Measuring the Higgs trilinear self-coupling at a high energy Muon Collider [Preliminary] Alexander Conway aconway@fnal.gov 1
Introduction V (η H )= 1 3 + 1 2 η H 2 +λ HHH v η H 4 4 λ HHHH η H [ 1 ] 2 m H ● Measuring the tri-linear Higgs self-coupling parameter, “λ,” is a crucial test of SM Higgs electroweak symmetry breaking [2]. ● In the Standard Model: 2 / 2v 2 λ HHH =λ HHHH =λ SM = m H [ 1 ] ● Best-case LHC limits on λ uncertainty are ~+30% and ~-20% [2]. ● Best-case CLIC limits are ~11% [1]. ● How (well) could a muon collider measure this? 2
Introduction ● Low energy (~2*m_h): ● High energy (1.5 – 10 TeV): – WW double-Higgs fusion: – S-channel: ● mu+ mu- → h h nu nu~ ● mu+ mu- → h* → h h – Cross section increases with – Inaccessible at e+e- (sqrt?)ecm collider. ● Higher cross section than e+e- because of tighter beam spread – More or less isotropic. ● Muon collider can go to higher energies with less beam spread – Analytic expression for – Process is more forward- cross section: boosted at higher energies ● ~1.4ab: too small to use ● Muon collider needs bigger cone; how does this affect signal? 3
What to Measure? WW Fusion (1) (2) ● These three diagrams interfere with each other. – Cross section of (1) is directly dependent on λ. – Therefore, total cross section of these diagrams is sensitive to the value of λ. (3) ● Decay angle θ* distribution is different for (1) – Distribution of |cosθ*| is sensitive to λ. ● Combined template fit to cross section and |cosθ*| distributions. 4
Decay Angle h * θ h * θ h ̂ p z Decay angle is the angle the decay products make with respect to the boost direction in 5 the h* reference frame.
Decay Angle 6
Cone Angle Effects @ 3TeV 7
How to Measure? WW Fusion ● Do template fit with λ as independent parameter. ● Cross section: – Not significantly larger than e+e- – Requires good ID of 2-Higgs events. – Strube et al. [1] used full jet/flavor/PFA recon. as inputs for ANN to tag Higgs events. ● Hard to replicate with bigger cone in short time. ● How else to estimate effect of cone on this measurement? ● Decay angle: – Requires good angular resolution. – How does cone affect resolution in decay angle? ● Generator level study of reconstruction using MC data? ● Bottom line: – Muon collider not significantly different from e+e- for this channel. – CLIC and ILC studies approximate the muon collider's potential. 8
Comparison of Cone Effects ● Look at h h → b + b~ + b + b~ at 3 and 6 TeV – Require all four b's can theoretically be tagged using tracker. ● Each b decay must have at least one lepton track or two other charged particle tracks. ● These tracks must have at least 5 (25) GeV of energy. ● Initial particle momentum must have |cos(theta)| < cos(theta_cone) – Compare acceptance for different cone half-angles ● 10 deg for high-energy MuC ● 2 deg for CLIC (From [4], p. 52: “95% electron tagging efficiency down to ≈ 40 mrad polar angle”) 9
Comparison of Cone Effects ● Acceptances for four 'taggable' b's – 5 GeV energy cut Self- 3 TeV 6 TeV Other hh 3 TeV 6 TeV Coupling Processes Process 2 Deg 93.8% 94.6% 2 Deg 93.6% 94.4% 10 Deg 87.4% 78.0% 10 Deg 90.2% 87.4% – 25 GeV energy cut Self- 3 TeV 6 TeV Other hh 3 TeV 6 TeV Coupling Processes Process 2 Deg 27.1% 36.8% 2 Deg 22.0% 34.6% 10 Deg 20.0% 20.9% 10 Deg 18.6% 24.6% 10
3TeV vs. 6TeV Visible Energy in Self-Coupling Process 11
S-Channel 2 m h 4 ( λ SM ) λ 9m μ + μ - → h * → h 0 h 0 )= σ(μ 2 √ 1 − 4m h 4 ( s − m h 2 ) 2 / s 64 π v ● Easier: calculate cross section for tau+tau- in MadGraph5* and use mass ratio to get muon cross section approximation: – Above expression has been confirmed to give same results [3] 0 )× ( m τ ) 2 m μ + τ + μ - → h * → h 0 h 0 )=σ(τ - → h * → h 0 h σ(μ + τ - → h * → h 0 h 0 )= 0.4fb σ(τ − 3 = 1.4ab + μ - → h * → h 0 h 0 )= 0.4fb × 3.6 × 10 σ(μ *MadGraph5 does not have mu+mu- → h vertex by default 12
What We Learned ● S-channel is indeed too small to use. – ~1 event per 500fb^-1! ● 10 degree cone has non-negligible effect on signal. ● Muon Collider can still do this physics at 6 TeV ● All about decay angles and template fitting ● Physics backgrounds at 3TeV should be very similar at MuC and CLIC – Lepton universality means only difference in cross sections comes from beam spread. – Machine background is the bigger issue. 13
My Focus Moving On: ● Continuing development and documentation of MCD analysis toolchain/environment. – Event generation, hadronization, simulation, background overlay, reconstruction, analysis. – Have to be using it to know what will be needed. – Continue providing support for people to work on analyses. ● Physics studies: – Develop understanding of/motivation for segmentation, fast timing and DR ● Demonstrate background reduction, show effect on signal, etc. – Full simulation, look at jet resolution ● Demonstrate W and Z separation 14
References (1) T. Laštovička, J. Strube. Measurement of the trilinear Higgs selfcoupling at CLIC. Slides accessed online on 08/13/13 at link. (2) F. Goertz et al . Higgs Boson self-coupling measurements using ratios of cross sections. MITP/13-002 (2013) (3) S. Dawson et al. Higgs Working Group Report . Draft accessed online 08/13/13 at link (4) "Physics and Detectors at CLIC - CLIC Conceptual Design Report" is now published, see: https://edms.cern.ch/document/1180032/ (290 pages, 20 Mb) 15
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