NLO Event Generation for Chargino Production at the ILC

Transcription

1 NLO Event Generation for Chargino Production at the ILC Jürgen Reuter University of Freiburg W. Kilian, JR, T. Robens, EPJ C 48 (26), 389; hep-ph/61425 Loopfest VI, Fermilab, April 18, 27

2 Motivation: Precision Analysis SUSY: stabilizes hierarchy, dark matter, radiative symmetry breaking Charginos SUSY partners of Higgs and EW gauge bosons Charginos/neutralinos at LHC only from gluino/squark decay chains ILC allows for precision measurements at least at per cent-level Measuring their properties helps proving SUSY Important for determination of SUSY dark matter content... and for determination of SUSY-breaking mechanism SPA project For the rest: always SPS1a SUGRA-scenario with m = 7 GeV m 1/2 = 25 GeV tan β = 1 sgn µ = 1 A = 3 GeV Chargino masses and widths: M Γ Γ/M χ GeV.77 GeV.42 χ GeV 3.1 GeV.75 SPS1a -preferred decay (2-step cascade): χ + 1 τ 1ν τ τ + χ 1 ν τ

3 The Born part e + χ + e + 6 e e + χ 1 χ + 1 χ + dσ + d cos θ [fb] (LO) + 4 e γ, χ e νe χ 2 s = 1 TeV / cos θ cos θ angle between e and χ 1 Born helicity amplitudes known analytically Choi et al., , 233 Implemented in narrow width approximation in many programs PYTHIA, Herwig, Isajet, Comphep, Grace,... Full processes in Sherpa, SMadgraph, WHiard No massless t-channel particles neglect m e for phase space to clarify notation σ Born (s) = dγ 2 M Born (s, cos θ) 2

4 Classification of NLO corrections Loop corrections to SUSY production and decay processes nonfactorizable, maximally resonant photon exchange between production and decay real radiation of photons off-shell kinematics for the signal process irreducible background from all other SUSY processes reducible, experimentally indistinguishable SM background processes implemented in Sherpa, Smadgraph, WHiard thoroughly checked Hagiwara et al., 51226; JR et al., Multi-pole approximation, justified from EW SM processes Denner et al., 637, 5263, 6411.

5 Classification of NLO corrections Loop corrections to SUSY production and decay processes nonfactorizable, maximally resonant photon exchange between production and decay real radiation of photons off-shell kinematics for the signal process irreducible background from all other SUSY processes reducible, experimentally indistinguishable SM background processes implemented in Sherpa, Smadgraph, WHiard thoroughly checked Hagiwara et al., 51226; JR et al., Multi-pole approximation, justified from EW SM processes Denner et al., 637, 5263, 6411.

6 Comparison of Automated Tools for Perturbative Interactions in SuperSymmetry cf. e.g. τ + τ X Process status Madgraph/Helas Whizard/O Mega Sherpa/A Megic.5 TeV 2 TeV.5 TeV 2 TeV.5 TeV 2 TeV τ 1 τ (7) 79.63(4) (1) (4) 257.3(1) (4) τ 2 τ (1) 66.86(2) (2) (3) (2) (3) τ 1 τ (3) 19.(1) (3) 19.15(8) (5) 19.(1) ντ ν τ 52.26(7) 272.1(8) 52.27(2) 272.1(1) 52.3(3) 272.1(1) χ 1 χ (2) (1) (9) (1) (1) (1) χ 1 χ (3) 9.894(3) (2) 9.894(4) (3) (5) χ 1 χ (3).7913(1) (1).79136(2) 17.4(1).79137(5) χ 1 χ (4) (3) (6) 1.575(5) 7.141(4) 1.574(8) χ 2 χ (7) (1) (3) (9) (4) (1) χ 2 χ (1) (5) (1) χ 2 χ (7) 2.964(1) (1) χ 3 χ (4) (9).46999(2) χ 3 χ (4) (3) (4) χ 4 χ (2) (5).26437(1) χ + 1 χ (3) 45.15(1) (6) (2) 185.1(1) (2) χ + 2 χ (1) (6) (1) χ + 1 χ (4) (9) (2) h h (3).1242(2).35339(2).12422(3).3534(2) (6) h H.5167(4).51669(3).51671(3) H H.7931(3).7931(6).79311(4) A A.7975(3).79758(6).79744(4) h (3) 3.183(8) (3) 3.182(1) 59.62(3) (2) H (3) 4.671(5) (9) 4.676(3) (1) 4.676(2) A (4) 4.682(5) (9) (3) (2) (2) A h.5143(4).51434(3).5144(3) A H 1.488(2) (9) (8) H + H (6) (2) (3)

7 Classification of NLO corrections Loop corrections to SUSY production and decay processes nonfactorizable, maximally resonant photon exchange between production and decay real radiation of photons off-shell kinematics for the signal process irreducible background from all other SUSY processes reducible, experimentally indistinguishable SM background processes Charginos quite narrow nonfactorizable corrections significantly suppressed be careful: D. Rainwater s talk

8 Virtual Corrections Virtual corrections from SUSY and SM particles: self energies, vertex corrections, box diagrams (as usual) (Semi-)automatized calculation with FeynArts/FormCalc Hahn et al., , 1226, ; Fritzsche, ; Fritzsche/Hollik, 4795 Independent check of numerical results Öller/Eberl/Majerotto, 5419 Regulators: Electron mass me for collinear photon radiation Fictitious photon mass λ for infrared divergencies Interference of Born and virtual corrections σ virt (s, λ 2, m 2 e) = dγ 2 [ 2Re ( MBorn (s) M 1-loop (s, λ 2, m 2 e) )] Eliminate dependence on λ by neglecting power corrections in λ Adding real (1st order) photon radiation with Eγ < E γ Correction (terms log Eγ) is shifted into soft-photon factor

9 Virtual Corrections Virtual corrections from SUSY and SM particles: self energies, vertex corrections, box diagrams (as usual) (Semi-)automatized calculation with FeynArts/FormCalc Hahn et al., , 1226, ; Fritzsche, ; Fritzsche/Hollik, 4795 Independent check of numerical results Öller/Eberl/Majerotto, 5419 Regulators: Electron mass me for collinear photon radiation Fictitious photon mass λ for infrared divergencies Interference of Born and virtual corrections σ virt (s, λ 2, m 2 e) = dγ 2 [ 2Re ( MBorn (s) M 1-loop (s, λ 2, m 2 e) )] Soft-photon factor: f soft = α 2 π i,j = e ±,eχ ± k E γ d 3 k (±)p i p j Q i Q j 2ω k (p i k)(p j k)

10 Real and Collinear Photons Virtual + Soft σ v+s(s, E γ, m 2 e) = h dγ 2 f soft ( Eγ λ ) M Born(s) 2 + 2Re `M Born (s) M 1-loop (s, λ 2, me) i 2 for simulation choose E γ E exp γ Real radiation (i.e. the process e e + χ + 1 χ 1 γ): σ 2 3 (s, E γ, m 2 e) = dγ 3 M 2 3 (s, m 2 e) 2. E γ Total cross section (fixed order): σ tot (s, m 2 e) = σ Born (s) + σ v+s (s, E γ, m 2 e) + σ 2 3 (s, E γ, m 2 e) should not depend on E γ, but power corrections only in σ 2 3, not in σ v+s

11 As usual, split 2 3 cross section: σ 2 3 (s, E γ, m 2 e) = σ hard,non-coll (s, E γ, θ γ )+σ hard,coll (s, E γ, θ γ, m 2 e) x = 1 2E γ / s electron energy fraction after radiation Approximate collinear radiation by convoluting the Born cross section with a structure function σ hard,coll (s, E γ, θ γ, m 2 e) = dγ 3 M 2 3 (s, m 2 e) 2 E γ, θ γ x = dx f(x; θ γ, m2 e s ) dγ 2 M Born (xs, m 2 e) 2. collinear structure functions (helicity conserving and helicity flip): Böhm/Dittmaier, x 2 1 x f + (x) = η 4 f (x) = α 2π (1 x) η := 2α π [ ( ) ] s log 4m 2 ( θ γ ) 2 1 e Cutoff E γ x = 1 2 E γ / s (no power corrections in θ γ )

12 Simulation Combining all parts: σ tot(s, m 2 e ) = dx f eff (x 1, x 2; E γ, θ γ, m2 e s ) + dγ 3 M 2 3(s) 2, Eγ, θγ dγ 2 M eff (s, x 1, x 2; m 2 e ) 2 with f eff (x 1, x 2 ; Eγ, θγ, m2 e s ) = δ(1 x 1 ) δ(1 x 2 ) + δ(1 x 1 ) f(x 2 ; θγ, m2 e s ) θ(x x 2 ) + f(x 1 ; θγ, m2 e s ) δ(1 x 2 ) θ(x x 1 ) M eff (s, x 1, x 2 ; m 2 h e ) 2 = 1 + f soft ( Eγ, λ 2 i ) θ(x 1, x 2 )) M Born (s) 2 + 2Re hm Born (s) M 1-loop (s, λ 2, m 2 i e ) θ(x 1 x )θ(x 2 x ) All corrections defined as a generalized structure function suitable for implementation in an event generator

13 The WHiard/O Mega Generator Generator Kilian/Ohl/JR Level of Complexity: e + e HH W W W W bbjjjjjjjj (12,, diagrams) pp χ 1 χ 1bbbb (32, diagrams, 22 color flows, 1, PS channels) pp V V jj jjllνν incl. anomalous TGC/QGC Current versions: WHiard 1.51 / O Mega.11beta Available from my homepage: Major upgrade this spring/summer: WHiard 2. / O Mega 1. Implemented models: Test models: QED, QCD SM Littlest/Simplest Little Higgs MSSM, NMSSM, extended SUSY models Extra dimensions Noncommutative Standard Model

14 Technical Details and Failure of Approach Generate Born by O Mega, convolute Born with generalized structure function ( user-defined structure function in WHiard) Sampling δ-functions: splitting sampling region [, x] [x, 1] map first region as exactly as possible set x = 1 in the 2nd region (δ-functions) reweighting according to w(x > x ) : w(x < x ) = 1 : x For fixed-order simulation avoid double-counting: f(x 1 < x, x 2 < x ) dx f(x; θ γ, m2 e s ) Numerical agreement: WHiard/O Mega and fixed-order calculation In the soft-photon region: negative event weights 2 2 and 2 3 runs separately Lowering the cutoff from Eγ/ s < 1 2 to E γ/ s < 1 3 : 2 2 NLO becomes negative, compensating the 2 3

15 Resumming photons e e + χ 1 χ + 1 Meff 2 ( + + ) LO e e + χ 1 χ + 1 Meff 2 ( + ++) s = 1 TeV s = 1 TeV E = 1 E = cos θ E = 1 E =.5 LO 1.5 cos θ Experimental resolution drives one into negative weights region Soft-collinear region: E γ < E γ, θ γ < θ γ : double logs α π log E2 γ s log θ γ invalidate perturbative series In that region resummation of all orders is possible σ Born+ISR (s, θ γ, m 2 e) = dx f ISR (x; θ γ, m2 e s ) dγ 2 M Born (xs) 2, f ISR includes all order soft-photon radiation (LLA), hard-collinear up to 3rd order Skrzypek/Jadach, 1991 For collinear photons cancellation of infrared divergencies built in, main source of negative weights removed

16 Matching with NLO Combine ISR-resummed LO with NLO, avoid double-counting Subtract contribution of one soft photon (already in soft-photon factor) f soft,isr ( E γ, θ γ, m 2 e) = η x 2 «dx 4 x 1 x + = η 4 2 ln(1 x ) + x + 1 «2 x2. After this subtraction we have» M f eff (ŝ; E γ, θ γ, m 2 e) 2 = 1 + f soft ( Eγ λ ) 2f soft,isr( E γ, θ γ, m2 e s ) M Born (ŝ) 2 + 2Re ˆM Born (ŝ) M 1-loop (ŝ, λ 2, m 2 e), contains Born, virtual + soft contr. with LL part of virtual and soft-coll. removed New s+v term (contains also soft/coll. corrections to Born/1-loop interference) σ v+s,isr (s, E γ, θ γ, m 2 e) = dx 1 f ISR (x 1 ; θ γ, m2 e s ) dx 2 f ISR (x 2 ; θ γ, m2 e s ) dγ 2 f M eff (ŝ; E γ, θ γ, m 2 e) 2

17 Simulation Resummation approach eliminates problem of negative weights: e e + χ 1 χ + 1 M res eff 2 (-++-) s = 1 TeV LO 1.5 e e + χ 1 χ + 1 M res eff 2 ( + ++) 1.5 LO s = 1 TeV cos θ 1.5 cos θ Only source for negative weights: soft-noncollinear region, does not cause problems Final improvement: convoluting 2 3 part with ISR structur function add 2 4 part σ tot,isr+ (s, m 2 e) = dx 1 f ISR (x 1 ; θ γ, m2 e s ) dγ 2 M f eff (ŝ; E γ, θ γ, m 2 e) E γ,i, θ γ,i dγ 4 M 2 4 (s) 2 dx 2 f ISR (x 2 ; θ γ, m2 e s )! E γ, θ γ dγ 3 M 2 3 (ŝ) 2

18 Choosing Cutoffs Collinear (angular) cutoff Collinear approximation breaks down at θ γ > 1 Higher-order effects for emission angles below.1 Energy cutoff Fixed order/semianalytic agree Small angles: interference term overshoots 5 correction from higher order γ radiation ILC statist. fluctuation: 2.5 E γ.5 GeV e e + χ 1 χ + 1 σtot [fb] s = 1 TeV e e + χ 1 χ + 1 σtot [fb] s = 1 TeV SPS1a LO res sa θγ [ ] Eγ [GeV] LO fix res sa fix

19 Results and Distributions 4 NLO corrections -5% (Xsec max.) 2 LO NLO e e + χ 1 χ + 1 σtot [fb] 2 e e + χ 1 χ + 1 σtot σlo [%] σlo -2% (-1.5%) fixedorder 1 TeV s [GeV] res fix 5 1 s [GeV] 15 Binned distribution of chargino scattering angle Cutoffs: θ γ = 1, E γ = 3 GeV (fixedorder) K-factor approach insufficient e e + χ 1 χ + 1 evt/bin s = 1 TeV L = 1 ab s = 1 TeV 1 L = 1 ab cos θ cos θ 5 e e + χ 1 χ + 1 evt/bin

20 Summary and Outlook Extended WHiard/O Mega: 1st NLO SUSY Monte Carlo Event Generator for the ILC All possible distributions available at NLO Matching of resummed soft-collinear photons and explicit NLO parts avoids negative weights Interface to FeynArts/FormCalc: all MSSM 2 2 processes for ILC available Maybe already part of new version WHiard 2./O Mega 1. Open issues/next step(s): Include chargino decays (work in progress: KKKRRR: Kalinowski/Kilian/Kovaric/JR/Robens/Rolbiecki) Resummation of Coulomb singularity: improved threshold behavior Corresponding LHC processes: More complicated parton shower More complicated matching Stay tuned!

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23 Reshuffling contributions by changing cut-offs Shifting cutoffs changes the type of higher-order contributions lowering cutoffs is not necessarily improvement Focus on O(α 2 ) (real or virtual) correction, Resummation method, 3 different ways for real+virtual photons: (a) Soft approximation (Denner, 1991) coll.+non-coll. soft γs; neglects contributions Eγ s ; (b) ISR (Skrzypek/Jadach, 199), coll. real+virtual γs; assumes k -ordering of P emitted γs, i.e. for j > i: kj > ki, and in n th order: n i=1 k i < kmax, where kmax is fixed (c) exact (hard non-collinear) matrix element M 2 3 Radiation from the same leg: O(α 2 ) ISR O(α) ISR O(α) soft ISR + O(α) ISR O(α) soft j = O(α) j,soft O(α) j,isr Radiation from different legs: O(α) 1,ISR O(α) 2,ISR +O(α) 1,ISR O(α) 2,soft O(α) soft 2,ISR + O(α) 1,soft O(α) soft 1,ISR O(α) 2,ISR. 1 O(α) 2,ISR + O(α) 1,ISR 2 + O(α) 1,ISR O(α) 2,ISR More details: T. Robens, PhD thesis, 26.