Outline Motivations for ILC: e + e γ/z q qg LHC: pp l + l + jet (q q l + l g + qg l + l q + qg l + l q) Existing literature The complete EW one-loop c

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1 Complete electroweak corrections to e + e 3 jets C.M. Carloni Calame INFN & University of Southampton Workshop LC08: e + e Physics at TeV scale September 22-25, 2008 in collaboration with S. Moretti, F. Piccinini and D.A. Ross arxiv: [hep-ph] C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 1 / 32

2 Outline Motivations for ILC: e + e γ/z q qg LHC: pp l + l + jet (q q l + l g + qg l + l q + qg l + l q) Existing literature The complete EW one-loop calculation calculation details the Monte Carlo event generator ew3jets results (technical checks & physics) Conclusions C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 2 / 32

3 Motivations at e + e colliders (e + e γ /Z 3 jets) e + e 3 jets was the golden process for QCD measurements and tests at LEP precise measurement of α s (O(1%) at LEP/SLC, O(0.1%) at GigaZ) O(α) EW RC roughly expected as large as NNLO QCD and, at high energies (Sudakov double-logs), as NLO QCD EW effects can induce asymmetries in 3 jets observables at hadron colliders (pp γ /Z l + l + jet) measurement of PDFs via p γ/z spectrum, in particular the gluon PDF large effects of EW Sudakov logs in Z+jet observables, e.g. at high p Z where BSM physics can show up detector calibration for jets measurements SM effects must be well under control to match the experimental accuracy and to disentangle SM from BSM physics C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 3 / 32

4 Literature Restricting to EW corrections E. Maina, S. Moretti, D.A. Ross, JHEP 0304:056 (2003) factorizable weak corrections to e + e 3 jets (no real & virtual QED, no RC connecting initial and final state), effects studied at s = MZ E. Maina, S. Moretti, D.A. Ross, PLB 593 (2004), Erratum PLB 614 (2005) purely weak corrections to pp Z or γ+ jet at high p γ/z T. γ and Z on-shell Kuhn, Kulesza, Pozzorini, Schulze, PLB 609 (2005) logarithmic weak corrections to pp Z+ jet (high p Z ) at one and two loop order with LL and NLL accuracy (Sudakov expansion) Kuhn, Kulesza, Pozzorini, Schulze, NPB 727 (2005) 368 Exact one loop corrections to pp Z+ jet QCD corrections to e + e 3 jets are known up to NNLO order (recent work by Gehrmann-De Ridder, Gehrmann, Glover, Heinrich) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 4 / 32

5 Weak factorizable RC at s = M Z Maina et al., PLB weak corrections have a O(1%) effect, which could be not negligible for α s determination at GigaZ at the 0.1% level larger effect for the b b sub-sample (due to top in the loops) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 5 / 32

6 Weak RC to γ/z+jet Maina et al., JHEP V p T LHC (NLO-LO)/LO (dσ NLO -dσ LO )/dσ LO γ blue Z red p T (GeV) large corrections (O(10%)) in the high boson p tail, where SM is a background to new physics signatures C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 6 / 32

7 Complete 1-loop EW RC to e + e 3 jets we calculated the full 1-loop EW corrections to e + e 3 jets QED can give a sizeable effect if realistic event selection criteria are considered non-factorizable RC are not negligible far from M Z non-factorizable RC can have a not trivial impact on asymmetries by crossing symmetry, EW RC to pp l + l + jet are straighfordwardly obtained the precise control of SM effects is mandatory for precision physics and new physics searches C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 7 / 32

8 Prototype diagrams The 1-loop diagrams to be evaluated are: e + e vertices. M M (a) (b) W W. (c) (d) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 8 / 32

9 Prototype diagrams q q and gluon vertices and fermion self-energies.. M W W M (a) (b) (a) (b) M M M M (c) (d) (c) (d) M M M M. (e) (f). (e) (f) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 9 / 32

10 Prototype diagrams box diagrams (factorizable and not factorizable). W (a) M M (b) (c) M1 M1 M2 (d) M2 (e) M1 M1 M2 M2. (f) (g) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 10 / 32

11 Prototype diagrams. pentagons and gauge-bosons self-energies M1 M1 M2 M2. (a) (b). + - (a) (b) (c) (d) (e) (f) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 11 / 32

12 Calculation details the calculation has been performed in the limit m 2 ext/s 0 collinear singularities cured with a small fermion & quark mass infrared divergencies regularized with a finite photon mass λ virtual corrections amplitudes evaluated with helicity techniques and manipulated with FORM two independend calculations up to 4-point functions: reduction of tensor integrals with Passarino-Veltman reduction 5-point functions, reduction according to PV or to Denner-Dittmaier (as coded in a our own library or in LoopTools) good agreement among different implementations the squared amplitude for the real emission process e + e q qgγ has been calculated with ALPHA (Moretti & Caravaglios) with MADGRAPH (Maltoni, Stelzer et al.) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 12 / 32

13 Gauge boson width in the real part of the calculation we have the Z propagator with fixed width switched on, in order to avoid the Z pole in the phase space integration the same propagator has to be retained in the virtual corrections (complex mass scheme) (e.g., in order to ensure the cancellation of IR singularities between virtual and real corrections) in LoopTools only scalar functions up to 3-points are available with finite width we implemented a 4-point scalar function with complex masses, according to t Hooft-Veltman (Nucl. Phys. B 153,1979) and to Denner-Beenakker (Nucl. Phys. B 338,1990) for IR configurations all the calculation can then be performed with complex Z (and W ) mass C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 13 / 32

14 Cross section calculation As usual, the cross section is split into two parts e + e q qg σ 2 3 = e + e q qgγ dφ 3 ( M0 2 +2R[M 0M virt α (λ)] ) σ 2 4 = dφ 4 M real α 2 + λ<ω<k 0 k 0 <ω λ<ω dφ 4 M real α 2 = dφ 4 M real α 2 = δ s (λ, k 0 )σ 0 + σ2 4 hard (k 0 ) σ σ 2 4 σ SV (k 0 )+σ hard (k 0 ) has to be independent from the unphysical parameters λ and k 0 the integral over 2 3 and 2 4 phase space is performed with a Monte Carlo generator C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 14 / 32

15 Initial state higher-order QED effects Large collinear logs ln(s/m 2 e) associated with ISR for reliable predictions they need to be resummed we use the SF formalism avoiding double counting G. Montagna, O. Nicrosini and F. Piccinini, Phys. Lett. B385 (1996) 348 dσ = dσ LL dσll α + dσexact α dσ LL = dx 1 dx 2 D(x 1,s)D(x 2,s)dσ 0 (x 1 x 2 s) dσll α = dx 1 dx 2 [D(x 1,s)D(x 2,s)] α dσ 0 (x 1 x 2 s) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 15 / 32

16 The Monte Carlo event generator ew3jets the calculation is implemented in the MC event generator ew3jets it s a fully exclusive EG (particles momenta, e ±, q q helicities, flavour can be accessed event by event) (unweighted or weighted) events can be stored in a Les Houches Accord compliant way (e.g. for futher processing with QCD Parton Shower codes) any cut can be imposed and any distribution can be looked at C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 16 / 32

17 Technical checks Only α EM contributions included independence of σ V + σ S from the photon mass (λ) λ 2 (GeV 2 ) σ V + σ S (pb) (5) (7) s = 300 GeV, k0 =0.15 GeV, independence of σ real from the soft-hard separator (k 0 ) 2k 0 / s σ real (pb) (5) (7) λ 2 = GeV 2, s = 300 GeV C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 17 / 32

18 Results numerical results for s = M Z and 1 TeV (and 350 GeV in the paper) cuts & parameters: momenta clustered into jets according to the Cambridge algorithm, i.e. if y ij <y min, where y ij =2 min(e2 i,e2 j )(1 cos θ ij) s photon (in 2 4) recombined according to the same algorithm at least 3 hadronic jets requested y min =0.001, 30 <θ jets < 150, M 3 jets > 0.75 s α s =0.118, α em =1/128, M Z = GeV, M W = 80.4 GeV summed over final state quarks (q q = uū, d d, c c, s s, b b) and over initial- and final-state helicities the final state b b has been treated retaining the full m top dependence C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 18 / 32

19 Energy scan % QED corrections gauge bosons self-energy non-factorizable WW graphs full weak - non-fact. WW graphs complete O(α) s (GeV) for d, s, b (u, c) only direct ( crossed ) WW virtual non-fact. diagrams survive (the ones giving negative correction) large negative corrections induced by lack of cancellation of WW direct and crossed diagrams, as it happens at LL level for ZZ diagrams C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 19 / 32

20 Leading jet angle at Z peak (%) dσ/dθlj (pb/ ) dσi dσborn dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL θ lj ( ) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 20 / 32

21 Leading jet angle at s =1TeV dσ/dθlj (fb/ ) (%) dσi dσborn dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL θ lj ( ) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 21 / 32

22 Leading jet energy at Z peak dσ/delj (pb/gev) (%) dσi dσborn dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL E lj (GeV) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 22 / 32

23 Leading jet energy at s =1TeV 10 dσ/delj (fb/gev) (%) dσi dσborn dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL E lj (GeV) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 23 / 32

24 Thrust at Z peak 2500 (1 T ) dσ/dt (pb) Born weak O(α) exact O(α) exact O(α) + h.o. LL (%) dσi dσborn dσborn i T = max p i n T i p i T C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 24 / 32

25 Thrust at s =1TeV (1 T ) dσ/dt (fb) Born weak O(α) exact O(α) exact O(α) + h.o. LL (%) dσi dσborn dσborn T C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 25 / 32

26 C parameter at Z peak dσ/dc (pb) (%) dσi dσborn dσborn C parameter Born weak O(α) exact O(α) exact O(α) + h.o. LL C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 26 / 32

27 C parameter at s =1TeV dσ/dc (pb) Born weak O(α) exact O(α) exact O(α) + h.o. LL 0.1 (%) dσi dσborn dσborn C parameter C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 27 / 32

28 y at Z peak 1e Born weak O(α) exact O(α) exact O(α) + h.o. LL dσ/dy (pb) (%) dσi dσborn dσborn y (Cambrigde) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 28 / 32

29 y at s =1TeV dσ/dy (fb) Born weak O(α) exact O(α) exact O(α) + h.o. LL 1 (%) dσi dσborn dσborn y (Cambridge) C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 29 / 32

30 y max at Z peak σ(ymax) (pb) (%) dσi dσborn dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL σ(y max ) y max ymax 0 dy dσ dy C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 30 / 32

31 y max at s =1TeV σ(ymax) (pb) dσi dσborn (%) dσborn Born weak O(α) exact O(α) exact O(α) + h.o. LL y max C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 31 / 32

32 Conclusions the complete one-loop EW corrections to e + e 3 jets have been calculated each contribution calculated independently twice good agreement between different implementations the calculation is implemented in the MC event generator ew3jets the effects of EW RC are important for future precision studies at ILC (e.g. α s determination) and BSM searches EW RC are expected to be even more relevant in presence of polarized beams, unlike QCD RC work in progress: study of the effects in presence of polarized beams crossing the process to study EW RC to Z+jet at hadron colliders C.M. Carloni Calame (INFN & Soton) EW RC to e + e 3 jets 32 / 32