UL-NTZ 03/98 Search for Next Generations of Quarks and Leptons at the Tevatron and LHC arxiv:hep-ph/9802364v1 19 Feb 1998 I.F. Ginzburg, I.P. Ivanov Institute of Mathematics, Novosibirsk, Russia, A. Schiller Institut für Theoretische Physik and NTZ, Universität Leipzig, D-04109 Leipzig, Germany February 19, 1998 Abstract If next heavy generations of quarks and leptons (with heavy neutrinos) within the Standard Model exist, they can be observed in experiments with Higgs boson production at the Tevatron and LHC before the discovery of these heavy fermions. For the case of one additional generation, the cross section of the Higgs boson production via gluon fusion at hadron colliders increases by a factor 6 9. So, the study of this process at the Tevatron and LHC can finally fix the number of generations in the SM. The Standard Model (SM ) does not fix the number of fermion generations. So far it is not known why there is more than one generation and what law of Nature determines their number. The studies at the Z peak at LEP proved that there are exactly three generations of quarks and leptons with light neutrinos. However, the existence of next generations with heavy neutrinos is not excluded. From data near the Z peak, the t quark mass was predicted to be near 170 GeV [1]. This value is very close to that obtained at the Tevatron. This means that new quarks and leptons (if they exist) should be heavier than the t-quark. At a first glance, one cannot determine precisely the number of generations in the SM in a foreseeable future, since the observation of new heavy quarks and leptons is not feasible at the existing colliders. Here we propose a simple way how to determine the number of such families before their direct discovery provided the simplest variant of the SM (with 1 Higgs E-mail: ginzburg@math.nsc.ru E-mail: igor@math.nsc.ru E-mail: schiller@tph204.physik.uni-leipzig.de 1
doublet) is valid. The key is given by experiments probing the Higgs boson production at hadron colliders (Tevatron and LHC). In our discussion we will assume that the quarks and leptons of extra families are heavier than the Higgs boson H. For definiteness, we limit ourselves to the case of one extra heavy generation the fourth generation. All modifications in the cases of more additional generations are evident. The proposal is based on well known facts. In p p or pp collisions, the Higgs boson is produced mainly via gluon fusion. The production cross section is proportional to the two gluon decay width of the Higgs boson Γ(H gg). This width is described by diagrams with quark loops, Fig. 1. The dominant contribution to Γ(H gg) comes from heavy g H g Figure 1: Dominant diagram for Higgs boson production in hadron collisions quark loops. Indeed, the amplitude corresponding to such a loop is g q α s /max{m H, m q } (M H, m q are the Higgs and quark masses, α s denotes the strong coupling). The Yukawa coupling constant g q between Higgs boson and quarks is equal to g q = m q /v (with v = 246 GeV the Higgs v.e.v.). At m q > M H, the quark contributions are finite and m q independent 1 (This fact is well known, see e.g. [2].) For this reason, in a qualitative discussion we restrict ourselves to the t quark and the possible fourth generation. Since the new fermion generation contains two extra quarks, the amplitude of this decay increases by a factor 3 and the two gluon width by a factor 2 9 for a Higgs boson lighter than 200 GeV. For higher M H, effects near the t t threshold become important. More precisely, the two gluon decay width of the Higgs boson can be written as Γ(H gg) = ( ) αs 2 MH 3 4π 8πv 2 Φ 2, Φ = q Φ q. (1) 1 The light quark contributions are suppressed as (m q /M H ) 2. 2 With k additional heavy generations the effect is roughly enhanced by a factor (2k + 1) 2. 2
The quantity Φ is the sum of loop integrals Φ q corresponding to different quarks q: Φ q = 2r q [1 + (1 r q )x 2 (r q )], r q = 4m2 q M 2 H, (2) x(r) = π 2 θ(r 1) arctan r 1 + iθ(1 r) ln 1 + 1 r r. Below we use the notation Γ n gg and σn for the cross section where the superscript n indicates the number of generations used, for n = 4 we have N q = 2. With reasonable accuracy we consider only the t quark and N q very heavy quarks from next generations (assuming that they are much heavier than H) 3. In this case Φ = 2r t [1 + (1 r t )x 2 (r t )] 4 3 N q. (3) The discussed dependence of the two gluon width Γ n gg on the Higgs mass M H is shown in Table 1. M H, GeV Γ 3 gg, MeV Γ 4 gg, MeV Γ 4 gg/γ 3 gg 50 0.014 0.123 8.93 100 0.093 0.812 8.77 120 0.155 1.34 8.67 140 0.241 2.06 8.54 160 0.357 3.00 8.40 180 0.507 4.18 8.24 200 0.702 5.65 8.05 250 1.46 10.9 7.47 300 2.87 19.2 6.69 350 6.28 33.9 5.44 Table 1: Two gluon width for three and four generations as function of M H The experimental cross section is given as convolution of the cross section for the subprocess gg H (Eq. (5)) with the gluon structure functions g(x, Q 2 ) (W 2 is the total two gluon c.m. energy squared) σ(p p H +...) = 1 1 0 0 g(x 1, W 2 )g(x 2, W 2 )σ gg H (W 2 )dx 1 dx 2, W 2 = x 1 x 2 s. (4) 3 If the quark masses are comparable with M H, all numbers will be changed similarly to the effect of the t quark mass seen in Table 1 at M H > 200 GeV. Besides, radiative corrections enhance considerably the Higgs boson production cross section [6]. 3
To estimate this cross section, we use the narrow width approximation for the subprocess cross section: σ gg H (W 2 ) = π2 Γ n gg δ(w 2 M 8M H) 2. (5) H This approximation is of high precision for M H < 300 GeV since here the total Higgs boson width is less than 10 GeV, whereas the distribution of colliding gluons is smooth enough. At higher values of M H one can use this approximation for estimates. Taking into account Eq. (5), the cross section (4) is σ(p p H +...) = π2 Γ n gg 8s 1 M H MH 2 /s dx 1 x 1 g(x 1, M 2 H)g(x 2, M 2 H), x 2 = M2 H sx 1. (6) The relative enhancement of the Higgs boson production due to the fourth generation is simply σ 4 (p p H +...) σ 3 (p p H +...) = Γ4 gg Γ 3. (7) gg The observable cross section for the production of the Higgs boson with its subsequent decay is also proportional to the branching ratio of the decay channel considered. Since the two gluon decay mode is not dominant, the new heavy generations hardly affect the total Higgs width and most of the branching ratios. Oppositely, the two photon decay width of the Higgs boson varies strongly taking into account the fourth generation. This decay originates from similar loops with leptons, quarks and W bosons. Below the WW threshold, contributions of fermions and W bosons are of opposite sign. For this reason, the contribution of the fourth generation reduces significantly the two photon width in this Higgs mass region (see Table 2). Nevertheless, M H, GeV 50 100 120 140 160 180 200 250 300 350 Γ 4 γγ Γ 3 γγ Γ 4 gg Γ4 γγ Γ 3 ggγ 3 γγ 0.114 0.158 0.193 0.250 0.403 0.485 0.539 0.710 0.96 1.36 1.02 1.39 1.67 2.13 3.39 4 4.34 5.3 6.4 7.4 Table 2: Ratios of two photon widths Γ 4 γγ/γ 3 γγ and of cross section gg H γγ for several Higgs boson masses the cross section of the process gg H γγ, being proportional to Γ n γγ Γn gg, increases if the fourth generation exists (Table 2). The influence of the fourth family becomes stronger for larger Higgs boson masses. Using the parametrization of the gluon structure functions from Ref. [3], we obtain the Higgs boson production cross sections for different decay channels at the Tevatron (Fig. 2) and LHC (Fig. 3) in the SM with three or four generations. The detector efficiency 4
σ, fb 10000 τ + τ bkgd Tevatron 1000 WW 100 τ + τ 10 ZZ 1 100 150 200 250 M H, GeV Figure 2: The cross section of Higgs boson production for different decay channels calculated for the Tevatron. The lower curves correspond to three generations, the upper ones to four generations. The τ τ background channel is also shown. certainly reduces the cross sections for both three and four generations, but their relative magnitude is independent from details of data recording (cf. Eq. (7)). For the τ τ channel the background is also shown. If the Higgs boson is supposed to be observed in a decay channel like q q, etc., the major background is given by (non resonant) production of the corresponding pair in collisions of quarks or gluons. Therefore, one needs a reasonable resolution M of the effective mass of this produced system and a cut off in transverse momenta p T > p T cut. For definiteness, in the estimates of S/B (signal to background ratio) we average the cross sections over M = 10 GeV and consider transverse momenta p T > 30 GeV. Let us now discuss different possible variants of the Higgs boson mass. M H < 135 GeV. For this Higgs boson mass the dominant decay channel is b b. The S/B value can be easily estimated since the main contribution to the non resonant background is given by b b production in the same gluon collisions. Therefore, it is sufficient to compare non resonant b b production with that occurring in the Higgs boson decay ignoring the particular distribution of the gluon flux. Using the just mentioned procedure to calculate the cross sections we find that S/B < 0.001 even in the case of four generations. Therefore, the b b channel cannot be used for our problem. The τ τ decay channel has a branching ratio of about 0.04. Its background arises from 5
σ, fb 100000 τ + τ - bkgd WW LHC 10000 1000 τ + τ - ZZ 100 γγ 10 100 150 200 250 300 M H, GeV Figure 3: Same as Fig. 2 for LHC the subprocesses q q τ τ (electroweak annihilation of quark pair into γ or Z). Since the gluon flux increases more rapidly with energy than the quark flux, the S/B ratio becomes improved with increasing energy. Figs. 2, 3 and Table 3 show the corresponding signal and the background cross sections at the Tevatron and LHC. Taking into account these estimates and the expected luminosity of the upgraded Tevatron of 2 fb 1 (and assuming a reasonable detection efficiency) we believe that the Higgs signal can be seen in this mode beyond the Z peak if the fourth generation exists. For LHC with luminosity of 200 fb 1 we expect a signal even in the case of three generations. The effect of the fourth generation should be observed at LHC up to M H 160 GeV. The γγ channel is also proposed for the Higgs boson study at LHC [4]. The accuracy needed to detect extra generations in this channel is seen from the Table 2. A precise enough knowledge of the gluon structure functions g(x i, Q 2 ) is necessary in this case. 135 GeV < M H < 190 GeV. In this mass region the WW decay channel is dominant. With a low detection efficiency this channel seems to be unsuitable to detect the Higgs boson at the Tevatron in the case of three generations. However, the extraction of a signal arising from the fourth generation is not excluded. The opportunities at LHC are significantly richer. One can even hope to use the ZZ channel to see Higgs boson in the cases of both three and four generations. M H > 190 GeV. 6
Tevatron M H, GeV τ τ, 3 gen., fb τ τ, 4 gen.,fb τ τ bkgd, fb 70 57 513 3300 80 42 369 6180 100 23 205 7090 110 18 154 1620 120 13 112 715 130 9.5 76 400 140 4.9 44 256 LHC M H, GeV τ τ, 3 gen., fb τ τ, 4 gen.,fb τ τ bkgd, fb 70 1650 14700 20200 80 1340 11800 42500 100 926 8120 53500 110 773 6740 12300 120 623 5400 5430 130 465 4000 3070 140 302 2580 1960 150 155 1310 1350 160 35 290 970 Table 3: Cross sections of τ τ production at the Tevatron and LHC for three and four generations and of non-resonant τ τ background In this case the ZZ channel is best suited for Higgs boson observation. The effect of the new generation should be seen well at LHC. The feasibility of using the WW channel should be examined too. M H M Z. Here only precise calculations and measurements at LHC in the γγ channel could solve the problem of the number of generations. Studies at the Tevatron. For Higgs boson masses lower than 125 GeV, recent calculations [4, 5] have shown that the best chance to find H at the upgraded Tevatron is the associative production p p WH +..., ZH +.... If the Higgs boson is discovered at LEP2 or in the associative production at the Tevatron within mass intervals (100 125) GeV or (60 80) GeV, the subsequent study of τ τ production at the Tevatron will give the final solution of the problem of the fourth generation. 7
The studies of τ τ production at effective masses below 150 GeV and of WW production above 135 GeV could reveal the existence of the fourth generation even without discovering the Higgs boson in the associative production. Studies at LHC. Here the Higgs boson is expected to be visible in different channels depending on its mass [4]. In all cases, strong signals of the fourth generation provide the opportunity to study the problem of new heavy generations in the SM EXHAUSTIVELY. Certainly, the presented numerical estimates are very rough. QCD corrections to the Higgs boson production are large [6] and have to be taken into account. Anyway, detailed simulations are needed to show real regions of Higgs boson masses where the effect of the fourth generation can be seen in particular channels at the Tevatron and LHC. Besides, the above simple estimates should be changed considerably in more complex models like SUSY; in that case similar calculations should be performed when an independent signature for such more complex models is observed. We acknowledge very useful discussions with Gregory Landsberg and Nikolai Mokhov. I.F.G. is grateful to David Finley, Peter Lucas and Hugh Montgomery for their hospitality to stay at FNAL. This work is supported by grants of INTAS 93 1180ext, RFBR 96-02-19079 and Volkswagen Stiftung I/72 302. References [1] J. Ellis, G. L. Fogli, E. Lisi, Phys. Lett. B 333 118 (1994); LEP Electroweak Working Group, Report No. CERN/PPE 95-172, 1995. [2] F. Wilczek, Phys. Rev. Lett. 39 1304 (1977); A. I. Vainshtein, M. B. Voloshin, V. I. Zakharov, and M. A. Shifman, Sov. J. Nucl. Phys. 30 711 (1979); L. B. Okun, Leptons and Quarks (North Holland, Amsterdam, 1982); B. A. Kniehl, Phys. Rep. 240 211 (1994). [3] M. Glück, E. Reya, A. Vogt, Z. Phys. C 67 433 (1995); we also considered the parametrizations from A. D. Martin, R. G. Roberts, M. G. Ryskin, W. J. Stirling, Durham university, Report No. DTP-96-102, 1996, hep-ph/9612449, the results differ weakly from those presented. [4] J. F. Gunion et al., Davies university, Report No. UCD-97-5, 1997, hep-ph/9703330; and references therein [5] G. Landsberg, private communication. [6] M. Spira, A. Djouadi, D. Graudenz, and P. M. Zerwas, Nucl. Phys. B453 17 (1995). 8