SLAC-PUB-2197. COO-1545-242. September 1978. (T/E). HIGGS BOSON PRODUCTION AT LARGE TRANSVERSE MOMENTUM IN QCD. 4. Risto Raitio*.
SLAC-PUB-2197 COO-1545-242 September 1978 (T/E)
HIGGS BOSONPRODUCTIONAT LARGE TRANSVERSEMOMENTUM IN QCD 4 Risto Stanford
Stanford University,
Raitio*
Linear Accelerator Center Stanford, California 94305 and
Research Institute for Theoretical University of Helsinki, Helsinki, Walter Stanford
Stanford University,
Physics Finland
W. Wadat
Linear Accelerator Center Stanford, California 94305 and
Department of Physics The Ohio State University, Columbus, Ohio 43210 ABSTRACT We estimate
the Higgs boson production
duldy and dcr/dydqG in p(p3p-collisions subprocess
cross
sections
by calculating
the
gluon + gluon - Higgs boson + heavy quark-anti-
quark pair.
(To be submitted
to Phys. Rev. D.)
*Supported by the Department of Energy under Contract No. EY-76-C-03-0515 and the Academy of Finland. tsupported in part by the Department of Energy under Contract No. EY-76-c02-1545.*000.
The problem of Higgs boson (H) production
has been studied
have been proposed, 5 it
Because of the lower bounds on the mass of H that appears @at
the possibility
to energetic
e+e- annihilation
the next generation analog
proton
into
subprocess
tributes
obviously
at small
it
able cross
gated in this H off levant a2S’
same as that
grams that
in the 14q
pair
and internal from two-gluons
To this
rapidity
process
gluon+gluon-H+heavy
Its
coupling
order
there
qT, such as that
sections
MeV,
Therefore,
that
we have investi-
production
of
The reis of order
are other
diaHowever,
these are expected
(Fig.2).
In this
do/dy and do/dydqG at y=O, arising
we
give measur-
in Fig.l(b).
of the nucleon,
under consideration
might
cross section
of H, for p(c) +p-HHanything
to
note we calwhere y
from the sub-
quark pair.
We assume the simplest H.
While only con-
in pp collisions.
(Fig.l(a)).
to-the
it
bremsstrahlung
of Ref.3
cross
that
The process
The resulting
referes
physical
processes
in Fig.2.
the differential
sections,
are most severe.
~~10 GeV region.
because of the small heavy quark content
culate
cross
are given
by the process
from the fusion
diagram is calculated.
problems
also other
can lead to non-vanishing
be dominated
arising
the two-gluon
nwmenta (qT) of the produced H, say (qT)w300
T work is the external
diagrams
hundred GeV3 of
In Ref.3
large
the background
heavy quark-antiquark
would be restricted
of several
facilities.
relatively
to invest-lgate
sections
ring
the quark triangle
transverse
desirable
and detection
mechanism (Fig.l(a))
gives
region
production
and pp collisions
storage
H through
in which kinematic find
~4
diagram of the Drell-Yan
of two-gluons this
of its
f-4
earlier.
spontaneously constant
broken gauge theory6
involving
one
to quarks is given by
$9 %I = mQ 2 GF'
(1)
I 3
where mQ is the quark mass and GF the Fermi coupling
constant.
gh is proportional
only
to m makes it Q
and t - are appreciable. ga(pl)
+gb(p2)
-H(q)
that
its
The amplitudes +a(k2>
+Q(k$
couplings
corresponding
The fact
that
to heavy quarks c, b,
to the diagrams of Fig.2
for
is of the fo-
(2)
with
I?ab
= T T A" abl
+ TbTaA;"+ TaTbAzV + TbTaAtv
+ TaTbA;;" + TbTaAgV + ifabcTc
where g is the gauge coupling Ta = *ha with [Ta,Tbl
ha the Gell-Mann It
= ifabcTc*
in accordance
with
is straightforward
gluons
should be summed over only to QED in which photon
These are given
As was pointed
polarizations
in QED, p
out previously7,
in the appendix.
the square of the amplitude of the gluons.
in which self-couplings familiar
of gluons,
the structure constants in abc to construct the amplitudes AyV...AiV
is always compled to conserved
conditions
to the octet
and f
in the protons,
(7) and (8) in Fig.2
the gauge-invariance do not occur.
in Fig.2.
the transverse
AFV + AIV > ,
of QGD, a and b refer
matrices,
the diagrams
Assuming on-shell
the diagrams
constant
(3)
this
charged current, of gluons
(2) Contrary because of
take place,
TPv = p2v?al = 0, in fact 1~ ab has the consequence that
the
in the Feynman gauge,& h hhE = -g would introduce spurious contribuWV’ PV coming from the longitudinal polarizations. A method to circumvent the com-
condition tions
plications
resulting
from this
terms in APv and APv proportional difference7between8TIl
was proposed previously8,
according
to py and pl are to be dropped,
of (3) and ?"ab thus obtained "
is proportional
to which the since
the
to pyeP(pl)
4
and p's (p ) and the amplitude 2v 2 is then found p p" = p2v!?ib 1~ ab the phyacal
gluons.
Needless
averaged
over the physical 9,lO the gluons. The coupling
an appropriate
is unchanged for = 0, allowing
constantOls(=g2/4n)
of QCD should depend upon Q2, where Q is It may be approximated
9 !h(Q2/A2>
'
(4)
particles
Crs(Q2) is found to be in the range 0.2-0.3
one takes Q2 to be equal to the mass square of the three
Because of the considerable situation,
culations,
i.e.
differential tions
uncertainty
we have adopted 11 as*0.3.
The cross section cross
according
in assigning
the value
for p+p -H+anything
section
for
g+g -H+Q+~
for Q2=25 -100
the value
for as commonly used in QCD cal-
is now obtained
F(xl)
F(x2)
by convoluting
over the gluon distribution
the func-
da(xlP1,x2P2,kl,k2,4),
where pl and p2 are the c.m. momenta of the protons, function
and F(x)
GeV2.
for Q2 in (4) in the
to
da = s dxldx2
tribution
by8
4ll
If
present
(2) should be
degrees of freedom of
where A = 500 MeV. produced,
It
the usage of the Feynman gauge for
and the octet
mass scale of the system.
=
polarizations.
to say, the square of the amplitude
polarizations
as(Q2)
the physical
the gluon dis-
which is taken to be
F(x) = ,tl-x)5,
X
(6)
I
5
to (x f-n)
corresponding
= 0.5.
The resulting cross sections da/dy(at h tions of /.s at two Higgs boson mass values from three
quarks c, b, and t with
are summed. Of these, mately
equal,
additional
while
The differential
%
are shown in Fig.3
= 5 and 10 GeV.
masses 1.5,
of the heaviest
quarks,
if
exist,
cross section
as func-
Contributions
5, and 15 GeV, respectively,
c and b quarks contributions
that
heavier
y=O)
are found to be approxi-
quark is roughly
should increase
do/dyqG (at y=O)
5% of the total.
the cross section
Thus,
only slightly.
for % = 10 GeV and &=400
GeV
is shown in Fig.4. A comparison diagram3
of da/dy obtained that
shows
the present
from the bremsstrahlung manitude tively
at all large
Js.
with
cross
offheavy
that section
arising
for H production
quarks is smaller
This disadvantage
from the triangle
by one or two orders
may perhaps be compensated by the rela-
by the previous
authors l-4 , the most serious
in the search of the Higgs boson is the experimental decays into
expected
pairs
l-4
previously.
that
meson pairs
hadrons,
situation
qT, say qTb5
arises
of these events
GeV/c, jets
for
for
if
its
mH 211 GeV. into
these b6 jets
a pair will
identifiaation.
corresponding
heavy quarks,
It
is then
of b6 jets.
be accompanied by
transverse
in momentum space is non-coplanar.
from the decay containing
then the signal
with
signal
problem
and photons have been discussed
the Higgs boson decays predominantly
of heavy quark-antiquark
The structure
stable,
of leptons,
An interesting
For an appreciable a pair
of
qT, as seen in Fig.4.
As has been emphasized
Its
arising
momenta. If
i.e.
bii, b3, etc.,
the Higgs boson is expected
to be relatively
the are clean.
6
Finally, sensitive _
we would like
to the largely
certainties
-
are typically
In sunxnary, it multihundred another
its
that
our cross section
unknown gluon structure factors
of two (squared
seems to us that
GeV proton
avenue for
to mention
rings
at large
function. in this
the production transverse
valuesNare
-
These uncase).
of the Higgs particle momenta may possibly
provide
search.
Acknowledgements We thank S. J. Brodsky, useful
discussions.
hospitality
We are grateful
extended
Group where this
J. Ellis,
P. H. Frampton, to Professor
to us at the Stanford
work was carried
out.
Linear
and E. Takasugi
in
for
S. D. Drell
for
the warm
Accelerator
Center Theory
7
APPENDIX Amplitudes in tiich2he
AyV, AgV, and,Ag'
two gluons
by the simultaneous
AVV = C(kl) 1
are given below. AClV
are crossed,
interchanges
3
APV = G(kl) 5
AC"" +A"= 7
8
l
respectively,
amplitudes are obtained
and pl*p2.
-$2yv + 2k; 1$" 2Wl)
2(Plkl)
4-2m YV
wq
Uqk2) +g
2ky - hl
$2~v - 2k;
2(plkl)
2(p2k2)
' 2(PlP2)
V(k2)
2(p2k2)
+G
2ky-Tfil ACIV = C(k1)
AclV, and Ai', 4
2'
p,*v
The corresponding
C(-Pl+P2)pgtiV
u(kl)
yP - yP
W2)
+ (2Pl+P2)v
gpp- (Pl+2P2)pgvq
W2).
8
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We have approximated
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in the square of the sum of the amplitudes
11.
We checked the case for da/dy (y=O) using quark mass m 10. Q =5 GeV at /s=400 GeV. The result was 27% increase of cross section commQ pared to the m =0 case. For other quark masses considered the effect upon Q do/dy was smaller. G. Altarelli, G. Parisi and R. Petronzio, Phys. Lett. z, 356 (1978); by setting
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I 9 FIGURE CAPTIONS 1.
8 for H production Diagrams of order asGF
2. >Diagrams for gluon+gluon 3.
The cross of /s with
Higgs masses %=5
masses 1.5,
quark-antiquark
pair.
do/dy at y= 0 in nb for pp-H+anything
section
we show for %=lO
4.
-H+heavy
in hadron collisons.
and 10 GeV, and as=0.3.
GeV the different
quark contributions
as a function In dashed line with
the quark
5 and 15 GeV indicated.
The differential
cross
Js=400
%=lO
GeV with
are shown in-dashed
line
section
do/dydqc
GeV and as=0.3. with
in nb/GeV2 for pp-HKanything The various
quark masses indicated.
quark contributions
at
I
-a W
9-78
(b) Fig. I
2. pq--
I.
P+--k2 3. -\
-3
5.
7.
2-4
-4
6.
\
-XE
8. Lr--