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Complementarity of a Low Energy Photon Collider and LHC Physics

a r X i v :h e p -p h /0308103v 1 9 A u g 2003

nuhep-exp/03-003

UCD-03-08

Complementarity of a Low Energy Photon Collider and LHC Physics

David Asner,1Stephen Asztalos,2Albert De Roeck,3Sven Heinemeyer,4Je?Gronberg,2John F.Gunion,5Heather E.Logan,6Victoria Martin,7Michal Szleper,7and Mayda M.Velasco 7

1

University of Pittsburgh,Pittsburgh,Pennsylvania 15260,USA

2

Lawrence Livermore National Laboratory,Livermore,California 94550,USA

3

CERN,CH-1211Geneva 23,Switzerland

4

Institut f¨u r theoretische Elementarteilchenphysik,LMU M¨u nchen,Theresienstr.37,D-80333M¨u nchen,Germany

5

University of California ,Davis,California 95616,USA 6

University of Wisconsin,Madison,Wisconsin,53706,USA 7

Northwestern University,Evanston,Illinois 60201,USA

We discuss the complementarity between the LHC and a low energy photon collider.We mostly consider the scenario,where the ?rst linear collider is a photon collider based on dual beam tech-nology like CLIC.

PACS numbers:

I.INTRODUCTION

The LHC is scheduled to turn on in the year 2007.Within the ?rst few years of operation LHC will discover the Higgs boson,if it exists.When this long awaited new particle is ?nally found,it will no doubt become the most important object to be studied in detail in high energy physics (HEP)–unless of course at the same time also many other new particles,such as SUSY sparticles,are copiously produced at the LHC –.

The LHC will be able to measure many characteristics of the Higgs boson rather precisely,such as mass and width.However,has not yet been demonstrated that the couplings to fermions and gauge bosons cannot be measured in a model independent way,rather ratios of couplings are directly accessible at LHC.The measurement of other properties,such as spin and CP quantum numbers and Higgs self coupling,will be even more tedious.Hence data on Higgs measurement in di?erent reactions such as in electron-positron and photon-photon collisions will be needed to determine the Higgs parameters in greater detail.

If the physics beyond the Standard Model is low energy supersymmetry,then the mass of the Higgs will be relatively low,e.g.below about 135GeV [1]as predicted in the minimal supersymmetric model (MSSM).This will put the production of Higgs bosons within reach of future lepton or photon colliders.Such colliders bene?t from a much cleaner production environment for Higgs particles as compared to hadron machines.

A linear e +e ?collider is seriously considered as an option for the next large accelerator in HEP [2]by international consensus.Such a machine would certainly be ideal to study the properties of the Higgs particle in detail.These linear colliders,for which presently several proposals exist [3,4,5]are generally huge machines,of a length of about 20-40km,to reach approximately 1TeV center of mass energy (E CM )with conventional accelerating techniques.Re-grettably,it is unlikely that the construction of such an accelerator will start any time before 2007-2009[6],and the construction/commissioning will take of the order of 10years.

Two beam acceleration (TBA)has been proposed as an alternative accelerating technique to reach higher accelerating gradients,and is presently studied most intensively at CERN through the CLIC R&D project [7,8].TBA is still in an experimental stage,but when ready it will allow to construct e +e ?colliders with higher E CM ,and/or,for a more compact e +e ?collider to reach the energy region of interest.That is,one 600m accelerating module with the CLIC technology will accelerate electrons by about 70GeV.The TBA technology has been demonstrated for low currents and small pulses in test facilities CTF1and CTF2at CERN.Presently,the CTF3test facility[9]is under construction and should demonstrate the feasibility of the machine parameters for the drive beam for CLIC.When successful this will allow to complete a technical design for a machine based on TBA.

In this paper we consider physics studies for a Higgs factory which could be decided upon and built,based on TBA, soon after the discovery of a light Higgs at the LHC during the last year of this decade.The smallest(but not necessary simplest)collider would be one based on two TBA modules,which accelerate each an electron beam up to70-75GeV. When these beams are converted into photon beams via Compton scattering using powerful lasers,Higgs particles with a mass of up to130GeV can be produced in the s-channel.Such photon colliders(γC)have been extensively proposed in Ref.[10],and all e+e?linear collider(LC)projects consider such an option as an upgrade of their base-line[3,4,5] program.R&D projects forγC are presently ongoing.To exploit the physics opportunities as discussed in this paper it is further imperative that the electron beams can be polarized,which is generally considered to be technologically feasible.

A low energy Higgs factory driven by aγC based on CLIC technology,such as the one assumed here,has already been elaborated in Ref.[11],and was coined CLICHE.The basic parameters of such a machine and initial physics studies have been presented.As discussed in Ref.[11],the H→γγvertex is due to loop diagrams making it sensitive to physics beyond the Standard Model,and as an example,they show how the precision obtained on the branching ratio measurements made at CLICHE could help us to distinguish between the Standard Model(SM)and its minimal supersymmetric extension, the MSSM.Further work on the comparison between the SM and the MSSM at aγC was discussed in Ref.[12].

Here we follow up on this opportunity,and we extend the physics arguments in favor of vigorously pursuing aγC col-lider,either at CLICHE,or possibly as an adjunct to an upcoming LC.We?nd that CLICHE by itself could provide invaluable complementarity to the LHC.For example,we show the crucial role that CLICHE could play in:(1)detecting and/or con?rming the LHC signal for a CP-even Higgs boson that decays to two light pseudo-scalar Higgs bosons,(2) providing a precise measurement of the H→γγpartial width,which allows us to test large scales in the Littlest Higgs model after combining with branching ratio measurements made at an e+e?collider or the LHC,and(3)in the presence of Higgs-Radion mixing in the Randall-Sundrum model,one could test possible gg andγγanomalous couplings to the h andφamong many other things,since the LHC will give access to the gg coupling,while theγC will give us the coupling toγγ.

II.MACHINE AND DETECTOR DESIGN UPDATE

As discussed in detailed in Ref.[11],the technical requirements to produce aγC with warm accelerating technology and for TBA are compatible,and therefore their R&D is in common.Details about the parameters forγC based on warm,cold and TBA technology can be found in Refs.[3,5,11].Here we will discuss the recent progress in the R&D, and detector requirements due to the environment at the interaction region of aγC.

A.R&D for photon collider technology

The straw man design for theγC technology for a warm machine that was presented at Snowmass2001by LLNL has continued to develop.The MERCURY laser has been commissioning and has reached it’s full repetition rate of10Hz with20Joule pulses.It is now undergoing a major re?t to include the second ampli?er head.Once that is completed it will reach its full power of100Joules.The basic layout of the optics has remained unchanged,but much work is going into the details of aligning the system and maintaining the laser pulse quality,which is critical to e?cient utilization of the laser power.

A collaboration of DESY and MBI have been exploring a design for a cavity laser system to reduce the total laser power by exploiting the larger bunch spacing of TESLA to reuse the laser pulses.This type of system cannot be used for the warm machine since the2.8ns bunch spacing does not allow time to reuse the laser pulse.

Choices in the operating parameters of the electron accelerator can improve the ratio of delivered luminosity to laser power.The percentage of electrons which Compton scatter is set by the laser photon density,and is independent of the electron bunch charge.Maximizing the bunch charge increases the luminosity at no cost in laser power and should always be pursued.In fact,since luminosity increases as the bunch charge squared,it can be a win to reduce the number of

FIG.1:Photon-photon Interactions.(left)Direct interactions involve only electroweak couplings.(center)Once resolved process where one photon probes the parton structure of the other photon,similar to deep inelastic scattering.(right)Twice resolved process where the partons of each photon interact,similar to aρ?ρcollisions.

bunches,while increasing the bunch charge to keep the total beam current constant.This can both increase luminosity, while reducing the total laser power needed,and therefore reduce cost.

B.Resolved photons and impact on detector

The photon is the gauge boson of QED that can couple to the electroweak and strong interactions via virtual charged fermion pairs.As a consequence,photon-photon interactions are more complex than e+e?interactions,and a careful simulation of the beam is extremely important.

In aγC we have a few×1010primary e?,in addition to~2

1At Snowmass2001,it was noted that the cross sections predicted by Pythia were much larger than naively expected from LEP data.At ECF A/DESY in St.Malo,the discrepancy was determined to be approximately an order of magnitude.A more detailed comparison by Asner and de Roeck,narrowed the discrepancy to a factor of six.It was reported at ECF A/DESY in Prague that Pythia predicted the

TABLE I:Pythia parameter settings for resolved photon processes.Other parameters are taken from Ref.[15].

Parameter Setting Explanation

s ee=160GeV and

√s=500GeV.The beam parameters for√

TABLE II:Laser and electron beam parameters for

s=160GeV machine and that this procedure is70%e?cient,thus more laser power is required.

Electron Beam Energy(GeV)80250

Events/Crossing0.6 1.8

Tracks/Crossing(p>0.2GeV,|cosθ|<0.9) 3.714.6

Energy/Track(p>0.2GeV,|cosθ|<0.9)0.70GeV0.74GeV

Clusters/Crossing(E>0.1GeV,|cosθ|<0.9) 5.521.8

Energy/Cluster(E>0.2GeV,|cosθ|<0.9)0.45GeV0.49GeV

beam crossing.For the TBA machine beam parameters discussed in Ref.[11],0.1overlay events per beam crossing are expected.Most of the products of theγγ→hadrons will be produced at small angles relative to the photon beam and will escape undetected down the beam pipe.We are interested in the decay products that enter the detector.For this reason we are only considering tracks and showers with|cosθ|<0.9in the laboratory frame,and we require tracks to have momentum greater than200MeV,while the showers must have energy greater than100MeV.The resulting track

and shower energy distributions integrated over17,000beam crossings for

s ee=500GeV are shown in Fig.4-7,and summarized in Table III.Experimental,theoretical and modeling errors have not yet been evaluated for these distributions.

Future studies of the physics possibilities of aγC should include the impact of the resolved photons on the event reconstruction,and we need to determine the appropriate number of beam crossing that we need to integrate over.It is generally assumed that theγC and e+e?detectors will be the same or at least have comparable performance.At e+e?,the plan is to integrate over100’s to1000’s of beam crossings.This depends,of course,on the choice of detector technology as well as the bunch structure of the electron beam.At aγC experiment,the desire to minimize the resolved photon backgrounds may drive the detector design to be able to minimize the number of crossings that are being readout together.In preliminary studies,integrating over about10crossings appears tractable.The required detector readout rate due to backgrounds from resolved photons call into question the assumptions that the e+e?andγγdetectors will be based on the same technology and/or have comparable performance.An important distinction between the TESLA

ee Luminosity Spectra

024

ee Center of Mass Energy (GeV)

L u m i n o s i t y x 1032

/3.328 G e V (c m -2 s -1

)

e γ Luminosity Spectra

02

4

e γ Center o

f Mass Energy (GeV)

L u m i n o s i t y x 1032

/3.328 G e V (c m -2 s -1

)

γγ Luminosity Spectra

02

4

50100150

γγ Center of Mass Energy (GeV)

L u m i n o s i t y x 1032

/3.328

G

e V (c m -2 s -1

)

Spin-0

Spin-2

ee Luminosity Spectrum

02468100

200400

ee Center of Mass Energy (GeV)L u m i n o s i t y x 1032

/10.4 G e V (c m -2 s -1

)

e γ Luminosity Spectrum

02468100

200400

e γ Center o

f Mass Energy (GeV)

L u m i n o s i t y x 1032

/10.4 G e V (c m -2 s -1

)

γγ Luminosity Spectrum

0246810γγ Center of Mass Energy (GeV)

L u m i n o s i t y x 1032

/10.4 G e V (c m -2 s -1

)

Spin-0

Spin-2

FIG.3:Luminosity for a 107sec year and associated expectation value for the product of photon polarizations, λλ′ ,are plotted

for

√2

The NLC-e +e ?design has 1.4ns bunch spacing –see the caption of Table II for discussion.

FIG.4:Tracks contributing to the resolved photon background for

=160GeV.Energy and cosθdistribution for showers

s

ee

with E>0.1GeV.The plots corresponds to6,700beam crossings.

A.Standard Model expactations at theγC Higgs factory

In the Standard Model,the branching ratios for B r(H→bˉb),B r(H→W W),B r(H→ZZ)and B r(H→γγ)for a Higgs mass of115GeV are:73.7%,8.8%0.9%and0.2%,respectively.In[11],it was shown that the most promising reaction for a115GeV Higgs,isγγ→H→ˉbb,but the expectations for other decay channels like H→W W and H→γγwere also given.Their results are summarized in Table IV.

However,since one of the objectives of aγC Higgs factory would be to test the prediction for these branching ratios,

FIG.6:Tracks contributing to the resolved photon background for

=500GeV.Energy and cosθdistribution for showers

s

ee

with E>0.1GeV.The plots corresponds to20,500beam crossings.

and use their measurements to distinguish between the Standard Model and its possible extensions,we are making an e?ort to also look at theγγ→H→ZZ.In order to evaluate the signal to background ratio in this decay mode,we need the cross sections forγγ→ZZ andγγ→four?fermions.

We have made progress adding the processesγγ→γγ,γγ→ZZ andγγ→γZ to Pandora[25].To date,these processes have not been included in Pandora as they are1-loop processes,and as such the cross section is di?cult to calculate.As it is the most interest to us,we have focused on theγγ→ZZ process.

The FormCalc and LoopTools packages[26]can be used to calculate the cross sections for various loop processes.

γγ Luminosity Spectra

00.5

1

γγ Center of Mass Energy (GeV)

L u m i n o s i t y x 1033

/3.12 G e V (c m -2 s -1

)

Spin-0

Spin-2

γγ Effective Polarization

0.5

1

γγ Center of Mass Energy (GeV)

<λλ′

>

FIG.8:Luminosity spectra and beam polarization as functions of E CM (γγ)for the CLIC 1parameters for 75GeV electrons obtained with DIMAD [24]and CAIN [13]for L ee =4.8×1034cm ?2s ?1.

We use code generated from these packages for us by Thomas Hahn,called AAAA ,which can be used to calculate one loop integrals for general 2to 2processes,and 2to 3process.Given the mass,charge,polarization and nature (scalar,fermion,vector or photon)of the initial and ?nal particles AAAA calculates the cross section for a given center of mass energy.We have modi?ed the AAAA code to create a subroutine that returns the cross section for the process γγ→ZZ given the masses of the Z ’s,the initial and ?nal polarizations,cos(θ)and center of mass energy.

We have based the Pandora class for the γγ→ZZ process on the γγ→W W class.When the cross section is required by Pandora we call the subroutine discussed above.

The tools that we have develop will allows us to use the CAIN prediction of the full γγenergy spectra and their corresponding polarization.The expected cross section for γγ→ZZ is smaller than 0.01fb,for the CLICHE luminosity spectra and polarization shown in Fig.8.

In order to determine the impact of γγ→four ?fermions ,background samples were generated with WHIZARD 1.24.For details concerning the usage of WHIZARD for four-fermion processes,please refer to point B 3below.

At the moment,we have only studied the prospects for the detection of γγ→ZZ based on the search for the heaviest decay b ˉbb ˉb ,and compare them to the light decays like e +e ?e +e ?,e +e ?μ+μ?and μ+μ?μ+μ??nal states.The signal sample for γγ→H →ZZ →b ˉbb ˉb was generated using Pythia 6.158with an interface to CAIN to get the correct CLICHE spectrum.Event reconstruction and analysis were done in the framework of the FastMC program and PAW.About 75%of generated events had four or more reconstructed jets.We required |cos Θj |<0.9for j =1,2,3,4,where Θj is the polar angle of the jet with respect to the beam direction,measured in the lab frame.The e?ciency of this cut for the four-fermion background processes depends strongly on the mass of the particle involved and for γγ→b ˉbb ˉb it produces a 20-fold reduction of the initial sample.Meanwhile,signal events are distributed nearly isotropically,so that ~70%of them will survive the cut.

Necessary signature to identify the ZZ intermediate state is the appearance of the Z mass peak.We therefore assume here that one Z must be on the mass shell,leaving at most a 24GeV mass for the other Z .Consequently,we selected only events for which one ?nds two jets with 85GeV 100GeV,which

TABLE IV:The statistical errors on selected decay modes of a115GeV Higgs boson in the Standard Model.Theγγ→h cross section for the full(peak)Lγγis assumed to be112(624)fb(see Ref.[11]).The expected yield for200(36)fb?1is22,400Higgs particles.

decay mode raw events/year S/B?sel B r?ΓγγB r/ΓγγB r

W+W?1971 1.20.328.8%5%

ZZ2010.9%11%

events is around25%.

No b tagging was simulated.We assume an additioanl70%e?ciency for tagging a single bˉb pair.Takingσ(γγ→H) =112fb,BR(H→ZZ)=0.009and BR(Z→bˉb)=0.15,we end up at0.6reconstructedγγ→H→ZZ→bˉbbˉb events per canonical year of107s.For the background,we have considered the direct bˉbbˉb production,as well asγγ→bˉbcˉc with a cˉc pair mistagged as bˉb andγγ→cˉc cˉc with a double cˉc mistagging.We assume a3.5%probability of mistagging cˉc as bˉb.Total selection acceptance for background processes as a function of energy was found to vary from less than0.01% for all three considered processes at100GeV and below to0.4%at120GeV forγγ→bˉbbˉb,to0.2%at120GeV for γγ→bˉbcˉc and to0.04%at120GeV forγγ→cˉc cˉc.Total cross sections in this energy region,calculated by WHIZARD 1.24,were found to be around300fb forγγ→bˉbbˉb,8pb forγγ→bˉbcˉc and90pb forγγ→cˉc cˉc,and slowly varying with energy.From all this input,we arrive at a?nal number of4.4bˉbbˉb events,4.7bˉbcˉc events and0.9cˉc cˉc events in the signal window per107s.Therefore,the signal to background is not optimal in this channel.

However,similar analysis for Z→ee,μμseem to give a better signal to background ratio,but higher monte carlo statistics is needed to be able to con?rm.The reasons are the following:the reconstruction e?ciency of the signal is much higher,and even though theσ(γγ→4l,l=e orμ)are higher that for bˉbbˉb,their stronger cosΘdependence causes most of the events to go down the beampipe.For example,σ(γγ→4μ)=0.16nb,but only1.7fb have at least all four μ’s in the detector.

Further work is needed before we can conclude,but the required tools are now available.

B.NMSSM Scenario with h→aa

In this section,we demonstrate that aγC add-on to the CLIC test machines could provide invaluable complementarity to the LHC when it comes to studying and verifying di?cult Higgs signals that can arise at the LHC in the context of the Next to Minimal Supersymmetric Model or other Higgs sectors in which a SM-like Higgs boson can decay to two lighter Higgs bosons.

1.Introduction

As repeatedly stressed,one of the key goals of the next generation of colliders is the discovery of Higgs boson(s) [27].Assuming the absence of CP violation in the Higgs sector,the Higgs bosons of the Minimal Supersymmetric Model(MSSM)comprise the CP-even h0and H0,the CP-odd A0and the charged Higgs,H±.Recent reviews of the prospects for Higgs discovery and study at di?erent colliders include[28,29].It has been established that the LHC with L>100fb?1will discover at least one of these Higgs bosons.A LC or aγC will be able to perform detailed precision measurements of great importance to testing the details of the MSSM Higgs sector and are very likely to discover those Higgs bosons of the MSSM that can not be seen at the LHC.For example,theγC can detect the H0and A0in the large-m A0,moderate-tanβwedge region where the LHC will not be able to detect them.

The results for the CP-conserving(CPC)MSSM do not generalize to supersymmetric models with more complicated

Higgs sectors.One highly motivated extension of the MSSM is the Next-to-Minimal Supersymmetric Model(NMSSM),in

which one additional singlet Higgs super?eld is introduced in order to naturally explain the poorly understoodμparameter

[27,30].The NMSSM Higgs sector comprises three(mixed)CP-even states(h1,2,3)two(mixed)CP-odd states(a1,2)

and a charged Higgs pair(H±).Guaranteeing discovery of at least one NMSSM Higgs boson is a considerable challenge. In particular,one of the key ingredients in the no-lose theorem for CPC MSSM Higgs boson discovery is the fact that the

SM-like Higgs boson(the h when m A>~125GeV or H when m A<~115GeV)never has signi?cant decays to other Higgs bosons(h→AA or H→AA,hh,respectively).In the NMSSM,Higgs boson masses are not very strongly correlated,

and h1→a1a1or h2→a1a1decays can be prominent[31,33].(If one-loop-induced CP violation is substantial in the MSSM Higgs sector,decays of one CP-mixed MSSM Higgs boson to two others are also possible[32].)Such decays fall outside the scope of the usual detection modes for the SM-like MSSM h on which the MSSM no-lose LHC theorem largely relies.The?rst question is whether this makes an absolute LHC no-lose theorem for the NMSSM impossible.Second, if there are regions of parameter space in which the LHC signal is marginal or of uncertain interpretation,could a LC or(our particular interest here)aγC alone(i.e.in the absence of a LC)guarantee Higgs discovery or help verify the nature of the signal for such regions.The purpose of this note is to remark on the complementarity of aγC to the LHC in such regions.We will?nd that it could be very crucial.

In earlier work[34],a partial no-lose theorem for NMSSM Higgs boson discovery at the LHC was established.In

particular,it was shown that the LHC would be able to detect at least one of the NMSSM Higgs bosons(typically,one

of the lighter CP-even Higgs states)throughout the full parameter space of the model,excluding only those parameter

choices for which there is sensitivity to the model-dependent decays of Higgs bosons to other Higgs bosons and/or

superparticles.

In more recent work,the assumption of a heavy superparticle spectrum has been retained and the focus was on the

question of whether or not this no-lose theorem can be extended to those regions of NMSSM parameter space for which

Higgs bosons can decay to other Higgs bosons.It is found[35]that the parameter choices such that the“standard”

discovery modes fail are such that either the h1or h2(numerically ordered according to increasing mass)is very SM-like

in its couplings,but mainly decays to a1a1.Detection of h1,2→a1a1will be di?cult since each a1will decay primarily to either b

b with a substantial branching

ratio even for these most di?cult cases,but it will be hard to be sure if the signal really corresponds to a Higgs boson.

We will show that aγC would be very important for clarifying the nature of the signal.

2.Details Regarding Earlier Results

In the earlier work,the simplest version of the NMSSM is considered,in which the termμ H1 H2in the superpotential of the MSSM is replaced by(using the notation A for the super?eld and A for its scalar component?eld)

λ H1 H2 S+κ

AκS3(2)

3

are considered as independent.The masses and/or couplings of sparticles are assumed to be such that their contributions

to the loop diagrams for gg→h andγγ→h couplings are negligible.In the stop sector,which appears in the radiative

corrections to the Higgs potential,the soft masses m Q=m T≡M susy=1TeV are chosen.Scans are perfomred over the stop mixing parameter,related to M susy and the soft mixing parameter A t by X t≡2A2t12(M2susy+m2t) .

As in the MSSM,the value X t=

In the studies of[35],a numerical scan over the free parameters is performed.For each point,the masses and mixings of the CP-even and CP-odd Higgs bosons,h i(i=1,2,3)and a j(j=1,2)are computed,taking into account radiative corrections up to the dominant two loop terms.Parameter choices excluded by LEP constraints on e+e?→Zh i and e+e?→h i a j are eliminated and m h±>155GeV is required,so that t→h±b would not be seen.LHC discovery modes

for a Higgs boson considered were(with?=e,μ):

1)gg→h/a→γγ;

2)associated W h/a or tˉt h/a production withγγ?±in the?nal state;

3)associated tˉt h/a production with h/a→bˉb;

4)associated bˉbh/a production with h/a→τ+τ?;

5)gg→h→ZZ(?)→4leptons;

6)gg→h→W W(?)→?+??νˉν;

7)W W→h→τ+τ?;

8)W W→h→W W(?).

The expected statistical signi?cances at the LHC in all Higgs boson detection modes1)–8)was estimated by rescaling results for the SM Higgs boson and/or the the MSSM h,H and/or A.Among these modes,the t tb

B (where S and B are the signal and background,respectively)assuming K S=K B=1were employed,awaiting the time when all K factors are known.(For all cases where both K S and K B are known,their inclusion improves the N SD value.) For each mode,the procedure was to use the results for the“best detector”(e.g.CMS for the t

th SM→t b N SD vales came in substantially larger than the ATLAS values.3)The experimental evaluations of the W W fusion channels yield lower N SD values than the original theoretical estimates.

The results from[34]can be summarized as follows.For parameter space regions where none of the“higgs-to-higgs”decays

i)h→h′h′,ii)h→aa,iii)h→h±h?,iv)h→aZ,

v)h→h±W?,vi)a′→ha,vii)a→hZ,viii)a→h±W?.

is kinematically allowed it is possible for the LHC signals to be much weaker than SM Higgs signals.In particular,one can?nd parameters such that the gg→h i→γγrates are all greatly suppressed and all the h i→W W branching fractions and couplings are suppressed.The result is greatly decreased N SD values for all the channels1)–8),and a not very wonderful combined statistical signi?cance after summing over various sets of channels.Nonetheless,the very worst parameter choices for the no-higgs-to-higgs decay part of parameter space does predict a≥5σsignal for at least one Higgs boson in at least one channel—in particular,in the t tb

evades LEP constraints.Further,in the case of the points1–3,the h2would not be detectable either at the LHC

or the LC.For points4–6,the h1,though light,is singlet in nature and would not be detectable.Further,the h3or

a2will only be detectable for points1–6if a super high energy LC is eventually built so that e+e?→Z→h3a2is possible.Thus,it was necessary to focus on searching for the SM-like h1(h2)for points1–3(4–6)using the dominant

h1(h2)→a1a1decay mode.

TABLE V:Properties of selected scenarios that could escape detection at the LHC.The production rate for gg→h i fusion

relative to the gg fusion rate for a SM Higgs boson with the same mass is given.Important absolute branching ratios are displayed.

For points2and6,BR(a1→jj)?1?BR(a1→τ+τ?).For the heavy h3and a2,only their masses are shown.For all points1–6,the statistical signi?cances for the detection of any Higgs boson in any of the channels1)–8)(as listed in the introduction) are tiny;their maximum is indicated in the last row,together with the process number and the corresponding Higgs state.

Point Number246

Bare Parameters

λ0.21240.33400.5212

0.53320.52040.0844

tanβ 3.5 2.5 2.5

200200200

Aλ(GeV)0500500

000

m h

(GeV)1197651

1

0.970.990.01

BR(h1→b0.020.010.91

BR(h1→τ+τ?)0.000.080.00

0.980.980.00

516594124

Relative gg Production Rate0.090.980.90

b)0.040.020.00

0.000.000.00

BR(h2→a1a1)0.020.970.96

(GeV)1064553535

m h

3

CP-odd Higgs Boson Masses and Couplings

563559

Relative gg Production Rate0.030.010.05

b)0.000.920.00

0.080.070.08

528643563

Charged Higgs Mass(GeV)640561539

Most Visible Process No.2(h1)2(h2)8(h2)

0.480.550.53

b decays are dominant with a1→τ+τ?making up the rest.In the case of points2and 6,m a

<2m b so that a1→τ+τ?decays are dominant,with a1→jj decays making up most of the rest.For points1 1

and3–5,the b jets will not be that energetic and b-tagging will be somewhat ine?cient.However,because of a large

jjτ+τ?background from Drell-Yanτ+τ?pair production,b-tagging will be needed.The situation is illustrated in Fig.9, where the cross section vs.the reconstructed M jjτ+τ?is plotted.The signals and backgrounds are plotted prior to the

LHC,√

t background rates will be reduced by a factor of about2and theτbackground will be negligible for points1and3–5.(Viable techniques for observation of points2and6have not yet been developed.)Although the signal

is somewhat amorphous in nature,statistics are signi?cant.To estimate S/

t background.(These K factors are not included in the plots of Fig.9.)Then,sum events over the region60≤M jjτ+τ?≤90GeV.Assuming a net e?ciency of50%for single b-tagging,the t

B of35,30,41and36,respectively.However,given the broad distribution of the signal,it is clear that a crucial question will be the accuracy with which the background shape can be predicted from theory.(The background normalization after the cuts imposed in the analysis would be very well known from the higher M jjτ+τ?regions.)Even more important is the question of how certain the interpretation of this signal will be,given that it would be the only signal for Higgs boson production.In this regard,detection of the a1a1→b b?nal state would be very valuable as it would allow us to determine if BR(a1→τ+τ?)/BR(a1→b

bb

order100GeV,discovery of the h would be very straightforward via e+e?→Zh using the e+e?→ZX reconstructed M X technique which is independent of the“unexpected”complexity of the h decay to a1a1.This would immediately provide a direct measurement of the ZZh coupling with very small error.The next stage would be to look at rates for the various h decay?nal states,F,and extract BR(h→F)=σ(e+e?→Zh→ZF)/σ(e+e?→Zh).For the NMSSM points considered here,the main channels would be F=b b,F=b

TABLE VI:NMSSM points 1,3,4,5.We give cross sections,acceptance after all cuts other than b -tagging,and the number of events (assuming a b -tagging e?ciency of ?b =0.5)in a canonical 106second year.

Scenario m a (GeV)

Acceptance

(1)

56

0.26

123

9.1

14.7

(4)

41

0.28

124

6.0

7.1

strongly depends on the h mass.This dependence is,however,almost entirely due to the luminosity spectrum assumed and the resulting sensitivity of the total h production cross section to m h .

The expected four-jet invariant mass distributions of all surviving signal and background events are depicted in

Fig.10(the background samples are the same in each case).Absolute numbers are again normalized to 106seconds.We ?nd a clear signal,visible over the background after a short time of running,even in the most disfavorable scenario (5).It is also clear that the particular choice of E CM =115GeV was not the most fortunate for this study and that an upgrade of E CM to 120-125GeV would very probably have the e?ect of producing signals for cases (3)and (5)that look much more like those shown here for cases (1)and (4).If the beam energy happens to be well tuned to m h (as was the case here for scenario (1)),a prominent signal peak in the four-jet invariant mass is bound to appear immediately.

m h = 115SIGNAL on top of BACKGROUND - 4 SCENARIOS

5101520

25M 4jet (GeV)

E v /106s

m h = 1230

0.5

11.52

2.5M 4jet (GeV)

E v /10s

m h = 1180

246810M 4jet (GeV)

E v /106s

m h = 1240

0.2

0.40.60.811.21.41.6M 4jet (GeV)

E v /10s

FIG.10:Four-jet invariant mass distributions after 106s of running,and after including b -tagging with ?b =0.5,in scenarios (1),

(3),(4)and (5).Signal γγ→h →aa →b ˉbb ˉb is shown in red,backgrounds:γγ→b ˉbb ˉb in green,γγ→b ˉbc ˉc in blue and γγ→c ˉc c ˉc in yellow.

potentially just as good as found here for the b b channel for scenarios(1)and(3–5).With the cross section for direct

4τproduction being of the order of500fb,the?nal signal to background ratio should,in fact,be very similar to the

one obtained here in the4b channel,except for the slightly di?erent h masses;the overall normalization will depend on

theτreconstruction e?ciency.The main di?culty will be the impossibility of fully reconstructing the mass peak in the

τ+τ?τ+τ?channel.A full study is needed.

Returning to scenarios(1),(3),(4)and(5)given Table VI,we note that BR(a→τ+τ?)≈0.1so that signal detection seems plausible also in the channel bˉbτ+τ?,provided m h is not too far away from E CM(a slight upgrade of E CM should be enough for this purpose).Combination of data obtained from the two channels will provide invaluable

information for physics studies.In particular,the very important ratio BR(a1→τ+τ?)/BR(a1→b

t and b

bτ+τ?channel.In particular,we have demonstrated a clear signal in the important complementary channel aa→b b.We have also argued that the other

two?nal state channels of aa→b

bb

b decays are not allowed,we believe that theγC will

be able to detect the aa→τ+τ?τ+τ?and possibly the aa→jjτ+τ??nal states that have not yet been shown to be detectable at the LHC.

C.Higgs boson physics in the Complex MSSM

The MSSM with complex parameters(cMSSM)o?ers an interesting extension of the“real MSSM”(rMSSM),especially

concerning Higgs boson physics.At the tree-level,CP-violation in the Higgs boson sector is absent.However,complex

phases of the trilinear couplings,A t,A b,...,of the gluino mass and of the gaugino masses,m g,M2and M1and possibly also from the Higgs mixing parameterμcan induce CP-violation at the loop-level.As a consequence all three neutral

Higgs bosons,h,H and A are no longer CP eigenstates,but can mix with each other[37],

(h,H,A)→(h1,h2,h3)with m h

1≤m h2≤m h3.(3) Higher order corrections to the Higgs boson masses and couplings have been evaluated in several approaches[38,39,40, 41].

Due to loop corrections,the lightest Higgs boson can decouple from the gauge bosons.In this case,at e+e?colliders, the main production modes for Higgs bosons can be

e+e?→Z→Z h2

e+e?→Z→h2h1.(4)

Higgs boson searches at LEP in the context of the cMSSM[42]have shown that in this case the decay h2→h1h1poses special experimental problems.This decay mode,which is often dominant in this case,results in a six jet?nal state topology(with the Higgs bosons decaying to b quarks).Such a?nal state can be quite complicated to handle,e.g.due

In aγC the situation is more favorable.Here the Higgs bosons are produced singly.Thus the decay h2→h1h1results in a four jet?nal state that is easy to handle.(In a similar fashion the problem at an e+e?collider could be overcome if the Higgs bosons are produced in the W W fusion mode at high energies.)The topology of the decay h2→h1h1 resembles strongly the topology that arises for h→AA in the rMSSM,the NMSSM or the THDM.Thus the analysis methods can(nearly)directly be taken over from these cases.

D.The Little Higgs boson at a Photon Collider

The Standard Model(SM)of the strong and electroweak interactions has passed stringent tests up to the highest energies accessible today.The precision electroweak data[43]point to the existence of a light Higgs boson in the SM, with mass m H<~200GeV.The Standard Model with such a light Higgs boson can be viewed as an e?ective theory valid up to a much higher energy scaleΛ,possibly all the way up to the Planck scale.In particular,the precision electroweak data exclude the presence of dimension-six operators arising from strongly coupled new physics below a scaleΛof order 10TeV[44];if new physics is to appear below this scale,it must be weakly coupled.However,without protection by a symmetry,the Higgs mass is quadratically sensitive to the cuto?scaleΛvia quantum corrections,rendering the theory with m H?Λrather unnatural.For example,forΛ=10TeV,the“bare”Higgs mass-squared parameter must be tuned against the quadratically divergent radiative corrections at the1%level.This gap between the electroweak scale m H and the cuto?scaleΛis called the“little hierarchy”.

Little Higgs models[45,46]revive an old idea to keep the Higgs boson naturally light:they make the Higgs particle a pseudo-Goldstone boson[47]of some broken global symmetry.The new ingredient of little Higgs models is that they are constructed in such a way that at least two interactions are needed to explicitly break all of the global symmetry that protects the Higgs mass.This forbids quadratic divergences in the Higgs mass at one-loop;the Higgs mass is then smaller than the cuto?scaleΛby two loop factors,making the cuto?scaleΛ~10TeV natural and solving the little hierarchy problem.

From the bottom-up point of view,in little Higgs models the most important quadratic divergences in the Higgs mass due to the top quark,gauge boson,and Higgs boson loops are canceled by loops of new weakly-coupled fermions,gauge bosons,and scalars with masses around a TeV.In contrast to supersymmetry,the cancellations in little Higgs models occur between loops of particles with the same statistics.Electroweak symmetry breaking is triggered by a Coleman-Weinberg[48]potential,generated by integrating out the heavy degrees of freedom,which also gives the Higgs boson a mass at the electroweak scale.

The Littlest Higgs model[46]is a minimal model of this type.It consists of a nonlinear sigma model with a global SU(5)symmetry which is broken down to SO(5)by a vacuum condensate f~Λ/4π~TeV.The gauged subgroup [SU(2)×U(1)]2is broken at the same time to its diagonal subgroup SU(2)×U(1),identi?ed as the SM electroweak gauge group.The breaking of the global symmetry leads to14Goldstone bosons,four of which are eaten by the broken gauge generators,leaving10states that transform under the SM gauge group as a doublet h(which becomes the SM Higgs doublet)and a tripletφ.A vector-like pair of colored Weyl fermions is also needed to cancel the divergence from the top quark loop.The particle content and interactions are laid out in detail in Ref.[49].

In the Littlest Higgs model,the tree-level couplings of the Higgs boson to SM particles are modi?ed from those of the SM Higgs boson by corrections of order v2/f2(where v?246GeV is the SM Higgs vacuum expectation value)that arise due to the nonlinear sigma model structure of the Higgs sector and,for the couplings to gauge bosons and the top quark, due to mixing between the SM particles and the new heavy states.The experimental sensitivity to the Higgs couplings to W and Z bosons in this model has been considered in Ref.[50].Here we focus on the loop-induced Higgs coupling to photon pairs,which receives corrections from the modi?cations of the Higgs couplings to the SM top quark and W boson,as well as from the new heavy particles running in the loop[51].Like the tree-level couplings,the loop-induced Higgs couplings receive corrections of order v2/f2.

Any charged particle that couples to the Higgs boson will contribute to H→γγ.In the Littlest Higgs model,those

Φ±,Φ±±.Besides the condensate f as the most important scale parameter,the mass and couplings of each new state depend upon additional dimensionless parameters.The mixing between the two gauge groups SU(2)1and SU(2)2,with couplings g1and g2respectively,is parameterized by c.The mixing between the top quark and the heavy vector-like quark T is parameterized by c t.In the Higgs sector,the ratio of the triplet and doublet vacuum expectation values(v′/v) is parameterized by x.More explicitly,we have(for additional details,see Refs.[49,51]):

0

g1

g21+g22

<1,0

λ1

λ21+λ22

<1,0≤x=

4fv′

1?c2and s t≡

2G Fα2m3H y2G

F

2G F y2G

F

,where[51]

y2G

F =1+

v2

12

+

1

f2 ?22x?1

f2 ?14(c2?s2)2?x2 .(8)

For the heavy particles in the loop,on the other hand,the y i factors are of order v2/f2.This re?ects the fact that the masses of the heavy particles are not generated by their couplings to the Higgs boson;rather,they are generated by the

f condensate.This behavior naturally respects the decouplin

g limit for physics at the scale f?v.The couplings are

[51]:

y T=?c2t(1+c2t)

v2

f2

,

yΦ+=v2

3

+

1

0.80.850.90.951

1.051.1500

1000

1500

200025003000

3500

4000

Γ(H → γγ) / S M

f (GeV)

Accessible

m H

120 GeV 150 GeV 180 GeV

FIG.11:Range of values of Γ(H →γγ)accessible in the Littlest Higgs model as a function of f ,normalized to the SM value,for m H =120,150and 180GeV.From Ref.[51].

an uncertainty of about 2%on the rate [11,53].(The uncertainty rises with increasing Higgs mass to about 10%for m H =160GeV.)This can be combined with the ~1.5?2%measurement of the branching ratio of H →b ˉb from the e +e ?collider [54,55,56]to extract Γ(H →γγ)with a precision of about 3%.Such a measurement could probe f <2700GeV at the 1σlevel,or f <1800GeV at the 2σlevel.A 5σdeviation is possible for f <1200GeV.For comparison,the electroweak precision constraints [52]on the Littlest Higgs model require f >~1TeV,while naturalness considerations prefer as low a value of f as possible.

In the absence of an e +e ?collider,a similar analysis could be done combining LHC and γC data on Higgs boson production and decay rates to look for deviations of the various Higgs couplings from their SM values that would indicate the little Higgs nature of the Higgs boson.Such an analysis has not yet been done.

E.Higgs-Radion Mixing

In this section,we demonstrate the important complementarity of a γC for probing the Higgs-radion sector of the Randall-Sundrum (RS)model [57].

工作励志正能量句子

工作励志正能量句子 1)对于攀登者来说,失掉往昔的足迹并不可惜,迷失了继续前时的方向却很危险。 2)奋斗者在汗水汇集的江河里,将事业之舟驶到了理想的彼岸。 3)含泪播种的人一定能含笑收获。 4)很多失败不是因为能力有限,而是因为没有坚持到底。 5)机会不会主动找到你,必须亮出你自己。 6)驾驭命运的舵是奋斗。不抱有一丝幻想,不放弃一点机会,不停止一日努力。 7)困难和挫折都不可怕,可怕的是丧失做人的志气和勇气。 8)漫漫长路,你愿一人独撑,忍受着孤独与寂寞,承受着体力与精神的压迫,只任汗水溶于泪水,可脚步却从不停歇。好样的,纵然得不了桂冠,可坚持的你,定会赢得最后的掌声。 9)莫找借口失败,只找理由成功。 10)世上没有绝望的处境,只有对处境绝望的人。 11)每一发奋努力的背后,必有加倍的赏赐。 12)赚钱之道很多,但是找不到赚钱的种子,便成不了事业家。 13)大多数人想要改造这个世界,但却罕有人想改造自己。 14)当一个人先从自己的内心开始奋斗,他就是个有价值的人。 15)即使爬到最高的山上,一次也只能脚踏实地地迈一步。 16)穷人缺的是钱而不是时间,富人缺的是时间而不是钱。

17)好心不一定会换来感恩,但千万不要因此而灰心。 18)若不给自己设限,则人生中就没有限制你发挥的藩篱。 19)最有效的资本是我们的信誉,它小时不停为我们工作。 20)人生不是一种享乐,而是一桩十分沉重的工作。 1)忙于采集的蜜蜂,无暇在人前高谈阔论。 2)你追我赶拼搏争先,流血流汗不留遗憾。 3)懦弱的人只会裹足不前,莽撞的人只能引为烧身,只有真正勇敢的人才能所向披靡。 4)勤奋是你生命的密码,能译出你一部壮丽的史诗。 5)人生伟业的建立,不在能知,乃在能行。 6)你的上司越忙,你的饭碗越危险。 7)如果你最近的工作很闲,注意了,这可能是危机的先兆。 8)到处都是有才华的穷人,千万别觉得自己无可替代。 9)每一个成功者都有一个开始。勇于开始,才能找到成功的路。 10)当一个人用工作去迎接光明,光明很快就会来照耀着他。 11)如果我们想要更多的玫瑰花,就必须种植更多的玫瑰树。 12)漂亮的脸孔是给别人看的,而有智慧的头脑才是给自己利用的。 13)人只有在布满陡峭的路上,才能使自己的脚跟变的更稳;人只有在布满荆棘的路上,才能使自己的身体变的不怕伤痕;人只有在布满危险的路上,才能使自己的战斗力变的无比之强! 14)选择自信,就是选择豁达坦然,就是选择在名利面前岿然不动,就是选择在势力面前昂首挺胸,撑开自信的帆破流向前,展示搏击的风采。

50条超励志的正能量经典句子

50条超励志的正能量经典句子 1、当你觉得自已充满斗志,充满信心,别人就会觉得你就是值得相信的你。 2、当你觉得没有人来爱你,别人看见的就是可怜兮兮,毫无魅力的你。 3、当你觉得自己满怀希望,对未来充满信心,别人看到的就是有魅力,风华绝代的你。 4、人生与其说你有不幸的事实存在,倒不如说是你的悲观的观念所带来的。 5、有一则谚语说,绵羊每"咩咩"叫上一次,它就会失掉一口干草,如果你的心态是沉重的,总是抱怨你的苦恼,那么每说一次你便失掉一个快乐的机会。 6、相信自已。 不要妄加评判自已,也不会把自已交给别人评判,更不会贬低自已。 7、你想要别人是你的朋友,你必须是别人的朋友,心要靠心来交换,感情只有用感情来博取。 8、人生的游戏不在于拿了一副好牌,而在于怎样去打好坏牌,世上没有常胜将军,勇于超越自我者才能得到最后的奖杯。 9、既然时间是最宝贵的财富,那么珍惜时间,合理地运用时间就很重要,如何合理地花费时间,就如同花钱的规划一样重要,钱花

完了可再挣,时间花完了就不能再生,因此,更要利用好你的时间。 10、解铃还需系铃人,躲避责任会解决不了任何问题,它只导致一个失败的人生。 11、人不怕走在黑夜里,就怕心中没有阳光。 12、逃避不一定躲得过,面对不一定难受.转身不一定最软 弱.13、话多不如话少,话少不如话好。 14、曾经拥有的不要忘记,已经得到的要珍惜,属于自已的不要放弃。 15、永远都不要停止微笑,即使是在你难过的时候,说不定哪一天有人会因为你的笑容面爱上你。 16、因为某人不如你所愿爱你,并不意味着你不被别人所爱。 17、一个真正的朋友会握着你的手,触动你的心。 18、也许上帝让遇见那个适合你的人之前,会遇见很多错误的人,所以当一切发生的时候,你应该心存感激。 19、勇敢的面对不一定成功,但你不面对就一定不成功。 20、黑夜的转弯是白天,愤怒的转弯是快乐,所以有的时候让心情转个弯就好了。 21、一天要做三件事,第一要笑,第二要微笑,第三要哈哈大笑。 22、小树会大,大树会老,老树会凋零。 23、如果你不想做,你可以找一个理由,如果你肯做,你也可以

(励志句子)激励自己奋斗的正能量励志句子

激励自己奋斗的正能量励志句子 励志句子 1、在别人肆意说你的时候,问问自己,到底怕不怕,输不输的起。不必害怕,不要后退,不须犹豫,难过的时候就一个人去看看这世界。多问问自己,你是不是已经为了梦想而竭尽全力了? 2、人生从来没有真正的绝境。无论遭受多少艰辛,无论经历多少苦难,只要一个人的心中还怀着一粒信念的种子,那么总有一天,他就能走出困境,让生命重新开花结果。 3、幻想一步成功者突遭失败,会觉得浪费了时间,付出了精力,却认为没有任何收获;在失败面前,懦弱者痛苦迷茫,彷徨畏缩;而强者却坚持不懈,紧追不舍。 4、进步和成长的过程总是有许多的困难与坎坷的。有时我们是由于志向不明,没有明确的目的而碌碌无为。但是还有另外一种情况,是由于我们自己的退缩,与自己亲密的妥协没有坚持到底的意志,才使得机会逝去,颗粒无收。 5、决不能习惯失败,因为你要知道,身体的疲惫,不是真正的疲惫;精神上的疲惫,才是真的劳累。 6、理想是什么?它不是口上说的计划,也不是敷衍的借口,它是自己的心,理想的最终汇集地,是幸福,为了自己有了理想,为了恋人有了理想,为了家人有了理想,有了理想才有梦,梦想与理想,一字之差千里之遥。

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