Production of CP-Odd Higgs Bosons with Large Transverse Momentum at Hadron Supercolliders

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FSU-HEP-930924-R Revised January 1994PRODUCTION OF CP-ODD HIGGS BOSONS WITH LARGE TRANSVERSE MOMENTUM AT HADRON SUPERCOLLIDERS Chung Kao ?Department of Physics,B-159,Florida State University Tallahassee,FL 32306-3016,USA Abstract A two Higgs doublet model is employed to study the production of a CP-odd Higgs boson (A )associated with a large transverse momen-tum jet (j )at hadron supercolliders.The cross section of pp →jA +X is evaluated with four subprocesses:gg →gA ,gq →qA ,g ˉq →ˉq A and q ˉq →gA .We ?nd that pp →jA +X is a signi?cant source of CP-odd

Higgs bosons at future hadron supercolliders.

1.Introduction

In the Standard Model(SM)of electroweak interactions,only one Higgs doublet is required to generate masses for the fermions as well as the gauge bosons.A single neutral CP-even Higgs boson(H0)appears after the spon-taneous symmetry breaking.Various extensions of the SM have more Higgs multiplets and lead to additional physical spin-0?elds[1].

A general two Higgs doublet model[2]has doubletsΦ1andΦ2with vacuum expectation values(VEV’s)v1and v2.If CP is invariant in the Higgs sector,there remain?ve physical Higgs bosons[1]after symmetry breaking: a pair of singly charged Higgs bosons H±,two neutral CP-even scalars H (heavier)and h(lighter),and a neutral CP-odd pseudoscalar A.

Two models with a discrete symmetry[3]have been considered for the Yukawa interactions among the Higgs bosons and fermions.In model I[4,6], all fermions couple toΦ2,and the Aqˉq interaction takes the form

L Aqˉq=+i m u v cotβˉdγ5dA(1) In model II[5,6],which is required in the minimal supersymmetry model (MSSM)?,Φ1couples to down-type quarks and charged leptons whileΦ2 couples to up-type quarks and neutrinos,and the Aqˉq interaction is

L Aqˉq=+i m u v tanβˉdγ5dA(2)

where tanβ≡v2/v1,

?I would like to thank Uli Baur for comparing the matrix elements in this reference.

2

of form factors[23]which are combinations of scalar one-loop integrals[24].

We have calculated all loop integrations with the computer code LOOP[25],

which evaluates one loop integrals analytically and generates numerical data.

If there exist just three generations of quarks,only the top quark loop

(t-loop)and the bottom quark loop(b-loop)make signi?cant contributions.

Therefore,only the third generation quark loops are considered in our cal-

culations with the following values of parameters:α=1/128,M Z=91.17

GeV,M W=80.0GeV,sin2θW=0.230,the bottom quark mass m b=5

GeV.If not speci?ed,the top quark mass(m t)is taken to be150GeV.The

mass of the CP-odd Higgs boson(m A)is considered to be between50and

1000GeV.The updated parton distribution functions of Owens[26]with

Λ=0.177GeV and Q2=m2A+P2T are chosen to evaluate the cross section

√

of pp→jA+X at the energies of the SSC(

s=14TeV).Since it is at the order ofα3s,the cross section of pp→jA+X

is very sensitive to the choice ofΛand Q2.To evaluate the production rate

of A with large P T as well as to avoid the singularities at P T→0,we impose a P T cut on the A and the jet:P T>50GeV.

Figure2shows the cross section of pp→jA+X at the SSC and the LHC

energies,as a function of m A,for m t=150GeV and various values of tanβ.

√s=14 The cross section is about5-19times larger at

TeV,for50GeV

mass of the CP-odd Higgs boson(m A),the quark mass in the loops(m q),

3

and the Mandelstam variables:?s,?t,?u.For m A

|M q?loop|2～m4q ln4(m2q).(3) The t-loop dominates in a large region of tanβ.The cross section is almost proportional to cot2βfor tanβ<10.Only for tanβclose to m t/m b,can the b-loop dominate and the total cross section be enhanced by large tanβ.Not shown is the interference between the t-loop and the b-loop.The t-loop and the b-loop interfere destructively if m A is close to2m t,but constructively if m A is away from2m t.

To compare the production rate of the CP-odd Higgs boson(A)to that of the SM Higgs boson(H0)at the SSC energy,we present the cross section of pp→φ+X,φ=H0or A from various subprocesses in Table I,for m t=150 GeV and tanβ=1.Several interesting aspects can be learned from Table I and Figure2:(1)If the Higgs bosons are produced from gg→φ,or the subprocesses of pp→jφ+X via quark loops,the cross section of A is at least twice that of the H0for mφ<500GeV.At mφ=2m t,the cross section of A is about5times that of the H0;which implies that the threshold enhancement at2m t is much larger for the A than for the H0.For larger mφ,their cross

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sections are about the same.(2)gg→gφdominates and contributes about 80%to the cross section of pp→jφ+X.(3)For mφ>400GeV,the number of Higgs bosons produced from gg→gφ+X with P T(φ)>50GeV,is almost comparable to that from gg→φ.(4)For mφ>50GeV,the cross sections of the A and H0are the same from gg→φbˉb,which is a good approximation to the‘exact’cross section ofφproduced from bˉb fusion[20].(5)For tanβ>10, gg→Abˉb becomes the major source of large P T CP-odd Higgs bosons.Its cross section is proportional to tan2βand it is greatly enhanced by large tanβ.

The e?ects of tanβand m t on the cross section of pp→jA+X at √

fusion in the appendix.

In Figure4,we show the P T distribution of pp→gA+X from gg→gA at

√

8

G aμν?G aμνA(4) whereλ=αs

32(

s4+t4+u4+m8A

24[?(

s2+u2

§In this section,tanβis taken to be1;αs is taken to be12π

|M(qˉq→gA)|2=f s)(7) where f=λ2g2s and the|M|2has been summed and averaged over all spins and colors.

√Table II shows the P T distribution(dσ/dP T)of pp→gA+X,at

cesses gg→gA and gg→Abˉb can be considered as complementary to each other for producing large P T CP-odd Higgs bosons at future hadron colliders.

The total cross section presented in this letter for pp→jA+X is less reliable for a much heavier A.It is likely to overestimate the production rates due to large ln(m2A/P2T0)contributions,since a constant minimal transverse momentum cuto?(P T>P T0=50GeV)has been applied.

√

The total cross section of pp→jA+X at

s=40TeV,for50GeV

I am grateful to Howie Baer,Bill Bardeen,Uli Baur,Joe Polchinski and Xerxes Tata for bene?cial discussions,to Sally Dawson and Duane Dicus for continuing encouragement as well as valuable comments and to Harvey Goldman for technical support.This research was supported in part by the DOE contract DE-FG05-87-ER40319.

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Appendix ?

At the lowest order,the cross sections of gg →φvia the top quark loops are

σ(gg →H 0)=1

M 2W

)(s )|F (ρ)|2δ(s ?M 0H 2

)

σ(gg →A )=1

M 2

W )(s )|G (ρ)|2δ(s ?M 2

A )

where αW =α/sin 2θW and ρ=m 2/m 2φ.

The functions F (ρ)and G (ρ)are

F (ρ)=+ρ[2+(4ρ?1)I (ρ)]

G (ρ)=?ρI (ρ)

and the function I (ρ)is

I (ρ)=+ 10dy

ρ?i?]}

=?2[sin ?1(1ρ)]2,ρ≥

1

2[ln (z

+

4

where z ±=[1±√

2[ln 2

(s

m 2)].

II.At the threshold,ρ=1/4,therefore

I(

1

4)=+

1

4)=+

π2

2ρ?

1

ρ3

),

F(ρ)=+1

ρ

),

G(ρ)=+1

ρ

).

Therefore,at the threshold of mφ=2m t,

σ(gg→A)

σ(gg→H0)

=9/4.

The same ratios appear in the cross sections of gg→gφat both limits.

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Tables

√

TABLE I.The cross section of pp→φ+X at

mφ(GeV)50100200300400600800

Raw Cross Section

gg→A6202701302908714 3.6 gg→Atˉt 6.9 4.6 2.2 1.20.710.290.13 gg→Abˉb467.9 1.00.270.0970.021 6.7×10?3 P T>50GeV

gg→Abˉb 2.6 1.00.260.0910.0390.010 3.6×10?3 gg→gA1368958125469.4 2.7 gq→qA22159.6217.5 1.60.45 gˉq→ˉq A9.5 6.1 3.77.6 2.60.470.12 qˉq→gA0.360.250.110.042 4.5×10?3 5.1×10?4 1.1×10?4

TABLE II.The P T distribution(dσ/dP T)of pp→gA+X in pb/GeV,at

√

m t\P T(GeV)1002004006008001000

15

Figures

FIG.1The Feynman diagrams of the subprocesses(a)gg→gA,(b) gq→qA and(c)qˉq→gA.We have not shown the diagrams with various permutations of the external legs.

FIG.2The cross section of pp→jA+X in pb versus m A,for m t=150

√

GeV,tanβ=1,2,5,10and30,at the energies:(a)

s=14TeV.

√FIG.3The cross section of pp→jA+X in pb versus tanβ,at

s=40 TeV,for m t=150GeV and tanβ=1,2,5,10and30.Two masses of the CP-odd Higgs boson are considered:(a)m A=200GeV and(b)m A=400 GeV.

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