Proposal for the measurement and combination of Higgs spin and CP properties

1. Proposal for the measurement and combination of Higgs spin and CP properties Peter Kluit HSG 7 17October / 12 September

2. Rediscuss The agreed procedure was discussed on 12 September (here appended to the talk) • Pros of the LHC style vs Tevatron style were addressed • Did not hear any new argument • Basically there are three main arguments that favour the LHC style: • LHC style uses a continuous fit with a fraction and will also be used for CP odd and even • For Tevatron “CP odd” it means one has to adopt the LHC style • LHC requires minimization of the fraction; Tevatron not it evaluates LL(0)-LL(1) • This minimum gives an additional physics interpretation • Time: everything has been changed and checked for the LHC style exclusion. Why a last minute change?

3. Proposal for the measurement and combination of Higgs spin and CP properties Tuan Vu Anh, Lashkar Kashif, Peter Kluit, Sven Kreiss, Bruno Lenzi, Kirill Prokofiev, Stefano Rosati, Jana Schaarschmidt,Wouter Verkerke HSG 7 12 September

4. Introduction Started an informal discussion on how to combine measurements of the CP and Spin properties of the Higgs with the three relevant final states: • ZZ, WW and gamma-gamma • Topics dicussed: • A common definition of the likelihood that will be used for spin and CP • The statistical recipe “test statistic” that will be used: LL(spin 2) – LL(minimum) • Common systematics and Higgs pT spectrum • Move code to the workspace and stats framework • Creation of an email list: atlas-phys-higgs-spinCPcombination

5. A common definition • A common definition of the likelihood that will be used for spin and CP • General considerations: • Use a common approach for both spin 2 vs spin 0 and CP odd vs even • Use the same free variables for different channels: • E.g. N events is different for each channel; the fraction of spin 2 events in the data set can be used in common. • Use a method that is sensitive to the shape differences between spin 0 and 2 (odd/even) • Therefore constraints are put on the background leaving the number of signal events free • Use a statistical treatment that fits in to e.g the LHC combination of the rate measurements

6. A likelihood definition • Mathematical expression: Log likelihood = log Poison (N(x),Nsig(x)+Nbkg(x)) + LLconstraint Nsig(x) = Nsig ( fraction * pdf_s2(x) + (1-fraction) * pdf_s0(x) ) Nbkg(x)= scale * Nbkg * pdf_bkg(x) LLconstraint = (scale-1)2 /(2 * error_scale2) • So three free parameters Nsig the total number of signal events, fraction the fraction of spin 2 events anda background scale factor. • Nbkg = fixed = expected number of background events from MC • pdf_s0(x) (for signal spin 0) and pdf_s2(x) (for signal spin 2) and pdf_bkg(x) from MC(dd). • Here a gaussian LL constraint on the background rate is used. Other type of constraints can also be used (e.g. in gamma-gamma a constraint from the side-bands). • Can extended to j backgrounds with j scale factors.

7. A likelihood definition • Some comments • The fraction can be treated common to all analyses e.g. to exclude a spin 2 particle hypothesis • Due to the fact that the total number of signal events is left free in the fit one is mostly sensitive to the shape differences between spin 2 and spin 0 and CP odd/even.

8. The spin 2 statistical test • The following LHC style recipe is chosen: • Generate samples with a spin 0 SM Higgs • Determine Log likelihood difference for spin 2 fraction = 1 minus the minimum: LL(spin 2; fraction = 1) – LL (minimum) • The median of the Log Likelihood distribution is the expected sensitivity to exclude a spin 2 (given a spin 0 Higgs) • The p0 value is calculated straight from the median LL with a simple analytic formula • A possible alternative Tevatron style recipe based on LL(fraction=1) – LL (fraction=0) is not chosen, basically because the above recipe is in line with what is done for the LHC rate measurements.

9. A possible interpretation • The fit will give a number for the fraction and an estimated error • This result should be interpreted • Most of us favour an interpretation of fully spin 2 or fully spin 0; similarly in case of CP odd and even • Still we feel it is important to perform the fit and see what fraction the data prefer and evaluate the compatibility a the minimum with a spin 0 or spin 2 hypothesis • Eventually plots can be made of superimposing full spin 0, full spin 2 and the fitted fraction • It is possible to have CP odd and even contributions (with interference): in that case the likelihood should be modified

10. Systematics, workspace and email • For the treatment of systematics (common and not-common) the same approach as is used for the rate measurement will be used • We did discuss a common systematic uncertainty that comes from the pT spectrum of the spin 2 Higgs • Need reweighting of JHU sample to PowHeg • By varying the fraction of produced in gg and qq the pT spectrum will change; will make a recipe to vary e.g. the qq (gg) fraction Decided to: • Move code to the workspace and stats framework • Distribute the histFactory workspace (when ready) • Creation of an email list: atlas-phys-higgs-spinCPcombination • Expect that e.g changing the likelihood definition and the statistical test will be done rather quickly