ir-improved dglap-cs parton shower effects in w+n jets
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PoS(ICHEP2016)1144
IR-Improved DGLAP-CS Parton Shower Effects inW+n Jets
B. Shakerin∗
Baylor UniversityE-mail: Bahram_Shakerin@Baylor.edu
B.F.L. WardBaylor UniversityE-mail: BFL_Ward@Baylor.edu
We use recently introduced MC realizations of IR-improved DGLAP-CS parton showers to studythe attendant improvement effects in W+n jets at the LHC in the MG5_aMC@NLO frameworkfor the exact O(αs) corrections.
38th International Conference on High Energy Physics3-10 August 2016Chicago, USA
∗Speaker.
c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/
PoS(ICHEP2016)1144
IR-Improved DGLAP-CS Parton Shower B. Shakerin
1. Theoretical Background
One can show that it is possible to improve the infrared aspects of the standard treatment ofthe DGLAP-CS evolution theory to take into account a large class of higher-order corrections thatsignificantly improve the precision of the theory for any given level of fixed-order calculation of itsrespective kernels.
1.1 QCD
Using equation (1) restricted to QCD allows us to improve in the IR regime the kernels inDGLAP-CS theory.
1.2 QCED=QED⊗QCD
QED and electroweak (EW) are handled by the simultaneous resummation of QED and QCDinfrared effects, QED⊗QCD resummation in the presence of parton showers.
2. HERWIRI1.031
Implementation of the new IR-improved kernels, equations (2-5) in the poster, in the frame-work of HERWIG6.5 results the new IR-improved parton shower MC HERWIRI1.031.
3. Methods
We use a computer program, MadGraph5_aMC@NLO, capable of computations of tree-leveland next-to-leading order cross sections, of their matching parton shower simulations, and of themerging of matched samples that differ by light-parton multiplicity.
4. Results
The events generated in the previous section are showered by HERWIG6 and HERWIRI1.031and histograms for Emiss
T , PLeptonT distribution and PW±
T distribution are presented for√
s = 7,8TeV. It is to be noted that there are, in general, differences between HERWIG6 and the exact IR-improved DGLAP-CS theory, HERWIRI1.031, in our distributions.
5. Conclusion and Future Work
Missing Transverse energy, EmissT , is used to study the non-detectable particles such as standard
model neutrino or particles do not interact with the detector such as light supersymmetric particles,Where
MET = /ET = |~/ET | and ~/ET =− ∑i ∈ tracks
~pT (i) (5.1)
for massless particles. The transverse momentum distribution of heavy particles has different ap-plications. Firstly, it is an important test of perturbative QCD. Secondly, it is central to the precisemeasurement of the W boson mass. In future work, we will compare our results with the availableLHC data and discuss the corresponding phenomenological implications.
1
PoS(ICHEP2016)1144
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One can prove that exact, amplitude-based resummation allows IR-improvement of the
usual DGLAP-CS theory. This results in a new set of kernels, parton distributions and
attendant reduced cross sections, so that the QCD perturbative result for the respective
hadron-hadron or lepton-hadron cross section is unchanged order-by-order in 𝛼𝑠 at large
squared-momentum transfer. Refs .[3,4]
We can repeat the analogous arguments of Refs. [1,2], following the corresponding
steps for 𝑆𝑄𝐶𝐷 to get the “YFS-like” result as follows
QCD:
𝑑𝜎 𝑒𝑥𝑝 = 𝑑𝜎 𝑛 = 𝑒𝑆𝑈𝑀𝐼𝑅(𝑄𝐶𝐷) 1
𝑛!
𝑑3𝑘𝑗
𝑘𝑗0
𝑑4 𝑦
(2𝜋)4 𝑒𝑖𝑦.(𝑝1+ 𝑞1 −𝑝2 −𝑞2 − 𝑘𝑗)+ 𝐷𝑄𝐶𝐷 ∗ 𝛽
𝑛 (𝑘1, … , 𝑘𝑛)𝑑3𝑝2
𝑝20
𝑑3𝑞2
𝑞20
𝑛
𝑗=1
∞
𝑛=0𝑛
(1)
With 𝑆𝑈𝑀𝐼𝑅 𝑄𝐶𝐷 = 2𝛼𝑠 𝑅𝑒 𝐵𝑄𝐶𝐷 + 2𝛼𝑠 𝐵 𝑄𝐶𝐷 𝐾𝑚𝑎𝑥 ,
2𝛼𝑠 𝐵 𝑄𝐶𝐷 𝐾𝑚𝑎𝑥 = 𝑑3𝑘
𝑘0 𝑆 𝑄𝐶𝐷 𝑘 𝜃 𝐾𝑚𝑎𝑥 − 𝑘 ,
𝐷𝑄𝐶𝐷 = 𝑑3𝑘
𝑘 𝑆 𝑄𝐶𝐷 𝑘 𝑒−𝑖𝑦.𝑘 − 𝜃 𝐾𝑚𝑎𝑥 − 𝑘 ,
1
2𝛽
0 = 𝑑𝜎(1−𝑙𝑜𝑜𝑝) − 2𝛼𝑠 𝑅𝑒 𝐵𝑄𝐶𝐷 𝑑𝜎𝐵,
1
2 𝛽
1 = 𝑑𝜎𝐵1 − 𝑆 𝑄𝐶𝐷 𝑘 𝑑𝜎𝐵, … ,
Where the 𝛽 𝑛 are the QCD hard gluon residuals defined above; they are the non-
Abelian analogs of the hard photon residuals defined by YFS.
DGLAP-CS IR-improved Kernels:
• 𝑃𝑞𝑞𝑒𝑥𝑝
𝑧 = 𝐶𝐹 𝐹𝑌𝐹𝑆 𝛾𝑞 𝑒1
2𝛿𝑞
1+𝑧2
1−𝑧 (1 − 𝑧)𝛾𝑞 −𝑓𝑞(𝛾𝑞)𝛿(1 − 𝑧) (2)
• 𝑃𝐺𝑞𝑒𝑥𝑝
𝑧 = 𝐶𝐹 𝐹𝑌𝐹𝑆 𝛾𝑞 𝑒1
2𝛿𝑞
1+ (1−𝑧)2
𝑧 𝑧𝛾𝑞 (3)
• 𝑃𝑞𝐺𝑒𝑥𝑝
𝑧 = 𝐹𝑌𝐹𝑆(𝛾𝐺)𝑒1
2𝛿𝐺 1
2(𝑧2(1 − 𝑧)𝛾𝐺+ 1 − 𝑧 2𝑧𝛾𝐺) (4)
• 𝑃𝐺𝐺𝑒𝑥𝑝
𝑧 =
𝐶𝐺 𝐹𝑌𝐹𝑆 𝛾𝐺 𝑒1
2𝛿𝐺 1−𝑧
𝑧𝑧𝛾𝐺 +
𝑧
1−𝑧(1 − 𝑧)𝛾𝐺+
1
2(𝑧1+𝛾𝐺 1 − 𝑧 + 𝑧 1 − 𝑧 1+𝛾𝐺 − 𝑓𝐺(𝛾𝐺)𝛿(1 − 𝑧)
(5)
Where
𝛾𝑞 = 𝐶𝐹
𝛼𝑠
𝜋=
4𝐶𝐹
𝛽0 , 𝛿𝑞 =
𝛾𝑞
2+
𝐶𝐹𝛼𝑠
𝜋
𝜋2
3−
1
2 , 𝐹𝑌𝐹𝑆 =
exp (−𝐶𝐸𝛾𝑞)
Γ(1 + 𝛾𝑞) , 𝛽0 = 11 −
2
3𝑛𝑓, 𝛾𝐺 = 𝐶𝐺
𝛼𝑠
𝜋𝑡 =
4𝐶𝐺
𝛽0,
𝛿𝐺 =𝛾𝐺
2+
𝛼𝑠𝐶𝐺
𝜋
𝜋2
2−
1
2, 𝑓𝑞 𝛾𝑞 , 𝑓𝐺 𝛾𝐺 𝑎𝑟𝑒 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑠
QCED: 𝑸𝑬𝑫 ⊗ 𝑸𝑪𝑫
Following the discussion in Refs. [1,3,4,5], wherein we have derived the following
expression for the hard cross sections in the SM 𝑆𝑈2𝐿 × 𝑈1 × 𝑆𝑈3𝑐 EW-QCD theory:
𝑑𝜎 𝑒𝑥𝑝 =
𝑒𝑆𝑈𝑀𝐼𝑅(𝑄𝐶𝐷) 1
𝑛!𝑚!
𝑑3𝑘𝑗1
𝑘𝑗1
𝑛𝑗1=1
𝑑3𝑘𝑗2
′
𝑘𝑗2′
𝑑4𝑦
(2𝜋)4 𝑒𝑖𝑦. 𝑝1+𝑞1−𝑝2−𝑞2− 𝑘𝑗1− 𝑘𝑗2
′ +𝐷𝑄𝐶𝐸𝐷𝑚𝑗2=1 ∞
𝑛,𝑚=0
𝛽 𝑛,𝑚 𝑘1, … , 𝑘𝑛; 𝑘1
′ , … , 𝑘𝑚′ 𝑑3𝑝2
𝑝20
𝑑3𝑞2
𝑞20 , (6)
Where the new YFS-style [1] residuals 𝛽 𝑛,𝑚 𝑘1, … , 𝑘𝑛; 𝑘1
′ , … , 𝑘𝑚′ have n hard gluons
and m hard photons.
With
𝑆𝑈𝑀𝐼𝑅 𝑄𝐶𝐸𝐷 = 2𝛼𝑠𝑅𝑒 𝐵𝑄𝐶𝐸𝐷𝑛𝑙𝑠 + 2𝛼𝑠𝐵 𝑄𝐶𝐸𝐷
𝑛𝑙𝑠
𝐷𝑄𝐶𝐸𝐷 = 𝑑3𝑘
𝑘0 𝑒−𝑖𝑘𝑦 − 𝜃 𝐾𝑚𝑎𝑥 − 𝑘0 𝑆 𝑄𝐶𝐸𝐷
𝑛𝑙𝑠
Where 𝐾𝑚𝑎𝑥 is “dummy” , “nls” ≡ DGLAP-CS synthesization and
𝐵𝑄𝐶𝐸𝐷𝑛𝑙𝑠 ≡ 𝐵𝑄𝐶𝐷
𝑛𝑙𝑠 + 𝛼
𝛼𝑠𝐵𝑄𝐸𝐷
𝑛𝑙𝑠 ,
𝐵 𝑄𝐶𝐸𝐷𝑛𝑙𝑠 ≡ 𝐵 𝑄𝐶𝐷
𝑛𝑙𝑠 + 𝛼
𝛼𝑠𝐵 𝑄𝐸𝐷
𝑛𝑙𝑠 ,
𝑆 𝑄𝐶𝐸𝐷𝑛𝑙𝑠 ≡ 𝑆 𝑄𝐶𝐷
𝑛𝑙𝑠 + 𝑆 𝑄𝐸𝐷𝑛𝑙𝑠 .
Theoretical Background
By implementing the new IR-improved Dokshitzer-Gribov-Lipatov-Atarelli-Parisi-
Callan-Symanzik (DGLAP-CS) kernels in the HERWIG6.5 environment one can
generate a new Monte Carlo (MC), HERWIRI1.0(31), for hadron-hadron scattering at
high energies. Refs. [2-7],[8]
HERWIRI 1.031
Results
1- Using mg5_aMC@NLO to generate the following processes:
• p p > l+ vl j j [QCD] for 𝑠 = 7 , 8 TeV
• p p > l- vl~ j j [QCD] for 𝑠 = 7 , 8 TeV
For nevents = 100000
2- Parton Shower (work in progress):
3- Cuts (work in progress):
• Jets:
• Lepton:
Methods
Conclusion and Future Work
We have introduced a new approach to QCD parton shower MC’s based on the new IR-
improved DGLAP-CS kernels in Refs. [3,4] and we have realized the new approach
with the MC HERWIRI1.031 in the HERWIG6.5.
We are going to repeat the same approach for n jets where n= 0, 1, 3 and compare our
results with the most recent available data.
References
[1]- The infrared divergence phenomena and high-energy processes, D. R. Yennie et al, Annals Phys.
13 (1961) 379-452
[2]- Improved treatment for the infrared divergence problem in quantum electrodynamics, D. R.
Yennie et al, Phys.Rev. D8 (1973) 4332-4344
[3]- IR-Improved DGLAP Theory: Kernels, Parton Distributions, Reduced Cross Sections, B. F. L
Ward, Annals Phys. 323 (2008) 2147-2171
[4]- IR-Improved Operator Product Expansions in non-Abelian Gauge Theory, B. F.L. Ward,
Mod.Phys.Lett. A28 (2013) 0069
[5]- IR-Improved DGLAP Theory, B. F. L. Ward, Adv.High Energy Phys.2009:682312
[6]- Partons in Quantum Chromodynamics, Guido Altarelli, Phys.Rept. 81 (1982) 1
[7]- Asymptotic Freedom in Parton Language, G. Altarelli and G. Parisi, Nucl.Phys. B126 (1977)
298
[8]- New Approach to Parton Shower MC’s for Precision QCD THEORY: HERWIRI 1.0(31), B. F
L. Ward et al, Phys. Rev. D81 (2010) 076008
Contact Information
BFL_Ward@baylor.edu
Bahram_Shakerin@baylor.edu
Department of Physics, Baylor University
B. Shakerin, B. F. L. Ward
IR-Improved DGLAP-CS Parton Shower Effects in W+n Jets
𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
Missing 𝑬𝑻 Distribution
Lepton 𝑷𝑻 Distribution
𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
Lepton 𝑷𝑻 Distribution (Cont.)
𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
W 𝑷𝑻 Distribution
𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊+ + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 7 TeV 𝑊− + 2 𝐽𝑒𝑡𝑠 @ 𝑠 = 8 TeV
• HERWIGPP • HERWIG 6521 • HERWIRI 1.031 • PYTHIA 8
𝑅 = 0.4 [anti-𝑘𝑇]
η𝑗𝑒𝑡 < 2.8
𝑝𝑇𝑗𝑒𝑡
> 30 𝐺𝑒𝑉
𝑝𝑇 > 25 𝐺𝑒𝑉 1.37 < η𝑒 < 1.51 𝐸𝑇 > 15 𝐺𝑒𝑉 𝐸𝑇
𝑚𝑖𝑠𝑠 > 25 𝐺𝑒𝑉 𝑀𝑇
𝑊 > 40 𝐺𝑒𝑉
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