Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSmall-$x$ Helicity Evolution: an Operator Treatment
388
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We rederive the small-$x$ evolution equations governing quark helicity distribution in a proton using solely an operator-based approach. In our previous works on the subject, the evolution equations were derived using a mix of diagrammatic and operator-based methods. In this work, we re-derive the double-logarithmic small-$x$ evolution equations for quark helicity in terms of the polarized Wilson lines, the operators consisting of light-cone Wilson lines with one or two non-eikonal local operator insertions which bring in helicity dependence. For the first time we give explicit and complete expressions for the quark and gluon polarized Wilson line operators, including insertions of both the gluon and quark sub-eikonal operators. We show that the double-logarithmic small-$x$ evolution of the polarized dipole amplitude operators, made out of regular light-cone Wilson lines along with the polarized ones constructed here, reproduces the equations derived in our earlier works. The method we present here can be used as a template for determining the small-$x$ asymptotics of any transverse momentum-dependent (TMD) quark (or gluon) parton distribution functions (PDFs), and is not limited to helicity.
rate research
Read More
We present a Monte Carlo based analysis of the combined world data on polarized lepton-nucleon deep-inelastic scattering at small Bjorken $x$ within the polarized quark dipole formalism. We show for the first time that double-spin asymmetries at $x<0.1$ can be successfully described using only small-$x$ evolution derived from first-principles QCD, allowing predictions to be made for the $g_1$ structure function at much smaller $x$. Anticipating future data from the Electron-Ion Collider, we assess the impact of electromagnetic and parity-violating polarization asymmetries on $g_1$ and demonstrate an extraction of the individual flavor helicity PDFs at small $x$.
Analytical study of the rapidity distribution of the final state particles in deep inelastic scattering at small x is presented. We separate and analyse three sources of particle production: fragmentation of the quark-antiquark pair, accompanying coherent soft gluon radiation due to octet color exchange in the t-channel, and fragmentation of gluons that form parton distribution functions. Connection to Catani-Ciafaloni-Fiorani-Marchesini (CCFM) equations and the role of gluon reggezation are also discussed.
Transverse momentum dependent (TMD) distributions at small x exhibit a rich infinite twist structure that encompasses the leading twist (partonic) distributions as well as the physics of gluon saturation. Progress to further the connection between the standard TMD framework at moderate x and small x has been recently made. In this context, we show that light cone Wilson line operators at small-x can be formulated in terms of transverse gauge links. This new formulation of small x operators allows a direct matching with the standard leading twist gluon TMD distributions and provides an efficient and general prescription for computing TMD distributions at small x beyond leading twist.
We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron $beta$ decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays $B_1 to B_2 + W_{rm off-shell}$ and $W_{rm off-shell} to ell + u_ell$ whereas neutron $beta$ decays are analyzed as true three-body decays $n to p + e^- +bar u_e$. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron $beta$ decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the $q^2$ averages of the observables up to NLO and NNLO in the recoil parameter $delta=(M_n-M_p)/(M_n+M_p)= 0.689cdot 10^{-3}$. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.
The nuclear modification factor $R_{pA}(p_T)$ provides information on the small-$x$ gluon distribution of a nucleus at hadron colliders. Several experiments have recently measured the nuclear modification factor not only in minimum bias but also for central $pA$ collisions. In this paper we analyze the bias on the configurations of soft gluon fields introduced by a centrality selection via the number of hard particles. Such bias can be viewed as reweighting of configurations of small-$x$ gluons. We find that the biased nuclear modification factor ${cal Q}_{pA}(p_T)$ for central collisions is above $R_{pA}(p_T)$ for minimum bias events, and that it may redevelop a Cronin peak even at small $x$. The magnitude of the peak is predicted to increase approximately like $1/{A_{perp}}^ u$, $ usim0.6pm0.1$, if one is able to select more compact configurations of the projectile proton where its gluons occupy a smaller transverse area $A_perp$. We predict an enhanced ${cal Q}_{pp}(p_T)-1 sim 1/(p_T^2)^ u$ and a Cronin peak even for central $pp$ collisions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
