igher order correcions o producion Nikolaos Kidonakis (Kennesaw Sae Universiy) producion channels igher-order correcions Charged is producion a he LC N. Kidonakis, c arged 008, Uppsala, Sepember 008
Charged is: sure sign of new physics (MSSM or oher DM) LC has good poenial for discovery Producion processes bg Zhu ( 0) [NLO QCD]; Belyaev, Garcia, Guasch, Sola ( 0, 0) [-loop SUSY]; ( b ) Plehn ( 0) [NLO QCD+SUSY]; Berger, an, Jiang, Plehn ( 03) [NLO QCD+SUSY]; Jin, Li, Oakes, Zhu ( 99) [Yukawa], ( 00) [SUSY elecroweak]; Alwall, Rahsman ( 04) [maching]; Kidonakis ( 04) [sof-gluons, approx NNLO], ( 05) [approx NNNLO] W Barrienos e al ( 98, 00); Brein, ollik, Kanemura ( 00) [quark, squark loops]; b b W ollik, Zhu ( 0); Gao, Li, Li ( 07) [NLO QCD] Eriksson, esselbach, Rahsman ( 06) [decays of, W ] Jiang e al ( 97); Krause, Plehn, Spira, Zerwas ( 97); Brein, ollik ( 99) [LO loops] b b ou e al ( 05) [NLO]; Alves, Plehn ( 05) [NLO] b b Morei, Rahsman ( 03) [LO] qq qqv V qq Morei ( 0) [LO] N. Kidonakis, c arged 008, Uppsala, Sepember 008
Associaed and op quark producion LO: bg b b b g g Born cross secion αα s m b an β m co β use MS m b in he coupling; m b 0 elsewhere N. Kidonakis, c arged 008, Uppsala, Sepember 008 3
Associaed and op quark producion NLO: bg (virual correcions) bg g b q q b bq q b q q bb b b b b QCD correcions large Reduced scale dependence SUSY correcions significan Issues: boom paron disribuion gluon spliing o b b in collinear approximaion valid for small b-quark p T N. Kidonakis, c arged 008, Uppsala, Sepember 008 4
b g g b b b g b g b Maching [Alwall, Rahsman] Find reliable descripion for all b-quark p T large p T : use marix elemens small p T : use paron showers simple adding gives double couning for small p T N. Kidonakis, c arged 008, Uppsala, Sepember 008 5
bg resums large logarihms α s ln µ F /m b n for small p T 3 process described by gluon spliing imes marix elemen of process b ougoing b-quark described by 3 marix elemen for large p T Mach analyic double-couning subracion erm: σ σ σ 3 σdc [Alwall, Rahsman] can be implemened in even generaors (PYTIA, ERWIG) smooh differenial disribuions N. Kidonakis, c arged 008, Uppsala, Sepember 008 6
Producion near hreshold b p b Define s g p g p b p g p, p b p p, u p g p and s 4 s u m m A hreshold s 4 Sof correcions 0 ln l s 4 /m s 4 Near hreshold sof correcions are dominan and provide excellen approximaions o he full cross secion For he order α n s correcions l LL: l=n- NLL: l=n- n Calculae NLO and NNLO correcions a NLL accuracy The hadronic cross secion σ f dx dx φ f /p x, µ F φ f / p x, µ F ˆσ s,, u, µ F, µ R, α s N. Kidonakis, c arged 008, Uppsala, Sepember 008 7
Resummed cross secion Resummaion follows from facorizaion properies of he cross secion - performed in momen space where ˆσ res N exp S f i f j exp i α s i E f i s N i dµ µ R µ β Ñ s exp exp α s µ s i s/ñ f i f j s dµ µ F µ γ i/i α s µ R dµ µ ReΓ f i f j S α s N i, α s µ µ i E f i N i i C i dz zn i 0 z z dλ λ α s λs π αs π z s α s C i C F N c / N c, B q 3C F /4 for quarks; C i C A N c, B g β 0 /4 for gluons Γ S is he sof anomalous dimension - a marix in color space Γ S C F ln m m s CA ln u m m CA iπ N. Kidonakis, c arged 008, Uppsala, Sepember 008 8
NNNLO expansions of resummed cross secion Inver back o momenum space and expand o arbirary order NLO sof gluon correcions ˆσ F B α s µ R π c 3 ln s 4 /m s 4 c s 4 c µ δ s 4 wih c 3 C F C A NNLO sof gluon correcions ˆσ F B α s µ R π c 3 ln 3 s 4 /m s 4 3 c 3 c β 0 4 c 3 ln s 4 /m s 4 NNNLO sof gluon correcions ˆσ 3 F B α3 s µ R π 3 8 c3 3 ln 5 s 4 /m s 4 5 8 c 3 c 5 4 β 0 c 3 ln 4 s 4 /m s 4 N. Kidonakis, c arged 008, Uppsala, Sepember 008 9
Charged is producion a he LC bg --> - a LC S / =4 TeV µ=m -+m bg --> - a LC S / =4 TeV µ=m -+m, (m -+m )/.8.4.7.6 NLO-exac/LO NLO-NLL/LO NLO-NLL/NLO-exac.3 Born NLO-NLL NNLO-NLL K-facor.5.4.3 σ(µ) / σ(m -).... 0.9 00 400 600 800 000 m - (GeV) 0.8 00 400 600 800 000 m - (GeV) various choices of cenral scale in he lieraure N. Kidonakis, c arged 008, Uppsala, Sepember 008 0
bg --> - a LC S / =4 TeV anβ=30 µ=m - bg --> - a LC S / =4 TeV µ=m - LO NLO-NLL NNLO-NLL NNNLO-NLL.8 NLO-NLL / LO NNLO-NLL / LO NNNLO-NLL/LO σ (pb) 0. 0.0 K-facor.6.4. 0.00 00 400 600 800 000 m - (GeV) 00 400 600 800 000 m - (GeV) K facors Mass (GeV) NNLO-NLL NNNLO-NLL 00.34.47 300.43.53 400.49.59 500.53.65 600.57.69 700.60.7 800.63.75 900.66.79 000.68.8 N. Kidonakis, c arged 008, Uppsala, Sepember 008
Scale dependence of he cross secion bg --> - a LC S / =4 TeV anβ=30 µ=m -/, m - bg --> - a LC S / =4 TeV anβ=30 m -=500 GeV LO NLO-NLL NNLO-NLL NNNLO-NLL 0. 0.5 LO NLO-NLL NNLO-NLL NNNLO-NLL 0. σ (pb) σ (pb) 0. 0.0 0.05 0.00 00 400 600 800 000 m - (GeV) 0 0. 0 µ / m - Reduced scale dependence over large range of scale 0. µ/m 0 σ max /σ min 3.39.50.38.3 LO NLO-NLL NNLO-NLL NNNLO-NLL N. Kidonakis, c arged 008, Uppsala, Sepember 008
Dependence of he cross secion on an β and op quark mass bg --> - a LC S / =4 TeV µ=m -=500 GeV bg --> - a LC S / =4 TeV anβ=30 µ=m -=500 GeV 0. Born NLO-NLL NNLO-NLL NNNLO-NLL 0.5 Born NLO-NLL NNLO-NLL NNNLO-NLL σ (pb) 0. σ (pb) 0. 0.05 0.0 0 0 0 30 40 50 an β 0 50 60 70 80 90 00 m (GeV) an β shape same for all curves Mild m dependence N. Kidonakis, c arged 008, Uppsala, Sepember 008 3
Associaed and W producion, b b W b b h 0, 0 b W b W σ (fb) 0 3 0 0 an β=50 an β=0 BR( ± ) τν 0 - an β=50 an β=0 0-00 400 600 800 000 m ± (GeV) 0-00 400 600 800 000 m ± (GeV) Eriksson, esselbach, Rahsman ( 06) N. Kidonakis, c arged 008, Uppsala, Sepember 008 4
Associaed pair producion 0 anβ = 30 pp + σ o [fb] anβ =.5 0 pp + σ o [fb] m = 00 GeV + s = 4TeV 0 - anβ = 6 oal cross secion wihou riangle conribuion 0-0 - 00 50 00 50 300 350 400 m + [GeV] 3 4 5 6 7 8 0 0 30 40 anβ Krause, Plehn, Spira, Zerwas ( 97) N. Kidonakis, c arged 008, Uppsala, Sepember 008 5
Associaed pair producion b b 0 qq,sum σ o,bb (pp + ) [fb] anβ = 0 0 sum qq σ o,bb (pp + ) [fb] anβ = 0 0 - bb 0 - bb 0-00 50 300 350 400 450 500 m [GeV] 00 50 300 350 400 450 500 m [GeV] 0 0 - sum qq bb σ o,bb (pp + ) [fb] anβ = 30 0 0 0 - sum qq bb σ o,bb (pp + ) [fb] anβ = 50 00 50 300 350 400 450 500 m [GeV] 00 50 300 350 400 450 500 m [GeV] Alves, Plehn ( 05) N. Kidonakis, c arged 008, Uppsala, Sepember 008 6
b b dominan pair producion mode a large an β relevan for riple-is couplings consider signaure: 4 b-jes + q-jes+ τ +p miss T Morei, Rahsman ( 03) N. Kidonakis, c arged 008, Uppsala, Sepember 008 7
Summary Several producion processes for a he LC NLO QCD and SUSY correcions bg, b a he LC - maching bg Sof and collinear correcions hrough NNNLO bg Large K facors -reduced scale dependence Associaed producion wih a W Charged is pair producion N. Kidonakis, c arged 008, Uppsala, Sepember 008 8