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1 Precision calculations for γγ 4 fermions (+γ) Stefan Dittmaier MPI Munich (in collaboration with A. Bredenstein and M. Roth) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 1

2 Contents 1 Introduction 2 The Monte Carlo generator 3 Selected lowest-order results 4 Radiative corrections 5 Conclusions LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 2

3 1 Introduction Four-fermion production at a future γγ collider: large γγ 4f cross section: σ total 80 pb at high energies precision signal / background to new physics test of γ and γγ couplings s-channel Higgs production γγ H /ZZ 4f Requirements from theory: Predictions at %-level or better achieved by thorough description of decays of resonant gauge bosons inclusion of radiative corrections optional inclusion of non-standard gauge-boson couplings special improvements for Higgs production Requirements neither fulfilled by multi-purpose Monte Carlo generators nor by previous dedicated analyses! Motivation for constructing the dedicated event generator COFFERγγ to fill this gap LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 3

4 2 The Monte Carlo generator Features of the generator COFFERγγ (COrrections to Four-FERmion production in γγ collisions) Complete lowest-order matrix elements γγ 4f Bredenstein, S.D., Roth compact results in terms of eyl van-der-aerden spinor products massless fermions (mass effects restored in corrections) loop-induced or effective γγh coupling anomalous triple and quartic gauge-boson couplings Radiative corrections to γγ 4f(+γ) in double-pole approximation (DPA) similar to e + e case Aeppli, v.oldenborgh, yler 93; Beenakker, Berends, Chapovsky 98 Jadach et al. 99; Denner, S.D., Roth, ackeroth 99 Multi-channel Monte Carlo integration with adaptive weight optimization Berends, Kleiss, Pittau 94 Kleiss, Pittau 94 Realistic γ beam spectrum, e.g., by COMPAZ Zarnecki 02 Note: all parts checked by a second independent Monte Carlo generator! LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 4

5 @ 4 & ) ' 21 ' C & &. 3 Selected lowest-order results A semileptonic integrated cross section Bredenstein, S.D., Roth 04? <AB )0 /.,- *3 () )0 /.,- *+ () DC D CD! & DC D D DE D DF D GD D DH D % $ #? > <= : ; Good agreement with HIZARD / MADGRAPH for all final states! Kilian 01 Stelzer, Long 94 LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 5

6 T LK J I I b V ] ] _ ] ^ ] U U V U Predictions with anomalous TGCs α Bφ δl = ig 1 M 2 (D µ Φ) B µν (D ν Φ) α φ ig 2 (D µ Φ) σ µν (D ν Φ) g 2 M 2 α 6M 2 µ ν ( ν ρ ρ µ) κ γ = α φ + α Bφ anomalous γ coupling λ γ = α anomalous γ and γγ couplings (elmg. gauge invariance!) R U [ V V \V V \V V [ V V YV VX c b ` ^b` ^b` ] _S` a b a ` b b a ` ZV V VX OQPSR KNM Bredenstein, S.D., Roth 04 ±1σ contours see = 500 GeV L = 100 fb 1 ZV V VX Above result based on cross section only. More stringent constraints will result from distributions! (See also Tupper, Samuel 81; Choi, Schrempp 91; Yehudai 91; Božović-Jelisavčić, Mönig, Šekarić 02) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 6

7 Ž ˆ Œ q ˆ ~ yx w v v ƒ ou ts nm j j j i h h e g h i d e g Ž ˆ Œ q ˆ ƒ Predictions with anomalous QGCs { Š xnz Bredenstein, S.D., Roth 04 δl = e2 16Λ 2 a 0 F µν F µν α α pnq o r e2 16Λ 2 a c F µα F µβ β α dfe g dfe g elk elk e2 16Λ 2 ã0 F µν Fµν α α a 0, a c, ã 0 anomalous γγ and γγzz couplings X ~ ~ {} ~ Š Above result based on cross section only ( s ee = 500 GeV, L = 100 fb 1 ). More stringent constraints will result from distributions! (See also Bélanger, Boudjema 92; Marfin, Mossolov, Shishkina 03) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 7

8 ÖÌ Õ Ð µ ³ Ô ÐÑÒ Ó Ü ¹ Þ º» È Ç Ã ª ½ ¼ ¹» Þ Ý š» Ü» Ý Ü Û Ú Ù» º ¹ ÏÎ ¼ ÌÍ ² ± š Naive -pair signal versus DPA in lowest order ² œ Ÿ œ ž Ï Bredenstein, S.D., Roth 04 Ä ÅÆ ¾Â Á ¾ À É Ê Ë Ë «signal = sum of diagrams with two resonant bosons non-gauge-invariant result, approximation out of control DPA = signal with on-shell-projected residue gauge-invariant result with accuracy of O(Γ /M ) = 1 3% (See also M. Moretti 96; Boos, Ohl 97; Baillargeon, Bélanger, Boudjema 97) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 8

9 4 Radiative corrections Strategy essentially follows approach of RACOON Denner, S.D., Roth, ackeroth Lowest-order predictions full matrix elements for γγ 4f Radiative corrections to γγ 4f Real photonic corrections full matrix elements for γγ 4f + γ Virtual corrections in DPA factorizable contributions results for on-shell s as building blocks: γγ Denner, S.D., Schuster 94, 95; Jikia 96 f f Bardin, S. Riemann, T. Riemann 86 Jegerlehner 86; Denner, Sack 90 non-factorizable contributions adapt known results for e + e annihilation Beenakker, Berends, Chapovsky 97; Denner, S.D., Roth 97 Combination of real and virtual corrections two methods: slicing and dipole subtraction S.D. 99; Roth 00 γ γ γ γ γ LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 9

10 More details about the corrections: Higgs resonance: interference term 2 Re{M Higgs M 0} with Born matrix element M 0 insufficient γ H inclusion of M Higgs 2 (with gauge-invariant residue at s = M 2 H) γ threshold region: DPA becomes unreliable use improved Born approximation for s γγ < 170 GeV (based on Coulomb singularity, Higgs resonance, and effective couplings) Final-state mass singularities versus photon recombination: phase-space cuts on bare momenta p f of charged fermions f yield large corrections α ln m f generalized dipole subtraction applied photon recombination: min{ (f, γ)} < θ rec = 5 p f p f + k γ, k γ 0 inclusiveness ensures cancellation of mass singularities α ln m f (KLN theorem) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 10

11 O(α)-corrected integrated cross section for γγ ν e e + dū: cuts: E l/q > 10 GeV, θ(l/q, beam) > 5, θ(l, q) > 5, m(q, q ) > 10 GeV σ [fb] best Born M H = 130GeV δ [%] M H = 130GeV M H = 170GeV Bredenstein, S.D., Roth see [GeV] see [GeV] photon spectrum from COMPAZ determines shape of Higgs resonance as function of e e CM energy s ee LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 11

12 O(α)-corrected integrated cross section for γγ ν e e + dū: σ [fb] 1000 M H = 130GeV δ [%] 4 3 M H = 130GeV best Bredenstein, S.D., Roth best Born see [GeV] see [GeV] O(α) corrections O(3%) off Higgs resonance LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 12

13 O(α)-corrected -production angle distribution for γγ ν e e + dū: s = 500 GeV dσ d cos θ + [fb] best, without γ spectrum Born, without γ spectrum best, with γ spectrum Born, with γ spectrum δ [%] without γ spectrum with γ spectrum Bredenstein, S.D., Roth cos θ cos θ pronounced forward-backward peaking behaviour, but moderate corrections after convolution with photon spectrum only small distortion of distribution by corrections LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 13

14 O(α)-corrected invariant-mass distribution for γγ ν e e + dū: s = 500 GeV, photon recombination applied! dσ dm [ ] fb GeV best, without γ spectrum Born, without γ spectrum best, with γ spectrum Born, with γ spectrum M + [GeV] δ [%] without γ spectrum with γ spectrum Bredenstein, S.D., Roth M + [GeV] important corrections to -line shape with and without convolution over photon spectrum LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 14

15 5 Conclusions Four-fermion production among most interesting processes at γγ collider large γγ 4f cross section precision signal / background to new physics test of γ and γγ couplings s-channel Higgs production New event generator COFFERγγ γγ 4f Bredenstein, S.D., Roth lowest-order predictions for all γγ 4f and 4f + γ processes with light f loop-induced or effective γγh coupling for Higgs production anomalous triple and quartic gauge-boson couplings radiative corrections to γγ 4f(+γ) in DPA Code well tested and ready to use! (available from authors upon request) LCS05, Stanford, March 2005 Stefan Dittmaier (MPI Munich), Precision calculations for γγ 4 fermions (+γ) 15

Four-fermion production near the W-pair production threshold. Giulia Zanderighi, Theory Division, CERN ILC Physics in Florence September

Four-fermion production near the W-pair production threshold Giulia Zanderighi, Theory Division, CERN ILC Physics in Florence September 12-14 2007 International Linear Collider we all believe that no matter