Production of CP-odd Higgs bosons with large transverse momentum at hadron supercolliders

2 June 1994 PHYSICS LETTERS B

ELSEVIER

Physics Letters B 328 (1994) 420-426

Production of CP-odd Higgs bosons with large transverse momentum at hadron supercolliders Chung Kao 1 Department of Physics, B-159, Florida State University, Tallahassee, FL 32306-3016, USA

Received 3 October 1993; revised manuscript received 7 February 1994 Editor: H. Georgi

Abstract

A two Higgs doublet model is employed to study the production of a CP-odd Higgs boson (A) associated with a large transverse momentum jet (j) at hadron supercolliders. The cross section o f p p ~ j A + X is evaluated with four subprocesses: gg ~ gA, gq ~ qA, gO ~ qA and q?l ~ gA. We find that pp --+ j A ÷ X is a significant 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 ( H °) appears after the spontaneous symmetry breaking, Various extensions of the SM have more Higgs multiplets and lead to additional physical spin-0 fields [ 1 ]. A general two Higgs doublet model [2] has doublets • ~ and @2 with vacuum expectation values (VEVs) vl and v2. If CP is invariant in the Higgs sector, there remain five 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

Internet Address: [email protected].

fermions couple to q~2, and the Aqgl interaction takes the form .md ~-~AqEI = +i mu cot /3~y5uA - t - - cot/3dysdA v u

(1)

In model II [5,6], which is required in the minimal supersymmetry model (MSSM) 2, qb~ couples to downtype quarks and charged leptons while qb2 couples to up-type quarks and neutrinos, and the AqO interaction is ~-~Aqg7 ~" + imu cot/3t~y5uA + i ma tan/3dy5dA u u

(2)

where tan/3 ~ v2/vl, v/-v~ + v~ = v = 2 M w / g , u and d are generic u-type and d-type quarks. Without loss of generality, Model II is chosen in all our calculations. In this model, the A d d coupling is enhanced when tan/3 is large. The cross section for Model I is usually dominated by the contribution from the top quark, and 2 Reviews of the MSSM can be found in [7-10]. Recent studies on the search for MSSM Higgs bosons at hadron supercolliders are to be found in [11-15].

0370-2693/94/$07.00 (~) 1994 Elsevier Science B.V. All rights reserved SSDI 0370-2693 (94) 00465-J

C. Kao / Physics Letters B 328 (1994) 420--426

g

g

g

g

(a)

q(qg ~ z ~

..... ?Aq)

(b)

~q

~

A

g

(c)

Fig. 1. The Feynman diagrams of the subprocesses (a) gg ---, gA, (b) gq --.->qA and (c) qgl --'* gA. We have not shown the diagrams with various permutations of the external legs.

can be well approximated by our data at tan/3 = 1 multiplied by cot 2/3. At hadron supercolliders, such as the SSC in the USA and the LHC at CERN, the SM Higgs boson can be produced dominantly from gluon fusion [ 16], and from vector boson fusion [ 17-19]. The A does not couple to the gauge bosons at the tree level, therefore, gluon fusion and heavy quark fusion [20] are the two major sources of the A in high energy hadron collisions.

2. CP-odd Higgs bosons with large Pr If the SM Higgs boson ( H °) can be produced in association with a large transverse momentum jet ( j ) , p p --* j H ° + X, via the following subprocesses: gg --~ g H°, gq --~ q H°, ggl ---' glH°, and q~ ---+ gH °, the mass of the Higgs boson might be reconstructed from its ~-+~-- decay channel [21] if the Higgs mass is in the intermediate range; or from the Z Z decay mode [22] 3 if the Higgs boson is heavier. The same subprocesses can also produce the CPodd Higgs bosons with large transverse momentum (Pr) via triangle and box diagrams, as shown in Fig. 1. The amplitudes of the quark loops can be expressed in terms of form factors [ 23 ] which are combinations of scalar one-loop integrals [24]. We have calculated 3 I would like to thank Uli Baur for comparing the matrix elements in this reference.

421

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 significant contributions. Therefore, only the third generation quark loops are considered in our calculations with the following values of parameters: a = 1/128, M z = 91.17 GeV, M w = 80.0 GeV, sin 20w = 0.230, the bottom quark mass rnb = 5 GeV. If not specified, the top quark mass (mr) is taken to be 150 GeV. The mass of the CP-odd Higgs boson (ma) is considered to be between 50 and 1000 GeV. The updated parton distribution functions of Owens [26] with A = 0.177 GeV a n d Q2 = m2a+ p 2 are chosen to evaluate the cross section of pp --+ j A + X at the energies of the SSC (x/~ = 40 TeV) and the LHC ( v ~ = 14 TeV). Since it is at the order of a,,3 the cross section of pp ---, j A + X is very sensitive to the choice of A and Q2. To evaluate the production rate of A with large Pr as well as to avoid the singularities at Pr --4 0, we impose a Pr cut on the A and the jet: Pr > 50 GeV. Fig. 2 shows the cross section of pp ---, j A + X at the SSC and the LHC energies, as a function of mA, for m, = 150 GeV and various values of tan/3. The cross section is about 5-19 times larger at v/-J = 40 TeV than at v/s = 14 TeV, for 50 GeV < ma < 1000 GeV. The loop integrals are functions of the mass of the CP-odd Higgs boson (ma), the quark mass in the l o o p s ( m q ) , and the Mandelstam variables: g, f, t~. For ma < mr, the t-loop is almost independent of mr, thus the amplitude is very sensitive to tan/3. For tan/3 larger than about 5, the cross section is dominated by the bloop. At the threshold of mA = 2rot, the imaginary part of the amplitude is turned on. Therefore, the amplitude squared ([M[ 2) grows rapidly when m a is close to 2mr. When mq2 << m2A < g, the amplitude squared behaves as 4 4 2 [Mq_loop[ 2 ~ m a i n ( m q ) .

(3)

The t-loop dominates in a large region of tan ft. The cross section is almost proportional to cot2fl for tanfl < 10. Only for tanfl close to mt/mb, can the b-loop dominate and the total cross section be enhanced by large tan ft. Not shown is the interference between the t-loop and the b-loop. The t-loop and the

422

C. Kao / P h y s i c s Letters B 328 (1994) 4 2 0 - 4 2 6

103 ~'''l

....

I ....

I ....

50 ~

102

} ....

~/s = 40

}

TeV

....

a) rn, = 200 GeV

I01

v

ioo I"

_

10 ~

i0 -I t9

,,,I

10-2

lO3 102

....

200

!'''[

....

(

I ....

I ....

400 600 mjt (GeV) I ....

I ....

I

....

800

1000

5

I ....

I0

''I

b) v's = 14 TeV

....

I ....

50

15 tan I ....

20

25

I ....

I ....

30

:

b) rnA = 400 GeV

lO1 +

t

~+

lo o 10 -1

't

r~

&t~

\,

\

\

'", ", \

lo-Z 10-3

I0

",.

b

200

400 600 rn, (GeV)

B00

1000

Fig. 2. The cross section of p p ---, j A + X in pb versus ma, for mt = 150 GeV, t a n f l = 1 , 2 , 5 , 1 0 and 30, at the energies: ( a )

x/~ = 40 TeV and (b) ~ = 14 TeV. b-loop interfere destructively if mA is close to 2mt, but constructively if ma is away from 2mt. To compare the production rate of the CP-odd Higgs boson (A) to that o f the SM Higgs boson ( H °) at the SSC energy, we present the cross section o f p p ---, & + X, ¢ = H ° or A from various subprocesses in Table 1, for m t = 150 GeV and tanfl = I. Several interesting aspects can be learned from Table 1 and Fig. 2: (1) If the Higgs bosons are produced from gg ~ ¢, or the subprocesses o f pp ~ j ¢ + X via quark loops, the cross section of A is at least twice that o f the H ° for me < 500 GeV. At me = 2mr, the cross section of A is about 5 times that of the H°; which implies that the threshold enhancement at 2mr is much larger for the A than for the H °. For larger me, their cross sections are about the same. (2) gg g& dominates and contributes about 80% to the cross section o f p p --~ j & + X. (3) For me > 400 GeV, the number of Higgs bosons produced from gg --~ g ¢ ÷ X with PT(&) > 50 GeV, is almost comparable to that from gg ~ &. (4) For me > 50 GeV, the cross sections of the A and H ° are the same from gg

\

5

-,,.

10

......,---

15 tan fl

20

25

30

Fig. 3. The cross section of p p ---* j A + X in pb versus tan fl, at v / s = 40 TeV, for mt = 120 (dotted), 150(solid) and 180 (dashed) GcV. Two masses of the CP-odd Higgs boson are considered: (a) mA = 200 GeV and (b) mA = 400 GeV.

ebb, which is a good approximation to the 'exact' cross section of ¢ produced from bb fusion [20]. (5) For tan fl > 10, gg ~ Ab[~ becomes the major source of large Pr CP-odd Higgs bosons. Its cross section is proportional to tan2fl and it is greatly enhanced by large tan ft. The effects of tan fl and rnt on the cross section of pp --+ j A + X at x/~ = 40 TeV are shown in Fig. 3, for mt = 120, 150 and 180 GeV, Two values of mA are considered: (a) mA = 200 GeV, which is less than 2mr; and (b) ma = 400 GeV, which is larger than 2mr. If tan fl is less than about 10, rnt slightly affects the total cross section: larger mt slightly enhances the cross section for mA = 200 GeV, but slightly reduces the cross section for mA -- 400 GeV. The total cross section is almost independent of m, for tan fl > 10. The top quark mass dependence on the matrix element squared of gg -+ g H ° has been studied in detail [21,22]. A similar study for gg ---+ gA is currently under investigation. At the threshold of 2mr, the enhancement on the IMI 2 for gg --+ gqb is very similar to that of gg --+ ¢, where & = H ° or A. Therefore,

423

C. Kao / Physics Letters B 328 (1994) 420-426

Table 1 The cross section of pp --+ 49 + X at v/s = 40 TeV, in pb, as a function of m4,, where 49 is the SM Higgs boson (H 0) or the CP-odd Higgs boson (A) m~(GeV) 50

100

200

300

400

600

800

Raw cross section

gg --+ H ° gg ---+HOt? gg ---+H°bb

310 27 43

120 7.7 7.8

52 1.4 1.0

47 0.68 0.27

40 0.44 0.097

9.6 0.21 0.021

2.7 0.11 6.7 × 10 -3

*Dr > 50 GeV

gg gg gq gq qq

2.5 64 10 4.4 0.17

1.0 40 6.5 2.7 0.12

0.26 23 3.7 1.4 0.041

0.091 22 3.6 1.3 7.2x10 -3

0.039 21 33 1.1 1.9x 10 -3

0.010 6.2 1.0 0.31 2.8x10 -4

3.6x 10 -3 2.0 0.33 0.092 6.7×10 -5

Raw cross section

gg ~ A gg ---+At? gg ---+Abb

620 6.9 46

270 4.6 7.9

130 2.2 1.0

290 1.2 0.27

87 0.71 0.097

14 0.29 0.021

3.6 0.13 6.7x10 -3

Pr > 50 GeV

gg ---+Ab[~ gg --+ gA gq --+ qA gq ---* qA qF:t---*gA

2.6 136 22 9.5 0.36

1.0 89 15 6.1 0.25

0.26 58 9.6 3.7 0.11

0.091 125 21 7.6 0.042

0.039 46 7.5 2.6 4.5X10 -3

0.010 9.4 1.6 0.47 5.1x10 -4

3.6 x 10 -3 2.7 0.45 0.12 1.1xl0 -4

---+H°bb ---+gH ° --+ qH ° ~ glH° ---, gH °

Various subprocesses are considered with rnt = 150 GeV and tan/3 = 1. We have imposed a cut on Pr (49) = Pr > 50 GeV for pp ---+j49 + X and pp ---+49b[~+ X. w e r e v i e w a n d d i s c u s s t h e p r o d u c t i o n o f p p ~ dp + X f r o m g l u o n f u s i o n in t h e a p p e n d i x . I n Fig. 4, w e s h o w t h e P r d i s t r i b u t i o n o f p p --+ g A + X f r o m g g --+ g A at v / s = 4 0 G e V for rnt = 150 GeV, m A ---- 2 0 0 a n d 4 0 0 GeV. T h e effect o f t a n / 3 is s i m i l a r to t h a t o n t h e c r o s s s e c t i o n v e r s u s m a i n Fig. 2. I f w e r e q u i r e P r ( A ) > 100 GeV, t h e c r o s s s e c t i o n will b e r e d u c e d to o n l y a b o u t 1 / 3 o f t h a t w i t h P r > 50 GeV for ma < 200 GeV while about 1/2 ofmA > 400 G e V will s u r v i v e .

m q2/ m 2A >> 1. A n effective L a g r a n g i a n [ 3 0 , 3 1 ] c a n b e

w r i t t e n as

w h e r e A = a s / 2 7 r v a n d O a ~ = elxup~rGapcr. A p p l y i n g t h e effective L a g r a n g i a n , w e o b t a i n t h e a m p l i t u d e s q u a r e d for v a r i o u s s u b p r o c e s s e s at t h e large q u a r k m a s s l i m i t

[M(gg ~

3. Large quark mass limit 4 I f t h e q u a r k m a s s in t h e l o o p d i a g r a m s is m u c h l a r g e r t h a n t h a t o f t h e C P - o d d H i g g s b o s o n , mq ~ m a , the ggA and gggA couplings can be obtained from the l o w e n e r g y t h e o r e m o f t h e axial a n o m a l y [ 2 7 - 2 9 ] or f r o m t h e e x a c t c a l c u l a t i o n o f gg --+ A at t h e l i m i t o f

4 In this section, tan/3 is taken to be 1; C~s is taken to be 12"/7"/ In (Q 2/ A 2 ); and only the top quark loop is considered. g5

(4)

Left = !8,"~~az v ~~a~v a~"

3f, gA)[ 2 = ~t

s 4 q- t 4 q-/l 4 -~- m 8 ) stu

f s2 + u2 I M ( g q - - * q A ) l 2 = }-~ [ - ( ~ ) ]

IM(qq---+ g A ) 1 2 =

f tZ+u 2 -9 ( s )

(5)

(6)

(7)

w h e r e f = A2gs2 a n d t h e IM[ 2 h a s b e e n s u m m e d a n d a v e r a g e d o v e r all s p i n s a n d colors. Table 2 shows the Pr distribution (do'/dPr) of p p ---+ g A + X , at v G = 14 TeV, f r o m t h e t o p q u a r k l o o p s o f gg --+ g A , for v a r i o u s m t a n d m t , w i t h t a n / 3 = 1. T h e large q u a r k m a s s l i m i t is a very g o o d a p p r o x i -

C. Kao /Physics Letters B 328 (1994) 420-426

424

Table 2 The Pr distribution ( d o - / d P r ) of p p ---+ gA + X in pb/GeV, at VG = 14 TeV, as a function of ma and mt mt(GeV)

ma = 100 G e V

ma = 400 GeV

mA = 600 G e V

mA = 1000 G e V

We

PT(GeV) 100

200

400

600

800

1000

100

I.lxl0 -1

8,9x10 -3

2.3x10 -4

1.5x10 -5

1.6xl0 -6

2.4x10 -7

150 200

1,0xl0 -I 9.9x10 -2

1,2x10 -2 1.3x10 -2

4.0x10 -4 5.6x10 -4

3.1x10 -5

3.8x10 -6

6.0×10 -7

4.9x10 -5

6 . 4 x 10 - 6

1.1xl0 -6

oc

9.5x10 -2

1.2x10 -2

8.1x10 -4

1.2x 10 - 4

2.5x10 -5

6.3×10 -6 2.7x10 -7

100

1.2x10 -2

2 . 2 x 10 - 3

1.4x10 -4

1.4x10 -5

1.7x10 -6

150

3.3x10 -2

6.2x10 -3

4.4x10 -4

4.3X10 -5

5.6x10 -6

9.1 x l 0 - 7

200

6.5x10 -2

1.2x10 -2

8.5xi0 -4

8.8;,<10 - 5

1.2x10 -5

2.0x10 -6

o~

1.2x10 -2

2.8x10 -3

3.8x10 -4

7.5×10 -5

1.8x10 -5

5 . 0 x 10 - 6

100

1.8×10 -3

3.9x10 -4

4.0x10 -5

5.4x10 -6

8.5XI0 -7

1.5x10 -7

150

5.0x10 -3

l.lxl0 -3

1.3xl0 -4

l.Sx10 -5

2.9X10 -6

200

1.0xl0 -2

2.3xl0 -3

2.7x10 -4

3.9x10 -5

6.5X 10 - 6

5 . 4 x 10 - 7 1.2×10 -6

oo

4.7xl0 -3

1.2x10 -3

2.0x10 -4

4 . 6 x 10 - 5

1.3X10 - 5

3.8x10 -6

100

1.1 × 1 0 - 4

2.7x10 -5

4.0x10 -6

8.1x10 -7

1.8×10 -7

4.2x10 -8

150

3.2x10 -4

8.2x10 -5

1.3x10 -5

2.7x10 -6

6.2X10 -7

1.5x10 -7

200

6.9x10 -4

1.7xl0 -4

2.9x10 -5

6.2x10 -6

1.5×10 -6

3.6×10 -7

oo

1.1×10 -3

3.0x10 -4

5.7x10 -5

1.6×10 -5

5.2X 10 - 6

1.8x10 -6

consider only the top quark loop diagrams of gg ---+ gA with tan fl = 1.

mation for Pr < mt and mA < mt. It provides a good check for the exact calculation. It slightly underestimates the exact cross section if ma is close to 2mr and Pr is less than 2mr, because the exact cross section is enhanced by the threshold effect. However, it overestimates the cross section if Pr is larger than 2mt or if ma is larger than about 4mr. Similar results have been found for the SM Higgs boson [21,22].

4. Conclusions The p p ~ j A + X is a very significant source of CPodd Higgs bosons at future hadron colliders for tan/3 less than about 10, especially for the detection modes that require a large PT for the A. The large quark mass limit of pp --~ j A + X is a good approximation for mA < mr, but overestimates the exact cross section for large m z and Pr. In the region of small PT, a complete description requires higher order corrections [ 3 !-33 ], and the resummation of gluon emission [34-36]. If the Abb coupling is proportional to tan/3, gg Abb is the dominant process to produce the A for tan/3 > 10 and mA > 100 GeV. The subprocesses gg ---, gA and gg ~ Abb can be considered as comple-

mentary to each other for producing large PT CP-odd Higgs bosons at future hadron colliders. The total cross section presented in this letter for pp --+ j A + X is less reliable for a much heavier A. It is likely to overestimate the production rates due to large In(m2A/Pr2o) contributions, since a constant minimal transverse momentum cutoff (Pr > PTO = 50 GeV) has been applied. The total cross section o f p p ~ j A + X at v/s = 14 TeV is about 5-19 times smaller than at x/~ = 40 TeV, for 50 GeV < ma < 1000 GeV.

Acknowledgements I am grateful to Howie Baer, Bill Bardeen, Uli Baur, Joe Polchinski and Xerxes Tata for beneficial 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.

C. Kao /Physics Letters B 328 (1994) 420-426 l

10 0

'1 . . . .

I ....

I ....

} ....

10-1

pp ~ gA+X ~/s = 40 TeV

~"

10-2

m t = 150 G e V 200 G e V

g

10_3

I(p) = +f

--

10

10-5 200

400 600 Px (CeV)

800

i000

]}

y ( 1 - y ): p-re

~{ln[1

o

10-4

b

425

= -2[sin-l(2~)]2

,

=+½[ln(Z+)-ier] z-

2,

p_>

1

p<~ 1

where z~: = [1 ± lx/]-Z~-4p]/2. I. W h e n m is very small, p << 1, therefore,

100 10-1

-

II. At the threshold, p = 1/4, therefore 10-2

I(¼) !

10-3

tariff = 1

= - }~2,

:-

F(¼)=+½,

=I 10-4

c(¼ , I ....

10-5

200

I~,

to.~r~f,

400 600 PT (GeV)

,,-7~<,800

I000

.

III. At very large m, p >> l, therefore,

1

]

2p

24p 2

Fig. 4. The PT distribution of pp --~ gA + X from gg --* gA at x/~ = 40 TeV, for rnt = 150 GeV and tanfl = 1,2,5, 10 and 30. Two masses of the CP-odd Higgs boson are considered: (a) mA 200 GeV and (b) ma = 400 GeV.

l(p) =

Appendix

G ( p ) = +3 + O(

=

s

+ o(p~)

F ( p ) = +½ + O ( 1 ) , P

1_). P

At the lowest order, the cross sections of gg --+ q5 via the top quark loops are

o-(gg --~ H °) = - ~ (

Therefore, at the threshold of m~ = 2mr,

o-(gg ~ A ) o'(gg ~ H °) = ~ . 4

~ 6;

)(s)[F(p)128(s - M °2) while at the large top quark mass limit,

o'(gg --+ A ) =

where cew =

( crsCew ~ ( s ) l G ( p ) 1 2 3 ( s - M2A)

M~v"

a~sin20w and p = m2/m~.

T h e f u n c t i o n s F ( p ) and G ( p ) are

F(p) = +p[2 + (4p-

o'(gg --+ A) ~ ( g g _ _ + H o)

_

9

4"

The same ratios appear in the cross sections o f gg --+ g~b at both limits.

l)l(p)] References

G(p) = -pl(p) and the function l ( p ) i s s In this appendix, m = mt; tanfl = 1; and & is the SM Higgs boson /40 or a CP odd Higgs boson A.

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