Top-quark pair production at hadron colliders: differential cross section and phenomenological applications with DiffTop

The results of phenomenological studies of top-quark pair production in proton-proton collisions are presented. Differential cross sections are calculated in perturbative QCD at approximate next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ by using methods of threshold resummation beyond the leading logarithmic accuracy. Predictions for the single-particle inclusive kinematics are presented for transverse momentum and rapidity distributions of final-state top quarks. Uncertainties related to the description of proton structure, top-quark mass and strong coupling constant are investigated in detail. The results are compared to the recent measurements by the ATLAS and CMS collaborations at the LHC at the center of mass energy of 7 TeV. The calculation presented here is implemented in the computer code \textsc{Difftop} and can be applied to the general case of heavy-quark pair production at hadron-hadron colliders. For the first time, a fit of parton distribution functions at NNLO is performed by using the differential cross sections of top-quark pair production together with other data sets. The impact of the top-pair production on the precision of the gluon distribution at high scales is illustrated.

In this paper, we present the results of a phenomenological analysis of differential cross section of tt production at the LHC, in which the estimate of the uncertainties due to the knowledge of the proton structure is addressed. The recent inclusive and, for the first time, differential measurements of tt production at hadron colliders are included in a QCD analysis at NNLO.
The impact of such data on the uncertainty of the gluon distribution is illustrated. For this purpose, the necessary developments of computing tools based on the available theory had to be performed. The approximate NNLO O(α 4 s ) calculation for the differential cross section in the single-particle inclusive (1PI) kinematic for heavy-flavor production at hadron colliders has been implemented in a novel computer code DiffTop which we provide at [44]. In this calculation, techniques of logarithmic expansion beyond the leading logarithmic accuracy in QCD threshold resummation are used.

Probing the proton structure through tt production
Top-pair production at the LHC probes parton distribution functions (PDFs) of the proton, in particular the gluon distribution. In proton-proton collisions at the LHC, tt production is mainly driven by the gluon, in fact approximately 85% of the total cross section is ascribed to the gluongluon channel at √ S = 7 TeV and this fraction grows with the increase of √ S. Measurements of the tt total and differential cross sections offer the possibility of probing the gluon in the large Bjorken x region (x ≈ 0.1) where gluon is currently poorly constrained. This has first been studied in [45] (see also [46]). However, strong correlations between α s , gluon distribution g(x), and the pole mass of the top quark m t , in the QCD description of tt production have to be taken into account. A simultaneous determination of g(x), α s and m t , using the tt measurements at the LHC in a QCD analysis, together with relevant measurements in Deep-Inelastic Scattering (DIS) and in proton-(anti)proton collisions might resolve these correlations.
The developed program and computational tools used for the phenomenological analyses presented in this paper, provide a basis for the inclusion of differential tt cross sections into QCD analyses at NNLO. For the purpose of a fast calculation within QCD analyses for PDF determination, DiffTop is interfaced to fastNLO [47][48][49][50] and included into the QCD analysis platform HERAFitter [51]. This allows the user to perform, for the first time, full genuine PDF fits including differential cross sections of tt production by using fast theoretical predictions for these observables. This not only represents a clear advantage in terms of the CPU-time consumption, but also opens the window to fully explore the potential of the tt measurements.
The exact NNLO calculation for the fully differential tt distributions, once available, will be of clear advantage. However, full global QCD analyses of the current and forthcoming highprecision LHC measurements set specific requirements to the representation of the experimental data and availability of fast computing tools. The present analysis addresses these requirements in the context of differential tt production cross sections for the first time, by using approximate calculations in order to facilitate future PDF fits using the exact NNLO theory.
Fast theoretical predictions for the full NNLO differential cross section calculation can be in principle obtained by using tools like fastNLO [47][48][49][50] or APPLgrid [52]. The grid files generated in the output of such codes can be directly read inside the HERAFitter open-source platform to determine the impact of the experimental tt data on PDFs by performing the QCD analysis. Presumably, the full NNLO calculation will be lengthy and CPU time consuming and the complication for creating an interface to fastNLO or APPLgrid will depend upon the structure of the calculation itself and the way the integration is done. One can forsee that the generation of fastNLO/APPLgrid grids will be feasible, but it might happen that it is dramatically CPU time consuming. If that will be the case, a possible way out will be to work on approximate calculations which can be highly improved once the full calculation is available.

Threshold resummation techniques
The new LHC measurements give us the possibility of investigating the applicability of QCD factorization for hadronic cross sections with high precision. In the past three decades QCD techniques have experienced stages of remarkable progress on theoretical and phenomenological ground. In particular, theoretical tools were introduced to estimate the importance of the perturbative higher orders in cross-section calculations [53][54][55][56][57][58]. In Fig. 1 we show the topquark transverse momentum, p t T , where higher orders are important and have reduced scale dependence.
The non-unique separation between long-and short-distance dynamics of partons in the proton is understood in terms of factorization theorems, in which inclusive hadronic cross sections are factorized in universal nonperturbative PDFs and fragmentation functions (FF), and hard scattering coefficients that can be computed in perturbative QCD. These hard scattering functions still contain, in certain kinematic regions, residuals of long-distance dynamic related to leftovers in the cancellation between real and virtual soft-gluon contributions. These finite reminders limit the predictive power of QCD in the kinematic region close to the partonic production threshold where singular logarithmic terms give large corrections to the cross section.
Threshold resummation methods, which are based on the universality of the factorization in the soft and collinear limit, allow us to resum these large contributions to all orders so that the predictive power of pQCD is extended to the phase space regions of the partonic threshold. By using threshold resummation methods one can derive approximate formulas at NNLO for differential distributions, in which the cross sections are expanded in terms of the logarith-   [10] and ATLAS (right) [12] measurements. Here MSTW08 NLO (NNLO) PDFs are used for the MCFM (DiffTop) calculation. Renormalization and factorization scales are set to µ R = µ F = m t and varied such as m t /2 ≤ µ R = µ F ≤ 2m t . For comparison, the central prediction by N. Kidonakis (solid line) using MSTW08 NNLO PDFs is shown. mic enhanced contributions (appearing as plus distributions), and can therefore be written at various degrees of logarithmic accuracy. Studies at the next-to-leading-logarithmic (NLL), nextto-next-to-leading-logarithmic (NNLL) accuracy and beyond can be found in Refs. [59][60][61][62][63][64][65][66][67][68] and references therein.
Recently, methods of heavy-quark effective theory (HQET) and soft-collinear effective theory (SCET) experienced enormous progress and received significant attention. Such methods can be also used to write the factorization formula for the hard-scattering kernels in the threshold region [69][70][71][72]. Approximate NNLO calculations, based on SCET, for differential cross sections for heavy-quark production can be found in [73][74][75][76][77][78][79] and references therein. A study of differences and similarities between the traditional QCD threshold resummation formalism and SCET can be found in [80] for the tt case.

Single particle kinematic
Top-quark pairs are produced in hadronic reactions in which the scattering process is defined by where H 1 and H 2 are the incoming hadrons with momenta P 1 and P 2 respectively, the final state top-quark has momentum p 1 , the anti-top momentum p 2 and X(k) represents any inclusive hadronic final state allowed by the reaction. At phenomenological level, the differential cross sections of interest are written in such a way that can be compared to measurements that are related to the detection of single particles or particle pairs.
When a single particle is detected in the final state, for instance the top-quark, the oneparticle inclusive (1PI) kinematic is used to determine the p t T spectrum and the rapidity y t distribution of the top-quark. These distributions are obtained by integrating over the phase space of the anti-top (not observed) together with any real emission of radiation [57].
When particle pairs are detected, the pair-invariant mass kinematic (PIM) is used to write a factorized cross section [53,54,56,58,81] in terms of the invariant mass of the heavy system, collective rapidity, and additional variables like the angle between the final-state quark direction and the beam axis. In what follows we will discuss differential distributions derived in the 1PI kinematic case and will leave the PIM kinematic [61] for a forthcoming analysis 2 .
In the case of single particle detection, the reaction in Eq.(1) is written as where p ′ 2 represents the recoil momentum. The Mandelstam invariants at hadronic level are defined as In the vicinity of the threshold the reaction is dominated by the following partonic subprocesses where the initial-state parton momenta expressed in terms of momentum fractions x 1 , x 2 are k 1 = x 1 P 1 and k 2 = x 2 P 2 . The recoil momentum p ′ 2 = p 2 + k accounts for momentum p 2 at the threshold and any additional radiation indicated by momentum k.
In the vicinity of the partonic threshold, the hadronic final state X[t(p ′ 2 )] ≡t(p 2 ) and the anti-top carry momentum p 2 . The Mandelstam invariants at parton level are defined as where the inelasticity of the reaction is accounted for by the invariant s 4 = p ′ 2 2 − m 2 t . The factorized differential cross section is written as where f j/H (x, µ 2 F ) is the probability of finding the parton j in hadron H, µ F and µ R are the factorization and renormalization scales respectively, and ω ij is the hard scattering cross section which depends on the kinematic of the reaction. Power suppressed terms Λ 2 /m 2 t are neglected here. The integration limits in the factorization formula are given by The double-differential cross section in Eq.(6) can be expressed in terms of the transverse momentum p t T of the top quark and its rapidity y by observing that where the transverse mass m T is defined as m T = p 2 T + m 2 t . According to QCD resummation, in the organization of the large logarithms at the threshold of the heavy system, the hard scattering ω ij functions are expanded in terms of singular functions which are plus-distributions of the type 3 where corrections are denoted as leading-logarithmic (LL) if l = 2i + 1 at O(α i+3 s ) with i = 0, 1, . . ., as next-to-leading logarithm (NLL) if l = 2i, as next-to-next-to-leading logarithm (NNLL) if l = 2i − 1, and so on.
Since QCD threshold resummation calculations and resummed formulae for inclusive cross sections for heavy-quark pair production have been extensively discussed in the literature in the past years, we will omit explicit derivations unless necessary and limit ourselves to general definitions. The calculation implemented in DiffTop strictly follows the derivation of Ref. [61] and references therein, which we refer to for details. Other particulars of this calculation can be found in [60,62,64,82].

Overview of the threshold resummation calculation
As described in [57,61] the fully resummed expression for the hard scattering cross section of Eq.(6) in 1PI kinematic is given by a trace in the color-tensor space of operators in the Mellin ij + · · · are the hard and soft functions respectively. The functions Γ S = (α s /π)Γ (1) S + · · · are the soft anomalous dimension matrices which are path-ordered in µ. Finally, γ i = (α s /π)γ i + · · · are the anomalous dimensions of the quantum field i = q, g. In our calculation, Γ S at two-loop for the massive case is given in [83,84].
The exponentials exp E i and exp E j represent resummed expressions for the collinear and soft radiation from incoming and outgoing partons respectively, and are defined as where γ i/i are the anomalous dimensions of the operator whose matrix element represents the parton density f i/i in the MS scheme. The vector ζ = p 2 /m t is used to define the distance from the threshold in 1PI kinematic: s 4 /m 2 t ≈ 2(ζ · k)/m t . The first exponential in Eq.(11) is defined as where functions A i and ν i have perturbative expansion in α s whose explicit expressions up to O(α 2 s ) can be found in [61,82] for the Feynman and axial gauge.
After an α s -expansion of the resummed hard-scattering cross section, the general structure of the double-differential cross section at parton level is given by where ω (0) ij is the cross section at the Born level and the one-loop soft-gluon correction beyond the LL approximation can be written as where coefficients C (in which we suppress the ij indices) and r 1 can be found in Appendix B of [61]. At the NNLL accuracy the coefficient R 1 which consists of virtual graph and soft-gluon radiation contributions, contains the NLO matching term Tr The expression of the NLO matching term is that of the soft plus virtual (S + V ) contributions in Eq.(6.19) of Ref. [18] for the gg channel, and that of the contributions in Eq.(4.7) of Ref. [20] for the qq channel. The Coulomb interactions, due to gluon exchange between the final-state heavy quarks, are included at 1-loop level.
The two-loop corrections at the NNLL accuracy can be written as where again, explicit expressions for the coefficients C 1 , . . . can be found in Appendix B of [61]. In the current implementation the scale-independent coefficient C (2) 0 contains the contribution from the soft anomalous dimension Γ (2) S given in [83,84] plus process-independent terms [63,82] which are universal in the qq and gg channels respectively. These contributions are formally at the next-to-next-to-next-leading logarithmic (NNNLL) accuracy. At this level of accuracy, C (2) 0 is therefore not exact due to incomplete separation of the individual color structures. From a comparison with the analogous approximation for the inclusive cross section we expect only small numerical deviations for the exact result. In the scale-independent coefficient R 2 we only include NNNLL subleading terms coming from moment to momentum space inversion [60]. The full knowledge of R 2 requires matching conditions at NNLO which include explicit analytical expressions for H (2) and S (2) . In the given kinematics (1PI), these are currently not available for H (2) and S (2) and those terms are thus set to zero. The current uncertainty on R 2 is therefore the dominant source.
To give an estimate of the dependence of the p T spectrum on the coefficients C (2) 0 and R 2 that are known only partially in our computation, we generated a set of predictions in which these coefficients are varied. In Fig. 2 we illustrate these variations separately, where the coefficient 0 is varied within 5% of its magnitude by keeping R 2 as fixed, and R 2 is varied by adding and subtracting R 2 or 2R 2 , and C (2) 0 is fixed. Variations of C (2) 0 produce modifications of magnitude and shape of the p T spectrum which are more pronounced in the peak region, where these are approximately 1% when R 2 is fixed. Being R 2 the less known contribution, we allow this coefficient to vary in a much larger interval to be more conservative. Variations of R 2 within its 5% when C (2) 0 is fixed, are found to be negligible. In Fig. 2 larger variations of R 2 have an impact over all the p T range beyond the peak, where modifications of the magnitude and shape can be approximately 7-10% or more at p T ≈ 200 GeV and are larger than those obtained by a simultaneous variation of factorization and renormalization scales. The uncertainties relative to C (2) 0 and R 2 are part of the systematic uncertainty associated to approximate calculations of this kind which are based on threshold expansions. Explicit expressions in SCET for S (2) in PIM kinematic, in the limit of boosted top quarks, can be found in Ref. [77]. Related studies are presented in Refs. [29,30,77,[85][86][87].
By setting µ R = µ F = µ one can write the inclusive total partonic cross section in terms of scaling functions f (k,l) ij that are dimensionless and depend only on To reduce the impact of threshold logarithms in the large-η regions of the scaling functions we made use of dumping factors as it is done in Ref. [19].  LHC 7 TeV, m t = 173 GeV, MSTW08 PDFs 0 is varied within its 5% while R 2 is kept fixed. Right: here the coefficient R 2 is varied by adding and subtracting 2R 2 while 4 Sensitivity of tt production to PDF-related aspects of QCD.
This section addresses details of the phenomenological analysis of the uncertainties on the predictions for differential tt production cross sections at the LHC. In particular, PDF uncertainties are studied and compared to the current experimental precision of the measurements. The approximate NNLO DiffTop predictions, obtained by using different PDF sets, are confronted to the recent measurements of differential distributions for tt production at √ S = 7 TeV by the CMS [10] and ATLAS [13,14] collaborations. The theoretical systematic uncertainties associated to variations of PDFs, α s (M Z ), scale, and m t , are investigated individually. In particular, transverse momentum p t T and rapidity y t distributions of the final state top-quark, measured by CMS, and the p t T distribution by ATLAS 4 are studied. The on-shell pole-mass definition for the top-quark mass is used, and the value of m t = 173 GeV is chosen. The scales are set to µ F = µ R = m t . The experimental measurements published by CMS and ATLAS are differential distributions that are normalized to the total cross section in bins of p t T and y t . This representation of experimental data is motivated by (partial) cancellation of systematic uncertainties.
The correlation between the p t T distribution for tt production at the LHC at √ S = 7 TeV and the gluon, as a function of x of the gluon (x gluon ) is illustrated in Fig. 3. A strong correlation is observed at x gluon ≥ 0.01. Here, the p t T distribution is averaged in 4 bins and the correlation cosine cos φ, as defined in [88], is evaluated for each bin. The predictions using MSTW08 [89] (left) and CT10 [90] (right) PDFs at NNLO are shown here, while those using ABM11 [91], HERAPDF1.5 [92], and NNPDF2.3 [93] have similar behaviors.
The uncertainties associated to the various PDFs are computed by using the prescription 4 In the data set we considered, y t is not provided by the ATLAS collaboration. The uncertainty related to the choice of the scale has been estimated by varying m t /2 ≤ µ R = µ F ≤ 2m t . As shown in Fig. 1, where the approximate NNLO prediction and the full NLO calculation obtained by MCFM [39] are compared, the reduction of the scale dependence is substantial. When these theory predictions are compared to the LHC data for the p t T distribution, the shape is also modified when passing from NLO to the approximate NNLO. In the approximate NNLO case, the theoretical description of the measurements is significantly improved.
The uncertainty associated to the pole mass m t has been assessed by considering variations ∆m t = ±1 GeV around the central value m t = 173 GeV.
4.1 Cross sections of tt production at approximate NNLO obtained with different PDFs.
In Tab. 1 we summarize the results for the tt total inclusive cross section at the LHC at √ S =7 TeV for each PDF set with relative uncertainties.
0 , in particular R 2 , which has impact on the large p T -spectrum. Also, missing contributions from the qg channel play a role at higher orders at large p T . These missing contributions spoil the agreement in the case of inclusive observables such as the total cross section. However, the local description of differential observables can still be approximated sufficiently well by threshold expansions in regions that are not strongly affected by hard gluon radiation. For example in the region 1 p T 250 − 300 GeV, where the bulk of the data is currently given. Exact predictions for the fixed-order NLO differential and total inclusive cross sections are in good agreement with the approximate NLO ones (see for example Ref. [95]) where the known one-loop soft and hard functions are included. This is an indication of the fact that the approximate NNLO predictions can be improved once the two-loop soft and hard functions from the full NNLO will be available and included in the calculation. A crude estimate of the systematic uncertainties associated to the missing contributions in functions for the total and differential cross sections was given in Sec. 3. A more realistic estimate of such uncertainties (variations can actually be combined) requires a separate analysis on which work is in progress and it will be addressed in a forthcoming paper by the authors. In the following figures these uncertainties are therefore not included.  and with the inclusion of threshold resummation, with scale dependence uncertainty obtained by using independent variations of µ F and µ R .
In Fig. 4 predictions for the absolute p t T and y t distributions are shown, with all used PDF sets that are compared within the respective total uncertainties. The spread of the central values is mostly due to the fact that the parton luminosities are driven by different gluon PDFs of each group. These differences arise from the different methodologies and inputs (heavy-flavor treatment, values of α s (M Z ), data selection, etc.) adopted by each PDF fitting group in their QCD analyses. The predictions using ABM11 are found to be generally lower with respect to the other sets, because the different methodology used in the ABM11 analysis leads to a lower gluon and smaller α s (M Z ) value. A larger value of the predicted cross section using ABM11 can be obtained by choosing a smaller value of the top-quark pole mass within the current uncertainties, see, e.g., [96].
Individual contributions to the total uncertainty on the prediction, arising from uncertainties of PDFs and variation of α s (M Z ), scales, and m t , are studied for each used PDF set separately.
The results for the CT10NNLO PDFs are shown in Fig. 5, while similar results obtained by using all the other PDF sets can be found in the Appendix. The total uncertainty on the theory prediction for the total and absolute differential tt cross section is dominated by the PDF errors. When theory predictions are compared to the data, CMS and ATLAS measurements exhibit some differences in the shape of the normalized p t T distribution, in particular in the first and third bin. In general, the first bins of transverse momentum 0 ≤ p t T ≤ 200 GeV and central bins of rapidity −1.5 ≤ y t ≤ 1.5 have potentially more constraining power, because of smaller experimental uncertainties. At the present stage, even though the CMS and ATLAS measurements exhibit relatively large uncertainties, these data might have some impact in PDF determination once included in QCD fit analyses. 4.2 QCD analysis using the tt production measurements.
To illustrate the possible impact of the current available measurements of tt production on PDF determination, we interfaced the DiffTop code to the HERAFitter [51] platform for QCD analyses. Fast theoretical calculations are obtained by using grids generated by the FastNLO package [48][49][50]. This allows the user to include measurements of differential tt production cross sections into NNLO QCD fits of PDFs. The NNLO PDF fit performed here uses the parton evolution implemented in the QCDNUM [98] code, that is the default parton-evolution package utilized in HERAFitter. The most important data sets for PDF determination are the combined HERA I measurements [104] of inclusive DIS, which we include in this analysis.
Constraints on the u and d-quark distributions in the x-range not properly covered by the HERA I measurements, are put by the CMS precise measurements of electron [105] and muon [106] charge asymmetry in W -boson production at √ S = 7 TeV. The theory predictions for the lepton charge asymmetry are obtained by using the MCFM program at NLO and K-factors are applied in the NNLO fit.
The tt measurements included in this analysis are the total inclusive cross sections at the LHC [99-102] at √ S of 7 and 8 TeV, and CDF [103] Tevatron, as well as the normalized differential cross-sections [10,13] of tt production at the LHC at √ S = 7 TeV as a function of p t T . The procedure for the determination of the PDFs follows the approach used in the QCD fits of the HERA [104] and CMS [106] collaborations. In our PDF analysis, the TR' [107,108] general mass variable flavor number scheme at NNLO is used for the treatment of heavy-quark contributions with input values of the heavy-quark masses given by m c = 1.4 GeV and m b = 4.75 GeV, while the choice of the QCD scales is µ R = µ F = Q. The strong coupling constant is set to α s (m Z ) = 0.1176 and the Q 2 range of the HERA data is restricted to the range Q 2 ≥ Q 2 min = 3.5 GeV 2 . The following independent combination of parton distributions is chosen at the QCD evolution initial scale Q 2 0 = 1.9 GeV 2 in the fitting procedure: xu v (x), xd v (x), xg(x) and xU(x), xD(x), where xU(x) = xū(x) and xD(x) = xd(x) + xs(x). At the scale Q 0 , the parton distributions are represented by The normalization parameters A u v , A d v , A g are determined by the QCD sum rules, the B parameter is responsible for small-x behavior of the PDFs, and the parameter C describes the shape of the distribution as x → 1. A flexible form for the gluon distribution is adopted with the choice of C ′ g = 25 motivated by the approach of the MSTW group [107,108]. The analysis is performed by fitting 14 free parameters in Eqs. (17)(18)(19)(20)(21). Additional constraints B U = B D and are imposed by f s that is the strangeness fraction defined as f s =s/(d +s), which is fixed to f s = 0.31 ± 0.08 as in the analysis of Ref. [108]. The inclusion the tt measurements in the current NNLO PDF fit leads to a change of the shape of the gluon distribution and a moderate improvement of its uncertainty at large x. This is observed in particular at high scales, as illustrated in Fig. 8. By increasing the scale, the quantitative reduction of the uncertainty of the gluon distribution remains similar, but it sets in at lower values of x. A similar effect is observed, although less pronounced, when only the total or only the differential tt cross section measurements are included in the fit. The results of our full PDF fit, demonstrating a moderate improvement of the uncertainty on the gluon distribution, confirm the observation reported in the reweighting analysis [46] which uses only the total tt cross sections.
The analysis presented here uses the normalized differential cross sections for tt production.
The use of normalized data leads to partial cancellation or reduction of the experimental uncertainties. However, a significant amount of information is lost by normalizing the data, in particular, in connection to uncertainty correlations, which are currently not provided by the experimental collaborations. Measurements of absolute differential cross sections supplied by full information about correlation of experimental uncertainties are of crucial importance to fully exploit the potential of the tt production to constrain the gluon distribution. Furthermore, the dependence of the experimentally measured differential tt cross section on the assumptions on the top-quark mass used in the Monte Carlo simulations used for efficiency calculation, is necessary. In the future, a reduction of the statistic and systematic uncertainties in the highenergy run of the LHC will be of clear advantage. A simultaneous determination of the gluon distribution and the top-quark mass is of particular interest.

Summary and conclusions
In this paper, we present results for the differential cross section of tt production at approximate NNLO that are of interest for phenomenological studies at hadron colliders. This calculation is implemented into the flexible computer code DiffTop, which is a useful tool for precision studies in QCD and phenomenological applications of the tt differential cross section.
In particular, details of the predicted distributions of top-quark transverse momentum and rapidity, generated by using different PDF sets are studied and compared to the recent measurements by the CMS and ATLAS collaborations. Individual uncertainties due to variations of PDFs, scale, α s and m t , are analyzed. The DiffTop code has been interfaced to FastNLO for fast evaluations of the theory predictions, and it has been included into the HERAFitter framework for QCD analysis to determine the PDFs of the proton. For the first time, it is possible to include measurements of the differential cross sections of tt production at the LHC into a full PDF fit. We studied the impact of the recent measurements of the inclusive and differential tt production cross sections in a PDF fit at NNLO together with the HERA I inclusive DIS data and the CMS measurements of the lepton charge asymmetries in W boson production. Given the current experimental precision of tt measurements, a moderate improvement of the uncertainty on the gluon distribution at high x is observed once the total and differential tt cross sections are included in the QCD analysis. Measurements of the p t T and y t differential cross sections of tt production in hadron collisions are going to play an important role in constraining the gluon PDF at large-x as the LHC will reach higher experimental precision in the forthcoming run II. Given the correlations between the strong coupling α s (M Z ), top-quark mass and gluon PDF, these measurements could be used to constrain the large-x gluon distribution and the top-quark mass simultaneously. In particular, investigations of absolute differential cross sections will bring complementary information related to the magnitude and other details of the distributions, which will be crucial to improve the constraining power of the experimental data.