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Threshold resummation for top pair associated W boson production at Hardron Colliders
Hai Tai Li
Institute of Theoretical Physics , Peking UniversityIn collaboration With C. S. Li, S. A. Li
2014 TeV workshop, Sun Yat-sen University, Guang ZhouMay 16 2014
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Associated top quark pair production
associated production production:
These processes are:
Important for direct measurements of and couplings As background to new physics searches such as , same sign
leptons……
In this talk, we concentrate on the production of .
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Associated top quark pair production
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CMS Collaboration 2013
The measurements at 7TeV LHC pb pb
Performed by a trilepton analysis of ttZ events and a same-sign dilepton analysis of ttV events
Current events samples are small and the LHC will produce sufficiently large samples in the future.
The measurement of production
The predictions at 7TeV LHC pb pb
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Fixed order results
The total cross section, V.Hrischi, et al. 2011 Production and decay at NLO, J.M Campbel etal. 2012
The total cross section for production
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How to improve the predictions Theroetical results
LO NLO NNLO NNNLOLLNLLNNLLNNNLL…
The Logarithmical enhancement comes from:
logarithms of ultra-violet (UV) originlogarithms of collinear originlogarithms of soft origin
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What are going to be resummed
Threshold definition: ,
Large logarithms:
Due to the fall-off of the parton distribution functions, threshold resummation can be justified even if
the invariant mass of top pair and W
In this case real gluon emission is soft.
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Factorization Formulla
𝝁𝒉
𝝁𝒔
𝝁
The partonic corss section is
The RG equarions
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The Soft Fucntions
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How to obtain the Hard FucntionsThe virtual corrections can be generated by MadLoop (V.Hrischi, et al. 2011 ), where ‘t hooft Velteman dimensional regularization scheme was adopted. However, the results in conventional
regularization scheme are needed
‘t hooft Velteman dimensional regularization
conventional regularization scheme
Kunszt et al, 1993
Comparing in ‘t hooft Velteman scheme to that in the conventional scheme, only the functions are different.
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How to Check Hard Fucntions
The Divergence in the hard functions
The scale dependence terms in the Hard fucntion
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Expansion to fixed order
Resumed hard-scattering kernels is
Set
𝑪 (𝒛 ,𝝁 𝒇 )𝑵𝑳𝑶𝒍𝒆𝒂𝒅𝒊𝒏𝒈
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The Scale Settings
The results are more stable in the range .We set the default hard scale at .
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The Scale Settings
We set the scale at the exact position where one-loop correction is minimal
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The resummation resultsThe NNLL distributions for the invariant mass of top pair and W boson
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The resummation results
Total Cross section for production
Total Cross section for production
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Summary and OutLook
Derive the factorization formula for the and production
Calculate the soft functions at NLO
Pergorm the NNLL resummation for the and production. The results reduce the scale dependence
This formula can be directly used for , and .
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Thanks for your attention !
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Back up
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Power corrections 8TeV LHCmuf 1 2 0.5
qqb channel 8.67 8.69 7.7
tota 12.23 9.56 16.00
Power corrections 13TeV LHCmuf 1 2 0.5
qqb channel 21.66 22.85 17.4
tota 45.28 34.38 60.89
𝒕 𝒕𝑾 +¿ ¿