The Higgs Boson Intrinsic Width

Transcription

1 The Higgs Boson Intrinsic Width Giampiero Passarino Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino, Italy LHC, 9 April 2014 Madrid

2 dσ off = µ r dσ peak Combined limit r = Γ H Γ SM assume µ = 1 measure r H peak, exp resolution / SM width 2 3 GeV /4 MeV Combined observed (expected) values r = / SM < % CL (p-value = 0.02) r = / SM = BINGO! equivalent to: < 17.4 (35.3) 95% CL = ( ) MeV 15 R. Covarelli

3 -1 [ pb] dσ dm V 2 V M 2 V V MW WW σ/σ SM ZZ dying line-shape g g g V rising decay s H = µ H 2 i µ H γ H CPS required 8 TeV Ý ÑÔ ÖÓ The big 8TeV Peak at Z mass due to singly resonant diagrams. Interference is an important effect. Destructive at large mass, as expected. With the standard model width, $H, challenging to see enhancement/deficit due to Higgs channel. Events/bin CMS preliminary Data CMS cuts CMS PAS HIG x 30 s = 8 TeV, L = 19.7 fb Keith Ellis,CERN, 9 December, 2013 gg+vv ZZ (Γ = 25 Γ, µ = 1) SM gg+vv ZZ (SM) qq ZZ Z+X m 4l (GeV) dynamic QCD scales MZ 2 Mt 2 Mt 1000 M V V [ GeV]

4 A short History of beyond ZWA (don't try xing something that is already broken in the rst place) ➀ There is an enhanced Higgs tail Kauer - Passarino (arxiv: ): away from the narrow peak the propagator and the off-shell H width behave like H 1 ( ) 2, Γ ( ) H VV MVV G F M MVV 2 VV 2 M VV µ2 H ➁ Introduce the notion of -degenerate solutions for the Higgs couplings to SM particles Dixon - Li (arxiv: ), Caola - Melnikov(arXiv: ) ➂ Observe that the enhanced tail is obviously γ H -independent and that this could be exploited to constrain the Higgs width model-independently ➃ Use a matrix element method (e.g. MELA) to construct a kinematic discriminant to sharpen the constraint Campbell, Ellis and Williams (arxiv: )

5 Off-shellness forever Madgraph VBF Signal 2 Phantom VBF Bkg pp gg H e + e γ Me γ > 0.1 M(e + e γ) Me + γ > 0.1 M(e + e γ) Phantom VBF Bkg + Sig σ [ fb] Me + e > 0.1 M(e+ e γ) arxiv: Me + e γ [ GeV] courtesy CMS

6 Scenario Improving ➊ On-shell -degeneracy: allow for a scaling of the Higgs couplings and of the total Higgs width defined by σprod Γ σ i H f = (σ BR) = i f σ γ i H f g2 i g f 2 H γ H g i,f = ξ g SM i,f γ H = ξ 4 γ SM H Remark Looking for ξ -dependent effects in the highly off-shell region is an approach that raises sharp questions on the nature of the underlying extension of the SM; furthermore it does not take into account variations in the SM background The signal strength in 4l, relative to the expectation for the SM Higgs boson, is measured to be CMS ATLAS

7 Scenario Improving ➁ Use κ-language, allowing for a consistent HEFT interpretation, Passarino:2012cb. Neglecting loop-induced vertices, we have Γ gg Γ SM gg(µ H ) = κ2 t Γ tt gg(µ H ) + κb 2 Γbb gg(µ H ) + κ t κ b Γ tb gg(µ H ) Γ tt gg(µ H ) + Γ bb gg(µ H ) + Γ tb gg(µ H ) σ i H f = κ2 i κ2 f κ 2 H σ SM i H f Remark The measure of off-shell effects can be interpreted as a constraint on γ H only when we scale couplings and total width to keep σ peak untouched, although its value is known with 15 20% accuracy.

8 Scenario Improving THE GENERALIZATION IS AN 2 -degeneracy, κ i κ f = κ H. ➂ On the whole, we have a constraint in the multidimensional κ-space, since κ g 2 = κ g(κ 2 t,κ b ) and κ H 2 = κ2 H (κ j, j). Only on the assumption of degeneracy one can prove that off-shell effects measure κ H ; a combination of on-shell effects (measuring κ i κ f /κ H ) and off-shell effects (measuring κ i κ f ) gives information on κ H without prejudices. Denoting by S the signal and by I the interference and assuming that I peak is negligible we have S off S peak κ 2 H + I off S peak κ H x if, x if = κ iκ f κ H for the normalized S + I off-shell cross section. The background, e.g. gg 4l, is also changed by the inclusion of d = 6 operators and one cannot claim that New Physics is modifying only the signal

9 The higher-order correction in gluon-gluon fusion have shown a huge K-factor K = σprod NNLO LO /σ prod, σ prod = σ gg H NNLO prod prod Ý ÑÔ ÖÓ K Ý ÑÔ ÖÓ Lineshape Kgg H virtuality [ GeV] LO

10 ➊ The zero-knowledge scenario Ý ÑÔ ÖÓ D NNLO = D eff NNLO (S) + D LO (I) + D LO (B) ] D NNLO (M) = K D [D LO (S) + D LO (I) + D LO (B) eff σ S+I ( D NNLO = K D D LO (S) + K gg ) 1/2 D D LO (I) + D LO (B) eff Ý ÑÔ ÖÓ multiplicative σ/σpeak intermediate H virtuality [ GeV] A-M THU QCD scale H virtuality [ GeV]

11 The soft-knowledge scenario: in a nutshell, one can σ = σ LO + σ LO α s 2π [universal + process dependent + reg] where universal (the + distribution) gives the bulk of the result while process dependent (the δ function) is known up to two loops for the signal but not for the background and reg is the regular part. A possible strategy (Bonvini et al. arxiv: ) would be to use for background the same process dependent coefficients and allow for their variation within some ad hoc factor.

12 The total systematic error is dominated by theoretical uncertainties, therefore one should never accept theoretical predictions that cannot provide uncertainty in a systematic way (i.e. providing an algorithm). vertical morphing Conway D ( λ, M4l ) = λdm ( M4l ) + (1 λ) DI ( M4l ) D + ( λ, M4l ) = λdi ( M4l ) + (1 λ) DA ( M4l ) 1 ε λ 1, has a flat distribution We will have D < D I < D + and a value for λ close to one (e.g. 0.9) gives less weight to the additive option, highly disfavored by the eikonal approximation.

13 1 Ý ÑÔ ÖÓ 0.75 QCD scales R S + I 0.50 λ = R S+I (i) = σ S+I (i)/σ S+I (1) σ S+I (i) is obtained by integrating dσ S+I /dm 4l 2 over bins of 2.25 GeV for M 4l > 212 GeV H virtuality [ GeV]

14 +5 +4 Ý ÑÔ ÖÓ δ H = G F s 2 2π 2 THU % H virtuality [ GeV]

15 THU summary ➀ PDF+α s ; these have a Gaussian distribution; ➁ µ R, µ F (renormalization and factorization QCD scales) variations; they are the standard substitute for missing higher order uncertainty (MHOU); MHOU are better treated in a Bayesian context with a flat prior; γ H ➂ uncertainty on γ H due to missing higher orders, negligible for a light Higgs; ➃ uncertainty for Γ H F (M f ) due to missing higher orders (mostly EW), especially for high values of the Higgs virtuality M f (i.e. the invariant mass in pp H f + X); ➄ uncertainty due to missing higher orders (mostly QCD) for the background

16 [from arxiv: ] FUTURE (Moriod EW ) 34 L =L 4 + n> 4 Nn i i =1 an Λ n i 4 O (d =n ) i e rov ge p a m to i langu as - NLO h TH h wit κ )

17 CONCLUSIONS The successful search for the on-shell Higgs-like boson did put little emphasis on the potential of the off-shell events. Wind of ange is blowing (CMS-PAS-HIG ), thanks Chiara. The associated THU is (almost) dominating the total systematic error and precision Higgs physics requires control of both systematics, not only the experimental one Very often THU is nothing more than educated guesswork but a workable falsehood is more useful than a complex incomprehensible truth. In other words, closeness to the whole truth is in part a matter of degree of informativeness of a proposition What can be said at all can be said clearly and whereof one cannot speak thereof one must be silent Ludwig Wittgenstein

18 Thanks for your attention