from D0 collaboration, hep-ex/

Transcription

1 At present at the Tevatron is extracted from the transverse-mass distribution Events / GeV/c Fit region from D0 collaboration, hep-ex/ Transverse Mass (GeV/c 2 )

2 3. Precise predictions for W and Z boson production at hadron colliders In the not so far future, we can look forward to improved and an independent measurement of at hadron colliders: measurements uncertainty now Tevatron Run II LHC LC GigaZ (6) 1.3 [GeV] [MeV] [%] (from all data) Projected uncertainties of themeasurement using the transverse mass ratio method at Run II (2 ): 45 MeV from U.Baur, hep-ph/ (Zeuthen 2003), Run-II workshop (1999), hep-ph/

3 For the envisioned high precision, it is crucial that the predictions for the observables to the underlying production processes are well under control. Examples of W and Z boson observables: W boson observables: transverse mass and momentum distributions ( measurement, measurement from high total W and Z production cross sections ( measurement (ratio) and ): as a luminosity monitor ): Z boson observables forward-backward asymmetry ( measurement of ) at the Z peak: invariant mass distributions of lepton pairs ( ) at the Z peak: measurement of and (detector calibration) and at high : scales of new physics, e.g. heavy gauge bosons ( see e.g. U.Baur, A.Bodek.,EPJC21 (2001) ), extra dimensions,

4 Impact of a 500 GeV Z boson on at the Tevatron from U.Baur, A.Bodek.,EPJC21 (2001)

5 W/Z production q p k + l + i, p i f, p f γ, Z W +, q q p k l i, p i f, p f Status of higher-order calculations QCD radiative corrections to W/Z production: exact up to sections) and soft gluon resummation ( (total cross distributions). R.Hamberg et al., NPB359 (1991); W.L.van Neerven et al, NBP382 (1992) ; W.T.Giele et al, NPB403 (1993); C.Balazs et al, PRD56 (1997) (RESBOS) Z boson production: complete QED complete electroweak PRD65 (2002). contribution (ZGRAD) U.Baur et al, PRD57 (1998) contribution (high ) (ZGRAD2) U.Baur et al,

6 Status of higher-order calculations: W boson production: extracted from final state QED (approximation) F.A.Berends et al, Z.Phys.C27 (1985) -65 extracted from full contribution to resonant W production in a pole approx. full at RUN I: MeV Shift due to FSR (RUN I): ( ) MeV in the electron (muon) case. MeV at RUN II: MeV shift in MeV W.Hollik, D.W, PRD55 (1997) theoretical uncertainty? U.Baur et al, PRD59 (1998) electroweak corrections S.Dittmaier,M.Krämer, PRD65 (2002) high :, MeV L.Akhushevich et al(2003); U.Baur, D.W., hep-ph/ real two-photon radiation in W, Z production significantly changes shape of U.Baur et al, PRD61 (2000) multiple final state photon radiation W.Placzek et al, hep-ph/ C.M.Carloni Calame et al, hep-ph/ MeV in the case

7 Parton level Monte Carlo generators for precise predictions for W and Z boson observables are available: RESBOS: QCD corrections to W/Z production, soft gluon resummation. C.Balazs, C.P.Yuan, PRD56 (1997) ZGRAD2: QED and weak corrections to Z boson production with proper treatment of higher-order terms around the Z resonance. U.Baur et al PRD65 (2002) baur/zgrad2.tar.gz WGRAD2: QED and weak corrections to W production. U.Baur et al., PRD59 (1999), U.Baur et al, in preparation. dow/wgrad.tar.gz see also S.Dittmaier, M.Krämer, PRD65 (2002) HORACE: Multiple photon radiation from final state as solution of QED DGLAP evolution for lepton SF. C.M.Carloni Calame et al, hep-ph/ WINHAC: Multiple photon radiation from final state, YFS exponentiation of soft photons. W.Placzek et al, hep-ph/

8 ' + and -' ' + ' ( ),+ /. (,+ 21 0!#" $ " % & Electroweak corrections to production via Drell-Yan The complete mechanism parton level cross section of production via the Drell-Yan is given by where the Born cross section,, is of Breit-Wigner form and usual Mandelstam variables in the parton center of mass frame. The observable section with the quark distribution functions ) and summing over all quark flavors ' (*),+ and are the cross section is obtained by convoluting the parton cross, ( + + with 43 for the Tevatron and for the LHC.

9 The Feynman diagrams contributing to production at shaded loop: non-photonic contributions (i.e. f,h,z,w in loop) : I γ, Z γ, Z, W II γ, Z III IV γ W + γ, Z γ Φ + u γ u + V W I II III

10 Treatment of mass singularities (same for Z boson production)!#" "! " - " % & " & "! " " from W.Hollik, D.W., PRD55, 6788 (1997)! and % " - " contain large mass singular logarithms: Final-state radiation (FSR): in sufficiently inclusive observables the mass singularities completely cancel (KLN theorem). Initial-state radiation (ISR): mass singularities always survive but can be absorbed by universal collinear counterterms to the parton distribution functions (in complete analogy to QCD). U.Baur et al., PRD59 (1999) introduces dependence on QED factorization scheme (in analogy to QCD, a and scheme has been introduced) currently no PDFs available which include QED corrections but the effects of QED on the PDFs are expected to be small (except at large x).

11 ? C J L P P@ B > = C KJ > I = % % : % ( * * P M N PO F D P D G P I R H P D QD P D,+,+ BA F D ED G AH./ %;& %;& %;&!!#" $ %'&," )( "+* The impact of QED corrections on PDFs from H.Spiesberger, LHC report, hep-ph/ (GLAP) from U.Baur et al PRD59 (1998)

12 The numerical impact on W boson observables At present at the Tevatron is extracted from the transverse-mass distribution separation cuts: GeV GeV Gaussian smearing of the lepton momenta and lepton identification requirements: electrons muons combine and and if momentum four vectors ifreject events with GeV for for reject events with reject events with GeV for for

13 The NLO/LO ratio of thedistribution at the Tevatron with WGRAD when taking into account realistic lepton identification requirements: from U.Baur et al, PRD59 (1999) The KLN theorem at work The effects of final-state radiation are largely reduced in the electron case.

14 Pole approximation vs.complete calculation at the Tevatron - above the W peak from U.Baur, D.W., hep-ph/

15 and! 3 The numerical impact on Z boson observables Effects of complete program ZGRAD2. corrections to studied with the MC : Using approximation by Berends,Kleiss: case. Full QED: additional shift of about -10 MeV, dominantly due to FSR. =-100 (-300) MeV for electron (muon) : with at the Tevatron (Collins-Soper frame, P ):

16 The impact of electroweak O O corrections on at the LHC - above the Z peak from U.Baur, D.W., in preparation Note: At the LHC at TeV, QCD NLO corrections enhance by about % (from U.Baur, private communications).

17 The impact of genuine weak from U.Baur, D.W., in preparation corrections on at the LHC observable?

18 Radiative Corrections Besides technical challenges a lot of interesting physics aspects enter the calculation of radiative corrections and their interpretation when comparing theory with experiment. scat- The techniques for QCD, EWK (and SUSY) 1-loop calculations of tering amplitudes are well under control. Explicit algebraic results available for 2-loop amplitudes for massless cesses (e.g. Bhabha, QCD parton scattering), 2-loop QCD amplitudes for jets. pro- A lot of progress in calculating master integrals for 4-loop massive tadpoles, 3-loop massless propagators. Recent progress in ewk 2-loop calculations for. Distributions at NNLO QCD: most tricky part is the PS integration of double real gluon radiation, but recent development for W,Z production in Drell-Yan (see eg talk by Anastasiou and Kilgore at LoopFest III)

19 Examples for remaining issues: Complete ewk 2-loop calculations for Complete 1-loop electroweak for processes. processes. Consistent gauge invariant treatment of unstable gauge bosons (most recent progress: use effective field theory methods (see eg talk by Beneke at LoopFestIII)) Implementation (or interface with) of NLO,NNLO calculations in multi-purpose Monte Carlo programs such as Pythia, Herwig. resummation of elec- Treatment of leading higher order corrections, e.g. troweak Sudakov logarithms. Automization Continued progress in the calculation of radiative corrections is needed to ensure that we fully exploit the potential of the Tevatron, LHC, and a future linear collider for precision physics and searches for new physics. These are long-term projects. To be ready in 2007, 2015 we have to start now!