Transverse-momentum resummation for Drell-Yan lepton pair production at NNLL accuracy Giancarlo Ferrera ferrera@fi.infn.it Universit` a di Firenze In collaboration with: G. Bozzi, S. Catani, D. de Florian & M. Grazzini
Outline Drell-Yan q T distribution and fixed order results 1 Transverse-momentum resummation 2 Resummed results 3 Conclusions and Perspectives 4 Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 2/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions Motivations The study of Drell-Yan lepton pair production is well motivated: Large production rates and clean experimental signatures: Important for detector calibration. Possible use as luminosity monitor. Transverse momentum distributions needed for: Precise prediction for M W . Beyond the Standard Model analysis. Test of perturbative QCD predictions. Constrain for fits of PDFs. Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 3/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions State of the art: fixed order calculations Historically the Drell-Yan process [Drell,Yan(’70)] was the first application of parton model ideas developed for deep inelastic scattering. QCD corrections: Total cross section known up to NNLO ( O ( α 2 S )) [Hamberg,Van Neerven,Matsuura(’91)], [Harlander,Kilgore(’02)] Rapidity distribution known up to NNLO [Anastasiou,Dixon,Melnikov,Petriello(’03)] Fully exclusive NNLO calculation completed [Melnikov,Petriello(’06)], [Catani,Cieri,de Florian,G.F., Grazzini(’09)] Vector boson transverse-momentum distribution known up to NLO ( O ( α 2 S )) [Ellis et al.(’83)],[Arnold,Reno(’89)], [Gonsalves et al.(’89)] Electroweak correction are know at O ( α ) [Dittmaier et al.(’02)],[Baur et al.(’02)] Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 4/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions h 1 ( x 1 ,µ 2 The Drell-Yan q T distribution h 1 ( p 1 ) f a F ) / . . > > > > ℓ 1 V ( M ) a ( x 1 p 1 ) ℓ 2 h 1 ( p 1 ) + h 2 ( p 2 ) → V ( M ) + X → ℓ 1 + ℓ 2 + X σ ˆ ab V = γ ∗ , Z 0 , W ± ℓ 1 ℓ 2 = ℓ + ℓ − , ℓν ℓ where and . . b ( x 2 p 2 ) X . > > > > . According to the QCD factorization theorem: h 2 ( p 2 ) h 2 ( x 2 ,µ 2 f b F ) / Z 1 Z 1 “ Λ 2 d σ F ) d ˆ σ ab ” X h 1 ( x 1 , µ 2 h 2 ( x 2 , µ 2 s ; α S ,µ 2 R ,µ 2 ( q T , M , s )= dx 1 dx 2 f a F ) f b ( q T , M , ˆ F ) + O . / / dq 2 dq 2 M 2 0 0 T T a , b The standard fixed-order QCD perturbative expansions gives: Z ∞ » – d ˆ σ q ¯ q c 12 log 2 ( M 2 / Q 2 M 2 / Q 2 dq T ∼ α S T ) + c 11 log( T ) + c 10 ( Q T ) dq 2 Q 2 T T » – + α 2 c 24 log 4 ( M 2 / Q 2 M 2 / Q 2 + O ( α 3 T ) + · · · + c 21 log( T ) + c 20 ( Q T ) S ) S Fixed order calculation theoretically justified only in the region q T ∼ M V For q T → 0 , α n S log m ( M 2 / q 2 T ) ≫ 1: need for resummation of logarithmic corrections Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 5/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions h 1 ( x 1 ,µ 2 The Drell-Yan q T distribution h 1 ( p 1 ) f a F ) / . . > > > > ℓ 1 V ( M ) a ( x 1 p 1 ) ℓ 2 h 1 ( p 1 ) + h 2 ( p 2 ) → V ( M ) + X → ℓ 1 + ℓ 2 + X σ ˆ ab V = γ ∗ , Z 0 , W ± ℓ 1 ℓ 2 = ℓ + ℓ − , ℓν ℓ where and . . b ( x 2 p 2 ) X . > > > > . According to the QCD factorization theorem: h 2 ( p 2 ) h 2 ( x 2 ,µ 2 f b F ) / Z 1 Z 1 “ Λ 2 d σ F ) d ˆ σ ab ” X h 1 ( x 1 , µ 2 h 2 ( x 2 , µ 2 s ; α S ,µ 2 R ,µ 2 ( q T , M , s )= dx 1 dx 2 f a F ) f b ( q T , M , ˆ F ) + O . / / dq 2 dq 2 M 2 0 0 T T a , b The standard fixed-order QCD perturbative expansions gives: Z ∞ » – d ˆ σ q ¯ q c 12 log 2 ( M 2 / Q 2 M 2 / Q 2 dq T ∼ α S T ) + c 11 log( T ) + c 10 ( Q T ) dq 2 Q 2 T T » – + α 2 c 24 log 4 ( M 2 / Q 2 M 2 / Q 2 + O ( α 3 T ) + · · · + c 21 log( T ) + c 20 ( Q T ) S ) S Fixed order calculation theoretically justified only in the region q T ∼ M V For q T → 0 , α n S log m ( M 2 / q 2 T ) ≫ 1: need for resummation of logarithmic corrections Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 5/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions h 1 ( x 1 ,µ 2 The Drell-Yan q T distribution h 1 ( p 1 ) f a F ) / . . > > > > ℓ 1 V ( M ) a ( x 1 p 1 ) ℓ 2 h 1 ( p 1 ) + h 2 ( p 2 ) → V ( M ) + X → ℓ 1 + ℓ 2 + X σ ˆ ab V = γ ∗ , Z 0 , W ± ℓ 1 ℓ 2 = ℓ + ℓ − , ℓν ℓ where and . . b ( x 2 p 2 ) X . > > > > . According to the QCD factorization theorem: h 2 ( p 2 ) h 2 ( x 2 ,µ 2 f b F ) / Z 1 Z 1 “ Λ 2 d σ F ) d ˆ σ ab ” X h 1 ( x 1 , µ 2 h 2 ( x 2 , µ 2 s ; α S ,µ 2 R ,µ 2 ( q T , M , s )= dx 1 dx 2 f a F ) f b ( q T , M , ˆ F ) + O . / / dq 2 dq 2 M 2 0 0 T T a , b The standard fixed-order QCD perturbative expansions gives: Z ∞ » – d ˆ σ q ¯ q c 12 log 2 ( M 2 / Q 2 M 2 / Q 2 dq T ∼ α S T ) + c 11 log( T ) + c 10 ( Q T ) dq 2 Q 2 T T » – + α 2 c 24 log 4 ( M 2 / Q 2 M 2 / Q 2 + O ( α 3 T ) + · · · + c 21 log( T ) + c 20 ( Q T ) S ) S Fixed order calculation theoretically justified only in the region q T ∼ M V For q T → 0 , α n S log m ( M 2 / q 2 T ) ≫ 1: need for resummation of logarithmic corrections Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 5/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions h 1 ( x 1 ,µ 2 The Drell-Yan q T distribution h 1 ( p 1 ) f a F ) / . . > > > > ℓ 1 V ( M ) a ( x 1 p 1 ) ℓ 2 h 1 ( p 1 ) + h 2 ( p 2 ) → V ( M ) + X → ℓ 1 + ℓ 2 + X σ ˆ ab V = γ ∗ , Z 0 , W ± ℓ 1 ℓ 2 = ℓ + ℓ − , ℓν ℓ where and . . b ( x 2 p 2 ) X . > > > > . According to the QCD factorization theorem: h 2 ( p 2 ) h 2 ( x 2 ,µ 2 f b F ) / Z 1 Z 1 “ Λ 2 d σ F ) d ˆ σ ab ” X h 1 ( x 1 , µ 2 h 2 ( x 2 , µ 2 s ; α S ,µ 2 R ,µ 2 ( q T , M , s )= dx 1 dx 2 f a F ) f b ( q T , M , ˆ F ) + O . / / dq 2 dq 2 M 2 0 0 T T a , b The standard fixed-order QCD perturbative expansions gives: Z ∞ » – d ˆ σ q ¯ q c 12 log 2 ( M 2 / Q 2 M 2 / Q 2 dq T ∼ α S T ) + c 11 log( T ) + c 10 ( Q T ) dq 2 Q 2 T T » – + α 2 c 24 log 4 ( M 2 / Q 2 M 2 / Q 2 + O ( α 3 T ) + · · · + c 21 log( T ) + c 20 ( Q T ) S ) S Fixed order calculation theoretically justified only in the region q T ∼ M V For q T → 0 , α n S log m ( M 2 / q 2 T ) ≫ 1: need for resummation of logarithmic corrections Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 5/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions Fixed order results: q T spectrum of Drell-Yan l + l − pairs at √ s = 1 . 96 TeV D0 data normalized to 1: [D0 Coll.(’08,’10)] Factorization and renormalization scale variations: µ F = µ R = m Z , m Z / 2 ≤ µ F , µ R ≤ 2 m Z , 1 / 2 ≤ µ F /µ R ≤ 2. LO and NLO scale variations bands overlap only for q T > 60 GeV Good agreement between NLO results and data up to q T ∼ 20 GeV . < 20 GeV ) LO and In the small q T region ( q T ∼ NLO result diverges to + ∞ and −∞ (accidental partial agreement at q T ∼ 5 − 7 GeV ): need for resummation. < 20 GeV ) effects of soft-gluon resummation are essential In the small q T region ( q T ∼ At Tevatron 90% of the W ± and Z 0 are produced with q T ∼ < 20 GeV Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 6/16
Drell-Yan q T distribution q T resummation Resummed results Conclusions Fixed order results: q T spectrum of Drell-Yan l + l − pairs at √ s = 1 . 96 TeV D0 data normalized to 1: [D0 Coll.(’08,’10)] Factorization and renormalization scale variations: µ F = µ R = m Z , m Z / 2 ≤ µ F , µ R ≤ 2 m Z , 1 / 2 ≤ µ F /µ R ≤ 2. LO and NLO scale variations bands overlap only for q T > 60 GeV Good agreement between NLO results and data up to q T ∼ 20 GeV . < 20 GeV ) LO and In the small q T region ( q T ∼ NLO result diverges to + ∞ and −∞ (accidental partial agreement at q T ∼ 5 − 7 GeV ): need for resummation. < 20 GeV ) effects of soft-gluon resummation are essential In the small q T region ( q T ∼ At Tevatron 90% of the W ± and Z 0 are produced with q T ∼ < 20 GeV Giancarlo Ferrera – Universit` a di Firenze HP2.3 Florence – 16/9/2010 Transverse-momentum resummation for DY at NNLL accuracy 6/16
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