Bounding the Higgs width at the LHC

Transcription

1 Bounding the Higgs width at the LHC Higgs XSWG workshop, June 2014 John Campbell, Fermilab with K. Ellis, C. Williams , ,

2 Reminder of the method This is the essence of the original proposal by Caola and Melnikov Example: map out the Z resonance as a function of the final-state virtuality. pp + - On-shell cross section in resonance region: ds σ on (s m 2 Z )2 + Γ 2 Z m2 Z 1 Γ Z Off-shell cross section above the resonance: ds σ off (s m 2 Z )2 + Γ 2 Z m2 Z s m 2 Z (approx.) independent of width. Linear relationship: Γ σ off σ on 2

3 How does it work for the Higgs boson? Naive expectation: ΓH / mh ~ 10-5 ; resonance peak so narrow that there is no off-shell cross section to measure. This is spectacularly wrong for the golden channel. tt loop threshold ZZ decay threshold About 15% of the total cross section in the region with m4l > 130 GeV. Kauer, Passarino,

4 Theoretical ingredients for 4-lepton (ZZ) analysis Need precision prediction for the 4-lepton final state. (a)+(b): gluon initiated (signal and background); diagrams interfere (c): dominant background (d)+(e): qg interference, same order as (a)*(b); not numerically important 4

5 Importance of interference Consider high-energy tt ZZ scattering (diagrams embedded in loops). straightforward to examine behavior using longitudinal modes of Z s ae 2 + (b + c)m t E ae 2 + (d c)m t E (b + d)m t E Inclusion of Higgs diagram essential to cancel bad high energy behaviour; observation of this mechanism at work would be evidence of the Higgs boson doing its job. Although the interference must be present, it is not essential for the method (c.f. other techniques such as diphoton mass shift). Destructive interference reduces the expected number of events observed and weakens bound: σ off /σ on a Γ b Γ 5

6 The result Cuts appropriate for CMS analysis of full data-set. Continuum (qq) background 1-2 orders of magnitude larger throughout most of range. Effect of destructive interference clear for high m4l. Difficult to observe interference (in the SM) since strong pdf suppression, small rate. 6

7 2-lepton, 2-neutrino (WW) analysis The ZZ channel is convenient: well-measured leptons allow the Higgs boson lineshape to be mapped out and peak/off-shell regions directly identified. However, exact mapping of lineshape is not crucial, just need well-separated regions corresponding to on- and off-resonance. Can therefore play the same game in WW channel: gg W + W e + µ ν e ν µ As proxy for invariant mass, use transverse mass of expected WW system: M 2 T = (E miss T + E ll T ) 2 p ll T + E miss T 2 Features washed out, but similar overall picture. 7

8 WW vs ZZ Advantages: threshold for two real W s much closer than for two real Z s branching ratio into leptons also larger combined, two orders of magnitude more events: Disadvantages: Br(H W W ) Br(W lν) 2 = Br(H ZZ) Br(Z l + l ) 2 = much less clean so many more backgrounds particularly, top-related that require a jet-veto to control effect of the jet-veto recently studied in a NLL resummed calculation; could weaken a fixed-order analysis by ~ factor of 2. Moult, Stewart,

9 Estimate of WW sensitivity Cuts to isolate Higgs peak signal remove tail, so some cuts must be lifted. Requires more of a leap of faith than ZZ estimates, since ATLAS uncertainties only presented in the resonance region. Extrapolation, estimation of backgrounds, systematic uncertainties,... <B>=336 events Try to be conservative by using systematic uncertainty on theory and your choice of experimental systematic uncertainties. Different flavour, 20 fb -1, δb=10%. 9

10 MCFM summary Matrix elements implemented in MCFM, in analytic form that is numerically stable without recourse to multiple precision. For these processes, possible to generate unweighted events in LHE format for subsequent showering etc. New version: 6.8, April includes: addition of identical-particle interference effects for ZZ 4l inclusion of interference between WW and ZZ for 2l2ν final state additional decays for W and Z bosons extra processes to streamline calculation of interference effects (unrelated to this topic) triphotons, diphoton+jet processes at NLO. 10

11 Comparison of 4l and 2l2l Assess effect of interference by comparing prediction for 4e+4µ [red] with 2e2µ, under the same set of cuts [magenta] (i.e. cannot distinguish e and µ). Almost no effect from interference, except at Higgs peak: 4l approx. 15% bigger. Under realistic cuts [blue], significant difference unrelated to interference, simply due to more combinations of 4l reconstructing on-shell Z. 11

12 Effect of higher orders Despite the presence of a loop, the effect of the interference is computed at LO; however the Higgs contribution alone is known to (at least) NNLO. Current CMS strategy: assume the higher-order corrections to the interference scale in the same way, additional 10% uncertainty. This strategy is based on a soft gluon approximation of the NLO and NNLO result for H WW for mh=600 GeV. Bonvini et al; Estimate performed using the equivalence theorem and HH rate, for which higher order corrections have been calculated in the heavy mt limit. Dawson et al, Longitudinal modes only dominate interference for m4l>400 GeV. 12

13 Estimate of uncertainty on interference Interference K-factor approximately described by: K 1 + α s 2π ( 2π 2 + c 1 ) c1 is the process-dependent piece; central value is extracted from HH production under the assumption that longitudinal modes dominate. Bonvini et al vary c1 between c1/5 and 5c1 in order to estimate uncertainty. For H WW with mh=600 GeV the overall effect of the interference is +15%; resulting uncertainty is ~6%. For H ZZ with mh=125 GeV the effect of the interference is approximately -150%, so varying c1 can lead to a larger effect (perhaps ~30% uncertainty). ( ) Noff 4l ΓH Γ H (m 4l > 300 GeV) = 2.02 Γ SM 2.91 H Γ SM H We will only know for sure when the interference is calculated to NLO, i.e. 2-loop virtual and 1-loop real radiation contributions. 13

14 Impact of uncertainty on constraint In the meantime, can estimate impact on cut-and-count result by changing interference term by ± 30% Example: With 4 off-shell events interpret bound at 5.5 x SM ± 30%: same no. of events limit interval ~ (4-7) x SM 14

15 Final thoughts The study of the off-shell method for constraining the Higgs width is just beginning. Even if subject to additional caveats in interpretation, measurements of the offf-shell cross section still provide valuable information on the Higgs boson. Measurements in multiple channels -- both in production and decay -- can be used to mitigate any caveats. Plenty of work remaining on the theory side to sharpen future constraints. 15