Next-to-leading order QCD analysis of parton distribution functions with LHC data

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Nuclear and Particle Physics Proceedings 282–284 (2017) 32–36 www.elsevier.com/locate/nppp

Next-to-leading order QCD analysis of parton distribution functions with LHC data ∗ A. Vafaee1,, A. Khorramian Faculty of Physics, Semnan University, 35131-19111, Semnan, Iran.

Abstract We present a next-to-leading order (NLO) QCD fit of parton distribution functions (PDFs) with and without the LHC data. In this analysis, we use the HERA I+II combine inclusive proton DIS cross sections, H1-ZEUS combined charm structure function, SLAC structure function, and EMC charm structure data as a base data, and then we investigate the effect of LHC data on the determination of PDFs. Our analysis and PDFs extraction is performed by xFitter framework. Keywords: QCD, PDFs, NLO, LHC.

1. Introduction The quarks inside the proton interact with each other through the exchange of gluons. The dynamics of this interacting system can describe the distribution of quark momenta within the proton, using DGLAP evaluation equations [1] in perturbetive Quantum Chromodynamics (pQCD). These distributions are expressed in terms of PDFs. At high energy momentum transfers, really the structure of the nucleon can be characterized by PDFs. Using factorization theorems we can describe the nucleon structure in terms of quarks and gluons distributions. The parton distribution fi (x, Q2 ) of the proton, is the number density of a parton with flavor i which is carrying a momentum fraction x at the scale of Q2 . The QCD theory have two main features which we know as confinement (as a short range feature) and asymptotic freedom (as a large range feature). The factorization theorem uses these features by separating them to ∗ Talk given at 19th International Conference in Quantum Chromodynamics (QCD 16, 31th anniversary), 4 - 8 July 2016, Montpellier FR Email addresses: [email protected] (A. Vafaee), [email protected] (A. Khorramian) 1 Speaker, Corresponding author.

http://dx.doi.org/10.1016/j.nuclphysbps.2016.12.007 2405-6014/© 2016 Elsevier B.V. All rights reserved.

short and long distances processes, such that structure functions of the nuclear and specially for proton can be written as a convolution between calculable parts (hard scattering coefficients) and non-calculable parts (PDFs), which are therefore parametrized and determined from a QCD fit of available experimental data. Extraction of the parton distribution functions using the deep inelastic scattering (DIS) data at lepton-proton colliders and also proton-proton colliders at the LHC and Tevatron, is an important subject in high energy hadron physics. In fact, HERA and LHC data have improved and affected the behavior of PDFs. By having precise PDFs at low and large x, we can develop our knowledge of the nucleon structure. Using QCD global analysis, recently some theoretical groups have extracted parton distribution functions in unpoalrized and polarized cases [2-13]. In this paper, we include HERA inclusive proton DIS cross sections [14], H1-ZEUS combined charm structure function [15], F2 structure functions SLAC data [16], the structure function of EMC charm [17], and also LHC data LHC data [18–23] on the determination of the PDFs. Our analysis of PDFs extraction is performed using xFitter framework [24]. The outline of the paper is as follows. In Sec. 2, we

A. Vafaee, A. Khorramian / Nuclear and Particle Physics Proceedings 282–284 (2017) 32–36

describe the deep inelastic scattering as a powerful tool for probing the structure of the nucleon and emphasis on the importance of the PDFs in the estimate of structure functions of the proton and double cross section of scattering. In Sec. 3, we discuss about the determination of the PDFs and explain our methodology which is performed by xFitter framework. Then, we discuss the importance of choosing the functional form which we used at the input scale in our QCD fit process using the xFitter standard functional form. In Sec. 4, we discuss about the impact of LHC data on the HERA I+II combine data, and DIS F2 structure functions SLAC and EMC data. Finally, we present our QCD fit results. 2. DIS experiments as a powerful tool for probing the proton structure High energy process such as deep inelastic scattering of electron proton (e− p → e− X), provides a powerful tool for probing the structure of the proton. Although, elastic scattering is described by the coherent interaction of a virtual photon with the proton as a whole, and thus provides a probe of the global properties of the proton, such as proton charge radius, but at high energies, the dominant process is deep inelastic scattering, where the proton breaks up. At the DIS level, the underlying process is the elastic scattering of the electron from one of the quarks within the proton. Consequently, deep inelastic scattering provides a probe of the momentum distribution of the quarks and gluons. For the present time, the DIS experiments provide the cleanest approach to measure the proton structure. To probe the structure of proton, deep inelastic scattering experiments are carried out either on the fixed targets or at the collider facilities using electrons or neutrinos to probe the structure of the proton. In the DIS process a lepton is scattered off the constituents of the proton by a virtual exchange of a neutral (NC) or charged (CC) boson producing a hadronic shower and a scattered lepton in the final state. The underlying physics which we have used in our QCD fit is on the base of NC-mode and it’s double cross section can be expressed in terms of the generalized structure functions such as follow: ±

d2 σeNCp

=

dxdQ2

2πα2 Y+ e± p σr,NC , xQ4

(1)

with: ±

p σer,NC

=

Y− ˜ ± y2 ˜ ± F˜ 2± ∓ xF − F , Y+ 3 Y+ L

(2)

where, Y± = 1 ± (1 − y)2 and α is the electromagnetic coupling constant [14].

33

Table 1: The list of experimental data included in our analysis, and for each data set, we indicated the χ2 /number of points. Data Set HERA1+2 CCep HERA1+2 CCem HERA1+2 NCem HERA1+2 NCep 820 HERA1+2 NCep 920 HERA1+2 NCep 460 HERA1+2 NCep 575 Charm cross section H1-ZEUS combined p SLAC F2 EMC Fc2 ATLAS Jet data 0.0 ≤|y|< 0.3 R=0.6 ATLAS Jet data 0.3 ≤|y|< 0.8 R=0.6 ATLAS Jet data 0.8 ≤|y|< 1.2 R=0.6 ATLAS Jet data 1.2 ≤|y|< 2.1 R=0.6 ATLAS Jet data 2.1 ≤|y|< 2.8 R=0.6 ATLAS Jet data 2.8 ≤|y|< 3.6 R=0.6 ATLAS Jet data 3.6 ≤|y|< 4.4 R=0.6 ATLAS high mass DY mass 2011 ATLAS Z rapidity, 2010 data ATLAS W+ lepton pseudorapidity ATLAS W- lepton pseudorapidity ATLAS low mass DY 2011 ATLAS DY mass 2010 extended data CMS electon Asymmetry rapidity CMS Boson rapidity Total χ2 / dof

BASE 58 / 39 49 / 42 238 / 159 72 / 68 459 / 363 211 / 200 221 / 249 44 / 47 84 / 59 96 / 16 1630 / 1228 =1.327

BASE+LHC 51 / 39 54 / 42 234 / 159 74 / 68 463 / 363 211 / 200 221 / 249 44 / 47 83 / 59 116 / 16 17 / 16 6.4 / 16 6.4 / 16 7.8 / 15 7.0 / 12 1.3 / 9 0.67 / 6 7.9 / 13 7.5 / 8 22 / 11 12 / 11 12 / 8 7.6 / 6 8.3 / 11 57 / 35 1860 / 1421 =1.310

3. Determination of the PDFs

The PDFs, reflect the underlying structure of the proton. PDFs cannot be calculated from the first principles and can be extracted from the measurements of the structure functions in deep inelastic scattering experiments. We can extract some information about the parton distribution functions of the proton by high-energy measurements involving protons, such as: fixed-target high-energy ep and νp scattering data, high-energy pp collider data from the Tevatron; and very-high-energy pp collider data from the LHC. Indeed, the different experimental measurements provide complementary information about the PDFs at high-energy physics. In this QCD analysis, we use the following experimental data: combined HERA inclusive proton DIS cross sections [14], H1-ZEUS combined charm structure function [15], DIS F2 SLAC data [16] and the structure function of EMC charm x [17], which can be labelled by “BASE”. Then we include the LHC data [18– 23] to determine the impact of the LHC data on PDF, which are labelled by “BASE+LHC”. There are several functional forms which theoretical groups choose them according to their necessity and underlying physics. In our calculation, we use the standard functional form from xFitter standard form [24] for valence xuv and xdv quark distribution at the starting scale

xuV(x,Q2)

0.9

xdV(x,Q2)

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Q2 = 1.4 GeV2 BASE +LHC

0.8

0.45

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0.05

0

0

4

10−2

10−1

x

Q2 = 1.4 GeV2 BASE +LHC

3

10−4

1

xΣ(x,Q2)

10−3

10−4

xg(x,Q2)

0.4

Q2 = 1.4 GeV2 BASE +LHC

1.4 1.2

10−3

10−2

10−1

10−2

10−1

x

1

Q2 = 1.4 GeV2 BASE +LHC

2 1 1 0.8

0 −1

0.6

−2

0.4

−3

0.2

−4

0 10−3

10−4

10−2

10−1

x

1

10−4

10−3

x

1

Figure 1: Our reults for xuv , xdv , xg, and xΣ PDFs as a function of x and for fixed value of Q2 = 1.4 GeV2 .

Table 2: The fit results for parameter values at NLO approximation at the initial scale of Q20 =1.4 GeV2 as defined in Eqs. (3-5) for Base and Base + LHC data. Parameter Buv Cuv Euv Bdv Cdv Bu¯ Cu¯ Du¯ AD¯ BD¯ C D¯ Bg Cg Ag Bg Cg

BASE 0.616 ± 0.037 4.624 ± 0.071 17.1 ± 2.7 0.754 ± 0.081 3.94 ± 0.39 −0.151 ± 0.016 7.79 ± 0.58 13.4 ± 3.5 0.158 ± 0.019 −0.151 ± 0.016 9.8 ± 2.6 −0.775 ± 0.023 1.23 ± 0.18 0.279 ± 0.023 −0.774 ± 0.022 25.00

of Q20 : xuv (x)

=

xdv (x)

=

BASE+LHC 0.710 ± 0.023 4.587 ± 0.072 11.8 ± 1.2 0.782 ± 0.059 4.01 ± 0.27 −0.129 ± 0.013 7.77 ± 0.89 7.3 ± 2.4 0.189 ± 0.017 −0.129 ± 0.013 7.4 ± 1.2 −0.708 ± 0.023 1.76 ± 0.17 0.338 ± 0.025 −0.711 ± 0.021 25.00

A dv x

(1 − x)

Cdv

.

=

Au¯ xBu¯ (1 − x)Cu¯ (1 + Du¯ x) ,

(4)

=





Ag xBg (1 − x)Cg − Ag xBg (1 − x)Cg . (5)

Here, to determine the normalization constants A for the valence and gluon distributions, we use the QCD number and momentum sum rules. In this analysis, we develop our QCD fit on the base of MS scheme and evolve our PDFs according the DGLAP evolution equations [1]. Our QCD analysis of parton distribution function at the NLO is performed using xFitter[24]. xFitter used QCDNUM packages [25] to determine the Q2 evolution of PDFs in x-space.

(3)

¯ and x s¯, we Also for light sea quark distributions, x¯u, xd, use the following from: x¯u(x)

=

¯ here xD(x) = AD¯ xBD¯ (1 − x)CD¯ , and finally for gluon distribution xg we use xg(x)

  Auv xBuv (1 − x)Cuv 1 + Euv x2 , Bdv

¯ (1 − f s )xD, ¯ x s¯(x) = f s xD,

¯ xd(x)

4. Impact of the LHC data on the HERA combine data In this paper, we first develop a next-to-leading order (NLO), QCD fit, HERA I+II combine, H1-ZEUS combined charm, SLAC, and EMC charm structure as a BASE and then we include the LHC data in our base

0.8 0.7

xdV(x,Q2)

xuV(x,Q2)

A. Vafaee, A. Khorramian / Nuclear and Particle Physics Proceedings 282–284 (2017) 32–36

Q2 = 4.0 GeV2 BASE +LHC

0.3

0.5

0.25

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0.05

0

7 6

0 10−3

10−2

10−1

x

10−4

1

xΣ(x,Q2)

10−4

Q2 = 4.0 GeV2 BASE +LHC

0.35

0.6

xg(x,Q2)

0.4

Q2 = 4.0 GeV2 BASE +LHC

5

2

10−3

10−2

10−1

10−2

10−1

x

1

Q2 = 4.0 GeV2 BASE +LHC

1.5

4 1

3 2

0.5 1 0 10−4

0 10−3

10−2

10−1

x

10−4

1

10−3

x

1

0.7 0.6

xdV(x,Q2)

xuV(x,Q2)

Figure 2: Our reults for xuv , xdv , xg, and xΣ PDFs as a function of x and for fixed value of Q2 = 4 GeV2

Q2 = 100 GeV2 BASE +LHC

0.35

Q2 = 100 GeV2 BASE +LHC

0.3 0.5

0.25

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0

45 40

0 10−3

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x

10−4

1

xΣ(x,Q2)

xg(x,Q2)

10−4

Q2 = 100 GeV2 BASE +LHC

35

8 7

10−3

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x

1

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6

30 5 25 4 20 3

15

2

10 5

1

0

0

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10−1

x

1

10−4

10−3

x

1

Figure 3: Our reults for xuv , xdv , xg, and xΣ PDFs as a function of x and for fixed value of Q2 = 100 GeV2

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A. Vafaee, A. Khorramian / Nuclear and Particle Physics Proceedings 282–284 (2017) 32–36

data set. Table 1 show a detailed comparison between these two data sets. As one can see in Table 1, the χ2 value as a estimate of agreement between experiment and theory is 1.327 for BASE data set and then reduce to 1.310 for BASE + LHC data set, which in turn clearly show the impact of LHC data set on the HERA I+II combine experimental data. Generally, in a QCD fit process when we take into account the underlying physics and organize our data set, the next step is the parametrized the PDFs on the base of an specific model and then evolve the PDFs and finally, finding the unknown parameters on the base of a minimization procedure. In Table 2, we show the QCD fit results for parameter values at NLO approximation at the initial scale of Q20 =1.4 GeV2 as defined in Eqs. (3-5) for BASE and Base plus LHC data. We set our initial Q20 value equal to 1.4 GeV2 and then extract our PDFs at the NLO at different values of Q2 . As a result of our next-toleading order QCD analysis of parton distribution functions with LHC data, we present our results for xuv , xdv , xg, and xΣ PDFs as a function of x and for different values of Q2 = 1.4, 4, 100 GeV2 in Figs. (1-3). References [1] V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972); G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1997); Yu. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977). [2] A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, Eur. Phys. J. C 63, 189 (2009) [arXiv:0901.0002 [hep-ph]]. [3] L. A. Harland-Lang, A. D. Martin, P. Motylinski and R. S. Thorne, Eur. Phys. J. C 76, no. 4, 186 (2016) [arXiv:1601.03413 [hep-ph]]. [4] R. D. Ball, V. Bertone, S. Carrazza, C. S. Deans, L. Del Debbio, S. Forte, A. Guffanti and N. P. Hartland et al., Nucl. Phys. B 867, 244 (2013) [arXiv:1207.1303 [hep-ph]]. [5] S. Alekhin, J. Bluemlein and S. Moch, Phys. Rev. D 89, no. 5, 054028 (2014) [arXiv:1310.3059 [hep-ph]]. [6] J. Gao, M. Guzzi, J. Huston, H. L. Lai, Z. Li, P. Nadolsky, J. Pumplin and D. Stump et al., Phys. Rev. D 89, no. 3, 033009 (2014) [arXiv:1302.6246 [hep-ph]]. [7] A. Khorramian, PoS EPS -HEP2015, 616 (2015). [8] A. Kusina, K. Kovaik, T. Jeo, D. B. Clark, F. I. Olness, I. Schienbein and J. Y. Yu, PoS DIS 2014, 047 (2014) [arXiv:1408.1114 [hep-ph]]. [9] P. Jimenez-Delgado and E. Reya, Phys. Rev. D 89, no. 7, 074049 (2014) [arXiv:1403.1852 [hep-ph]]. [10] A. N. Khorramian, S. Atashbar Tehrani, S. Taheri Monfared, F. Arbabifar and F. I. Olness, Phys. Rev. D 83, 054017 (2011) [arXiv:1011.4873 [hep-ph]]. [11] A. Vafaee, A. Khorramian, S. Rostami and A. Aleedaneshvar, Nucl. Part. Phys. Proc. 270-272, 27 (2016). [12] H. Khanpour, A. N. Khorramian and S. A. Tehrani, J. Phys. G 40, 045002 (2013) [arXiv:1205.5194 [hep-ph]]. [13] F. Arbabifar, A. N. Khorramian and M. Soleymaninia, Phys. Rev. D 89, no. 3, 034006 (2014) [arXiv:1311.1830 [hep-ph]].

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