Higgs Pseudo - Observables

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1 Higgs Pseudo - Observables Giampiero PASSARINO Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino, Italy HEPTOOLS Network Loops and Legs in Quantum Field Theory, April 2010, Wörlitz, Germany

2 Based on work done in collaboration with Christian Sturm and Sandro Uccirati Thanks: A. Denner, S. Dittmaier, M. Dührssen, M. Grünewald, S. Heinemeyer, C. Mariotti, R. Tanaka But I talk, so it s my responsibility All that theories can tell us is how the world could be (van Fraassen 1991)

3 Outlines (1, 2,) 1 From signal and background at LHC to the definition of Pseudo - Obervables 2 and Feynman diagrams on the second Riemann sheet, what else, but the inevitable! The suggestion that particles might be seen as aspects of pseudo-observability fits nicely with structural realism, even in the absence of further metaphysical explication (Higgs)

4 Outlines (1, 2,) 1 From signal and background at LHC to the definition of Pseudo - Obervables 2 and Feynman diagrams on the second Riemann sheet, what else, but the inevitable! The suggestion that particles might be seen as aspects of pseudo-observability fits nicely with structural realism, even in the absence of further metaphysical explication (Higgs)

5 Outlines (1, 2,) 1 From signal and background at LHC to the definition of Pseudo - Obervables 2 and Feynman diagrams on the second Riemann sheet, what else, but the inevitable! The suggestion that particles might be seen as aspects of pseudo-observability fits nicely with structural realism, even in the absence of further metaphysical explication (Higgs)

6 o o os Before the entry of the chorus All the questions in this talk are not really urgent, as nothing will be really measurable by LHC before 2013, 2014 or beyond but they will be if you consider as relevant to have results published in such a way that theorists can later enter their general model parameters, calculate resulting POs and see how well data constrains this model. even if it will take 10 years to reach enough fb 1 ; even if it is not LEP anymore study tools that Exps can use in future analysis to extract Higgs POs

7 Oldies but Goldies Experimenter s (should) extract (unfold?) so-called realistic observables from raw data, e.g. M in pp X and need to present results in a form that can be useful for comparing them with theoretical predictions, i.e. the results should be transformed into POs Theorists (should) compute POs using the best available technology and satisfying a list of demands from the self-consistency of the underlying theory

8 Prolegomena The search for a mechanism explaining EWSB has been a major goal for many years, in particular the search for a SM Higgs boson. As a result of this an intense effort in the theoretical community has been made to produce the most accurate NLO and NNLO predictions However, there is a point that has been ignored: the Higgs boson is an unstable particle and should be removed from the in out bases in the H - space, without destroying unitarity of the theory. Therefore, concepts as the production or partial decay widths of an unstable particle should be replaced by a conventionalized definition which respects first principles of QFT

9 Prolegomena The search for a mechanism explaining EWSB has been a major goal for many years, in particular the search for a SM Higgs boson. As a result of this an intense effort in the theoretical community has been made to produce the most accurate NLO and NNLO predictions However, there is a point that has been ignored: the Higgs boson is an unstable particle and should be removed from the in out bases in the H - space, without destroying unitarity of the theory. Therefore, concepts as the production or partial decay widths of an unstable particle should be replaced by a conventionalized definition which respects first principles of QFT

10 Prolegomena The search for a mechanism explaining EWSB has been a major goal for many years, in particular the search for a SM Higgs boson. As a result of this an intense effort in the theoretical community has been made to produce the most accurate NLO and NNLO predictions However, there is a point that has been ignored: the Higgs boson is an unstable particle and should be removed from the in out bases in the H - space, without destroying unitarity of the theory. Therefore, concepts as the production or partial decay widths of an unstable particle should be replaced by a conventionalized definition which respects first principles of QFT

11 Prolegomena The search for a mechanism explaining EWSB has been a major goal for many years, in particular the search for a SM Higgs boson. As a result of this an intense effort in the theoretical community has been made to produce the most accurate NLO and NNLO predictions However, there is a point that has been ignored: the Higgs boson is an unstable particle and should be removed from the in out bases in the H - space, without destroying unitarity of the theory. Therefore, concepts as the production or partial decay widths of an unstable particle should be replaced by a conventionalized definition which respects first principles of QFT

12 Prolegomena The search for a mechanism explaining EWSB has been a major goal for many years, in particular the search for a SM Higgs boson. As a result of this an intense effort in the theoretical community has been made to produce the most accurate NLO and NNLO predictions However, there is a point that has been ignored: the Higgs boson is an unstable particle and should be removed from the in out bases in the H - space, without destroying unitarity of the theory. Therefore, concepts as the production or partial decay widths of an unstable particle should be replaced by a conventionalized definition which respects first principles of QFT

13 $ # Prolegomena II Example Combine gg H with H. The full process is pp X Signal pp gg H X! and by a non-resonant background. The question is: how to extract from the data, without ambiguities, a PO H partial decay width into which does not violate first principles? Once again, Higgs boson " out H in in ; not definable in QFT.

14 Background: comment but Perhaps we have been too busy with polynomial 20 gluons, The qq background was computed with NLO XX. However, XX is not an event Monte Carlos suitable for the detector simulation. Hence LO YY is used to produce events and then, the p T and the M&'& distributions are reweighted to XX. Theory issues exist independently of those experimental detector-related aspects and must be tackled anyway ('('()('('( %

15 / /! / The mother of all POs resummed propagators Skeleton expansion of the self-energy S i, with propagators that are resummed up to -. n / i s / 0 n2 i s 3 s 3 m 2 i / 0 02 i s 1 / 0 02 i s4, 0 n2 ii s! / 0 n5 12 i s 5 1! a dressed propagator is the formal limit i s n687 lim i s 3 /10 n2 i s9! / 0 02 i s 1 / 0 02 i s4, ii s! i s * 5 1!

16 / /! / The mother of all POs resummed propagators Skeleton expansion of the self-energy S i, with propagators that are resummed up to -. n / i s / 0 n2 i s 3 s 3 m 2 i / 0 02 i s 1 / 0 02 i s4, 0 n2 ii s! / 0 n5 12 i s 5 1! a dressed propagator is the formal limit i s n687 lim i s 3 /10 n2 i s9! / 0 02 i s 1 / 0 02 i s4, ii s! i s : 5 1!

17 @ = Complex pole The Higgs boson complex pole s H is the solution of the equation s H 3 M 2 H <, HH s H! M 2 H!>=? 0! where M 2 H is the renormalized mass; all local CTs have been introduced to make the off-shell, UV finite. NI 1 s H 0 NI 2, HH s H! M 2 H!>=? 0! ;

18 @ = Complex pole The Higgs boson complex pole s H is the solution of the equation s H 3 M 2 H <, HH s H! M 2 H!>=? 0! where M 2 H is the renormalized mass; all local CTs have been introduced to make the off-shell, UV finite. NI 1 s H 0 NI 2, HH s H! M 2 H!>=? 0! A

19 =, Corollary From NIs it follows: 0 12 HH s H! s H!>=? 0! at one-loop, the Higgs complex pole is gauge parameter independent if the self-energy is computed at M 2 H s H, the basis of the so-called complex-mass scheme higher than one-loop C'C'C no time C'C'C B

20 / / S - matrix At the parton level the S -matrix for the process i S fi V i s f can be written as H s V f se B if s9! V i is the production vertex i H V f is the decay vertex H f H the H re-summed propagator B if is the non-resonant background D

21 J $ / N $ N $ N $ Modification of the LSZ reduction Step 1 f out H H i in G n IH H f out n n i in nkml H is a complete set of states Step 2 HH s, HH so3p, HH s H s 3 s H! HH s s 3 s H Z H 1 HHC HH s 5 1! F

22 Modification of the LSZ reduction Step 3 S fi Z 5 1R 2 H s V i s 1 s 3 s H Z 5 1R 2 H s V f s B if s Step 4 S H c f Z 5 1R 2 H s H V f s H 9! Q S i H c S H c f S fi non resonant termsc s 3 s H

23 J W W J Main result Example: gg 1 s dt f P H! p f KU S i s H S f s H 2 5 V H s 3 s H s s 3 s H 2 V H gg6 H XZY V H H6 &'& C V H Y H c f 2+[ 4 2 spins S H c dt f P H! f 2! p f KU S

24 real life: ] \

25 c b real life: 4 leptons /dm [fb/10gev/c dσ 2 ] Hf ZZ*f 2e2eµ After Selection d Zb b ZZ* H130 H150 H200 H ma 2e2` µ ^ _ [GeV/c 2 ]

26 i V Strategy We have four parameters, all PO s H 2 H 3 i V H HCh V H ij6 H! Y V H H6 XX! to use in a fit to the (box-detector) experimental distribution (of course, after folding with PDFs); these quantities are universal, uniquely defined, and in one-to-one correspondence with corrected experimental data; after that one could start comparing the results of the fit with a XM calculation. Proposed initial step: unfold RO into something with idealised cuts and then use the PO approach to fit that. g

27 PO, once again Why PO language? POs are the the moneta franca of LHC, creating an awful lot of wealth C'C'C)C'C'C. There are reasons why the chain MCT detector simulation-selection cuts realistic distributions unfolded distributions should be replaced by MCT box acceptance (unfolded particle-level) distributions Since detector-experimental issues are a moving target only PO are the Frankish language to understand LHC. j

28 Why? PO POs transform the universal intuition of a QFT-non-existing quantity into an archetype, PO l the archetypal model after which theoretical calculations are patterned without worries on generating and detector-simulating events for signal and background k

29 Glossary Example RD = real data RO = from real data distributions with cuts l RO diphoton pairs n Eo pprq Mnts?sp ; PO = transform the universal intuition of a QFT-non-existing quantity into an archetype, e.g. gg H9! Y H, RO th n m H ovuwn H qxs?spyo{z{z9z p fitted to RO exp (e.g. RO m } Mn~ssp ) defines and extracts m H etc.

30 Steps go via idealised (model-independent?) RO distributions and from there then going to the POs. Step 0) Use a (new) MCT the PO code to fit ROs Step 1) Understand differences with a standard event generator plus detector simulation plus calibrating the method/event generator used (which differ from the PO-code in its theoretical content) Step 2) Let s see z{z9z{z{z9z

31 Lep example of RO 1 L3 ˆ e ˆ + e e ˆ + e (γ) Š 44 o < θ < 136 o σ [nb] ƒs-channel t-channel interference ratio

32 Plan Example RO exp PO XM 1 C'C'C PO XM n XM = any Model 5U6 fit Ž 5 comparison RO th PO 1 C'C'C PO n PO 1 C'C'C PO n PO 1 X PO 2 C'C'C PO n Œ

33 Once again on-shell H FS does not exist well defined RO th FS m H Y H c FS! C'C'Cw RO exp FS m H! Y H c FS extracted conventional but unique

34 Generalization s H signal into gg q H production, H q W W decay and subsequent s W Figure: Gauge-invariant breakdown of the triply-resonant gg q W q f f decays. 4 f

35 œ œ œ General setup 2 theor y with Mš 2 m ; the propagator is The inverse function, œ s ž MŸ 2 ŸvŸ? s 1 s is analytic in the entire s -plane except for a cut 4 m «ª 2 ; is defined above the cut, œ 1 1 s i 0 and the analytical continuation downwards is to the 2nd Riemann sheet 1 2 s ž i 0 1 s i 0 œ 2 i ± s is the discontinuity across the cut. 1 s ž i 0 2 i ± s

36 The logarithm We need ³ a few definitions which will help the understanding of the procedure for the analytical continuation of functions defined through a parametric integral representation Logarithm Step 1 ln kµ z ln 0µ z 2 i k k 0 1 ' ' where ln 0µ z denotes the principal branch (ž¹»º arg z ¹¼ ). Step 2 Let z½ z 0 i 0 and z z R i z I, define ² ln ½ z ¾ z½ ln z 2 i 1 ž z 0 À ÂÁ z I ln z 2 i 1 ž z R À 9Á z I

37 The logarithm II first definition of the ln ½ -functions is most natural in defining analytical continuation of Feynman integrals with a smooth limit into the theory of stable particles; the reason is simple, in case some of the particles are taken to be unstable we have to perform analytical continuation only when the corresponding Feynman diagram, in the limit of all (internal) stable particles, develops an imaginary part (e.g. above some normal threshold); However, in all cases where the analytical expression for the diagram is known, one can easily see that the result does not change when replacing z 0 with z R, the second variant. Ã

38 ž The di-logarithm Example Å Li 0Æ 0µ 2 z 0 º arg z ž 1 º 2 Li næ mµ 2 z Li 0Æ 0µ 2 z 2 n i ln 0µ 2 z 4 m Question: given Li 2 M 2 i 0 Im Li 2 M 2 i 0 1 dx 0 x ln 1 ž M2 x ž i 0 Ä ln M 2 M 2 ž 1 how do we understandbf analytical continuation in terms of an integral representation?

39 ž di-logarithm II Let us consider the analytical continuation from zè M 2 i 0 to z M 2 ž i M É and define Ê x I 0 1 dx x ln 1 ž z x ¾ 1 ž zè x 1 ž z x 1 ž M 2 ž i MÉU x If M 2 Ë 1 Ê crosses the positive imaginary axis I Li 0Æ 0µ 2 z 2 i ln M 2 Ç which is not the expected result

40 Ð di-logarithm III The mismatch can be understood by observing that Ê has a cut 0 i Í and, in the process of ln continuation, with x Î 0 1, we have been crossing the cut. The solution consists in deforming the integration contour, therefore defining a new integral, I C C dx x ln 1 ž z x ¾ 1 ž zè x where C C 0 CÏ xð C 0 0 ¼ x ¼ 1Ñ M 2 ž<ò Ó 1Ñ M 2 ÒÔ¼ x ¼ 1, CÏ u GÕ x u i 1 M 2 u 1 1 M ÖØ, M 2 È Ö 2 ¼ u ¼ M 2 Ì

41 di-logarithm IV Result: The integral over CÏ is downwards on the first quadrant an upwards on the second (along the cut of ln ); Integration of ln over CÏ gives ž 2 i ln M 2 ž ln z, showing that Li 1Æ 0µ 2 z the correct analytical continuation. Therefore we can extend our integral, by modifying the contour of integration, to reproduce the right analytical continuation Ù I C AnalytÚ ContÚ Li n Ûžª Li n Li n 1 È z 8Ü 0 z dx x Li x n

42 Deformation: example v 0 u cut Im[V]=0 contour Ý 0 x ª u iv in 1 0 dx ln V. 1

43 ž ß Complexification: example t t s m 2 H s H natural choice: real kin ª complex inv PO à gg ª Hj s H s t t u ž s 2 1 ž s H s 2 1 ž s H s s ž 1 ž 4 s H s 1 ž 4 s H s 1á 2 cos 1á 2 cos Þ

44 Schemes Schemes RMRP the usual on-shell scheme where all masses and all Mandelstam invariants are real; CMRP the complex mass scheme with complex internal W and Z poles (extendable to top complex pole) but with real, external, on-shell Higgs, W Z, etc. legs and with the standard LSZ wave-function renormalization; CMCP the (complete) complex mass scheme with complex, external, Higgs (W Z, etc.) where the LSZ procedure is carried out at the Higgs complex pole (on the second â Riemann sheet). No theoretical uncertainty; only the CMCP scheme is fully consistent.

45 å ä ì æ ç 25 íh ë γë ê γ (gg) 20 CMCP/CMRP-1 [%] å é 5 è å µ [GeV] H ç 300 ã Figure: H îxï?ï (blue), H î gg (red)

46 è ç ä ñ ñ Outlines Introduction Complex poles Extracting POs Complexity Numerica ç 35 ç 30 Γ(H gg) [MeV] å 15 å 10 é ç 320 Figure: òwó H î ç µ [GeV] H ñ ð ggô CMRP (dashed), CMCP (dotted) 500

47 è ç ä Outlines Introduction Complex poles Extracting POs Complexity Numerica 0.5 è 0.4 /σ CMRP -1 σ CMCP è 0.3 è 0.2 è 0.1 è ç 320 ç [GeV] H Figure: ù CMCPú ù CMRP ó pp î Hôrû s ü 3 TeV (red), û s ü 10 TeV (blue) and û s ü 14 TeV (black) µö õ

48 ç ä 0.14 σ(pp H) [pb] 0.12 è è ç 320 Figure: ùó pp î þs= 3 TeV ç [GeV] H µö Hô at û s ü 3 TeV for CMRP (red) and CMCP (blue). Dashed lines give the scale uncertainty ý

49 ç ä ç Outlines Introduction Complex poles Extracting POs Complexity Numerica è 0 H bb [%] δ w µö [GeV] H Figure: Weak one-loop radiative corrections to H î CMRP (black dotted) and CMCP scheme (black) ÿ bb; RMRP (red),

50 ä ç ç γ) [kev] γ Γ(H ñ è µö [GeV] H 350 Figure: òwó H îxïïô ; RMRP (dotted line), CMRP (dashed line) and the CMCP (solid line) 400

51 o os (1, 2,) 1 We get a consistent PO definition of mass, width, couplings, meaning we can write à pp ª H BR H ª X as product of POs 2 This is needed if we want published results in such a way that theorists can later enter their general model parameters, calculate resulting POs and see how well data constrains this model Happening at Higgs Cross Section Working Group

52 o os (1, 2,) 1 We get a consistent PO definition of mass, width, couplings, meaning we can write à pp ª H BR H ª X as product of POs 2 This is needed if we want published results in such a way that theorists can later enter their general model parameters, calculate resulting POs and see how well data constrains this model Happening at Higgs Cross Section Working Group

53 o os (1, 2,) 1 We get a consistent PO definition of mass, width, couplings, meaning we can write à pp ª H BR H ª X as product of POs 2 This is needed if we want published results in such a way that theorists can later enter their general model parameters, calculate resulting POs and see how well data constrains this model Happening at Higgs Cross Section Working Group

Higgs production at the Tevatron and LHC

Higgs production at the Tevatron and LHC at the Tevatron and LHC Dipartimento di Fisica Teorica, Università di Torino, Italy INFN, Sezione di Torino, Italy E-mail: giampiero@to.infn.it Status of the art in the calculation of Higgs cross sections