Charge Asymmetry in Production t t and Threshold Resummation - PowerPoint PPT Presentation

Charge Asymmetry in Production t ¯ t and Threshold Resummation Leandro G. Almeida YITP , Stony Brook University LGA, G. Sterman, W. Vogelsang :: arXiv:0805.1885 [hep-ph] Pheno 09

Outline Charge Asymmetry in QCD Threshold Resummation in t ¯ t Production Threshold Behavior of Charge Asym. Charge Asymmetry at LHC vs TeVatron Threshold Resummation at fixed Pair Rapidity

Charge Asymmetry in QCD � d 2 � H A H B ! t � t d cos � � d 2 � H A H B ! � tX ttX d � � t d cos � � 1 � ; dM 2 dM 2 dM 2 t d cos � 2 t � t � t � � d 2 � H A H B ! t � t d cos � þ d 2 � H A H B ! � tX ttX d � t d cos � � 1 � � ; dM 2 dM 2 dM 2 t d cos � 2 t � t � t � angle of top with proton in partonic cms Inclusive Asymmetry t ; cos � Þ � d � � Differential: A c ð M 2 t � d � � dXd ∆ σ Total: A T = � dXd ¯ σ Exclusive Asymmetry t ¯ Opposite sign to inclusive tj 1 · · · j n (S. Dittmaier, P . Uwer and S. Weinzierl)

Contributions to Asymmetric x-section (Kuhn, Rodrigo) (M. T. Bowen, S. D. Ellis and D. Rainwater) + flavour excitation 1 xsec contributions ~ 2 3 cos θ 16 d abc � s At Tevatron lead to sizable Forward Backward Asymmetry Incl. Asym. measured at CDF/D0: 0 . 24 ± 0 . 13 / 0 . 12 ± 0 . 08 SM ~ 0.08 Resum. ~1%

Threshold Corrections in t ¯ t Production X Z Z d 2 � H A H B ! t � tX d 2 ^ Z 1 Z 1 � ; cos � ; � 2 =s Þ � ab ð ^ � 1 X 0 dx b f H A a ð x a ; � 2 Þ f H B b ð x b ; � 2 Þ t d cos � ¼ 0 dx a ; dM 2 s d ^ � d cos � t � ab (Kidonakis, Sterman) τ = M 2 partonic threshold thus, t ¯ t τ → 1 ˆ ˆ s ˆ mis-cancelations will lead to large logarithmic corrections. At , one finds: α 3 � s � d 2 ^ � NLO q ð ^ � ; cos � Þ � log ð 1 � ^ � Þ 1 � � � q � ¼ C 1 ð � Þ � ð 1 � ^ � Þ þ C 2 ð � Þ þ C 3 ð � Þ þ . . . d ^ � d cos � 1 � ^ � 1 � ^ � þ þ � �

Resummation of threshold logarithms d 2 � Z 1 d � N Mellin moment space: 0 d �� N � 1 � d � d cos � : d cos � d � N X x-section factors f H A ;N ð � 2 Þ f H B ;N ð � 2 Þ ^ ¼ � ab ð N; � Þ ; a b d cos � ab � N � 1 d 2 ^ Z 1 � ab ð ^ � ; cos � Þ � ab ð N; � Þ ¼ 0 d ^ ^ � ^ d ^ � d cos � Resumm. can be schematically written ð Þ ð Þ ð Þ f ð � ð res Þ ab ð N; � Þ ¼ C ab ð � Þ � a ð N Þ � b ð N Þ Tr f H ð 0 Þ � ½ S ab ð N; � Þ� y S ð 0 Þ ab ð � Þ ab S ab ð N; � Þ g ; ^ � � 1 + β cos θ (8 C F − 3 C A ) ln(1 − 2 λ ) e − CA σ (Born) 2 π b 0 ln(1 − 2 λ ) ( θ ) ( ∆ q ( N )) 2 ) = ˆ q ¯ q π b 0

t Dependence M 2 √ p ¯ p @ S = 1 . 8 TeV t ¯

t Dependence of Charge Asymmetry M 2 THRESHOLD RESUMMATION FOR THE TOP QUARK . . . t ¯ At high gg fusion is suppressed and CA increases M 2 t ¯ t

Scale Dependence:

pp VS p ¯ p @ LHC, Total FB Asymmetry Vanishes However, the charge asymmetry in QCD still leads to the same sign asym. (Kuhn, Rodrigo) More work needed to perform threshold resummation in this regime.

Summary Charge Asymmetry in tt production robust with respect to higher orders generated by threshold resummation Charge Asymmetries from QCD increase with At LHC, need increased information on tops to exploit differences in top distributions.