-to-ba
k)
Z boson momenta in the rest frame of the Higgs boson [67℄. As shown in Fig. 12, in the rest
frame of Higgs boson, the ba
k-to-ba
k Z bosons like to lie in the dire
tion perpendi
ular to
the z−axis, whi
h is the moving dire
tion of the Higgs boson in the lab frame. After being
0 20 40 60 80 100
 (GeV)
0 20 40 60 80 100
 (GeV)
0 20 40 60 80 100
 (GeV)
(a) (b) (c)
Figure 11: Normalized transverse momentum of Z boson in gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− at the
LHC: (a) is the pT distributions of o�-shell Z boson for MH = 140GeV, (b) is the pT distributions
of on-shell Z boson for MH = 140GeV and (
) is the pT distributions of on-shell Z boson for
MH = 200GeV.
0 0.5 1 1.5
0 0.5 1 1.5
(a) (b)M
 = 140 GeV M
 = 200 GeV
Figure 12: Normalized polar angle of the (ba
k-to-ba
k) Z boson momenta distributions in the rest
frame of the Higgs boson in gg → H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− at the LHC: (a) is for MH = 140GeV
, (b) is for MH = 200GeV.
boosted to the lab frame, two Z bosons will move 
lose to ea
h other, 
.f. Fig. 13(b), where
θZZ is the opening angle between the two Z bosons in the lab frame. Another interesting
angular variable is the angle between the two on-shell Z boson de
ay planes (φDP ) in the rest
frame of the Higgs boson, whi
h is shown in Fig. 13(a). The two Z bosons are re
onstru
ted
as explained above. Sin
e the angle θ∗Z and φDP are de�ned in the rest frame of the Higgs
boson, the non-zero transverse momentum of the Higgs boson does not a�e
t these two
variables. Therefore, as 
learly shown in the �gures, all the distributions of the angular
variables mentioned above are the same for the RES, NLO and LO 
al
ulations.
-1 -0.5 0 0.5 1
cos φ
-1 -0.5 0 0.5 1
cos θ
(a) (b)
Figure 13: Normalized distributions of cosφDP and cos θZZ in the rest frame of the Higgs boson
with mass 200GeV in gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′− at the LHC.
B. gg → H → ZZ → ℓ+ℓ−νν̄
Although the �gold-plated� mode, H → ZZ → ℓ+ℓ−ℓ′+ℓ′−, is 
onsidered to be the most
e�e
tive 
hannel for the SM Higgs boson dis
overy at the LHC, it su�ers from the small
de
ay bran
hing of Z → ℓ+ℓ−. Moreover, the larger the Higgs mass be
omes, the smaller
the produ
tion rate is. When the Higgs boson mass is larger than 600 GeV, the H →
ZZ → ℓ+ℓ−νν̄ 
hannel may be
ome important be
ause the de
ay bran
hing ratio (Br) of
H → ZZ → ℓ+ℓ−νν̄ is six times of the Br of H → ZZ → ℓ+ℓ−ℓ′+ℓ′−. The drawba
k is that
one 
annot re
onstru
t the Higgs mass from the �nal state parti
les due to the presen
e of
two neutrinos. In this dis
overy 
hannel, the missing transverse energy ( 6ET ) is 
ru
ial to
suppress the ba
kground [37℄. The 6ET distribution is shown in Fig. 14(a) whi
h exhibits a
Ja
obian peak around MH/2, and the soft-gluon resummation e�e
ts smear the Ja
obian
peak and shift more events to the larger 6ET region. Similar to the H → WW mode, the
kinemati
s of this 
hannel is similar to the W boson produ
tion and de
ay in the Drell-Yan
pro
ess, therefore the shape of 6ET distribution 
hange signi�
antly by the RES 
ontributions.
The Higgs boson mass 
an be measured from the peaks of the distributions of the transverse
mass MT and the 
luster mass MC , 
f. Eq. (3), as shown in Fig. 14(b) and (
). Although
the upper endpoint of MT is insensitive to high order 
orre
tions as we mentioned in the
study of H → WW (∗) mode, the Ja
obian peak is smeared out by the width (ΓH) e�e
ts
of the Higgs boson. For MH = 600GeV, the total de
ay width of the Higgs boson is about
0 100 200 300 400 500
/ET (GeV)
0 200 400 600 800
 (GeV)
0 200 400 600 800
 (GeV)
(a) (b) (c)
Figure 14: Normalized distributions of 6ET , MT and MC in gg → H → ZZ → ℓ+ℓ−νν 
hannel with
MH = 600GeV at the LHC.
Table III: A

eptan
e of the pro
ess gg → H → ZZ → ℓ+ℓ−ℓ′+ℓ′− for MH = 140 (200)GeV and
the pro
ess gg → H → ZZ → ℓ+ℓ−νν̄ for MH = 600GeV after imposing 
uts.
MH = 140GeV MH = 200GeV MH = 600GeV
basi
 (Eq. 8) optimal (Eq. 9) basi
 (Eq. 8) optimal (Eq. 9) basi
 (Eq. 10)
RES 0.53 0.15 0.67 0.14 0.55
NLO 0.54 0.12 0.67 0.11 0.56
LO 0.53 0 0.67 0 0.58
120 GeV, whi
h is quite sizable and generates a noti
eable smearing e�e
t on the Ja
obian
peak.
C. A

eptan
e study
The dis
overy potential of the H → ZZ → ℓ+ℓ−ℓ′+ℓ′− and H → ZZ → ℓ+ℓ−νν̄ modes
has been studied in Ref. [37℄ after imposing the following 
uts:
• For MH = 140GeV and 200GeV, the intermediate mass range, we impose the basi

uts:
pET > 7.0GeV, |YL| < 2.5, pLT > 20GeV, (8)
and the optimal 
uts:
, (9)
where pET and YL are the transverse momentum and rapidity of ea
h 
harged lepton,
respe
tively, and p
T is the pT of the harder Z boson.
• For MH = 600GeV, we require:
pLT > 40GeV, |YL| < 2.5 ,
pLLT > 200GeV, 6ET > 150GeV, (10)
where pLLT is the transverse momentum of the two 
harged lepton system. The numeri-

al results of the a

eptan
es of the various 
uts are summarized in Table III. For the
H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− mode, the RES and NLO 
ontributions have almost the same
a

eptan
es after imposing the basi
 
uts. However, after imposing the optimal 
uts the
a

eptan
e of the RES 
ontribution is larger than the one of the NLO 
ontribution by 25%,
and the LO 
ontribution is largely suppressed. For the H → ZZ → ℓ+ℓ−νν̄ mode, the
a

eptan
es of the RES and NLO 
al
ulations are similar to ea
h other.
VI. CONCLUSION
The sear
h for the SM Higgs boson is one of the major goals of the high energy physi
s
experiments at the LHC, and the ve
tor boson de
ay modes, H → WW (∗) or H → ZZ(∗),
provide powerful and reliable dis
overy 
hannels. The LHC has a great potential to dis-

over the Higgs boson even with low luminosity (∼ 30 fb−1) during the early years of run-
ning [37, 38, 68℄. In order to extra
t the signal from huge ba
kground events, we should
have better theoreti
al predi
tions of the signal events as well as ba
kground events. In
this paper, we examine the soft gluon resummation e�e
ts on the sear
h of SM Higgs boson
via the dominant produ
tion pro
ess gg → H at the LHC and dis
uss the impa
ts of the
resummation e�e
ts on various kinemati
s variables whi
h are relevant to the Higgs sear
h.
A 
omparison between the resummation e�e
ts and the NLO 
al
ulation is also presented.
For H → WW (∗) → ℓ+ℓ−νν̄ mode, we study MH = 140GeV at the Tevatron and
MH = 170GeV at the LHC. Due to the spin 
orrelations between the �nal state parti
les,
this pro
ess is similar to the W boson produ
tion and de
ay in the Drell-Yan pro
ess.
The shapes of the kinemati
s distributions are modi�ed signi�
antly by RES e�e
ts. For
example, the e�e
ts 
ould 
ause ∼ 50% di�eren
e 
ompared to NLO 
al
ulation in the
transverse momentum distribution of the leading lepton (p
T ), when MH = 170GeV. The
Higgs boson mass 
annot be re
onstru
ted dire
tly from the �nal state parti
les be
ause of
two neutrinos. Therefore, the upper endpoint in the transverse mass distribution 
an be
used to determine the mass of the Higgs boson, and we found that it is insensitive to the
RES e�e
ts. After imposing various kinemati
s 
uts, the LO, NLO and RES 
al
ulations
yield similar a

eptan
e of the signal events.
For the H → ZZ(∗) → ℓ+ℓ−ℓ′+ℓ′− mode, the so-
alled �gold-plated� mode, we study
MH = 140GeV and MH = 200GeV at the LHC in this paper. We pursue an algorithm,

alled minimal deviation algorithm in this paper, to re
onstru
t the two Z bosons when the
four 
harged leptons in the �nal state have the same �avors. The RES e�e
ts 
hange the
shapes of kinemati
s signi�
antly, e.g. pLmaxT and p
T distributions. However, the variables
φDP and θ
Z , de�ned in the Higgs rest frame, are insensitive to RES e�e
ts. After imposing
the optimal kinemati
s 
uts, the RES e�e
ts 
ould in
rease the a

eptan
e by 25% 
ompared
to that of NLO 
al
ulation while the LO 
ontribution is largely suppressed. When the Higgs
boson is heavy (600GeV), we 
onsider the H → ZZ → ℓ+ℓ−νν̄ mode be
ause of its larger
de
ay bran
hing ratio, as 
ompared to the H → ZZ → ℓ+ℓ−ℓ′+ℓ′− mode. The shape of 6ET
distribution, whi
h is 
ru
ial to suppress the ba
kgrounds, is largely modi�ed be
ause it is
sensitive to the transverse momentum of the Higgs boson.
In summary, we have presented a study of initial state soft-gluon resummation e�e
ts
on the sear
h for the SM Higgs boson via gluon-gluon fusion at the LHC. The e�e
ts not
only signi�
antly modify some of the kinemati
 distributions of the �nal state parti
les, as

ompared to the NLO and LO predi
tions, but also enhan
e the a

eptan
e of the signal
events after imposing the kinemati
 
uts to suppress the large ba
kground events. Therefore,
we 
on
lude that the initial state soft-gluon resummation e�e
ts should be taken into a

ount
as sear
hing for the Higgs boson at the LHC. In addition, we note that the spin 
orrelations
among the �nal state leptons 
ould be modi�ed by the ele
troweak 
orre
tions to the Higgs
boson de
ay. Therefore, we have implemented the NLO QED 
orre
tion in the ResBos 
ode,
and the phenomenologi
al study will be presented in the forth
oming paper.
A
knowledgments
We thank Professor C.-P. Yuan for a 
riti
al reading and useful suggestions. We also
thank Dr. Kazuhiro Tobe for useful dis
ussions. Q.-H. Cao is supported in part by the U.S.
Department of Energy under grant No. DE-FG03-94ER40837. C.-R. Chen is supported in
part by the U.S. National S
ien
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	introduction
	Transverse momentum resummation formalism
	Inclusive cross sections
	Phenomenological study of the HWW mode
	Basic kinematics distributions
	Higgs mass measurement
	Acceptance study
	Phenomenological study of the HZZ mode
	ggHZZ(*)+-+-
	ggHZZ+-
	Acceptance study
	Conclusion
	Acknowledgments
	References
