Excited QCD 2014 Bjelasnica Mountain, Sarajevo

Outline Sara Taheri Monfared (IPM) 2

Motivation 3 Structure functions are a measure of the partonic structure of hadrons, which is important for any process which involves colliding hadrons. They are key ingredient for deriving PDFs in nucleons. These PDFs allow us to predict scattering cross sections at particle colliders. A good knowledge of PDFs is of prime importance for the success of the physics program.

Deep Inelastic Scattering (DIS) Sara Taheri Monfared (IPM) 4

Polarization 5 For the lepton and target nucleon polarized longitudinally For nucleons polarized transversely Very little information is available on the g 2. This structure function is of special interest, because of its unique sensitivity to quark-gluon correlations.

Data and theory comparison with other groups Sara Taheri Monfared (IPM) 6 DISSIDISRHICTMCHT g 1 HT g 2 DSSV 09 AAC 09 BB 10 LSS 10 NNPDF 13 JAM KATAO AKS MODEL Long-term objective is to tick all the boxes (including SIDIS and RHIC data)

Cross Section Sara Taheri Monfared (IPM) 7 Leading twist contribution Higher twist correction It is formally of order 1/Q 2 but not precisely known. The correction is often neglected in extracting PDFs from the cross sections. QPM + Perturbative QCD Operator Product Expansion (OPE)

Corrections Sara Taheri Monfared (IPM) 8

g 1 p & g 1 n & g 1 d Sara Taheri Monfared (IPM) 9

g 1 (x,Q 2 ) LT Sara Taheri Monfared (IPM) 10

g 2 WW Sara Taheri Monfared (IPM) 11

Target Mass Correction Sara Taheri Monfared (IPM) 12

Basic Concepts Sara Taheri Monfared (IPM) 13 Bjorken & Natchman variable : In the massless target & quark limit or equivalently Q²→∞ : At finite Q², the effects of target and quark masses modify the identification of the Bjorken variable. For massless quarks : At large values of Q²: X=ξ

First Correction: TMC First Correction: TMC Sara Taheri Monfared (IPM) 14 Y. B. Dong, Phys. Lett. B 641, 272 (2006). A.Piccione and G. Ridolfi, Nucl. Phys. B513, 301 (1998); B.J. Blumlein and A. Tkabladze, Nucl. Phys. B553,427 (1999); W. Detmold, Phys. Lett. B 632, 261 (2006). Georgi and Politzer (1976) : TMC to the g ₁ In order to take into account all TMCs, g ₁ can be written in the following form, and the exact formula is achieved:

Second Correction: Higher Twist Second Correction: Higher Twist Sara Taheri Monfared (IPM) 15

Sara Taheri Monfared (IPM) 16

The Effect of HT +TMC on PPDFs Sara Taheri Monfared (IPM) 17 Polarized parton distribution at Q 0 2 as a function of x in NLO approximation.

Sara Taheri Monfared (IPM) 18 Polarized structure functions as a function of x and for different low values of Q 2 is compared with the curves obtained by the other theoretical groups.

Full g 2 Full g 2 Sara Taheri Monfared (IPM) 19

Higher Twist Effect on g 2 Higher Twist Effect on g 2 Sara Taheri Monfared (IPM) 20

Higher Twist Effect on g 1 Higher Twist Effect on g 1 Sara Taheri Monfared (IPM) 21

Twist 3 evolution Sara Taheri Monfared (IPM) 22 Twist-3 contribution of g 1 and g 2 for proton, neutron and deuteron as a function of x and for different values of Q 2.

The effect of HT +TMC on QCD Fit Sara Taheri Monfared (IPM) 23

Sum Rules Sara Taheri Monfared (IPM) 24 PDFs and SFs follow a series of sum rules. These sum rules which are based on the moments of SFs, provide an opportunity to test QCD. Moments of PDFs contain valuable information about total momentum fraction carried by partons or the total contribution of parton helicities to the spin of nucleons in unpolarized and polarized case.

OPE sum rule Sara Taheri Monfared (IPM) 25 OPE sum rule relates the moments of g 1 and g 2 at fixed Q 2 to the twist-2 and twist-3 reduced matrix elements of spin-dependent operators in nucleon, a n and d n.

Twist-3 Contributions to Polarized Nucleon Structure Functions Sum Rule Sara Taheri Monfared (IPM) 26

Burkhardt-Cottingham (BC) Sum Rule Sara Taheri Monfared (IPM) 27 In all Q 2

Bjorken Sum Rule Sara Taheri Monfared (IPM) 28 We achieved the value of for the above ratio. Bjorken sum rule relates the integral over all x at fixed Q 2 of difference between the proton and neutron polarized structure function to the neutron beta decay coupling constant. This sum rule can be explicitly conclude for the 3 He– 3 H system. Considering the ratio of these two relations, one gets

Ellis-Jaffe Sum Rule Sara Taheri Monfared (IPM) 29

First Moment Sum Rule Sara Taheri Monfared (IPM) 30 The spin contribution of parton i to the nucleon spin can be found by its first moment. This is why there are universal efforts to determine precise PPDF from different experimental data.

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Conclusion Sara Taheri Monfared (IPM) 32 In conclusion, this has been a general overview of what really fascinated me through the course of this study. We present here an updated, more accurate, version of our calculations on performing a global fit to the existing data by imposing TMC & HT effects. In deriving polarized distribution some unknown parameters are introduced which should be determined by fitting to experimental data. Our results for polarized structure functions are in good agreement with available experimental data.

Thanks for your paying attention Sara Taheri Monfared (IPM) 33

Sara Taheri Monfared (IPM) 34

Sara Taheri Monfared (IPM) 35 Back up

Efremov-Leader-Teryaev (ELT) Sum Rule Sara Taheri Monfared (IPM) 36 E155 Our Model

OPE Sara Taheri Monfared (IPM) 37 C coefficient functions represent the hard scattering of the boson from the parton. τ denote the twist of the operator O. i represents different operators with the same twist. Perturbative partNon Perturbative part The separation of distances is a key point in the OPE, so we need to have scale : Λ ₌ 243  62 (exp) MeV For Q²<Λ² the QCD perturbation theory is invalid and we must use the non perturbation theory. A quantitative framework which follows this picture and incorporates both short- and long- distance Contributions was developed in a form of OPE.

Description of OPE from g 2 Sara Taheri Monfared (IPM) 38 If m=0 Leading twist contribution determined entirely from g1 through the Wandzura-Wilczek relation Another twist-2 structure function depicting quark transverse polarization. Twist-3 part from quark-gluon interactions.

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Sara Taheri Monfared (IPM) 40

Twist: In general an operator of dimension d has a coefficient function in the OPE of current that has dimension (mass)^(6-d). However, if the operator has spin s.thus the relative size of contributions from the OPE to DIS is controlled, not exactly by dimension of the operator. But rather by twist, defined as: t=d-s Leading twist:  The logarithmic scale dependence is therefore related to the leading twist operators, Which in the parton language are one-body operators whose matrix elements yield the contribution of the individual partons To the nucleon.  t=2 is the smallest value for QCD operators and denotes the leading twist contributions.  at leading twist only longitudinal polarization contributes to DIS. 41

Higher twist:  HT denotes the contribution to g₁ arising from QCD operators of higher twist, namely t  3.  Power type corrections are related to higher-twist operators measuring the relevance of correlations among quarks and gluons in the nucleon.  In HT processes more than one parton from a hadron take part in the scattering.  The region of intermediate Q² exposes quark-gluon correlation effects.  They are non perturbative effects.  their effects are small but are nonzero. qqGqqGG 42

Sara Taheri Monfared (IPM) 43 Twist: If an operator of dimension d in OPE has spin s t=d-s Leading twist: t=2 is the smallest value for QCD operators and denotes the leading twist contributions. Higher Twist : HT denotes the contribution to g ₁ arising from QCD operators of higher twist, namely t  3. Power type corrections are related to higher-twist operators measuring the relevance of correlations among quarks and gluons in the nucleon. In HT processes more than one parton from a hadron take part in the scattering. They are non perturbative effects. their effects are small but are nonzero.

Sara Taheri Monfared (IPM) 44 As in the unpolarized case the main goal is: to test QCD to extract from the DIS data the polarized PD where "+" and "-" denote the helicity of the parton, along or opposite to the helicity of the parent nucleon, respectively.