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Register a new userGeneralisation of DGLAP equations to massive partons
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C. Pascaud
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DGLAP evolution equations are modified in order to use all the quark families in the full scale range, satisfying kinematical constraints and sumrules, thus having complete continuity for the pdfs and observables. Some consequences of this new approach are shown.
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We have studied the effects of nonlinear scale evolution of the parton distribution functions to charm production in $pp$ collisions at center-of-mass energies of 5.5, 8.8 and 14 TeV. We find that the differential charm cross section can be enhanced up to a factor of 4-5 at low $p_T$. The enhancement is quite sensitive to the charm quark mass and the renormalization/factorization scales.
We have studied how parton distributions based on the inclusion of nonlinear scale evolution and constraints from HERA data affect charm production in $pp$ collisions at center-of-mass energies of 5.5, 8.8 and 14 TeV. We find that, while the resulting enhancement can be substantial, it is very sensitive to the charm quark mass and the scale entering the parton densities and the strong coupling constant.
The effects of the first nonlinear corrections to the DGLAP evolution equations are studied by using the recent HERA data for the structure function $F_2(x,Q^2)$ of the free proton and the parton distributions from CTEQ5L and CTEQ6L as a baseline. By requiring a good fit to the H1 data, we determine initial parton distributions at $Q_0^2=1.4$ GeV$^2$ for the nonlinear scale evolution. We show that the nonlinear corrections improve the agreement with the $F_2(x,Q^2)$ data in the region of $xsim 3cdot 10^{-5}$ and $Q^2sim 1.5$ GeV$^2$ without paying the price of obtaining a worse agreement at larger values of $x$ and $Q^2$. For the gluon distribution the nonlinear effects are found to play an increasingly important role at $xlsim 10^{-3}$ and $Q^2lsim10$ GeV$^2$, but rapidly vanish at larger values of $x$ and $Q^2$. Consequently, contrary to CTEQ6L, the obtained gluon distribution at $Q^2=1.4$ GeV$^2$ shows a power-like growth at small $x$. Relative to the CTEQ6L gluons, an enhancement up to a factor $sim6$ at $x=10^{-5}$, $Q_0^2=1.4$ GeV$^2$ reduces to a negligible difference at $Q^2gsim 10$ GeV$^2$.
The effects of the first nonlinear corrections to the DGLAP equations are studied in light of the HERA data. Saturation limits are determined in the DGLAP+GLRMQ approach for the free proton and for the Pb nucleus.
We complete the study of two-loop infrared singularities of scattering amplitudes with an arbitrary number of massive and massless partons in non-abelian gauge theories. To this end, we calculate the universal functions F_1 and f_2, which completely specify the structure of three-parton correlations in the soft anomalous-dimension matrix, at two-loop order in closed analytic form. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, they are unsuppressed and diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the two-loop anomalous-dimension matrix for q q_bar --> t t_bar near threshold and show that it is not diagonal in the s-channel singlet-octet basis.
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