Constraining the Higgs boson width with ZZ production at the LHC
aa r X i v : . [ h e p - ph ] N ov Constraining the Higgs boson width with ZZ production at the LHC Fabrizio Caola ∗ and Kirill Melnikov † Department of Physics and Astronomy, Johns Hopkins University, Baltimore, USA
We point out that existing measurements of pp → ZZ cross-section at the LHC in a broad range of ZZ invariant masses allow one to derive a model-independent upper bound on the Higgs boson width,thanks to strongly enhanced off-shell Higgs contribution. Using CMS data and considering eventsin the interval of ZZ invariant masses from 100 to 800 GeV, we find Γ H ≤ . SM H ≈
163 MeV, atthe 95% confidence level. Restricting ZZ invariant masses to M ZZ ≥
300 GeV range, we estimatethat this bound can be improved to Γ H ≤
21 Γ SM H ≈
88 MeV. Under the assumption that allcouplings of the Higgs boson to Standard Model particles scale in a universal way, our result can betranslated into an upper limit on the branching fraction of the Higgs boson decay to invisible finalstates. We obtain Br( H → inv) < .
84 (0 . ZZ invariant masses thatare used to constrain the width. We believe that an analysis along these lines should be performedby experimental collaborations in the near future and also in run II of the LHC. We estimate thatsuch analyses can, eventually, be sensitive to a Higgs boson width as small as Γ H ∼
10 Γ SM H . Since the discovery of the Higgs-like particle by ATLASand CMS collaborations about a year ago [1, 2], muchhas been learned about its properties. We know that themass of the new particle is around 126 GeV [3, 4], thatits spin-parity is most likely 0 + [5–7] and that its produc-tion cross-sections as observed in particular productionand decay channels are consistent with Standard Modelexpectations [4, 8]. It is customary to translate the latterresult into a statement about Higgs boson couplings toStandard Model particles but, as it is well-known, sucha translation is only possible under the assumption thatthe Higgs boson width is the same as in the StandardModel (SM). Indeed, since after imposing selection cutsthe Higgs boson production at the LHC can be describedin a narrow width approximation [9–13], we can write aproduction cross-section for the process i → H → f as σ i → H → f ∼ g i g f Γ H , (1)where g i,f are the Higgs boson couplings to initial and fi-nal states and Γ H is the Higgs boson width. Therefore, allmeasured cross-sections can be kept fixed if one simulta-neously rescales couplings of the Higgs boson to StandardModel particles and the Higgs boson width by appropri-ate factors. Indeed, if g = ξg SM and Γ H = ξ Γ H , SM ,the measured Higgs production cross-sections in all chan-nels will coincide with expected Standard Model values, σ i → H → f = σ SM i → H → f . We conclude that current LHCdata allow for infinitely many solutions for the Higgs cou-plings to SM particles, the Higgs width and the branch-ing fraction of the Higgs boson to invisible (or so farunobserved) states. To break this degeneracy, indepen-dent measurements of the Higgs boson width or the Higgscouplings are required.Direct measurement of the Higgs boson width is notpossible at a hadron collider unless Γ H ∼ > O (1) GeV, ∗ Electronic address: [email protected] † Electronic address: [email protected] or more than 250 times larger than its Standard Modelvalue. The only facility where a direct measurementof the width can be performed is a future muon col-lider where by scanning the production cross-section for µ + µ − → H → X around m H , the Higgs width can bedirectly measured to high precision [14, 15]. At any otherfacility, the Higgs boson width should be obtained indi-rectly, using information on the Higgs couplings to Stan-dard Model particles or information about the Higgs bo-son branching ratio to invisible final states, provided thatsuch information is available from independent sources.A number of ways were suggested to constrain theHiggs couplings and the Higgs branching fraction intoinvisible final states. For example, under certain theo-retical assumptions about electroweak symmetry break-ing, one can argue [16] that the SM value of the Higgsboson coupling to W -bosons provides an upper boundfor all possible HW W couplings. From this, the upperlimit on the Higgs width Γ H < .
43 Γ SM H is obtained[17]. Imposing even stronger constraints on the Higgscouplings to Standard Model particles, one can obtaintighter bounds on the Higgs boson width [18, 19]. Underthe assumption of the Standard Model production ratefor pp → ZH , the ATLAS collaboration derives an up-per bound on the Higgs branching ratio to invisible finalstate Br( H → inv) < .
65 at the 95% confidence level[20]. A related CMS study with a similar conclusion hasalso appeared recently [21].On the other hand, it is more difficult to obtain model-independent constraints on the Higgs boson couplings.It was suggested in Ref. [22] to use differences in themeasured values of the Higgs boson masses in γγ and ZZ channels, caused by the interference of gg → H → γγ and gg → γγ amplitudes, as a tool to constrain the product of Hgg and
Hγγ couplings, independent of the Higgs bosonwidth. Once the couplings are measured, one can derivethe value of the Higgs boson width from the narrow widthcross-section, see Eq.(1).The purpose of this paper is to point out that a con-straint on the product of
Hgg and
HZZ couplings andthe resulting model-independent constraint on the Higgs
FIG. 1: Sample signal (left) and background gg → ZZ (right)diagrams for the process pp → ZZ → l . The two amplitudescan interfere. boson width can be obtained from the observed numberof ZZ events at the LHC above the Higgs boson masspeak in the pp → ZZ process. Interestingly, this can al-ready be done with the current data. The main reasonfor that is an enhanced contribution to the Higgs signalfrom invariant masses above the ZZ threshold, as wasfirst pointed out in Ref. [12]. Interestingly, useful lim-its on the Higgs width can already be derived with thecurrent data. To show how this works, we recall howEq.(1) is obtained. We focus on the H → ZZ → eeµµ final state and write the production cross-section as afunction of the invariant mass of four leptons M l d σ pp → H → ZZ d M l ∼ g Hgg g HZZ ( M l − m H ) + m H Γ H . (2)The total cross-section receives the dominant contri-bution from the resonant region M l − m H ∼ m H Γ H ,where integral of Eq.(2) gives Eq.(1). However, the to-tal cross-section also receives off-peak contributions fromlarger or smaller invariant masses, where Eq.(2) is stillproportional to squares of Hgg and
HZZ couplings butit is independent of Γ H .Suppose now that in Eq.(2), the product of couplingconstants c gZ = g Hgg g HZZ and the width Γ H are scaledby a common factor ξ and that this factor is still suf-ficiently small to make the narrow width approxima-tion applicable. Under this circumstance, the reso-nance contribution remains unchanged and is given byEq.(1), while the off-shell contribution from the region M l ≫ m H increases linearly with ξ and can, therefore,be bounded from above by the total number of events ob-served in pp → ZZ process above the Higgs boson peakin the ZZ invariant mass spectrum. This is the mainidea behind this paper.There are two sources of Higgs-related ZZ events offthe peak. One is the off-shell production of the Higgsboson followed by its decay to ZZ final states. The sec-ond source of events is the interference between gg → H → ZZ and gg → ZZ amplitudes, see Fig. 1. Theinterference exists, but is numerically irrelevant in thepeak [12, 13] while, as we show below, it significantlychanges the number of expected Higgs-related events offthe peak. We account for both of these effects in thefollowing discussion. To estimate the number of Higgsevents in gg → H → ZZ , including the interference, weuse the program gg2VV described in Refs. [12, 23].To calculate the number of Higgs-related events thatare expected off peak, we compute 7 and 8 TeV produc- Energy σ Hpeak σ H off σ intoff N SM2 e µ N SMtot pp → H → ZZ → e µ in fb, and the corresponding number of events expected forintegrated luminosities L = 5 . − at 7 TeV and L =19 . − at 8 TeV. All cross-sections are computed withleading order MSTW 2008 parton distribution functions [24].The renormalization and factorization scales are set to µ = m H /
2. The peak cross-section is defined with the cut M l <
130 GeV, while off-peak and interference cross-sections aredefined with the cut M l >
130 GeV. The total number ofevents in the last row includes contributions from 4 e and 4 µ channels. The number of events is obtained using proceduresoutlined in the text. tion cross-sections for pp → H → ZZ → e + e − µ + µ − at leading order in perturbative QCD requiring that the in-variant mass of four leptons is either smaller or largerthan 130 GeV. We refer to the former case as the “onpeak” cross-section and to the latter case as the “offpeak” one .We employ the CMS selection cuts [6] requiring p ⊥ ,µ > p ⊥ ,e > | η µ | < . | η e | < . M l − l + > M l >
100 GeV. In addition, the transverse mo-mentum of the hardest (next-to-hardest) lepton shouldbe larger than 20 (10) GeV, the invariant mass of a pairof same-flavor leptons closest to the Z -mass should be inthe interval 40 < m ll <
120 GeV and the invariant massof the other pair should be in the interval 12 −
120 GeV.We also take the Higgs boson mass to be 126 GeV, andset renormalization and factorization scales to m H / e µ events in that Table is computed startingfrom the number of on-peak events reported in Table Iof Ref. [6]. According to Table I in [6], the CMS col-laboration expects 9 . eeµµ channel on the peak . We estimate the number of Higgs-related events for M l >
130 GeV by taking ratios ofcross-sections weighted with luminosity factors. We alsoinclude additional suppression factor due to the fact This number of events is a combination of gg → H (88%), weakboson fusion (7%) and V H production (5%). Although a detailedstudy of the channels besides gg → H is beyond the scope of thispaper, we believe that they will contribute to the number of high-mass ZZ events in a way that is similar to gg → H → ZZ ; forthis reason we decided to keep the number of events in the peakunchanged when performing numerical estimates. that the appropriate scale choice for the strong cou-pling constant in gg → H ∗ → ZZ is the invariantmass of the Z boson pair divided by two, rather than m H /
2, as appropriate for the on-shell cross-section [25].We take 300 GeV as a typical value of the invariantmass for Higgs-related events produced off the peak.The corresponding suppression factor is then given by η = ( α s (150 GeV) /α s ( m H / ≈ .
75. We find N H, off2 e µ = 9 . × η L σ H off (7) + L σ H off (8) L σ H peak (7) + L σ H peak (8) ≈ . , (3)where we use the integrated luminosities L = 5 . − at 7 TeV and L = 19 . − at 8 TeV.We combine this estimate with results for other lep-ton channels by similarly rescaling CMS data on 4 e and4 µ , and conclude that 3 .
72 four-lepton events producedby decays of an off-shell Higgs boson can be expectedin the current data. Repeating this calculation with theinterference contribution, we find that − .
91 events areexpected. Since cross-sections that we use are computedin the leading order QCD approximation and do not in-clude any detector effects, one may wonder if the numberof events estimated using them is reliable. While a de-tailed answer to this question requires careful studies, webelieve that, by taking ratios of cross-sections, account-ing for the dominant effects of the running of the strongcoupling constant when relating on- and off-peak eventsand by normalizing our computation to the CMS num-ber of the expected Higgs events in the peak, we obtainestimates for the off-peak number of events that are suf-ficiently reliable for the purposes of this paper. We note that the estimated number of events in Table Ilooks quite striking for two reasons. The first one is thatthe off-shell contributions related to gg → H → ZZ are large ; the off-peak cross-section is close to twenty percentof the peak cross-section. This large off-peak contribu-tion in ZZ final state was first emphasized in Ref. [12].It was explained as the consequence of a relatively largeprobability to produce the Higgs boson with the off-shellness larger than 2 m Z where decays to longitudinally-polarized Z -bosons rapidly become important and com-pensate for the decrease in the cross-section caused bythe off-shell Higgs propagator. This leads to a contri-bution to the invariant mass distribution Eq.(2) which,although small, extends over a large invariant mass range2 m Z ∼ < M l ∼ <
800 GeV and gives rise to a sizable con-tribution to the total cross-section. The second reasonis due to a large destructive interference. Note, however,that the interference is an off-peak phenomenon; it does We note that by rescaling both off-peak and interference contri-butions in the same way, we implicitly assume that QCD cor-rections to the signal and the interference are comparable. Thisis supported by the analysis of higher-order corrections to theinterference in pp → H → W + W − process reported in [26]. not contribute to the peak cross-section to a very goodapproximation [12, 13].The expected number of Higgs-related events shown inTable I refers to the Standard Model. Relaxing this as-sumption by allowing for correlated changes in the Higgscouplings and the Higgs boson width, so that the numberof events in the peak remains intact, we write the numberof off-peak events as N off4 l = 3 . × Γ H Γ SM H − . × s Γ H Γ SM H . (4)For Γ H ≫ Γ SM H , we can interpret Eq.(4) as an addi-tional source of ZZ events in the current data; these ZZ events are broadly distributed over a large invariant massrange, roughly from the ZZ threshold up to the highest ZZ invariant masses of order 800 GeV. Therefore, as thefirst step, we can look at the total number of ZZ -events inthe current data and ask how many additional events canbe tolerated given the number of observed events and thecurrent uncertainty on the number of expected events.CMS currently observes 451 events in the pp → ZZ → l channel, while 432 ±
31 events are expected [6]. The ex-pected number of events does not include the off-shellHiggs production and the off-shell interference. There-fore, we estimate the total number of events that areexpected if the Higgs couplings and width differ from theStandard Model using the following equation N exp = 432 + 3 . × Γ H Γ SM H − . × s Γ H Γ SM H ± , (5)where we assume that the sign of the interference is thesame as in the Standard Model. Note that we obtainthe above error estimate by adding errors for the 4 e , 4 µ and 2 e µ channels reported in Ref. [6] in quadratures,assuming that they are uncorrelated. While not exact,this is also not an unreasonable assumption, but a de-tailed analysis of error correlations is beyond the scopeof this paper.Requiring that the expected and observed numbersof events are within two standard deviations from eachother, we derive an upper limit on Γ H at the 95% confi-dence level. We findΓ H ≤ . SM H ≈
163 MeV , (6)where we used Γ SM H ≈ . The upper limit on the Higgs boson width can beturned into an upper limit on the branching fraction for Note that errors for the expected number of background eventsfor all channels in Table I of Ref. [6] are of the same order as thesquare root of the expected number of events reported there. We note that, if we add the errors for the number of expectedevents in the 4 e , 4 µ and 2 e µ channels linearly , the 95% confi-dence level limit for the width will degrade to Γ H ≤
52 Γ SM H . Energy σ Hpeak σ H off σ intoff N SM2 e µ N SMtot M l >
300 GeVapplied to the off-peak cross-section and interference. See textfor details. the Higgs boson decay into invisible final states. To thisend, we write Γ H = Γ inv + X i ∈ vis Γ i , (7)where the sum extends over all visible channels. We notethat Γ i ∈ vis ∼ g i , and that ratios g i g f / Γ H should be equalto their Standard Model values, to keep all narrow-widthHiggs boson production cross-sections to be the same asin the Standard Model. Assuming that all Higgs cou-plings to SM particles differ by identical factors relativeto their Standard Model values, we find that the Higgsboson width and the branching fraction to invisible finalstates satisfy the following constraintΓ H (1 − Br inv ) = Γ SM H . (8)This constraint translates into an upper limit on Br inv Br inv = 1 − q Γ H / Γ SM H < . . (9)Can the above analysis be improved? We believe thatthere is, most likely, an affirmative answer to this ques-tion. To show this, we note that an upper bound on theHiggs width was derived by using the total number of pp → ZZ events observed in a broad range of four-leptoninvariant masses. However, this may not be an optimalmass range since the invariant mass distribution of thefour-lepton events produced in the “decays” of the off-shell Higgs boson is almost flat. To illustrate this point,we repeat the above analysis but now select events wherethe invariant mass of four leptons is larger than 300 GeV.The corresponding leading order cross-sections are shownin Table II. By comparing Tables I and II, it is clear thatthe off-shell production decreases by a smaller amountthan the interference. The observed number of eventsfor M l >
300 GeV is N obs = 87 and the expected num-ber of events is estimated to be N exp = 70 . δN exp = 10 which is about 15 percent of N exp . Re-peating the same analysis as in the case of the full massrange, we find an improved 95% confidence level limit on the Higgs boson widthΓ H ≤
21 Γ SM H ≈
88 MeV . (10)Further refinements should, therefore, include a carefulselection of the invariant mass window and, perhaps, theuse of angular correlations of four lepton momenta to dis-entangle gg → H → ZZ off-peak events from q ¯ q → ZZ background. Such angular correlations are already usedby the CMS collaboration [6] to improve their measure-ment in the Higgs peak region; it is probably straightfor-ward to apply these techniques off the peak as well. Wenote that polarization effects may play a more substan-tial role at high-invariant masses since Z bosons that areproduced in decays of the off-shell Higgs boson are, mostlikely, longitudinally polarized.With increased luminosity, one can expect the erroron the number of ZZ events to be dominated by sys-tematic uncertainties; we will optimistically assume thatthis uncertainty will, eventually, become as small as 3%.This may require extending existing theoretical compu-tations for pp → ZZ to NNLO QCD but this appearsto be a realistic target on a few years time-scale; see e.g.Ref. [28] as an example of recent progress. If such anerror is reached and about half of the background eventsare rejected, the 95% confidence level upper limit on theHiggs boson width Γ H ∼ < −
10 Γ SM H = 20 −
40 MeV may,eventually, be obtained. This appears to be the ultimatelimit of what can be reached with the methods that areadvocated in this paper.In conclusion, we suggested that the total Higgs bo-son width can be constrained in a model-independentway by studying the ZZ events off the Higgs bosoninvariant-mass peak. We pointed out that already withthe current data one can put a 95% confidence limitΓ H ≤ −
38 Γ SM H depending on the four-lepton invariantmass range chosen for the analysis. We also note that ifthe interference contribution in Eq.(4) changes sign andbecomes constructive, bounds on the Higgs width becomemuch stronger, Γ H ≤ −
13 Γ SM H . While we believe thatour estimates are sufficiently accurate, the present studyis crude and ignores the many details of experimentalevent selection. We tried to mitigate that by normaliz-ing our calculations to the number of Higgs boson eventsthat CMS collaboration expects to observe in the peak.However, it will be best if experimental collaborationsperform a detailed analysis of ZZ events at high invari-ant masses and, as suggested in this paper, derive model-independent constraints on the Higgs boson width. Acknowledgments
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