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