Assuming that a Higgs sector is responsible for electroweak symmetry
breaking, we attempt to address two important questions: How much better
precision are various measurements of Higgs boson properties at a future linear
collider than at the LHC? What can a future linear collider do for Higgs
physics that the LHC cannot?Comment: 10 pp, 4 eps fig, econf, invited talk at RADCOR 2000 (Carmel, CA,
  Sept 2000), includes additional comments and citations on multiple Higgs
  productio

Rainwater, D.

English

arXiv

Assuming that a Higgs sector is responsible for electroweak symmetry breaking, we attempt to address two important questions: How much better precision are various measurements of Higgs boson properties at a future linear collider than at the LHC? What can a future linear collider do for Higgs physics that the LHC cannot

Rainwater, Dave

UNT Digital Library

Fermilab FERMILAB-Conf-01/049-T  April 2001arXiv:hep-ph/0101135 v2   11 Feb 2001February 11, 2001hep-ph/0101135Precision Higgs Physics at aFuture Linear ColliderDave RainwaterTheoretical Physics Dept.Fermi National Accelerator Laboratory, Batavia, IL 60510 USAAssuming that a Higgs sector is responsible for electroweak symmetrybreaking, we attempt to address two important questions: How muchbetter precision are various measurements of Higgs boson properties at afuture linear collider than at the LHC? What can a future linear colliderdo for Higgs physics that the LHC cannot?Presented at the5th International Symposium on Radiative Corrections(RADCOR{2000)Carmel CA, USA, 11{15 September, 20001 IntroductionThe origin of electroweak symmetry breaking (EWSB) and fermion mass gener-ation remains one of the most pertinent in the eld of high energy physics today.Although there exist several explanations for EWSB, some dynamical and othersspontaneous, preeminent among those is the existence of a Higgs sector, either one ortwo complex scalar doublets which acquire a vacuum expectation value (vev), or vevs,providing longitudinal degrees of freedom for the weak gauge bosons and additionalphysical observable Higgs boson states. For a single Higgs doublet, as in the Stan-dard Model (SM), one neutral CP even Higgs (H) would be observed. In a two-Higgsdoublet model (2HDM), such as the MSSM, ve physical Higgses would exist: lightand heavy CP even neutral scalars (h;H), a CP odd scalar (A), and a charged Higgsand its conjugate H. Additionally, a set of Yukawa couplings of the Higgs to SMfermions (Yf ), of unknown origin, generates the fermion masses.No physical Higgs boson has yet been observed, although electroweak precisiondata has long suggested that the Higgs is light, of order 100 GeV. As such, it canpossibly be accessed by present experiments, i.e. CERN's LEP II or the FermilabTevatron II. If neither of those experiments turns up evidence for a Higgs, the com-munity will turn to the LHC, which will have the capability to detect a SM or atleast one MSSM Higgs of any mass up to the unitarity limit.Let us suppose that the LHC nds a Higgs candidate resonance, which could beeither the solitary physical Higgs of a single Higgs doublet model, or a 2HDM neutralstate. This could be conrmation of previous observation at LEP or Tevatron, or anLHC discovery. Either way, a narrow resonance  is found in one or more anticipatedchannels with rate commensurate with expectations. The task is then to determinethe quantum numbers of , rst to conrm that it is a Higgs of some avor, secondto determine what model the Higgs belongs to. These quantum numbers are, withthe expected value for a Higgs in brackets: charge [neutral] color [none] mass [O(100) GeV] spin [0] couplings (gauge, Yukawa) [model dependent] total width self-coupling () [model dependent] CP [even, odd, mixture?]1The nature of the nal state of the observed channel(s) gives us at least the rsttwo quantum numbers, charge and color, immediately. For example, detecting aJacobian peak in the dilepton-missing transverse momentum spectrum in `+` jj=pTevents, as expected in weak boson fusion and decay to a pair of W bosons, wouldindicate that the state is neutral and colorless. Likewise for nding a resonance inthe two photon invariant mass spectrum, i.e. due to Higgs production, gg ! ! .The latter process would further imply by Yang's Theorem that the state cannot bespin 1, also consistent with a Higgs boson. A fairly precise measurement of the state'smass would also be obtained.These determinations are necessary, but not sucient conditions for conrmingthe Higgs nature of an observed resonance. To go further we must measure the state'scoupling to weak bosons, which must be a gauge coupling, perhaps modied by a massmixing parameter  and ratio of vevs in a 2HDM tan; and its couplings to fermions,which must be Yukawa, i.e. proportional to the fermion mass. Were these couplingsfound to meet the requirements of a Higgs sector, it is likely that most members ofthe community would agree that a Higgs had been discovered. However, the issue ofmeasuring a self-coupling clouds this. One could argue that this is merely an aspectof determining the exact model that is realized in nature. To this end we would alsowant to know the CP state of the resonance.For a SM or MSSM Higgs, the LHC can, in fact, make quite good determinationsof the mass and gauge coupling, a very good measurement of the total width (evenfor a Higgs width smaller than the width resolution of the detectors), and a goodmeasurement of at least one Yukawa coupling, Y [1]. CP-dependent distributions inHiggs production are known [2], however observing them appears not to be possiblein practice, due to detector eects [3]. A future International Linear Collider (ILC)can certainly do better than the LHC for the case of a light Higgs, approximately110 MH  200 GeV. How much better an ILC could measure these couplings, whatadditional couplings it would have access to, and its ability to go signicantly beyondLHC physics by measuring a self-coupling  or the CP nature of the Higgs sector arewhat I review here.2 The Easy Quantum NumbersOf greatest interest in Higgs physics is \Where is the Higgs?" That is, what is itsmass? Precision ts to electroweak data suggest [4] it is very near the lower boundfrom experiment,MH > 113 GeV [5]. If a Higgs is found in the range MH < 135 GeVor so, then the MSSM is still a viable theory. Finding a much heavier Higgs wouldsuggest a dierent form of new physics. At the LHC, MH would be determinedprincipally by observing the process gg ! H ! ZZ ! 4`, which is accessible atall masses. For example, at ATLAS for MH < 400 GeV, this would yield a 0:1%2or better mass measurement, depending ultimately on uncertainty in the calorimetercalibration [3].For a light Higgs, an ILC would improve this roughly by a factor of two to three,around 0:03   0:05% uncertainty for a light Higgs, using a combination of data fromthe recoil mass spectrum in e+e  ! HZ ! `+`  + X and direct reconstruction ofHiggs decay into dijets. A simulated recoil mass spectrum forMH = 120 GeV is shownin Fig. 1. Fig. 2 shows a comparison between CMS expectations and some dierentILC energies and luminosities. However, this level of precision may be overkill. Itwould correspond to, for example, 4-loop radiative corrections in the MSSM! Theseare currently far from achievable. Additionally, the leading uncertainty in MH inthis case is due to the large uncertainty in the top quark mass, mt, which will notimprove enough in the LHC or conceivable ILC experiments to warrant calculationof MSSM 4-loop corrections to MH , possibly even the 3-loop contributions.µµ Recoil Mass (GeV/c2)Entries/3 GeV/c2 /100 fb-105010015020025060 80 100 120 140 160 180Figure 1:  recoil mass for e+e  ! ZH !  +X , taken from Ref. [6].Determining consistency of a resonance with spin-0 has been studied thoroughlyfor the LHC. There exist two methods: angular distributions in H ! , and alsoin the reconstructed Z bosons in H ! ZZ![3]. The LHC has no diculty with thisconsistency check for MH < 400 GeV, so I do not discuss it further here.Measurement of the resonance's couplings to the weak bosons, photon, gluons,and fermions is of much greater interest. Conrming that gHWW ; gHZZ are gaugecouplings and related by SU(2) is one of the key determinations to identifying theresonance as a Higgs boson. These couplings may be modied by mixing or otherparameters of a 2HDM, which are well dened and appear only as overall factors.300.050.10.150.20.250.30.350.4125 150 175 200 225 250 275 300 325 350Higgs mass [GeV/c2]∆m/m [%]CMS: Lint = 3⋅105 pb-1 µµµµLC350: Lint = 5⋅105 pb-1 HllLC500: Lint = 5⋅105 pb-1 HllLC500: Lint = 5⋅105 pb-1 bbqqFigure 2: The expected Higgs mass resolution at CMS and at three linear collider options,taken from Ref. [7].For example, the hWW;HWW verticies are modied at tree level in the MSSM bysin( ); cos( ), respectively. In this same vein, we would require that gH; gHggare demonstrated to be loop-induced.At the LHC, gHWW may be determined to better than 5% for a light Higgs,MH < 200 GeV, for scenarios where the Higgs is relatively SM-like [1]; non-SM-likeHiggs coupling extraction scenarios are just now beginning to be examined [8]. This isachieved by combining information from various decay channels in weak boson fusionHiggs production. This same method also allows the total width to be extractedindirectly, to about the 10  15% level. The best Yukawa coupling measurement canbe made for taus, which is quite good at about 5  15% over the mass region 115 <MH < 150 GeV, and work is progressing onH ! bb but this measurement is not likelyto be better than about 30% in the end [9]. Decays to cc are completely inaccessibleat the LHC, but the width to gluons could be determined to about 20% from the ratefor gg ! H ! W+W  and the highly accurately known BR(WW ). These resultswould already be quite good and allow for considerable model determination, but anILC could do far better.The procedure for extracting couplings1 is equally involved at the ILC. First, therecoil mass spectrum in ZH production would be used to determine ZH to about1We may alternatively discuss the measurement of partial widths, which are directly proportionalto the coupling squared. If the total width cannot be determined, it is more appropriate to discussmeasurement of branching ratios.42% (TESLA) for a light Higgs, say 110 < MH < 150 GeV. This measurement isthe basis for extracting absolute branching ratios. Once the WW branching ratio isknown (< 5% for a light Higgs, possibly as good as 2%), gHWW could be obtainedto better than 2%. From there, Yukawa couplings could be extracted directly. Theexpected uncertainty in the branching ratio for decay to bb is anticipated to be thelowest, about 2% for MH = 120 with reasonable luminosity; 8% for cc and 6% for+ . Additionally, BR(gg) could be determined to about 8% for the same mass.Fig. 3 shows the probable branching ratio measurement precision at TESLA.mH (GeV/c2)SM Higgs Branching Ratio10-210-1190 100 110 120 130 140 150Figure 3: Estimated accuracy for SM Higgs branching fractions for 500 fb 1 of data atTESLA, taken from Ref. [6].ttH production is possible for a high-energy ILC, being optimum at aboutps =800 GeV for MH = 120 GeV. There is considerable discrepancy in the literature,however, as to the achievable precision in gHtt=gHtt, ranging from 6% [10] on theoptimistic end to as pessimistic as about 50% [11]. Clearly, more study is needed toresolve this disagreement. Finally, the total width could be had to better than 5%for MH = 120 GeV, or about 3% for MH = 140 GeV, using the H cross section askey input, which contains the already determined gauge coupling.As far as distinguishing the SM from the MSSM, prospects appear good at theILC but this subject begs for more study. Ratios of branching ratios are important,especially BR(bb)/BR(W+W ), which could yield an indirect measurement of MA.(It is possible that observing the CP odd state A itself could prove dicult.) Otherimportant ratios are BR(cc)/BR(bb) and BR(gg)/BR(bb). It is known that an MSSMHiggs sector can be established as non-SM-like at the 95% CL for MA < 550 or so at5TESLA, depending somewhat on tan . This is shown in Fig. 4 for 500 fb 1 of data.TESLA  L = 500 fb-1mA (GeV/c2)tan β51015202530200 300 400 500 600 700 800 900Figure 4: SM v. MSSM discriminating power as a function of MA and tan for 500 fb 1of data at TESLA, taken from Ref. [6]. Parameter space to the right of the curves wouldappear SM-like. The blue curve is 95% CL, red is 90% CL, and green is 68% CL.For a Higgs heavier than about 150 GeV, measurement of Yukawa couplings (otherthan to the top quark) are essentially inaccessible at any machine, except in certainrestricted regions of a 2HDM. However, it is still highly desirable to know the gaugecouplings and total width in this regions. Preliminary results indicate [12] that forthe mass region 150 < MH < 300 GeV an ILC could achieve 10% uncertainty forBR(WW ) and 10   25% uncertainty for BR(ZZ), the latter depending strongly onMH . For MH > 300 GeV, BR(V V ) could be determined to a few percent, andBR(tt) becomes accessible, probably at the 6% level. It is currently not known how tomeasure this at all at the LHC. ForMH > 230 GeV or so, the Higgs width is expectedto exceed detector resolution; the LHC and an ILC would have comparable abilityhere, at the few percent level for a heavy Higgs. A heavy Higgs is widely regardedas less interesting, and as such this scenario has not received as much attention instudies for an ILC.It is easy to nd already in the SM that radiative corrections are important. Forexample,  BR(bb)> 30% forMH = 120 GeV, simply due to the gluonic corrections. Inextensions to the SM, such as the MSSM, large radiative corrections to the couplings(partial widths) lurk behind every corner. To take a couple examples, light squarkcorrections to h ! gg can be as large as factors of 2-3 in the partial width, butdisappear as the squarks get heavy, greater than a few hundred GeV. Also, gluino6or chargino corrections to the b-H verticies and H1;H2 mixing can lead to order 1corrections to the partial widths to b quarks or  leptons [13]. Considerable eorthas been invested in calculating such corrections over the past decade, but the stateof the art advances and interesting phenomenology continues to be revealed.3 The Tough Quantum NumbersWhile the \easy-to-determine" quantum numbers of a newly discovered resonancemay be sucient to establish it as part of a Higgs sector, in some sense the moredicult measurements are the interesting ones. These are the CP nature of theresonance, more specically if there is any CP mixing in the neutral states in the caseof a two Higgs doublet sector; and the self-coupling(s) i. In the SM  is related tothe Higgs mass via M2H = 2v2, and as it is a free parameter, MH is undetermined.In the MSSM, the various i are gauge couplings, thus MH is constrained. To beconvinced that an observed Higgs sector (and perhaps other MSSM candidate states)belong to the MSSM, we would need to verify that these are, indeed, gauge couplings.Thus, multiple Higgs production would have to be observed.Several studies have addressed the issue of multiple Higgs production at an ILC,highlighting scenarios where the cross section is large enough to obtain a substantialrate [14]. Only two groups have performed a signal v. background study at thephenomenological level (in the ZHH channel for the SM), and only one of those twogroups, Castanier et al., included detector simulation. However, their results are quitepromising. For a light SM Higgs, i.e. 120 < MH < 140 GeV, their study suggeststhat the ZHH cross section could potentially be measured at the 12  18% level forlarge integrated luminosity, 2000 fb 1. They further show that this would translateto about a 20% measurement of hhh. It is clear that studies such as these at a futurelinear collider will depend critically on b-tagging performance. The studies go on topoint out that in some MSSM parameter space regions, heavy Higgs decay to lighterHiggs states has signicantly larger rates than the SM case, making the prospects forobservation quite good. In contrst, it remains to be shown that the LHC has anycapability to measure a Higgs sector self-coupling.Research into methods to extract the CP nature of observed neutral Higgses iseven less developed. Studies so far indicate that a CP = +1 state can be qualitativelydistinguished from a CP = -1 state via angular distributions in ZH production [15],but if the state has mixed CP, the -1 component is very easily washed out. Additionalwork is sorely needed in this area, as the LHC again has no capability here, primarilydue to the strong backgrounds and detector eects that hide the relevant distributions.74 ConclusionsProspects for observing a Higgs sector as the responsible mechanism for EWSBare quite good: precision ts to electroweak data suggest that the Higgs is light andthus accessible, perhaps by the Tevatron, and the LHC has the capability to observe aHiggs boson of any mass up to the unitarity limit. While the Tevatron could not makeany serious measurements of couplings or other important properties of an observedresonance to completely convince one that it is part of a Higgs sector, the LHC cango a long way toward this goal. The LHC would determine the mass to a greaterprecision than can be matched theoretically, and would be able to determine the gaugecoupling and total width of a Higgs boson, either directly or indirectly, to better thanthe 10% level. However, the LHC will have considerable diculty to observe mostfermionic decays, and will not have the capability to observe any self-couplings oridentify CP mixing among the states of multiple physical Higgses.An ILC extends our knowledge of a Higgs sector considerably. Its measurementsof both gauge and Yukawa couplings would be superior over most of the mass rangeof a possible Higgs, and it would have access to additional fermionic decays as well asself-couplings and probably CP mixing, improving model discrimination. However,the state of the art on the last goal is still somewhat underdeveloped. Also lackingis a detailed overview of the capability of an ILC to distinguish dierent modelsbased on coupling and mass measurements, although at least one study to addressthis is nearing completion [16]. So far, studies have presented levels of measurementprecision based only on cross sections in the SM. If a Higgs sector turns out to be notvery SM-like, then some of these levels of precision could be quite poor, while othersare better than expected, and the restriction in model parameter space may or maynot be satisfyingly small.AcknowledgmentsI am grateful to the organizers of the conference and to the many physicists who haveperformed the LHC and LC Higgs studies which I have attempted to summarize here.References[1] D. Zeppenfeld, R. Kinnunen, A. Nikitenko and E. Richter-Was, Phys. Rev. D62, 013009 (2000) [hep-ph/0002036].[2] J. F. Gunion and X. He, Phys. Rev. Lett. 76, 4468 (1996) [hep-ph/9602226];J. F. Gunion and J. Pliszka, Phys. Lett. B444, 136 (1998) [hep-ph/9809306].8[3] ATLAS Collaboration, ATLAS TDR, report CERN/LHCC/99-15 (1999).[4] See, e.g.: W. J. Marciano, hep-ph/0003181;J. Erler, hep-ph/0010153.[5] P. Igo-Kemenes, LEP seminar, CERN, Nov.3, 2000;R. Barate et al. [ALEPH Collaboration], hep-ex/0011045;M. Acciarri et al. [L3 Collaboration], hep-ex/0011043.[6] M. Battaglia, talk presented at the Fermilab Linear Collider Study Group meet-ing, April 5, 2000.[7] A. Sopczak, talk presented at the 2nd ECFA/DESY Linear Collider Conference,Obernai, Oct. 16-19, 1999.[8] M. Carena, S. Heinemeyer, D. Rainwater, G. Weiglein and D. Zeppenfeld, inpreparation.[9] D. Rainwater, hep-ph/0004119, to appear in Phys. Lett. B.[10] A. Juste and G. Merino, hep-ph/9910301.[11] H. Baer, S. Dawson and L. Reina, Phys. Rev. D 61, 013002 (2000) [hep-ph/9906419][12] A. Kronfeld et al., Fermilab Linear Collider Study Group Physics Report, FNAL-FN-701.[13] M. Carena, S. Mrenna and C. E. Wagner, Phys. Rev. D 60, 075010 (1999) [hep-ph/9808312].[14] C. Castanier, P. Gay, P. Lutz and J. Orlo, talk presented at the 2ndECFA/DESY Linear Collider Conference, Obernai, Oct. 16-19, 1999; hep-ex/0101028;D. J. Miller and S. Moretti, Eur. Phys. J. C13, 459 (2000) [hep-ph/9906395];A. Djouadi, W. Kilian, M. Muhlleitner and P. M. Zerwas, hep-ph/0001169;P. Osland and P. N. Pandita, Phys. Rev. D 59, 055013 (1999) [hep-ph/9806351].[15] See e.g. talk presented by A. Skjold and P. Osland, hep-ph/9508223.[16] M. Carena, H. Haber, H. Logan and S. Mrenna, FNAL-00/334-T, in preparation.9

Precision Higgs physics at a future linear collider

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Precision Higgs Physics at a Future Linear Collider

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