We present a general formalism for the evaluation of time-reversal odd parton distributions. This formalism is applied to the evaluation of the two T-odd TMDs allowed at the twist-2 level, i.e., the Sivers and the Boer-Mulders functions. We have performed the calculation for two different models of proton structure: a non relativistic constituent quark model and the MIT bag model. The results obtained in both models are compared. So are the two T-odd functions. We comment on the fulfilment of the Burkardt sum rule as well as on the current status of T-odd TMDs in phenomenology.
A formula for the single transverse spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision is derived. We focuss on the chiral-odd contribution where the transversity distribution and the chiral-odd spin-independent twist-3 distribution contributes. This contribution is expected to give rise to a large effect at $x_F\to -1$.
We present an estimate of a chiral-odd contribution to the single transverse-spin asymmetry in the large-$p_T$ pion production in the nucleon-nucleon collision. In this contribution the transversity distribution and the chiral-odd spin-independent twist-3 distribution appear. Because of the smallness of the corresponding hard cross section, this term turned out to be negligible in all kinematic regions compared with the chiral-even contribution.
A two Higgs doublet model is employed to study the production of a CP-odd Higgs boson ($A$) associated with a large transverse momentum jet ($j$) at hadron supercolliders. The cross section of $pp \to jA+X$ is evaluated with four subprocesses: $gg \to gA$, $gq \to qA$, $g\bar{q} \to \bar{q}A$ and $q\bar{q} \to gA$. We find that $pp \to jA+X$ is a significant source of CP-odd Higgs bosons at future hadron supercolliders.
We study the transverse momentum dependent quark-gluon-quark correlation function. Using a spectator diquark model, we calculate the eight time-reversal-odd interaction-dependent twist-3 quark distributions appearing in the decomposition of the transverse momentum dependent quark-gluon-quark correlator. In order to obtain finite results, we assume a dipole form factor for the nucleon-quark-diquark coupling, instead of a point-like coupling. The results are compared with the time-reversal-odd interaction-independent twist-3 TMDs calculated in the same model.
We have scrutinized the transverse momentum dependent quark-gluon-quark correlation function. We have utilized the light-front quark-diquark model to study the time-reversal-odd interaction-dependent twist-3 gluon distributions which we have obtained from the disintegration of the transverse momentum dependent quark-gluon-quark correlator. Specifically, we have studied the behavior of $\tilde{e}_{L}$ and $\tilde{e}_{T}$ while considering our diquark to be an axial-vector.
We investigate the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively. We present overlap formulas for the chiral-odd GPDs in terms of light-front wave functions (LFWFs) of the proton both in the ERBL and DGLAP regions. We calculate them in a field theory inspired model of a relativistic spin 1/2 composite state with the correct correlation between the different LFWFs in Fock space, namely that of the quantum fluctua…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
We study the time-reversal odd quark fragmentation function and its consequences on the hard processes. T-odd quark fragmentation function may arise, although QCD is T-invariant, from the non-perturbative dynamics in the fragmentation process. Assuming the factorization, we extract the T-odd fragmentation function from the inclusive pion production in the transversely polarized proton-proton collision. We then estimate the single spin asymmetry $A_{OT}$ of the semi-inclusive deep inelastic scattering with unpolarized lepton and the transversely polarized proton. We also discuss the meson cloud…
The T-odd quark distrbutions are shown to vanish in the chiral sigma model in contrast to the opposite widespread opinion. This failure of the chiral sigma model is a feature of the model itself and has nothing to do with the recent progress in the clarification of the status of the T-odd distributions in QCD.
Within the framework of light-cone quantization we derive the overlap representation of generalized parton distributions for transversely polarized quarks using the Fock-state decomposition in the transverse-spin basis. We apply this formalism to the case of light-cone wave functions in a constituent quark model giving numerical results for the four chiral-odd generalized parton distributions in a region where they describe the emission and reabsorption of a quark by the nucleon. With the transversity distribution obtained in the forward limit of the generalized distribution, we provide some p…
We compute the transverse single spin asymmetry in forward $p^\uparrow p \to hX$ and $p^\uparrow A \to hX$ collisions from the odderon mechanism originally suggested by Kovchegov and Sievert [1]. Working in the hybrid approach of the Color Glass Condensate effective theory we firstly identify the relevant collinear parton distribution function (PDF) of the transversely polarized proton $p^\uparrow$ as the intrinsic twist-3 $g_T(x)$ distribution. We further argue that the complete polarized cross section also contains contributions from the kinematical and the dynamical twist-3 PDFs, in additio…
The bounds on the neutron electric dipole moment and T-odd nucleon-nucleon interaction are used to extract the limits on the effective CP-odd four-fermion operators containing strange quark field. This completes the study of the dim=5,6 CP-odd operators built from the light-quark fields. The limits are very strong and comparable to those obtained previously for operators containing up and down flavors. We also analyze the shift of the axionic vacuum, $θ_{eff}$, induced by four-fermion operators in the presence of PQ mechanism and conclude that this gives subleading contributions to CP-odd obse…
In a class of beyond-standard-model theories, CP-odd observables, such as the neutron electric dipole moment, receive significant contributions from flavor-neutral P-odd and CP-odd four-quark operators. However, considerable uncertainties exist in the hadronic matrix elements of these operators strongly affecting the experimental constraints on CP-violating parameters in the theories. Here we study their hadronic matrix elements in combined chiral perturbation theory and nucleon models. We first classify the operators in chiral representations and present the leading-order QCD evolutions. We t…
We present a study of the chiral-odd generalized parton distributions for $u$ and $d$ quarks in a proton using the light front wave functions of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We obtain the GPDs in terms of overlaps of the LFWFs. Numerical results for chiral-odd GPDs in momentum as well as transverse position spaces considering both zero and nonzero skewness($ζ$) are presented. For nonzero skewness, the GPDs are also evaluated in longitudinal position space.
We present preliminary results on the leading-twist transverse-momentum-dependent (TMD) gluon linearity function, which is directly connected to nucleon transverse-spin asymmetries originating from the density of linearly-polarized gluons. The function is calculated in a spectator-model framework for the parent proton and for the $f$-type gauge-link structure. Our work represents a further step toward the definition of a complete set of gluon TMD distributions at twist-2 that can be used to access the gluon dynamics inside nucleons and nuclei at new-generation colliders.
We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon.
The interaction dependent part of the $x^2$-moment of the twist-3 polarized parton distribution $g_2(x)$ is related to the transverse force acting on the active quark in deep-inelastic scattering off a transversely polarized nucleon immediately after it has absorbed the virtual photon. Similarly, the $x^2$-moment of the chirally odd twist-3 unpolarized parton distribution $e(x)$ can be related to the transverse force experienced by a transversely polarized quark ejected from a transversely polarized nucleon.
The azimuthal dependence of hadrons produced in lepton scattering off a polarized hadron probes the quark transverse-spin distributions. In the calculation of the asymmetries, transverse momenta of quarks in the distribution and fragmentation functions must be incorporated. In addition to the $\sin (ϕ+ ϕ_S)$ asymmetry for transversely polarized hadrons, known as the Collins effect, we find $\sin 2ϕ$ asymmetries for both transversely and longitudinally polarized hadrons.
We define a number of quark fragmentation functions for spin-0, -1/2 and -1 hadrons, and classify them according to their twist, spin and chirality. As an example of their applications, we use them to analyze semi-inclusive deep-inelastic scattering on a transversely polarized nucleon.
The T-odd top-quark chromoelectric dipole moment, $d_t$, is probed through top-quark-pair production via gluon fusion at the CERN LHC with the possibility of having polarized proton beams in account. At 1-$σ$ level, the typical CP-odd lepton energy and tensor correlations enable us to measure $Re(d_t)$ and $Im(d_t)$ up to the order of 10$^{-18}$ ($g_scm$) in the unpolarized case and the initial CP-odd gluon spin correlation allows us to probe $Im(d_t)$ up to the order of 10$^{-20}$ ($g_scm$) for $\sqrt{s}=14$ TeV and the integrated luminosity $L_{pp}=10 fb^{-1}$.
Generalized Parton Distributions (GPDs) provide information on the distribution of quarks in impact paarmeter space. For transversely polarized nucleons, these impact parameter distributions are transversely distorted and this deviation from axial symmetry leads on average to a net transverse force from the spectators on the active quark in a DIS experiment. %The strength of that force can be related to twist-3 PDFs. This force when acting along the whole trajectory of the active quark leads to a transverse single-spin asymmetries. For a longitudinally polarized nucleon target, the transverse …
The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration has opened up new possibility to measure chiral-odd distribution functions through semi-inclusive deep-inelastic scatterings. Here, predictions are given for the twist-2 and twist-3 chiral-odd distribution functions of the nucleon within the framework of the chiral quark soliton model, with full inclusion of the vacuum polarization effects as well as the subleading $1/N_c$ corrections. The importance of the vacuum polarization effects is demonstrated by showing that the so-called Soffer inequality holds no…
We derive a nonperturbative transverse momentum distribution for partons using a potential model to describe the quark-quark interaction inside the proton. We use this distribution to calculate the diferential cross-section of $π^0$-production for intermediate values of transverse momentum in $p-p$ collisions at high energies. Assuming a variable string tension constant for the quark-quark potential we obtain a very good description of the experimental data at different energies. The corresponding values of the mean transverse momentum of the partons are essentially lower than those obtained u…
We calculate the q q correlation function associated to transverse target lepton-nucleon inclusive deep-inelastic scattering by direct evaluation of the corresponding matrix element. We use the electromagnetic impact parameter potential for a transversely polarized nucleon to define the q q correlation function for each avor in terms of the field components of that avor. The results are compared with the two existing models for the q q correlator. Using the calculated q q correlation function, we estimated the transverse target SSA in IDIS process.
Accounting for transverse momenta of the quarks, a longitudinal quark spin asymmetry exists in a transversely polarized nucleon target. The relevant leading quark distribution $g_{1T}(x,k_T^2)$ can be measured in the semi-inclusive deep-inelastic scattering. The average $k_T^2$ weighted distribution function $g^{(1)}_{1T}$ can be obtained directly from the inclusive measurement of $g_2$.
Quarkonium production in hadron collisions at low transverse momentum $q_\perp \ll M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of $η_c$ or $η_b$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft d…
In the symmetric string fragmentation recipe adopted by PYTHIA for jet simulations, the transverse momenta of successive quarks are uncorrelated. This is a simplification but has no theoretical reason. Transverse momentum correlations are naturally expected, for instance, in a covariant multiperipheral model of quark hadronization. We propose a simple recipe of string fragmentation which lead to such correlations. The definition of the jet axis and its relation with the primordial transverse momentum of the quark is also discussed.
The 2+1 dimensional (2 space dimensions and 1 time dimension) Transverse Lattice is constructed using the Color Dielectric formalism. The dynamics of the Color Dielectric link fields are not known from first principles, so an ansatz for the effective action is made, which is truncated at fourth order in the fields. Since the Transverse Lattice is a Light-Front field theory, it lacks manifest rotational invariance. This lack of manifest rotational invariance is exploited to determine the couplings in the effective action by calculating the Quark/Anti-quark Potential, an observable that is very …
We study the semi-classical interpretation of the $x^3$ and $x^4$ moments of twist-3 parton distribution functions (PDFs). While no semi-classical interpretation for the higher moments of $g_T(x)$ and $e(x)$ was find, the $x^3$ moment of the chirally odd spin-dependent twist-3 PDF $h_L^3(x)$ can be related to the longitudinal gradient of the transverse force on transversely polarized quarks in longitudinally polarized nucleons in a DIS experiment. We discuss how this result relates to the torque acting on a quark in the same experiment. This has further implications for comparisons between tha…
We study the spin-dependent quark distributions at large transverse momentum. We derive their transverse momentum behaviors in the collinear factorization approach in this region. We further calculate the angular distribution of the Drell-Yan lepton pair production with polarized beams and present the results in terms of the collinear twist-three quark-gluon correlation functions. In the intermediate transverse momentum region, we find that the two pproaches: the collinear factorization and the transverse momentum dependent factorization approaches are consistent in the description of the lept…
The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon ver…
Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent(TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with $J^{PC}=0^{++}, 2^{++}$ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop.
We study the angular distribution of the charged lepton in the top-quark decay into a bottom quark and a W boson which subsequently decays into \ellν_{\ell}, when a hard gluon is radiated off. The absorptive part of the t \to bWg decay amplitudes, which gives rise to T-odd asymmetries in the distribution, is calculated at the one-loop level in perturbative QCD. The asymmetries at a few percent level are predicted, which may be observable at future colliders.
We revisit the effect of CP violating anomalous top-quark couplings in $t\bar{t}$ production and decay. We consider $t\bar{t}$ production through gluon fusion (and light $q{\bar q}$ annihilation) followed by top-quark decay into $bW$ or $b\ellν$. We find explicit analytic expressions for all the triple products generated by the anomalous couplings that fully incorporate all spin correlations. Our results serve as a starting point for numerical simulations for the LHC.
We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a $ W $-gauge boson where the helicities of the $ W $ are specified as longitudinal, transverse-plus and transverse-minus. Together with the $ O(α_s) $ corrections these corrections may become relevant for the determination of the mass of the top quark through angular decay measurements.
We present a calculation of the perturbative quark-to-quark transverse parton distribution function at next-to-next-to-leading order based on a gauge invariant operator definition. We demonstrate for the first time that such a definition works beyond the first non-trivial order. We extract from our calculation the coefficient functions relevant for a next-to-next-to-next-to-leading logarithmic $Q_T$ resummation in a large class of processes at hadron colliders.
I present NNLO approximate calculations, based on NNLL resummation, for top quark differential transverse momentum and rapidity distributions. In particular recent results are presented for top-pair production and single-top production processes and compared to the latest experimental data from the LHC.
The chirally-odd twist-3 nucleon distribution e(x) is studied in the large-Nc limit in the framework of the chiral quark-soliton model at a low normalization point of about 0.6 GeV. The remarkable result is that in the model e(x) contains a delta-function-type singularity at x=0. The regular part of e(x) is found to be sizeable at the low scale of the model and in qualitative agreement with bag model calculations.
We study the transverse momentum distribution for a $pair$ of heavy quarks produced in hadron-hadron interactions. Predictions for the large transverse momentum region are based on exact order $α_s^3$ QCD perturbation theory. For the small transverse momentum region, we use techniques for all orders resummation of leading logarithmic contributions associated with initial state soft gluon radiation. The combination provides the transverse momentum distribution of heavy quark pairs for all transverse momenta. Explicit results are presented for $b\bar b$ pair production at the Fermilab Tevatron c…
There exist several recent studies of the top-quark CEDM in the context of searching for CP violating signals in top-quark pair production at the LHC. Most of these studies constrain the CEDM either from deviations in the top-pair cross section from its standard model value, or from T-odd asymmetries in the dimuon channel. Motivated by ATLAS and CMS interest, we extend the study of T-odd asymmetries to the lepton plus jets channel. At the parton level, using MadGraph, we identify the most promising signals and their statistical sensitivity. We find that the signals with larger sensitivity to t…
Transverse polarization of $Λ^0$ hyperons in inclusive photoproduction at x_F>0 is tackled within the framework of the quark recombination model, which has been successfully applied to the polarization of different hyperons in a variety of unpolarized hadron-hadron reactions. The results are compared with recent experimental data of HERMES.
We present the general framework to calculate chiral-odd generalized parton distributions in the overlap representation using the Fock-state decomposition in the transverse spin basis. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon. Numerical results are obtained by applying the formalism to the case of light-cone wavefunctions of constituent quark models.
We report progresses on leading-twist transverse-momentum-dependent (TMD) gluon distributions, calculated in a spectator-model framework for the parent nucleon. We encode in our formalism a fit-based parameterization for the spectator-mass density, suited to describe the gluon content of the proton in a wide range of $x$. We present preliminary results on the $f$-type Sivers function, a key ingredient to access relevant spin-asymmetries emerging when the nucleon is transversely polarized. These studies are helpful to shed light on the gluon dynamics inside nucleons and nuclei, which is one of …
We study the detectability of the lightest CP-odd Higgs boson of the NMSSM, $a_1$, at the LHC through its production in association with a bottom-quark pair followed by the $a_1\to b\bar b$ decay. It is shown that, for large $\tanβ$ and very high luminosity of the LHC, there exist regions of the NMSSM parameter space that can be exploited to detect the $a_1$ through this channel. This signature is a characteristic feature of the NMSSM in comparison to the MSSM, as $a_1$ masses involved are well below those allowed in the MSSM for the corresponding CP-odd Higgs state.
We present the calculation of the leading contribution to the quark Sivers function at small-Bjorken $x$. This calculation uses the high energy scattering approximation and operator formalism developed by Kovchegov and Sievert to obtain a dominant contribution to the quark Sivers function coming from the spin-dependent odderon, in agreement with the results of Dong, Zhen, and Zhou. We then calculate this dominant contribution in the diquark model of the proton to obtain a small-$x$ estimate for the Sivers function.
I present some results about transverse momentum dependent distribution and fragmentation functions. Firstly I illustrate a simple model, with predictive power about the energy behavior, for T-odd, chiral odd functions. Moreover I propose a slight modification in extracting transversity from HERMES data, so as to apply correctly factorization. Lastly I suggest a method for determining the quark transverse polarization in an unpolarized or spinless hadron.
We present results for leading-twist azimuthal asymmetries in semi-inclusive lepton-nucleon deep-inelastic scattering due to naively time-reversal odd transverse-momentum dependent parton distribution functions from the light-cone constituent quark model. We carefully discuss the range of applicability of the model, especially with regard to positivity constraints and evolution effects. We find good agreement with available experimental data from COMPASS and HERMES, and present predictions to be tested in forthcoming experiments at Jefferson Lab.
We report on a calculation of the chiral odd generalized parton distributions (GPDs) for non-zero skewness $ζ$ in transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively using overlaps of light-front wave functions (LFWFs).
We present a detailed analysis of the Bc form factors in the BSW framework, by investigating the effects of the flavor dependence on the average transverse quark momentum inside a meson. Branching ratios of two body decays of Bc meson to pseudoscalar and vector mesons are predicted.
We present the results of an O(alpha_s) calculation of the transverse polarization of top quarks produced in e+e- annihilation. In a first step we determine the transverse polarization of the top with regard to the hadron plane spanned by the (q,bar q,g) system. We then rotate the transverse components of the polarization to the lepton plane spanned by the (q,e+,e-) system. After azimuthal averaging we determine the three remaining inclusive transversely polarized structure functions. Together with the one-loop and Born term contributions they determine the sin(theta) and sin(2*theta) beam-qua…
The T-odd top-quark chromoelectric dipole moment (tCEDM) is probed through top-quark-pair production via gluon fusion at the CERN Large Hadron Collider (LHC) by considering the possibility of having polarized protons. The complete analytic expressions for the tree-level helicity amplitudes of gg-> ttbar is also presented. For the derived analytic results we determine the 1-sigma statistical sensitivities to the tCEDM form factor for (i) typical CP-odd observables composed of lepton and anti-lepton momenta from t and tbar semileptonic decays for unpolarized protons, and (ii) a CP-odd event asym…
We calculate transverse momentum dependent quark splitting kernels $P_{gq}$ and $P_{qq}$ within $k_T$-factorization, completing earlier results which concentrated on gluon splitting functions $P_{gg}$ and $P_{qg}$. The complete set of splitting kernels is an essential requirement for the formulation of a complete set of evolution equations for transverse momentum dependent parton distribution functions and the development of corresponding parton shower algorithms.
We consider the leading order result for polarized leptoproduction, putting emphasis on transverse momentum dependent effects appearing in azimuthal asymmetries. Measurements of weighted cross sections enable extraction of the distribution of transversely polarized quarks. We focus on the distribution in a longitudinally polarized hadron and estimate the expected asymmetries in leptoproduction.
Little Higgs models are often endowed with a T-parity in order to satisfy electroweak precision tests and give at the same time a stable particle which is a candidate for cold dark matter. This type of models predicts a set of new T-odd fermions in addition to the heavy gauge bosons of the Little Higgs models, which may show interesting signatures at colliders. In this paper, we study the signatures of strong and electroweak pair production of the first two generations of T-odd quarks at the LHC. We focus on the dileptonic signatures (p p to l l j j MET) with (a) opposite-sign dileptons and (b…
We consider neutralino production and decay e^+e^ --> chi^0_i chi^0_j, chi^0_j --> chi^0_1 f \bar{f} at a linear collider with transverse e^+ and e^- beam polarization. We propose CP asymmetries by means of the azimuthal distribution of the produced neutralinos and of that of the final leptons, while taking also into account the subsequent decays of the neutralinos. We include the complete spin correlations between production and decay. Our framework is the Minimal Supersymmetric Standard Model with complex parameters. In a numerical study we show that there are good prospects to observe these…
We show that soft-gluon twist-3 contributions to single-spin asymmetries (SSA) in hard processes may be expressed in the form of effective T-odd Sivers distributions, whose signs and scales are modified by process-dependent colour factors. We thus prove that the Sivers mechanism may also be applied at large transverse momenta. We stress that twist-3 SSA in semi-inclusive deeply inelastic scattering and Drell-Yan processes are suppressed by transverse momentum rather than a virtual-photon momentum transfer and thus naively correspond to twist two at the hadronic level. More rigorously, the tran…
We calculate the contribution arising from nonperturbative quark-gluon chromomagnetic interaction to the high energy total quark-quark cross section and to gluon distributions in nucleon. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons. We argue that the Odderon, which is the $P=C=-1$ partner of Pomeron, is governed by the spin-flip component related to nonpert…
