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S. I. Troyan

Publications and source records attributed to S. I. Troyan.

At least 37 records · Page 2Linked to original sources
arXiv2008

Parametrization of the QCD coupling in Hard and Regge processes

We examine the parametrization of the QCD coupling in the Bethe-Salpeter equations for the hard and Regge processes and determine the argument of alpha_s of the factorized gluon. Our analysis shows that for the hard processes alpha_s = alpha_s(k^2_T/(1- beta)) where k^2_T and beta are the longitudinal and transverse moment of the soft parton. On the other hand, in the Regge processes alpha_s = alpha_s(k^2_T}/beta). We have also shown that the well-known parametrization alpha_s = alpha_s(k^2_T) in the DGLAP equations stands only if the lowest integration limit, mu^2, over k^2_T (the starting point of the Q^2 -evolution) obeys the relation mu >> Lambda_{QCD} exp {(π/2)}, otherwise the coupling should be replaced by the more complicated expression.

hep-ph↗
arXiv2008

Comment on the recent COMPASS data on the spin structure function g_1

We examine the recent COMPASS data on the spin structure function g_1 singlet. We show that it is rather difficult to use the data in the present form in order to draw conclusions on the initial parton densities. However, our tentative estimate is that the data better agree with positive rather than negative initial gluon densities.

hep-ph↗
arXiv2008

Parametrization of the QCD coupling in the Evolution Equations

We examine the parametrization of the QCD coupling in the Evolution Equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k^2_{\perp}/βor just k^2_{\perp}, stands only if the lowest integration limit in the transverse momentum space (the starting point mu^2 of the Q^2 -evolution) obeys the relation mu >> Lambda_{QCD} \exp {(π/2)}, otherwise the coupling should be replaced by the more complicated expression presented in Eq. (37).

hep-ph↗
arXiv2007

Impact of double-logarithmic electroweak radiative corrections on the non-singlet structure functions at small x

In the QCD context, the non-singlet structure functions of u and d -quarks are identical, save the initial quark densities. Electroweak radiative corrections, being flavor-dependent, bring further difference between the non-singlets. This difference is calculated in the double-logarithmic approximation and the impact of the electroweak corrections on the non-singlet intercepts is estimated numerically.

hep-ph↗
arXiv2007

Description of the spin structure function g_1 at arbitrary $x$ and arbitrary Q^2

The explicit expressions describing the structure function g_1 at arbitrary x and Q^2 are obtained. In the first place, they combine the well-known DGLAP expressions for g_1 with the total resummation of leading logarithms of x, which makes possible to cover the kinematic region of arbitrary x and large Q^2. In order to cover the small-Q^2 region the shift Q^2 -> Q^2 + mu^2 in the large-Q^2 expressions for g_1 is suggested and values of mu are estimated. The expressions obtained do not require singular factors x^{-a} in the fits for initial parton densities.

hep-ph↗
arXiv2007

Spin structure function g_1 at small x and arbitrary $Q^2: Total resummaion of leading logarithms vs Standard Approach

The Standard Approach (SA) for description of the structure function g_1 combines the DGLAP evolution equations and Standard Fits for the initial parton densities. The DGLAP equations describe the region of large Q^2 and large x, so there are not theoretical grounds to exploit them at small x. In practice, extrapolation of DGLAP into the region of large Q^2 and small x is done with complementing DGLAP with special, singular (~x^{-a}) phenomenological fits for the initial parton densities. The factors x^{-a} are wrongly believed to be of the non-perturbative origin. Actually, they mimic the resummation of logs of x and should be expelled from the fits when the resummation is accounted for. Contrary to SA, the resummaton of logarithms of x is a straightforward and natural way to describe g_1 in the small-x region. This approach can be used at both large and small Q^2 where DGLAP cannot be used by definition. Confronting this approach and SA demonstrates that the singular initial parton densities and the power Q^2-corrections (or at least a sizable part of them) are rather not real physical phenomena but the artefacts caused by extrapolating DGLAP into the small-x region.

hep-ph↗
arXiv2007

Perturbative power Q^2-corrections to the structure function g(1)

We prove that regulating infrared divergencies generates power (~1/(Q^2)^k) corrections to the spin structure function g_1 at small x and large Q^2. At the same time it leads to the corrections ~(Q^2)^k at small Q^2. We present the explicit series of such terms as well as the formulae for their resummation. These contributions are not included in the standard analysis of the experimental data. We argue that accounting for such terms can sizably change the impact of the other power corrections conventionally attributed to the higher twists.

hep-ph↗
arXiv2007

Infrared Evolution Equations: Method and Applications

It is a brief review on composing and solving Infrared Evolution Equations. They can be used in order to calculate amplitudes of high-energy reactions in different kinematic regions in the double-logarithmic approximation.

hep-ph↗
arXiv2006

Total resummation of leading logarithms vs standard description of the Polarized DIS

Total resummation of leading logarithms of x contributing to the spin-dependent structure function g_1 ensures its steep rise at small x. DGLAP lacks such a resummation. Instead, the DGLAP expressions for g_1 are complemented with special phenomenological fits for the initial parton densities. The singular factors x^{-α} in the fits mimic the resummation and also ensure the steep (power-like) rise of g_1 at the small-x region. Furthermore, DGLAP by definition cannot describe the region of small Q^2 whereas our approach can do it.

hep-ph↗
arXiv2006

Singlet structure function g_1 at small x and small Q^2

Explicit expressions for the singlet g_1 at small x and small Q^2 are obtained with the total resummation of the leading logarithmic contributions. It is shown that g_1 practically does not depend on Q^2 in this kinematic region. In contrast, it would be interesting to investigate its dependence on the invariant energy 2pq because, being g_1 positive at small 2pq, it can turn negative at greater values of this variable. The position of the turning point is sensitive to the ratio between the initial quark and gluon densities, so its experimental detection would enable to estimate this ratio

hep-ph↗
arXiv2006

Deep Inelastic Structure Functions at small x

Explicit expressions for the non-singlet and singlet structure functions g_1 in the small-x region are obtained. They include the total resummation of the double- and single- logarithms of x and account for the running QCD coupling effects. Both the non-singlet and singlet structure functions are Regge behavied asymptotically, with the intercepts predicted in agreement with experiments. A detailed comparison with the DGLAP evolution equations for different values of x and Q^2 is performed. Finally, the role played by singular terms in DGLAP fits is discussed and explicitly shown to mimic the resummation of leading logarithms at small x.

hep-ph↗
arXiv2005

Role of the singular factors in the standard fits for initial parton densities

Total resummation of double- and single- logarithms of x contributing to the spin-dependent structure function g_1 ensures its steep rise at small $x$. In the asymptotic limit x ->0, the resummation leads to the Regge behavior of g_1 and allows to calculate the non-singlet and singlet intercepts of g_1. DGLAP lacks such a resummation but suggests special phenomenological fits for the initial parton densities such that the singular factors x^{-α} in the fits mimic the resummation and also provide g_1 with the steep (power-like) rise at the small-x region. Accounting for the total resummaton of logarithms of x allows to drop the singular factors in the fits and leads to remarkable simplifications of the fits.

hep-ph↗
arXiv2005

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

The explicit expressions for the non-singlet DIS structure functions obtained at small x by resumming the most singular logarithmic contributions are discussed and compared in detail with the DGLAP evolution for different values of x and Q^2. The role played by the initial conditions for the parton densities currently used in the DGLAP analysis, on the small-$x$ behavior of the non-singlet structure functions is discussed. Explicit expressions are presented which implement the NLO DGLAP contributions with our small-x results.

hep-ph↗
arXiv2005

Off-shell scattering amplitudes in the double-logarithmic approximation

When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and the ElectroWeak Standard Model. The off-shell amplitudes are considered in the hard and the Regge kinematic limits. We compare our results in both the Feynman and Coulomb gauges.

hep-ph↗
arXiv2004

Spin-Dependent Structure Function g_1 at Small x

Accounting for double-logarithms of x and running QCD coupling leads to expressions for both the non-singlet and singlet components of $g_1$. These expressions manifest the Regge asymptotics when x ->0 and differ considerably from the DGLAP expressions at small values of x.

hep-ph↗
arXiv2003

Small -x behavior of the non-singlet and singlet structure functions g_1

Explicit expressions for the non-singlet and singlet structure functions g_1 at the small $x$-region are obtained. They include the total resummation of double-logarithmic contributions and accounting for the running QCD coupling effects. We predict that both the non-singlet and singlet g_1 asymptotically ~ x^{- Δ}, with the singlet intercept = 0.86 and being more than twice larger than the non-singlet intercept = 0.4. The impact of the initial quark and gluon densities on the sign of g_1 at x << 1 is discussed.

hep-ph↗