arXiv subjects
Publications and source records attributed to J. P. Ma.
A new method is proposed to calculate wave functions in $k_T$-factorization in \cite{LiMi} as a comment about our paper \cite{FMW}. We point out that the results obtained with the method are in conflict with the translation invariance and depend on the chosen contours for loop-integrals. Therefore, the method is in principle unacceptable and the results with the method cannot be correct.
In the $k_T$-factorization for exclusive processes, the nontrivial $k_T$-dependence of perturbative coefficients, or hard parts, is obtained by taking off-shell partons. This brings up the question of whether the $k_T$-factorization is gauge invariant. We study the $k_T$-factorization for the case $πγ^* \to γ$ at one-loop in a general covariant gauge. Our results show that the hard part contains a light-cone singularity that is absent in the Feynman gauge, which indicates that the $k_T$-factorization is {\it not} gauge invariant. These divergent contributions come from the $k_T$-dependent wave function of $π$ and are not related to a special process. Because of this fact the $k_T$-factorization for any process is not gauge invariant and is violated. Our study also indicates that the $k_T$-factorization used widely for exclusive B-decays is not gauge invariant and is violated.
The k_T-factorization has been widely used for exclusive decays of B-mesons. In this factorization the pertubative coefficients are extracted from scattering of off-shell partons. Because the off-shellness of partons the extracted pertubative coefficients in general are not gauge-invariant. We show that these perturbative coefficients contain gauge-dependent singularities beyond tree-level. This leads to that the k_T-factorization is gauge-dependent and violated in the general covariant gauge. This is not consistent with expectations of physics. In the factorization there exist two different wave functions for a B-meson in general. We show that the two wave functions satisfy different evolution equations whose solutions are used to re-sum large log's. Based on this fact, the rseummation of large log's at leading log approximation in the widely used k_T-factorization with only one wave function is inconsistent.
Single transverse-spin asymmetries have been studied intensively both in experiment and theory. Theoretically, two factorization approaches have been proposed. One is by using transverse-momentum-dependent factorization and the asymmetry comes from the so called Sivers function. Another is by using collinear factorization where the nonperturbative effect is parameterized by a twist-3 hadronic matrix element. However, the factorized formulas for the asymmetries in the two approaches are derived at hadron level formally by diagram expansion, where one works with various parton density matrices of hadrons. If the two factorizations hold, they should also hold at parton level. We examine this for Drell-Yan processes by replacing hadrons with partons. By calculating the asymmetry, Sivers function and the twist-3 matrix element at nontrivial leading order of $α_s$, we find that we can reproduce the result of the transverse-momentum-dependent factorization. But we can only verify the result of the collinear factorization partly. Two formally derived relations between Sivers function and the twist-3 matrix element are also examined with negative results.
This physics book provides detailed discussions on important topics in $τ$-charm physics that will be explored during the next few years at \bes3 . Both theoretical and experimental issues are covered, including extensive reviews of recent theoretical developments and experimental techniques. Among the subjects covered are: innovations in Partial Wave Analysis (PWA), theoretical and experimental techniques for Dalitz-plot analyses, analysis tools to extract absolute branching fractions and measurements of decay constants, form factors, and CP-violation and \DzDzb-oscillation parameters. Programs of QCD studies and near-threshold tau-lepton physics measurements are also discussed.
We study the observed enhancement of a $p\bar p$ system near the threshold in the process $J/ψ\to γp\bar p$ and $e^+ e^- \to p\bar p$. From early studies the enhancement can be explained by final state interactions, which are in general taken into account with some potential models. In this work we offer a simple approach within quantum field theory to explain the observed enhancement. We point out that among different final state interactions the rescattering in a $N\bar N$ system though exchange of $π$ is the most important. The effects of the rescattering is completely fixed by the well-known coupling $g_{πNN}$. Our results show that the enhancement in $J/ψ\to γp\bar p$ and $e^+ e^- \to p\bar p$ can be well described with the rescattering effects.
The recently discovered $X$(3872) has many possible interpretations. We study the production of $X$(3872) with PANDA at GSI for the antiproton-proton collision with two possible interpretations of X(3872). One is as a loosely-bound molecule of $D$-mesons, while another is a 2P charmonium state $χ_{c1}$ (2P). Using effective couplings we are able to give numerical predictions for the production near the threshold and the production associated with $π^0$. The produced $X$(3872) can be identified with its decay $J/ψπ^+π^-$. We also study the possible background near the threshold production for $X(3872) \to J/ψπ^+π^-$. With the designed luminosity $1.5{\rm fb}^{-1}$ per year of PANDA we find that the event number of $p\bar p \to J/ψπ^+π^-$ near the threshold is at the order of $10^6 \sim 10^8$, where the large uncertainty comes from the total decay width of X(3872). Our study shows that at the threshold more than about 60% events come from the decay of X(3872) and two interpretations are distinguishable from the line-shape of the production. With our results we except that the PANDA experiments will shed light on the property of X(3872).
We study two body decays of a scalar glueball. We show that in QCD a spin-0 pure glueball (a state only with gluons) cannot decay into a pair of light quarks if chiral symmetry holds exactly, i.e., the decay amplitude is chirally suppressed. However, this chiral suppression does not materialize itself at the hadron level such as in decays into $π^+π^-$ and $K^+K^-$, because in perturbative QCD the glueball couples to two (but not one) light quark pairs that hadronize to two mesons. Using QCD factorization based on an effective Lagrangian, we show that the difference of hadronization into $ππ$ and $KK$ already leads to a large difference between ${\rm Br} (π^+π^-)$ and ${\rm Br}(K^+K^-)$, even the decay amplitude is not chirally suppressed. Moreover, the small ratio of $R={\rm Br}(ππ)/{\rm Br}(K\bar K)$ of $f_0(1710)$ measured in experiment does not imply $f_0(1710)$ to be a pure glueball. With our results it is helpful to understand the partonic contents if ${\rm Br}(ππ)$ or ${\rm Br}(K\bar K)$ is measured reliably.
We propose to study hadron-hadron scattering using lattice QCD in an asymmetric box which allows one to access more non-degenerate low-momentum modes for a given volume. The conventional Lüscher's formula applicable in a symmetric box is modified accordingly. To illustrate the feasibility of this approach, pion-pion elastic scattering phase shifts in the I=2, J=0 channel are calculated within quenched approximation using improved gauge and Wilson fermion actions on anisotropic lattices in an asymmetric box. After the chiral and continuum extrapolation, we find that our quenched results for the scattering phase shifts in this channel are consistent with the experimental data when the three-momentum of the pion is below 300MeV. Agreement is also found when compared with previous theoretical results from lattice and other means. Moreover, with the usage of asymmetric volume, we are able to compute the scattering phases in the low-momentum range (pion three momentum less than about 350MeV in the center of mass frame) for over a dozen values of the pion three-momenta, much more than using the conventional symmetric box with comparable volume.
In the collinear factorization of the form factor for the transition $γ^* π^0 \to γ$ the hard part contains double log terms as $\ln^2 x$ with $x$ as the momentum fraction of partons from 0 to 1. A simple exponentiation for resummation leads to divergent results. We study the resummation of these $\ln^2 x$ terms. We show that the $\ln^2 x$ terms come partly from the light-cone wave function(LCWF) and partly from the form factor. We introduce a jet factor to factorize the $\ln^2 x$ term in the form factor. To handel the $\ln^2 x$ terms from the LCWF we introduce a nonstandard light-cone wave function(NLCWF) with the gauge links off the light-cone direction. An interesting relation between two wave function is found. With the introduced NLCWF and the jet factor we can re-factorize the form factor and obtain a new hard part which does not contain terms with $\ln^2 x$. Beside the renormalization scale $μ$ the introduce NLCWF and jet factor have extra scales to characterize their $x$-behaviors. Using the evolutions of the extra scales and the relation we can do the resummation perturbatively in sense that the LCWF is the only nonpertubative object in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with the resummation and that without the resummation, and the resummed predictions can describe the experimental data.
Nonrelativistic QCD provides a systematic approach for inclusive decays and productions of a quarkonium. By taking color-octet components into account, the approach can explain the $ψ'$-anomaly at Tevatron, where the measured production rate at large transverse momentum $p_\perp$ is in order of magnitude larger than the predicted with color-singlet components only. With the approach one can predict that the produced $J/ψ$ and $ψ'$ at large $p_\perp$ will be transversely polarized. But the prediction fails in confronting with experimental measurements and this generates a puzzle. We examine the role of spin-flip interactions in the spin density matrix of the transition of a color-octet charm quark pair into $J/ψ$ and $ψ'$. These interactions will introduce new nonperturbative parameters in the spin density matrix. Our result shows that the impact of the interactions is always to dilute the polarization and can be very significant. Taking the impact into account, predictions for the polarization are more close to the measured than the previous predicted. The same can also be expected for the polarization of $J/ψ$.
With a consistent definition of transverse-momentum dependent (TMD) light-cone wave function, we show that the amplitude for the process $γ^* π^0 \toγ$ can be factorized when the virtuality of the initial photon is large. In contrast to the collinear factorization in which the amplitude is factorized as a convolution of the standard light-cone wave function and a hard part, the TMD factorization yields a convolution of a TMD light-cone wave function, a soft factor and a hard part. We explicitly show that the TMD factorization holds at one loop level. It is expected that the factorization holds beyond one-loop level because the cancelation of soft divergences is on a diagram-by-diagram basis. We also show that the TMD factorization helps to resum large logarithms of type $\ln^2x$.
Recently the BES collaboration has announced observation of a resonant state in the $π^+π^- η'$ spectrum in $J/ψ\to γπ^+π^-η'$ decay. Fitting the data with a $0^{-+}$ state, the mass is determined to be 1833.7 MeV with $7.7σ$ statistic significance. This state is consistent with the one extracted from previously reported $p \bar p$ threshold enhancement data in $J/ψ\to γp \bar p$. We study the properties of this state using QCD anomaly and QCD sum rules assuming X(1835) to be a pseudoscalar and show that it is consistent with data. We find that this state has a sizeable matrix element $<0|G\tilde G|G_p>$ leading to branching ratios of $(2.61\sim 7.37)\times 10^{-3}$ and $(2.21\sim 10.61)\times 10^{-2}$ for $J/ψ\to γG_p$ and for $G_p \to π^+π^- η'$, respectively. Combining the calculated branching ratio of $J/ψ\to γG_p$ and data on threshold enhancement in $J/ψ\to γp \bar p$, we determine the coupling for $G_p- p-\bar p$ interaction. We finally study branching ratios of other $J/ψ\to γ+ {three mesons}$ decay modes. We find that $J/ψ\to γG_p \to γ(π^+π^- η, K K π^0)$ can provide useful tests for the mechanism proposed.
Transverse-momentum dependent (TMD) light-cone wave functions of a light meson are important ingredients in the TMD QCD factorization of exclusive processes. This factorization allows one conveniently resum Sudakov logarithms appearing in collinear factorization. The TMD light-cone wave functions are not simply related to the standard light-cone wave functions in collinear factorization by integrating them over the transverse momentum. We explore relations between TMD light-cone wave functions and those in the collinear factorization. Two factorized relations can be found. One is helpful for constructing models for TMD light-cone wave functions, and the other can be used for resummation. These relations will be useful to establish a link between two types of factorization.
We show that the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. The factorization is achieved by expanding the small velocity v, which the c- or \bar c- quark moves inside a rest quarkonium with. At leading order of v the twist-2 light-cone wave-functions of eta_c and J/ψcan be factorized as the product of a perturbative function and a NRQCD matrix element. The perturbative function is calculated at one-loop level and free from any soft divergence. Our results can be used for the production of J/ψη_c through e^+e^- -annihilation and of a charmonium in B-decays, which are studied in experiment of two B-factories.
With a consistent definition of transverse-momentum-dependent(TMD) light-cone wave function of $B$-meson, we show that the amplitude of the radiative leptonic B-decay can be factorized at one-loop level as a convolution with the wave function and a perturbative coefficient function, combined with a soft factor. In this TMD factorization, the transverse momenta of partons in the $B$-meson are taken into account and all soft divergences are contained in the wave function and the soft factor. The coefficient function is infrared-safe. The factorization works on a diagram-by-diagram basis and is possible to extend beyond one loop. With the factorization the large logarithms in the perturbative function can be simply resummed. Our work shows that the result of collinear factorization for the decay can be derived from that of TMD factorization. Therefore, the two factorizations for the case here are simply related to each other.
The approach of nonrelativistic QCD(NRQCD) factorization was proposed to study inclusive production of a quarkonium. It is widely used and successful. However, a recent study of gluon fragmentation into a quarkonium at two-loop level shows that the factorization is broken. It is suggested that the color-octet NRQCD matrix elements should be modified by adding a gauge link to restore the factorization. The modified matrix elements may have extra soft-divergences at one-loop level which the unmodified can not have, and this can lead to a violation of the universality of these matrix elements. In this letter, we examine in detail the NRQCD factorization for inclusive quarkonium production in $e^+ e^-$ annihilation at one-loop level. Our results show that the factorization can be made without the modification of NRQCD matrix elements and it can also be made for relativistic corrections. It turns out that the suggested gauge link will not lead to nonzero contributions to color-octet NRQCD matrix elements at one-loop level and at any order of $v$. Therefore the universality holds at least at one-loop level.