HP2.3rd - GGI Florence High Precision for Hard Processes at the LHC ����������������� ����� ����������������������������������� Markus Schulze in collaboration with K. Melnikov
����������������������� events from ≈ 200 k LHC (7 TeV) : σ t � t ≈ 200 pb LHC (7 TeV) with 1 fb #1 vs. Tevatron : σ t � t ≈ 7 pb events from ≈ 30 k Tevatron with 5 fb #1 Markus Schulze, Johns Hopkins University 2/16
������� NLO QCD corrections to production and decay t � t Calculation framework Top quark spin correlations Top quark mass measurements at NLO QCD + [S. Biswas] ������������������������ ��������������������� � Markus Schulze, Johns Hopkins University 2/20
������������������ ����� !������"��# Literature on hadronic top production beyond leading#order is rich: ● stable top quarks: Classic NLO QCD corrections: Beenakker,Dawson,Ellis, Frixione,Meng,Nason,v.Neerven,Schuler,Smith; Czakon,Mitov Threshold resummation & Coulomb corrections: Banfi,Bonciani,Catani,Czakon,Frixione,Kidonakis,Kiyo,Kühn,Laenen,Mangano,Mitov,Moch,Nason,Ridolfi,Steinhause,Sterman,Uwer,Vogt Electroweak corrections: Beenakker,Bernreuther,Fuecker,Denner,Hollik,Kao,Kollar,Kühn,Ladinsky,Mertig,Moretti,Nolten,Ross,Sack,Scharf,Si,Uwer,Wackeroth,Yuan NNLO QCD contributions: Anastasiou,Aybat,Bonciani,Czakon,Ferroglia,Gehrmann,Körner,Langenfeld,Maitre,Merebashvili,Mitov,Moch,Rogal,Studerus,Uwer ● decays of top quarks: Study of non-factorizable corrections: Beenakker,Berends,Chapovsky,Fadin,Khoze,Martin,Melnikov,Yakovlev Factorizable correction to top decays: Czarnecki,Jezabek,Kühn; Bernreuther,Brandenburg,Si,Uwer Spin correlations: Mahlon,Parke; Bernreuther,Brandenburg,Si,Uwer ● event generators: MC@NLO: Frixione,Webber; Laenen,Motylinski,Nason,White POWHEG: Frixione,Nason,Oleari,Ridolfi Markus Schulze, Johns Hopkins University 3/16
������������������ ����� !������"��# Only very recently: NLO QCD corrections to top quark pair production and decay at hadron colliders Bernreuther, Si (2010); Melnikov, M.S. (2009) Top quark decays: leptonic or hadronic decays at NLO � Narrow Width Approximation Γ t m t → 0 neglect non#factorizable corrections Allows for: ● realistic description of the final state ● implementation of arbitrary detector cuts ● accounting for all spin correlations Markus Schulze, Johns Hopkins University 4/16
������������������ �������������$ ℓ + ν b t 1 We calculate M tree = LO helicity amplitudes. 2 � � b t q , q � Generate phase space of top quarks ● Generate phase space of decay particles ● ● u ( p t ) = M ( t → bℓ + ν ) i( p t + m t ) � u ( p t ) � ˜ √ 2 m t Γ t M tree = � u ( p t ) ˜ ● M (12 → � t ) + O ( Γ t ˜ tt ) ˜ v ( p � m t ) Markus Schulze, Johns Hopkins University 5/16
������������������ !�%������������������$ real Production virt Dipole subtraction D -dimensional generalized unitarity with alpha dependence + OPP Markus Schulze, Johns Hopkins University 6/16
������������������ !�%������������������$ real Production virt Dipole subtraction D -dimensional generalized unitarity with alpha dependence + OPP Decay + extra: b B B#meson fragmentation Markus Schulze, Johns Hopkins University 6/16
&�������'����������� ● Measurement of the total cross section t � t The total cross section is claimed to be measured with 5#10% accuracy NLO QCD corrections: typically 10#30% Markus Schulze, Johns Hopkins University 7/16
&�������'����������� ● Measurement of the total cross section t � t The total cross section is claimed to be measured with 5#10% accuracy NLO QCD corrections: typically 10#30% Note: The total cross section is never measured in an experiment σ tot = N ��� � 1 with A = σ ���� σ ��� L A To claim that the total cross section has been measured with NLO accuracy, we need to calculate at NLO QCD. Otherwise, we introduce potential biases. A Markus Schulze, Johns Hopkins University 7/16
● Top quark spin correlations Spins of production and decay mechanism are interlocked t t J=1 J=0 close to threshold: q q � S-wave production g g (L=0) � t � t � leptons preferably parallel � leptons preferably anti-parallel ℓ + ℓ + ℓ − ℓ − Markus Schulze, Johns Hopkins University 8/16
● Top quark spin correlations These effects are only observable for top quarks m ��� spin�flip time ∼ ��� � Γ top Λ � life time Markus Schulze, Johns Hopkins University 9/16
● Top quark spin correlations These effects are only observable for top quarks m ��� spin�flip time ∼ ��� � Γ top Λ � life time So far, only one measurement exists: d � σ 1 d cos φ i d cos φ j = 1 4 (1 − C cos φ i cos φ j ) σ requires boost into top rest frames and specification of a quantization axis C (Tevatron) = 0 . 32 +0 . 55 C (SM theory) = 0 . 78 − 0 . 78 [Bernreuther et..al.] [CDF+D0, 4.3fb -1 ] Markus Schulze, Johns Hopkins University 9/16
Mahlon, Parke: measure lepton opening angle with m t � t < 400 GeV is not an observable m t � t Cut can be applied to the average, <m t � t > Markus Schulze, Johns Hopkins University 10/16
our suggestion: measure lepton opening angle with special cuts on leptons Cuts: 0.38 spin correlated 0.36 p T ,ℓ > 20GeV 0.34 p T , bjet > 25GeV 0.32 d σ 0.3 p T , miss > 40GeV σ d∆ φ ℓℓ 0.28 uncorrelated η ℓ ,η bjet < 2 . 5 0.26 + 0.24 m ℓℓ < 100GeV NLO NLO NLO NLO LHC (7 TeV) 0.22 p T ,ℓ < 50GeV 0 0.5 1 1.5 2 2.5 3 ∆ φ ℓℓ advantage: clean observable, simpler measurement Markus Schulze, Johns Hopkins University 11/16
New ideas (under development): define indicator that is sensitive to spin correlations r |M ���� | � r (Φ) = |M ���� | � + |M ���� | � depends on neutrino momenta which are unobservable Φ integration of over neutrino momenta yields up to 8 solutions r (Φ) r obs = � i r (Φ i ) we calculate , weighted with the cross section r obs for spin correlated and uncorrelated top quarks Markus Schulze, Johns Hopkins University 12/16
preliminary LO result LHC(10TeV) di#leptonic final state with standard acceptance cuts 10 file_LHCc using ($2):(($1)==1?($3)/totLHCc:1/0) file_LHCu using ($2):(($1)==1?($3)/totLHu:1/0) uncorrelated 1 0.1 d( rσ ) σ d r 0.01 spin correlated 0.001 0.0001 1e-05 0 0.2 0.4 0.6 0.8 1 r obs we find similar results for the Tevatron Markus Schulze, Johns Hopkins University 13/16
● Top quark mass measurement at the LHC Target precision is about 1 GeV, dominated by systematics. Clean measurements involve kinematics of top quark decay products. So far, systematics of all those studies were estimated by parton showers whose reliability at this level of precision is questionable. one example: average invariant mass of B#meson and lepton J/Psi decay mode allows for very precise measurements already with 20 fb #1 calculate as a function of <m Bℓ > m top Markus Schulze, Johns Hopkins University 14/16
parton show studies neglect production process t � t deviations in slope lead <m Bℓ > Herwig = 0 . 61 m top − 25 . 31GeV to uncertainty ≈ 3GeV <m Bℓ > Pythia = 0 . 59 m top − 24 . 11GeV uncertanties from scale variations comparable to <m Bℓ > NLO = 0 . 60 m top − 26 . 7GeV expected experimental errors Markus Schulze, Johns Hopkins University 15/16
parton show studies neglect production process t � t deviations in slope lead <m Bℓ > Herwig = 0 . 61 m top − 25 . 31GeV to uncertainty ≈ 3GeV <m Bℓ > Pythia = 0 . 59 m top − 24 . 11GeV uncertanties from scale variations comparable to <m Bℓ > NLO = 0 . 60 m top − 26 . 7GeV expected experimental errors t → b � complete NLO study of pp → t � bℓνjj 84 < m Bℓ > NLO [GeV] <m Bℓ > prod NLO = 0 . 64 m top − 32 . 12GeV 80 ⇒ uncertainty of 1.5 GeV on 76 m top 72 170 172 174 176 178 180 m t [GeV] Markus Schulze, Johns Hopkins University 15/16
(������ ● NLO QCD corrections to production and decay t � t ● important contributions have been neglected in the past ● realistic description of the final state incl. spin correlations is crucial for a precise understanding ● allows for new improved studies of e.g. top mass measurement or spin correlations ● I left out: NLO QCD corrections to production t � t + jet Markus Schulze, Johns Hopkins University 16/16
)%���� Markus Schulze, Johns Hopkins University
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