HIGGS BOSON PRODUCTION AT LARGE TRANSVERSE ...

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

REFERENCES 1.

J. Ellis, (1976),

M. K. Gaillard, and references

H. M. Georgi, Rev. Lett.

Nucl.

Phys. B106, 292

therein.

Phys. Rev. Lett.

2;" F. Wilczek, 3.

and D. V. Nanopoulos,

2,

1304 (1977).

S. L. Glashow, M. E. Machacek, and D. V. Nanopoulos,

40, 692 (1978).

4.

P. H. Frampton and W. W. Wada, Phys. Rev. (to be published).

5.

S. Weinberg, 296 (1976), Lett.

6.

Phys.

Phys. Rev. Lett. and Phys. Lett.

36, 296 (1976); 7OB, 306 (1977);

A. D. Linde,

JETP Lett.

P. H. Frampton,

2,

Phys. Rev.

37, 1378 (1976).

S. Weinberg, Particle

Phys. Rev. Lett.

Physics,

l-9, 1264 (1967);

ed. N. Svartholm

(Almquist

A. Salam, in Elementary and Wiksell,

Stockholm,

1968),

p. 367. 7.

R. Cutler

8.

H. M. Georgi, Particles preprint

-9.

The trace

and D. Sivers,

Phys. Rev. Dz,

196 (1978).

S. L. Glashow, M. E. Machacek, and D. V. Nanopoulous "Charmed

from Two-Gluon Annihilation

in Proton-Proton

Collisions,11

Harvard

(1978). of the squared matrix

gram REDUCE. The xl9 x2, by the Monte Carol

element was obtained

and phase space integrations

by the computer prowere carried

out

program SHEP.

10.

We have approximated

the numerators

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

H. Fritzsch R. Raitio,

and P. Minkowski, Nucl.

Phys. Lett.

Phys. B139, 72 (1978).

m,

80 (1978);

K. Kajantie

and

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--