Precision measurements of Higgs-chargino couplings in chargino pair production at a muon co

a r X i v :h e p -p h /0303044v 2 9 J u l 2003WUE-ITP-2003-003IPPP-03-03DCPT-03-06hep-ph/0303044Precision measurements of Higgs-chargino couplings in chargino pair production at a muon collider H.Fraas ?,F.Franke ?,G.Moortgat-Pick ?,F.von der Pahlen ?,A.Wagner ??Institut f¨u r Theoretische Physik,Universit¨a t W¨u rzburg,Am Hubland,D-97074W¨u rzburg,Germany ?Institute for Particle Physics and Phenomenology,University of Durham,Durham DH13LE,UK Abstract We study chargino pair production on the heavy Higgs resonances at a muon collider in the MSSM.At √

muon collider is the by far more suitable machine to study their couplings to Higgs bosons.The MSSM contains three neutral Higgs bosons:a light scalar h and two

heavier Higgs particles,a scalar H and a pseudoscalar A.Higgs bosons are ex-pected to be discovered at the LHC and studied in the clean environment of a linear e+e?collider.However,a linear collider will probably not reveal all properties of the heavy supersymmetric Higgs bosons in detail.The cross sections for the pro-cesses e+e?→Z{H,A}are heavily suppressed close to the Higgs decoupling limit [7].The main production mechanism for heavy Higgs bosons is the associated pro-

duction e+e?→HA,which yields cross sections in the fb range[6].But for a subsequent determination of the Higgs chargino couplings one has to discriminate

between charginos from H and A decay.Here it turns out to be rather complicated to?nd observables which allow to identify the CP quantum number of the mother particle of the chargino pairs[8].For beam energies below the HA threshold single Higgs production e+e?→Hνˉνhas been studied in[9].The small cross section of this process,however,signi?cantly restricts the potential for precision studies of the Higgs properties.

Also theγγmode of a linear collider will not be suitable for a precise measure-

ment of the heavy Higgs bosons to charginos.Although H or A can be resonantly produced,the background from chargino pair productionγγ→?χ+?χ?is one order of magnitude larger than the signalγγ→H,A→?χ+?χ?[10].Furthermore one has to deal with a signi?cantly larger energy spread compared to a muon collider.

A muon collider could overcome these di?culties by providing a heavy Higgs factory[1,2].In a relevant part of the parameter space the Higgs branching ratios for the decay into chargino pairs is su?cient to perform precise measurements of the Higgs chargino couplings.In order to be independent of the speci?c chargino decay mechanism we focus on the ratio of the chargino couplings to the scalar and pseudoscalar Higgs.Then the relevant observables are merely the total cross sections at the H and A resonances and the contribution of the non-Higgs channels that can be measured without any model-dependent assumptions.

The achievable precision is generally limited by the energy resolution of the muon

collider and the separation of the relevant Higgs channel from the non-resonant contribution in the chargino production process.An essential requirement is that the H and A signals can be clearly separated.Therefore we also study the overlap of the Higgs resonances as a function of the energy resolution and tanβ.

This paper is organized as follows:In Section2we give analytical formulae for the cross sections and characterize the observables for the determination of the Higgs-chargino couplings.Section3contains numerical results for representative supersymmetric scenarios with di?erent chargino mixing,Higgs masses and values of tanβ.We show cross sections for the pair production of the light charginoμ+μ?→?χ+1?χ?1and estimate the relative systematic error in the determination of the Higgs chargino couplings.

2

2Analytical formulae

2.1Lagrangians and cross sections

We study chargino pair production in the MSSM

μ+μ?→?χ+i?χ?j(1) for CMS-energies

√

s.Therefore the total cross section of the production of chargino pairs?χ+i?χ?j can be separated into the

dominating contributionsσij

H andσij

A

from H and A exchange and the background

σij

B,SUSY

fromγ,Z,?νμand h exchange

σij=σij

H +σij

A

+σij

B,SUSY

.(4)

Chargino production via theγ,Z,?νμchannels will have been thoroughly studied at linear colliders[6].The h exchange contribution can be neglected at the H and A resonances.

At CMS energy

√

4π|c(φμ)|2·|c(φ)R ij|2·B i,jφ(s)Kφ(s),φ=H,A(5) with

Kφ(s)=

s

B ij

H (s)=

λ(s,m2i,m2j)3/2

s

,(8)

λ(s,m2i,m2j)=s2?2s(m2i+m2j)?(m2i?m2j)2(9) The total cross sectionσf+f?for the pair productionμ+μ?→?χ+i?χ?j with sub-

sequent decays?χ+i→f+and?χ?j→f?factorizes into the production cross section σij and the branching ratios for the respective decay channels:

σf+f?(√s)×BR(?χ+

i→f+)×BR(?χ?j→f?).(10)

This holds for each of the contributionsσf+f?

H from H exchange,σf+f?

A

from A

exchange andσf+f?

B,SUSY

from the background channels in eq.(4).

2.2Determination of the Higgs-chargino couplings

In the following we consider the pair production of the light chargino?χ±1that is expected to be among the?rst kinematically accessible supersymmetric particles at a muon collider.In order to determine the Higgs-chargino couplings one has to

separate the Higgs exchange contributionsσf+f?

H +σf+f?

A

from the total measured

cross sectionsσf+f?

meas ,at

√s=m

A

,respectively.Since the interference

between the Higgs channels and the background is negligible we can subtract the contributionsσf+f?

B,SUSY

from the total cross section.

Besides the non-resonant contributions to the chargino pair production one has to consider further background sources from standard model processes.Here W pair production and single W production constitute the main standard model back-ground,which is in principle rather large[6]but can be strongly reduced by appro-priate cuts[12].Then the resonance peaks remain clearly visible above the smooth

standard model backgroundσf+f?

B,SM which can therefore be included in the subtrac-

tion of the non-resonant contribution from the total cross section.

We determine the total background contributionσf+f?

B =σf+f?

B,SUSY

+σf+f?

B,SM

by lin-

ear interpolation ofσf+f?

meas far below and above the resonance energies.The precision

of this estimate obviously depends on the variation of the background contributions around the heavy Higgs resonances.By this procedure we avoid,however,reference to other experiments at di?erent energy scales as e.g.chargino production at e+e?colliders combined with speci?c model calculations.

Due to their factorization into production and decay the ratio of the measured contribution from H and A exchange

r=σf+f?

meas

(m H)?σf+f?

B

(m H)

σ11

H

(m A)+σ11

A

(m A)

(11)

is independent of the speci?c chargino decay channel which may be chosen to give the best experimental signal.Then the measurement of the total cross section

4

for chargino production and decay at the Higgs resonances o?ers an interesting possibility to determine the ratio of the Higgs-chargino couplings

x= c(H)R11

C·1?C1/r

xμ

,(13)

with

C=β3(m2H)

Γ2

H

,(14)

C1=

β(m2H)

β(m2

H

) 3K H(m2A)Γ2H,(16)β(s)= λ(s,m21,m21)s 1/2,(17) xμ= c(Hμ)

Scenarios A C E

217.3169.5400

217.3400169.5

-0.632-0.943-0.184

0.7750.3330.983

0.7750.9830.333

-0.632-0.184-0.943 m H/GeV352.1351.9352.2

ΓH/GeV0.670.310.32

ΓA/GeV 1.050.430.43

0.5130.2070.207

c(H)R

11

c(A)R

0.4170.1920.192

11

Scenarios B400B180B7C7

154.9180.7212.8157.5

-400-420212.8-400

5588

155180155155

0.9580.959-0.6220.954

0.2880.2830.7830.300

0.99840.99770.7830.9967

-0.056-0.068-0.622-0.081 m A/GeV400400350350

m H/GeV402.0402.0351.2351.0

ΓH/GeV 1.170.820.710.44

ΓA/GeV 2.43 1.96 1.420.57

BR (A →?χ+?χ?

)

M 2/GeV

μ/GeV BR (H →?χ+?χ?)

M 2/GeV μ/GeV

Figure 1:Branching ratios of the heavy Higgs bosons A and H into light chargino pairs for m A =350GeV,tan β=5and sfermions masses larger than M H /2,computed with the program HDECAY [14].The contour lines correspond to 0.1(dotted),0.2(dashed),0.3(dash-dotted),0.4(large dashed)and 0.5(solid).The gray area is the experimentally excluded region given here by m ?χ±

1<100GeV,the thick dots are the scenarios A –F of table 1.

and larger than in the higgsino scenario ?g.2e,inversely proportional to the widths.The H resonance is largest in the scenario with the largest Higgs-chargino coupling ?g.2a.Only comparing ?g.2e and f the relative height of the H peak is determined by their width since the couplings are equal due to an approximate symmetry under |μ|?M 2.

Essential requirements for a precise determination of the Higgs-chargino cou-plings are distinct resonance peaks and a clear separation of the Higgs resonances.Near threshold the A resonance peak is suppressed by a factor β,compared to a suppression by β3of the H resonance.This e?ect explains the relative height of the resonances in ?g.2.

Whether the resonances can be separated depends on both the Higgs line shape and the energy spread of the muon beams.In ?gs.2a –f we compare the cross sections without and with a Gaussian energy spread of 150MeV which corresponds to an energy resolution R ≈0.06%.

The energy spread clearly suppresses the resonance peaks especially in scenarios with gaugino-like and higgsino-like light charginos where the resonances are narrower than in the mixed scenarios.However,also with an energy spread of 150MeV the H and A resonances are well separated in all scenarios (A –F).

The in?uence of the Higgs mass m A and the chargino mass m ?χ±

1is illustrated in ?g.3for mixed scenarios with μ>0and for scenarios with a gaugino-like light

chargino and μ<0.In scenarios B400and C400with m A =400GeV and m ?χ±

1=155GeV the overlap of the Higgs resonances is larger than in the corresponding

scenarios with m A =350GeV and the same chargino mass,see ?gs.2b and 2c.

The overlap diminishes when the chargino mass is increased to m ?χ±

1=180GeV in scenarios B180and C180due to the smaller phase space of the Higgs decays.

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σ11/pb

√s/GeV

(a)(b)

σ11/pb

√s/GeV

(c)(d)

σ11/pb

√s/GeV

(e)(f)

Figure2:Total cross sectionσ11forμ+μ?→?χ+1?χ?1in mixed,gaugino and higgsino scenarios withμ<0(μ>0),a(b),c(d)and e(f)respectively,corresponding to the scenarios A(B),C(D)and E(F)of table1.In all scenarios tanβ=5,M A=

350GeV,m

?χ+1=155GeV and m?ν

μ

=261GeV.The dashed line corresponds to an

energy spread of150MeV,the solid line to no energy spread.

For larger values of tanβthe A and H resonances tend to overlap since the mass di?erence diminishes.As an example we compare in?g.4for m A=350GeV the total cross sections for the gaugino scenarios C,C7and C8with tanβ=5,tanβ=7 and tanβ=8respectively,without and with an energy spread of150MeV.Without

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σ11/pb √s/GeV

(a )(b )Figure 3:Total cross section σ11for μ+μ?→?χ+1?χ?1with tan β=5,M A =400GeV,m ?νμ=261GeV and m ?χ+1=155GeV (solid)and m ?χ+

1=180GeV (dashed).(a)shows the mixed scenarios of table 2with μ>0,B400and B180,and (b)the gaugino scenarios

with μ<0,C400and C180,given in table 2.

energy spread both resonances are well separated up to tan β=7whereas for tan β=8the H resonance can barely be discerned.With energy spread,however,the overlap for tan β=7is already so large that the resonances nearly merge.Here the separation of the resonance contributions may not be possible with a good precision.The same conclusion applies to other chargino scenarios,as can be seen for the mixed scenarios B (tan β=5),B7(tan β=7)and B8(tan β=8)in ?gs.4c and ?g.4d without and with energy spread of 150MeV,respectively.

4Precision measurements of the Higgs-chargino

couplings

The error in the determination of the ratio x of the squared Higgs-chargino couplings eq.(12)depends both on the energy resolution R of the muon beams and on the error ?σB /σB in the measurement of the non-resonant channels (γ,Z ,?νμand h exchange as well as irreducible standard model background)at the H and A resonances.This background contribution can be estimated from cross section measurements su?ciently far o?the Higgs resonances.

In ?g.5we plot contours of the relative error in the determination of x in the R and ?σB /σB plane for the scenarios A –F.The contours are shown for the two cases that the irreducible standard model background is neglected or reduced to 25%of the non-resonant supersymmetric channels by appropriate cuts,respectively.For a detailed background analysis Monte Carlo simulations taking into account the de-tailed detector characteristics have to be performed and are expected to correspond to the considered range in ?g.5[12].

As a result of the error propagation one observes a stronger dependence on R than on ?σB /σB .Since the energy spread only changes the shape of the resonance

10

σ11/pb

(a)(b)

√s/GeV

σ11/pb

(c)(d)

√s/GeV Figure4:Dependence on tanβof the total cross sectionσ11forμ+μ?→?χ+1?χ?1with M A=350GeV and m?ν

=261GeV.The gaugino scenarios withμ<0,C,C7and C8,

μ

are plotted without energy spread(a)and with an energy spread of150MeV(b),for tanβ=5(solid),7(dashed)and8(dotted),and the mixed scenarios withμ>0,B,B7 and B8,in(c)and(d),without and with energy spread respectively and tanβ=5(solid), 7(dashed)and8(dotted).

the relative errors in the peak cross sections and in the widths are correlated.Gen-erally,an irreducible standard model background up to25%of the supersymmetric background leads to a slightly reduced precision for the determination of x.

Due to the narrower resonance widths the energy resolution R a?ects the relative error in x in scenarios C,D and E,F with gaugino-like or higgsino-like light charginos signi?cantly more than in the mixed scenarios A and B.The in?uence of the error in the background measurement is largest in the scenarios with a higgsino-like light chargino and much smaller in the other chargino mixing scenarios.In all cases only minor di?erences appear between the scenarios with positive and negativeμ.

In order to achieve a relative error?x/x<10%an energy resolution R<0.04% is necessary in the mixed scenarios and less than0.02%in the gaugino and higgsino scenarios.These values lie in the range between0.01%and0.06%of the expected energy resolution at a muon collider[3,4].In addition,the background contributions have to be known with a relative error?σB/σB<10%in the mixed and gaugino

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0.020.040.06

0.05

0.1

0.150.2

0.020.040.06

0.05

0.1

0.15

0.2

(a )

(b )

?σB

σB

2%

5%

10%

20%

2%

5%10%

20%

R [%]

R [%]

0.020.04

0.060.050.1

0.150.2

0.020.04

0.06

0.05

0.1

0.15

0.2

(c )(d )

?σB

σB

2%

5%

10%

20%

50%

2%

5%

10%

20%

50%

R [%]

R [%]

0.020.04

0.060.050.1

0.150.2

0.020.04

0.06

0.05

0.1

0.15

0.2

(e )

(f )

?σB

σB

2%

5%10%20%

50%

2%

5%10%

20%50%

R [%]

R [%]

Figure 5:Relative error in the ratio of the Higgs-chargino couplings x as a function of the energy resolution and the relative error in the non-resonant contributions.The irreducible standard model background is neglected (solid)and 25%of the supersymmetric background (dashed).Plots (a)–(f)correspond to the scenarios A –F in table 1.

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scenarios whereas in the higgsino scenarios a much higher precision?σB/σB<6% is necessary.

For a energy resolution R=0.04%the error in the measurement of x becomes ?x/x≈40%in the scenarios C and D with gaugino-like charginos and practically independent of the background error.A similar error is expected in scenario E with higgsino-like charginos,which decreases to27%for?σB/σB<10%.

If on the other hand an energy resolution R=0.01%is achieved and the con-tributions of the background channels are well known(?σB/σB<5%in the mixed and gaugino scenarios and?σB/σB<2.5%in the higgsino scenarios)the error can be reduced to the order of a few percent.

5Conclusion

In this paper we have studied chargino pair production at a future muon collider via resonant heavy Higgs boson exchange in the MSSM.This process yields large cross sections of up to a few pb in relevant regions of the supersymmetric parameter space. Due to the sharp energy resolution that allows to separate the CP-even and CP-odd resonances a muon collider is an accurate tool to investigate the Higgs couplings to its decay products.Here we have focused on the determination of the Higgs-chargino couplings.We have shown that the ratio of H-chargino and A-chargino couplings can be precisely determined independently of the chargino decay mechanism.This method avoids reference to other experiments and makes only a few model depen-dent assumptions,namely the existence of a CP-even and a CP-odd resonance and the approximate decoupling limit for the Higgs-muon couplings.In representative supersymmetric scenarios we have analyzed the e?ect of the energy spread and of the error from the non-resonant channels including an irreducible standard model background up to25%of the supersymmetric background.With a good energy resolution a precision as good as a few percent can be obtained for tanβ<8and M A≤400GeV,where the Higgs resonances can be separated.

The precision could be further improved by appropriate beam polarization that enhances the resonant scalar exchange channels and suppresses the background.A loss of luminosity[1,4]as well as e?ects from initial state radiation and radiative corrections should be taken into account for real simulation studies.The qualitative conclusions of this study,however,remain unchanged.

Acknowledgement

This work was supported by the Bundesministerium f¨u r Bildung und Forschung, Contract No.057WZ91P(0),by DFG FR1064/4-2and by the EU TMR-Network Contract No.HPRN-CT-2000-00149.

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