Discovering the Higgs Bosons of Minimal Supersymmetry with Bottom Quarks

We investigate the prospects for the discovery of a neutral Higgs boson produced with one bottom quark followed by Higgs decay into a pair of bottom quarks at the CERN Large Hadron Collider (LHC) and the Fermilab Tevatron Collider. We work within the framework of the minimal supersymmetric standard model. The dominant physics background is calculated with realistic acceptance cuts and efficiencies including the production of $bb\bar{b}$, $\bar{b}b\bar{b}$, $jb\bar{b}$ ($j = g, q, \bar{q}$; $q = u, d, s, c$), $t\bar{t} \to b\bar{b}jj\ell\nu$, and $t\bar{t} \to b\bar{b}jjjj$. Promising results are found for the CP-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with masses up to 800 GeV for the LHC with an integrated luminosity ($L$) of 30 fb$^{-1}$ and up to 1 TeV for $L =$ 300 fb$^{-1}$.


I. INTRODUCTION
The Fermilab Tevatron Run II has been taking data since March 2001, and the CERN Large Hadron Collider (LHC) is planned to start running in Autumn 2009. One of the most important experimental goals of the Tevatron Run II and the LHC is the search for the mechanism of electroweak symmetry breaking-to discover the Higgs bosons or to prove their non-existence.
In the Standard Model, only one Higgs doublet is required to generate mass for both gauge bosons and elementary fermions, and the Higgs boson is the only particle remaining to be discovered in high energy experiments. In the minimal supersymmetric standard model (MSSM) [1], the Higgs sector has Yukawa interactions with two doublets, φ 1 and φ 2 , whose neutral components couple to fermions with weak isospin t 3 = −1/2 and t 3 = +1/2 respectively [2]. After spontaneous symmetry breaking, there remain five physical Higgs bosons: a pair of singly charged Higgs bosons H ± , two neutral CP-even scalars H 0 (heavier) and h 0 (lighter), and a neutral CP-odd pseudoscalar A 0 . The Higgs potential is constrained by supersymmetry such that all tree-level Higgs boson masses and couplings are determined by just two independent parameters, commonly chosen to be the mass of the CP-odd pseudoscalar (M A ) and the ratio of vacuum expectation values of neutral Higgs fields (tan β ≡ v 2 /v 1 ).
At the LHC, gluon fusion (gg → φ 0 ; φ 0 = h 0 , H 0 , A 0 ) is the major source of neutral Higgs bosons in the MSSM for tan β less than 5. For tan β > 7, neutral Higgs bosons are dominantly produced from bottom quark fusion bb → φ 0 [3,4,5,6,7]. Since the Yukawa couplings of φ 0 bb are enhanced by 1/ cos β, the production rate of neutral Higgs bosons associated with bottom quarks, especially that of the A 0 or the H 0 , is enhanced at large tan β.
For a Higgs boson produced along with a single bottom quark at high transverse momentum (p T ), the leading-order subprocess is bg → bφ 0 [8,9,10,11,12]. If two high p T bottom quarks are required in association with a Higgs boson, the leading order subprocess should be gg → bbφ [3,13,14,15,16]. In 2002, it was suggested that the search at the LHC for a Higgs boson produced along with a single bottom quark with large p T should be more promising than the production of a Higgs boson associated with two high p T bottom quarks [10]. This has already been shown to be the case for the µ + µ − decay mode of the Higgs bosons [17].
For large tan β, the τ + τ − decay mode [18,19] can be a promising discovery channel for the A 0 and the H 0 in the MSSM. Recently, the discovery channel bφ 0 → bτ + τ − has been demonstrated to offer great promise at the LHC to search for the A 0 and the H 0 up to M A = 1 TeV [20].
The Higgs decay into bb has the largest branching fraction for large values of tan β. However, the inclusive channel of pp → φ 0 → bb + X is very challenging at the LHC owing to the extremely large QCD background. Previous theoretical studies have focused on the associated production of bbφ 0 → bbbb [21,22,23]. Realistic simulations by the ATLAS and the CMS collaborations with parton showering lead to pessimistic results [24,25,26], because the trigger for the 4b final state requires high p T bottom quarks for pp → bbφ 0 → bbbb + X. The requirement of four high p T b-quarks removes most of the Higgs events. Moreover, integrating over the fourth b-quark to study a 3b signal requires a careful inclusion of higher order corrections in the four-flavor scheme. These potentially large leading-log corrections are absorbed into the b-quark PDFs in the five flavor scheme which we employ.
In this article, we present the prospects for discovering the MSSM neutral Higgs bosons produced with a single high p T bottom quark (b orb) followed by Higgs decay into a pair of bottom quarks . We calculate the Higgs signal and the dominant Standard Model (SM) backgrounds with exact matrix elements as well as realistic cuts and efficiencies. Furthermore, we present promising 5σ discovery contours at the LHC in the (M A , tan β) plane. Section II shows the production cross sections and branching fractions for the Higgs signal. The SM physics background is discussed in Section III. Sections IV and V present the discovery potential at the LHC and the Fermilab Tevatron Run II. Optimistic conclusions are drawn in Section VI.

II. THE PRODUCTION CROSS SECTIONS AND BRANCHING FRACTIONS
At the LHC or the Tevatron Run II, the production cross section of bg → bφ 0 → bbb, where φ 0 = H 0 , h 0 , A 0 , is evaluated with the parton distribution functions of CTEQ6L1 [27] and the factorization scale µ F = M H /4 [10]. In this article, b represents a bottom quark (b) or a bottom anti-quark (b) unless it is explicitly specified. The bottom quark mass in the φ 0 bb Yukawa coupling is chosen to be the next-to-leading-order (NLO) running mass m b (µ R ) [28], which is calculated with m b (pole) = 4.7 GeV and the NLO evolution of the strong coupling [29]. We have also taken the renormalization scale to be M H /4. This choice of scale effectively reproduces the effects of next-to-leading order (NLO) corrections [10]. Therefore, we take the K factor to be one for the Higgs signal.
At the LHC, we calculate the Higgs cross section σ(pp → bφ 0 → bbb + X) with a Breit-Wigner resonance via bg → bφ 0 → bbb. In addition, we check the cross section with the narrow width approximation where B(φ 0 → bb) is the branching fraction of a Higgs boson decay into bb. Figure 1 shows the invariant mass distribution (M ij , i,j = 1,2,3) of the b i b j or b ibj pairs for the Higgs signal pp → bA 0 → bbb + X via bg → bA 0 . The bottom quarks are ordered according to their transverse momenta, . We note that with energymomentum smearing, the cross section in the narrow width approximation (NWA) agrees very well with that evaluated via a Breit-Wigner resonance (BWR) for most parameters that we have chosen. Based on the ATLAS [24] specifications, we model these effects by Gaussian smearing of momenta: for jets at the LHC, with individual terms added in quadrature. For the Tevatron we use based on CDF parameters [30]. For M A = 800 GeV and tan β = 50, the cross sections are in agreement within 10%. For large values of M A , the increased width of the Higgs may lead to a reduced signal due to cuts on the dijet invariant-mass acceptance window. This effect is less well-modeled in the NWA than with BWR, although the total cross-sections remain in good agreement.

III. THE PHYSICS BACKGROUND
The final state of bbb has dominant physics backgrounds coming from (a) bg → bbb, (b) cg → cbb, (c) qg → qbb with q = u, d, s, (d) qq → gbb with q = u, d, s, c, and (e) gg, qq → tt → bbjjℓν, or gg, qq → tt → bbjjjj. We have computed the cross section of the Higgs signal and physics background utilizing MadGraph [31,32] and HELAS [33] to generate matrix elements. To reduce the physics background while keeping most of the signal events, we require that in each event there are three jets (at least two b-jets) which satisfy the following requirements: (a) we consider two sets of cuts for an integrated luminosity (L) of 30 fb −1 (low luminosity, LL): (i) p T (j 1 ) > 50 GeV, p T (j 2 ) > 30 GeV and p T (j 3 ) > 20 GeV (low p T cuts), or (ii) p T (j 1 , j 2 , j 3 ) > 70 GeV (CMS 3-jet trigger) [26] as well as the pseudorapidity, |η| < 2.5 for all jets, where GeV (ATLAS 3-jet trigger) [25] or (ii) p T (j 1 , j 2 , j 3 ) > 150 GeV (ATLAS 3-jet trigger for high luminosity) [25] as well as |η| < 2.5 for all jets, (c) there is at least one pair of bottom quarks in the Higgs mass window such that (d) all three jets are separated with ∆R = √ ∆φ 2 + ∆η 2 > 0.7 (where φ is the angle between two jets in the transverse plane), (e) the missing transverse energy ( E / T ) should be less than 40 GeV.
In addition, we veto events with more than three jets passing the cuts p T (j) > 15 GeV and |η| < 2.5. We take the b−tagging efficiency to be ǫ b = 0.6 (LL) or ǫ b = 0.5 (HL), the probability that charm quark may be misidentified is ǫ c = 0.15, and the probability that a light quark or a gluon may be misidentified as a bottom quark is ǫ j = 0.01. For the backgrounds arising from bbb and jbb [21] as well as those from tt [34], we assume a K factor of 2 when computing the significance as discussed below. In practice we find that the tt backgrounds are negligible after cuts, although we include them for completeness.
In Figure 2, we present the transverse momentum distribution (dσ/dp T ) of the bottom quarks (b orb), for the Higgs signal pp → bA 0 → bbb + X. Also shown is the p T distribution for bottom quarks from the SM background bg → bbb. We have required p T (b) > 10 GeV and |η b | < 2.5 in this figure.

IV. THE DISCOVERY POTENTIAL AT THE LHC
To study the discovery potential of pp → bφ 0 → bbb + X (φ 0 = H 0 , h 0 , A 0 ) at the LHC, we calculate the Higgs signal as well as the SM physics background in the mass window of M φ ± ∆M bb where ∆M bb = MAX(22 GeV, 0.10 × M φ ), or ∆M bb = MAX(22 GeV, 0.15 × M φ ) for an integrated luminosity of 30 fb −1 .
In Figure 3 we show the cross section of σ(pp → bA 0 → bbb + X), for tan β = 10 and 50, with a common mass for scalar quarks, scalar leptons and the gluino mf = mg = µ = 1 TeV. We also present the background cross sections with no K factor in the mass window of M A ± ∆M bb for the dominant SM processes pp → bbb + X and pp → jbb + X, j = q,q, g, with (a) low p T cuts and (b) CMS 3-jet trigger. The cuts and tagging efficiencies are included with ∆M bb = 0.10 × M A . In addition, we present the 5σ cross section for L = 30 fb −1 . The cross section of the Higgs signal with tan β ≃ 50 can be larger than the 5σ cross section for M A < ∼ 800 after acceptance cuts. Requiring higher transverse momenta (p T > 70 GeV) greatly reduces the background and the Higgs signal for M A < 200 GeV.
We define the signal to be observable if the lower limit on the signal plus background is larger than the corresponding upper limit on the background [35,36], namely, which corresponds to Here L is the integrated luminosity, σ s is the cross section of the Higgs signal, and σ b is the background cross section. Both cross sections are taken to be within a bin of width ±∆M bb centered at M φ . In this convention, N = 2.5 corresponds to a 5σ signal. We take the integrated luminosity L to be 30 fb −1 and 300 fb −1 [24]. For tan β > ∼ 10, M A and M H are almost degenerate when M A > ∼ 125 GeV, while M A and m h are very close to each other for M A < ∼ 125 GeV in the MSSM [37]. Therefore, when computing the discovery reach, we add the cross sections of the A 0 and the h 0 for M A < 125 GeV and those of the A 0 and the H 0 for M A ≥ 125 GeV [24,26,38]. Figure 4 shows the 5σ discovery contours for the MSSM Higgs bosons where the discovery region is the part of the parameter space above the contour. We have chosen M SUSY = mq = mg = ml = µ = 1 TeV. If M SUSY is smaller, the discovery region of A 0 , H 0 → bb will be slightly reduced for M A > ∼ 250 GeV, because the Higgs bosons can decay into supersymmetric (SUSY) particles [39] and the branching fraction of φ 0 → bb is suppressed. For M A < ∼ 125 GeV, the discovery region of H 0 → bb is slightly enlarged for a smaller M SUSY , but the observable region of h 0 → bb is slightly reduced because the lighter top squarks make the H 0 and the h 0 lighter; also the H 0 bb coupling is enhanced while the h 0 bb coupling is reduced [38]. In addition, we have studied the effect of an invariant mass cut, using only the two jets with highest p T as the candidate pair. Table I presents the cross section corresponding to two schemes: (a) requiring |M 12 − M φ | < ∆M bb , and (b) requiring |M ij − M φ | < ∆M bb ; i, j = 1, 2, 3. We find that for M A > ∼ 400, it is more advantageous to apply an invariant mass cut only on the two leading b jets. For lower masses using any pair of the three leading jets leads to higher significance. We also show the ratio of signal to background in this figure.
We have chosen a set of cuts, p T (j 1 , j 2 , j 3 ) > 100, 80, 70 GeV, which tends to maximize this ratio. Less stringent cuts can improve the nominal statistical significance in the low mass regions, but for high masses and low tan β the small signal to background ratio would require excellent understanding of backgrounds and systematic errors. Furthermore, we have studied the effects of SUSY particles on the φ 0 bb Yukawa couplings at large tan β. The SUSY contributions can be described with an effective Lagrangian and a

Mass(GeV)
Signal Background Significance (  [40,41,42,43] such that the bottom quark mass in Yukawa couplings becomes where SUSY QCD corrections lead to for bottom squarks and gluinos, and the auxiliary function is Then the cross section can be estimated with a simple formula [43] σ(pp In our analysis of SUSY effects, we adopt the conventions in Refs. [12,44] and have used a more complete estimate, including the effects of the modified Higgs width in the full BWR calculation. Table II where α t ≡ λ 2 t /4π (λ t = √ 2m t /v 2 being the top Yukawa coupling), and A t is the trilinear Higgs-stop coupling. It is clear that SUSY effects reduce the Higgs cross section for a positive µ while they enhance the Higgs cross section for a negative µ. The effect of the Higgsino/stop loops is highly dependant on the size of A t . We present two scenarios, M max h and no-mixing, as defined in Ref. [43]. In the former the Higgsino/stop contribution is comparable to the gluino/bottom-squark term, in the latter it is almost negligible.

V. THE DISCOVERY POTENTIAL AT THE FERMILAB TEVATRON
To study the discovery potential of Higgs decays into bottom quark pairs at the Fermilab Tevatron Run II, we require (i) three b quarks or 3 jets (at least two b jets) with p T > 15 GeV or p T (j 1 , j 2 , j 3 ) > 50, 30, 15 GeV, |η(b, j)| < 2.0, and a b−tagging efficiency ǫ b = 50% [30], (ii) the angular separation between each pair of jets should be ∆R > 0.4 [45], (iii) the invariant mass of the reconstructed bottom quark pairs should be within the mass window of the Higgs mass with ∆M bb = MAX(0.1 × M φ , 20GeV). Figure 5 show the 5σ discovery contours for the MSSM Higgs bosons, where the discovery region is the part of the parameter space above the curves. The discovery contours for ∆M bb = 0.10 × M φ [46] are comparable to those presented in this figure.
We find that the Tevatron Run II can discover neutral Higgs bosons in the MSSM for a value of tan β slightly less than 30 with an integrated luminosity of 4 fb −1 and M A < 120 GeV. For tan β ∼ 50, the Tevatron Run II will be able to discovery the Higgs bosons up to M A ∼ 160 GeV with L = 4 fb −1 , and up to M A ∼ 200 GeV with L = 20 fb −1 . Our results are consistent with those found in Refs. [23,45,47].

VI. CONCLUSIONS
The associated production of a Higgs boson with a bottom quark, followed by the Higgs decay into bottom quark pairs, is a promising channel for the discovery of the neutral Higgs bosons in the minimal supersymmetric standard model at the LHC. The A 0 and the H 0 should be observable in a large region of parameter space with tan β > ∼ 10. The associated final state of bφ 0 → bbb could discover the A 0 and the H 0 at the LHC with an integrated luminosity of 30 fb −1 if M A < ∼ 800 GeV. At a higher luminosity of 300 fb −1 , the discovery region in M A is expanded up to M A = 1 TeV for tan β ∼ 50.
In our analysis, we apply a mass cut, requiring the reconstructed Higgs mass to lie in the mass window M φ ± ∆M bb . We note that improvements in the discovery potential will be possible by narrowing ∆M bb if the bottom quark pair mass resolution can be improved. In regions of high mass and low tan β the ratio of signal to background events is very low. Discovery in these regions would require either excellent understanding of backgrounds in order to lower systematic errors below the few percent level, or better discrimination between signal and background due to narrower ∆M bb or improved b-tagging. Our results using three b's are more promising than those found in previous studies based on 4b analyses [21,22,25,26].
The discovery of the associated final state of bφ 0 → bbb along with bφ 0 → bτ + τ − [20] and bφ → bµ + µ − [17] will provide information about the Yukawa couplings of ff φ 0 ; f = b, τ, µ, for fermions with t 3 = −1/2. Furthermore, the muon pair channel can also be observable in a significantly large region and the muon pair channel will provide a good opportunity to precisely reconstruct the masses for MSSM Higgs bosons [13,17,38]. In concert, this family of channels may provide an excellent window on the Yukawa sector of the MSSM.