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arXiv:hep-ph/0005313v1 31 May 2000

KEK–TH–698

KIAS–P00028

OCHA–PP–160

hep–ph/0005313

February 1, 2008

Measuring the Higgs CP Property through Top Quark

Pair Production at Photon Linear Colliders

Eri Asakawa1, S.Y. Choi2, Kaoru Hagiwara3and Jae Sik Lee4

1Graduate School of Humanities and Sciences, Ochanomizu University,

1–1 Otsuka 2–chome, Bunkyo, Tokyo 112-8610, Japan

2Department of Physics, Chonbuk National University, Chonju 561–756, Korea

3Theory Group, KEK, Tsukuba, Ibaraki 305-0801, Japan

4Korea Institute for Advanced Study, Seoul 130–012, Korea

Abstract

We present a model–independent study of the effects of a neutral Higgs boson without

definite CP–parity in the process γγ → t¯t around the mass pole of the Higgs boson. Near the

resonance pole, the interference between the Higgs–exchange and the continuum amplitudes

can be sizable if the photon beams are polarized and helicities of the top and anti–top quarks

are measured. Study of these interference effects enables one to determine the CP property

of the Higgs boson completely. An example of the complete determination is demonstrated

in the context of the minimal supersymmetric standard model.

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1Introduction

Search for Higgs bosons and precise measurements of their properties such as their masses, the

decay widths and the decay branching ratios [1] are among the most important subjects in our

study of the electroweak symmetry breaking. In the standard model (SM), only one physical

neutral Higgs boson appears and its couplings to all the massive particles are uniquely deter-

mined. On the other hand, models with multiple Higgs doublets have neutral Higgs bosons of

definite CP parity as well as charged Higgs bosons, if CP is a good symmetry. If CP is not a

good symmetry of the symmetry breaking physics, these neutral Higgs bosons do not necessarily

carry definite CP parity.

The CP–violating interactions beyond the Kobayashi–Maskawa mechanism and their conse-

quences at high–energy colliders have been intensively studied. This is motivated in part by the

search of an efficient mechanisms of generating the cosmological baryon asymmetry at the elec-

troweak scale [2]. An extended Higgs–boson sector, as predicted by many extensions of the SM

such as the minimal supersymmetric SM (MSSM), can provide such CP–violating interactions

in a natural way. One attractive scenario is to make use of explicit CP violations in the MSSM

Higgs sector [3, 4] which are induced through loop corrections with complex supersymmetric pa-

rameters in the mass matrices of the third generation squarks. Such interactions cause mixings

among CP–even and CP–odd Higgs bosons.

It is of great interest to examine the possibility of studying these Higgs bosons in detail in

CP non–invariant theories. A two–photon collision option [5] of the future linear e+e−colliders

offers one of the ideal places to look for such Higgs signals [6]. There, neutral Higgs bosons can

be produced via loop diagrams of charged particles. If the Higgs boson is lighter than about

140 GeV, its two-photon decay width can be measured accurately by looking for its main de-

cay mode, which is usually the bb mode [7]. When the Higgs boson is heavy, the processes

γγ → W+W−,ZZ and t¯t can be useful to detect its signal [8]. In theories with weakly coupled

Higgs sector, such as the MSSM, heavier Higgs bosons have suppressed branching fractions to

the WW/ZZ modes [9]. Furthermore, CP-odd Higgs bosons do not have the ZZ decay modes

in the tree level. On the other hand, the tt decay mode can be significant irrespective of the CP

property of the Higgs boson φ. In this case, it is expected that the heavy Higgs boson contributes

to the process γγ → tt significantly around its mass pole.

The s–channel resonant amplitude of γγ → φ(∗)→ tt can interfere with the tree–level t– and

u–channel continuum amplitudes, if the resonant and the continuum amplitudes have comparable

magnitudes near the resonance pole [10]. This often happens for heavy Higgs bosons where both

the peak resonant amplitudes and their total decay widths are large enough to make the interfer-

ence effects significant. In this article, we study the contribution of a heavy Higgs boson without

definite CP–parity to the process γγ → tt and describe an efficient method to determine its CP

property completely by making use of the photon and t¯t polarizations; the procedure is crucially

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based upon the interference effects among various helicity amplitudes. We also demonstrate the

feasibility of determining the heavy Higgs–boson contribution in the context of the MSSM.

The remainder of this article is organized as follows. In Sect. 2, the helicity amplitudes of the

process γγ → t¯t are calculated with model–independent parametrizations of the couplings of the

Higgs boson φ to a photon pair and a top–quark pair. In Sect. 3 we present all the observables

constructed by use of photon polarizations and by measuring the helicities of the final top and

anti–top quarks. Section 4 gives the description of the procedure to determine the CP property of

the Higgs boson completely. In Sect. 5 we study the properties of polarized photon beams through

the Compton laser backscattering. In Sect. 6 we demonstrate the complete determination of the

CP property of the heaviest neutral Higgs boson in the MSSM. Finally, we give conclusions in

Sect. 7.

2Helicity amplitudes

In CP non–invariant theories, the lowest–dimensional interaction of the Higgs boson φ with a

top–quark pair can be described in a model–independent way by the vertex:

Vφtt= −iemt

mW

(St+ iγ5Pt) ,(1)

and the loop–induced interaction of the Higgs boson with a photon pair is parameterized in a

model–independent form as follows:

Vγγφ =

√sα

4π

?

Sγ(s)

?

ǫ1· ǫ2−2

s(ǫ1· k2)(ǫ2· k1)

?

− Pγ(s)2

s?ǫ1ǫ2k1k2?

?

,(2)

where the form factors depend on the c.m. energy squared s of two colliding photons, ǫ1,2stand

for the wave vectors of the two photons, k1,2are the four–momenta of the two photons, and

?ǫ1ǫ2k1k2? = ǫµναβǫµ

1ǫν

2kα

1kβ

2,(3)

with ǫ0123= 1. Since we are interested in the s–channel virtual (and real) Higgs–boson exchange,

for the sake of consistency the s–dependence of the form factors Sγand Pγis exhibited explicitly

in Eq. (2). We note that a simultaneous presence of {Sγ,Pγ} or/and {St,Pt} implies CP non–

invariance of the theory.

In the two–photon c.m coordinate system with?k1along the positive z direction and?k2along

the negative z direction, the wave vectors ǫ1,2of two photons are given by

ǫµ

1(λ) = ǫµ∗

2(λ) =−λ

√2

?

0,1,iλ,0

?

.(4)

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where λ = ±1 denote the right and left photon helicities, respectively. Using Eqs. (1), (2) and

(4) one can derive the explicit forms of the helicity amplitudes for the process γγ → tt which con-

sist of two parts; the s–channel Higgs–boson exchange and the tree–level continuum contributions:

(i) Higgs–exchange contribution:

M(λ1λ2:σσ)

φ

=eαmt

4πmW

s

s − m2

φ+ imφΓφ[Sγ(s) + iλ1Pγ(s)][σβSt− iPt]δλ1,λ2δσσ.(5)

(ii) Tree–level continuum contribution:

M(λ1λ2:σσ)

cont

=

4παQ2

1 − β2cos2Θ

−4mt

t

?4mt

√s(λ1+ σβ)δλ1λ2δσσ

√sσβ sin2Θδλ1,−λ2δσσ− 2β(cosΘ + λ1σ)sinΘδλ1,−λ2δσ,−σ

?

,(6)

where Θ is the scattering angle of the top quark with respect to the positive z direction,

β =

1 − 4m2

with its three–momentum along the positive (negative) direction, respectively, in units of ¯ h, and

σ = ±1 (σ = ±1) denote the right and left helicities of t (t), respectively, in units of ¯ h/2. There

exists the interference between the Higgs–boson and the continuum contributions for equal t and

¯t helicities which can be used to observe the CP property of the Higgs boson. On the other hand,

the continuum contribution with opposite t and¯t helicities dominates the γγ → t¯t events at

high energies so that it is important to distinguish events with equal t and¯t helicities from those

with opposite t and¯t helicities. With the above points in mind, we concentrate on the helicity

amplitudes of equal t and¯t helicities in the present work.

?

t/s, λ1= ±1 (λ2= ±1) denote the right and left helicities of the incident photon

When the helicities of the top and anti–top quarks are equal, i.e. σ = σ, the helicity ampli-

tudes for the process γγ → tt can be rewritten in the following simple form

M(λλ:σσ)

M(λ,−λ:σσ)

where for the sake of brevity the explicit s–dependence of the form factors Sγ and Pγ is not

denoted and two s–dependent functions Acont(s) and Aφ(s) are introduced:

= Acont(s)(λ + σβ) + Aφ(s)[Sγ+ iλPγ][σβSt− iPt] ,

= −Acont(s)σβ sin2Θ,(7)

Acont(s) =

16παQ2

√s(1 − β2cos2Θ),

tmt

Aφ(s) =eα

4π

mt

mW

Dφ(s). (8)

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Here Dφ(s) is the s–channel propagator of the Higgs boson

Dφ(s) =

s

s − m2

φ+ imφΓφ. (9)

A few important comments concerning the helicity amplitudes (7) are in order:

• Only the amplitudes with equal photon helicities have contributions from the Higgs–boson

exchange.

• The spin–0 Higgs–boson contributions are independent of the scattering angle Θ.

• The s–dependent form factors Sγ and Pγ as well as Aφare in general complex while the

other form factors are real in the leading order.

• The continuum part is CP–preserving while the Higgs–exchange part can be CP–violating

if the ‘scalar’ (CP–even) form factors, Sγand St, and ‘pseudoscalar’ (CP–odd) form factors,

Pγand Pt, are present simultaneously.

3Polarized cross sections

3.1 Equal photon helicities and top–quark helicities

In this section, we investigate what physics information on the Higgs–boson contribution can be

extracted from the cross section with equal photon and top–quark helicities. First of all, we can

construct four independent squared amplitudes:

???M(++:++)???

???M(−−:−−)???

???M(++:−−)???

???M(−−:++)???

2= |M|2

2= |M|2

2= |M|2

2= |M|2

0

?

?

?

?

1 + A0+ A1− (1 + β)(A2− A3)

?

?

?

?

,

0

1 + A0− A1+ (1 + β)(A2− A3),

0

1 − A0+ A1+ (1 − β)(A2+ A3),

0

1 − A0− A1− (1 − β)(A2+ A3), (10)

where |M|2

0is the unpolarized squared amplitude, i.e. the average

|M|2

0=1

4

????M(++:++)???

2+

???M(−−:−−)???

2+

???M(++:−−)???

2+

???M(−−:++)???

2?

.(11)

The explicit form (7) of the helicity amplitudes then leads to the following expressions for |M|2

and the quantities Ai(i = 0,1,2,3):

|M|2

0

0

= (1 + β2)A2

cont+ (β2S2

t+ P2

t)(|Sγ|2+ |Pγ|2)|Aφ|2

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