arXiv subjects

T. N. Pham

Publications and source records attributed to T. N. Pham.

At least 19 recordsLinked to original sources

arXiv2018

A Simple Expression for Heavy to Light Meson Semileptonic Decays Form Factors

Like the two-photon and two-gluon decays of the $P$-wave $χ_{c0,2}$ and $χ_{b0,2}$ charmonium state for which the Born term produces a very simple decgays amplitude in terms of an effective Lagrangian with two-quark local operator, the Born term for the processes $c\bar{d} \to (π,K) \ell ν$ and $b \bar{d}\to (π, K) \ellν$, could also produce the $D$ and $B$ meson semileptonic decays with the light meson $π, K$ in the final state. In this approach to heavy-light meson form factors with the $π$, K meson treated as Goldstone boson, a simple expression is found for the decays form factors, given as~: $ f_{+}(0)/(1 -q^{2}/(m_{H}^{2}+ m_π^{2}))$, with $H=D,B$ for $D,B \to π$ form factors, and $f_{+}(0)/(1 -q^{2}/(m_{H}^{2}+ m_{K}^{2}))$ for $B,D\to K$ form factor. The purpose of this paper is to show that this expression for the form factors could describe rather well the $q^{2}$- behaviour observed in the BaBar, Belle and BESIII measurements and lattice simulation. In particular, the $D\to K$ form factors are in good agreement with the measured values in the whole range of $q^{2}$ showing evidence for $SU(3)$ breaking with the presence of $m_{K}^{2}$ term in the quark propagator, but some corrections to the Born term are needed at large $q^{2}$ for $D,B \to π$ form factors.

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arXiv2016

Testing QCD factorization with phase determinations in $B\to Kπ$,$Kρ$ and $ K^{*}π$ decays

The success of QCD factorization(QCDF) in predicting branching ratios for charmless $B$ decays to light pseudoscalar and vector mesons and the small CP asymmetries measured at $BABAR$, Belle and LHCb show that the phase in these decays, as predicted by QCDF, are not large. For a precise test of QCDF one needs to extract from the measured decay rates, the phase of the decay amplitude which appears in the interference terms between the tree and penguin contribution. Since the tree amplitude is known at the leading order in $Λ_{\rm QCD}/m_{b}$ and is consistent with the measured tree-dominated decay rates, the QCDF value for the tree amplitude can be used with the measured decay rates to obtain the phases in $B\to Kπ$,$Kρ$, and $ K^{*}π$ decay rates. This is similar to the extraction of the final-state interaction phases in the interference term between $p\bar{p}\to J/Ψ\to e^{+}e^{-}$ and $p\bar{p}\to e^{+}e^{-} $ and in $J/Ψ\to 0^{-}0^{-}$ done previously. In this paper, we present a determination of the phase between the $I=3/2$ tree and $I=1/2$ penguin amplitudes in $B\to Kπ$,$Kρ$ , and $ K^{*}π$ decays using the measured decay rates and the QCDF $I=3/2$ tree amplitude obtained from the $I=2$ $B^{+}\to π^{+}π^{0},ρ^{0}π^{+}, ρ^{+}π^{0 tree-dominated decays and compare the result with the phase given by QCDF. It is remarkable that the phase extracted from experiments differs only slightly from the QCDF values. This shows that there is no large final-state interaction strong phase in $B\to Kπ$,$Kρ$, and $ K^{*}π$ decays.

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arXiv2015

$η-η^{\prime}$ mixing

The $η-η^{\prime}$ mixing mass term due to the derivative coupling $SU(3)\times SU(3)$ symmetry breaking term, produces an additional momentum-dependent pole term for processes with $η^{\prime}$, but is suppressed in the $η$ amplitude by a factor $m_η^{2}/m_{η^{\prime}}^{2}$. This seems to be the origin of the two-angle description of the pseudo-scalar decay constants used in the literature. In this paper, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, we show that the $η-η^{\prime}$ system could be described by a meson field renormalization and a new mixing angle $θ$ which differs from the usual mixing angle $θ_{P}$ by a small momentum-dependent mixing $d$ term. This new mixing scheme with exact treatment of the momentum-dependent mixing term, is actually simpler than the perturbation treatment and should be used in any determination of the $η-η^{\prime}$ mixing angle and the momentum-dependent mixing term. Assuming nonet symmetry for the $η_{0}$ singlet amplitude, from the sum rules relating $θ$ and $d$ to the measured vector meson radiative decays amplitudes, we obtain consistent solutions with $θ=-(13.99\pm 3.1)^{\circ}$, $d=0.12\pm 0.03$ from $ρ\toηγ$ and $η^{\prime}\toργ$ decays, for $ω$ , $θ=-(15.47\pm 3.1)^{\circ}$, $d=0.11\pm 0.03$, and for $ϕ$, $θ=-(12.66\pm 2.1)^{\circ}$, $d=0.10\pm 0.03$. It seems that vector meson radiative decays would favor a small $η-η^{\prime}$ mixing angle and a small momentum-dependent mixing term.

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arXiv2014

Test of SU(3) Symmetry in Hyperon Semileptonic Decays

Existing analyzes of baryon semileptonic decays indicate the presence of a small SU(3) symmetry breaking in hyperon semileptonic decays, but to provide evidence for SU(3) symmetry breaking, one would need a relation similar to the Gell-Mann--Okubo (GMO) baryon mass formula which is satisfied to a few percents, showing evidence for a small SU(3) symmetry breaking effect in the GMO mass formula. In this talk, I would like to present a similar GMO relation obtained in a recent work for hyperon semileptonic decay axial vector current matrix elements. Using these generalized GMO relations for the measured axial vector current to vector current form factor ratios, it is shown that SU(3) symmetry breaking in hyperon semileptonic decays is of $5-11%$ and confirms the validity of the Cabibbo model for hyperon semi-leptonic decays.

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arXiv2013

Pion as a Longitudinal Axial-Vector Meson $q\bar{q}$ Bound State

The success of the Adler-Bell-Jackiw(ABJ) chiral anomaly prediction for $π^{0}\to γγ$ decay rate shows that non-anomaly terms would make a negligible contribution to the decay rate, in agreement with the Sutherland-Veltman theorem. Thus the conventional $q\bar{q}$ bound-state description of the pion could not be valid since it would produce a $π^{0}\to γγ$ decay amplitude not suppressed in the soft pion limit, in contradiction with the Sutherland-Veltman theorem. Therefore, if the pion is to be treated as a $q\bar{q}$ bound state, this bound state would be a longitudinal axial-vector meson. In this paper, we consider the pion to be a longitudinal axial-vector meson $q\bar{q}$ bound state with derivative coupling for the pion $q\bar{q}$ Bethe-Salpeter(BS) wave function. We shall show that this BS wave function could produce a suppressed $π^{0}\to γγ$ decay amplitude in the soft pion limit, in agreement with the Sutherland-Veltman theorem. This explains the almost perfect agreement of the anomaly prediction with experiment and the suppression of the virtual one-photon exchange contribution in $η\to 3π$ decay. The Goldstone boson equivalence theorem used for longitudinal gauge bosons scattering in the electroweak standard model then identifies the longitudinal axial-vector meson $q\bar{q}$ bound state with the pion.

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arXiv2013

Test of SU(3) Symmetry in Hyperon Semileptonic Decays

Existing analyzes of baryon semileptonic decays indicate the presence of a small SU(3) symmetry breaking in hyperon semileptonic decays, but to provide evidence for SU(3) symmetry breaking, one would need a relation similar to the Gell-Mann Okubo(GMO) baryon mass formula which is satisfied to a few percents, showing evidence for SU(3) symmetry breaking in the divergence of the vector current matrix element. In this paper, we shall present a similar GMO relation for the hyperon semileptonic decay axial vector form factors. Using these relations and the measured axial vector current to vector current form factor ratios, we show that SU(3) symmetry breaking in hyperon semileptonic decays is of 5-11%.

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arXiv2011

CKM Matrix Elements

The current analysis of the Cabibbo-Kobayashi-Maskawa(CKM) quark mixing matrix uses the standard parametrisation by 3 mixing angles and the CP-violating KM phase. However it would be more convenient to express these mixing angle parameters in terms of the known CKM matrix elements like $V_{ud}$, $ V_{us}$, $ V_{ub}$, $V_{cb}$ and the CP-violating phase $δ$. The other CKM matrix elements are then expressed in terms of these known matrix elements instead of the standard mixing angles. In this paper, using $V_{ud}$, $ V_{us}$, $ V_{ub}$ and $V_{cb}$ from the current global fit, we show that the measured values for $|V_{td}/V_{ts}|$ and $\sinβ$ imply $γ=(68\pm 3)^{\circ}$ at which $\sinβ$ and $\sinα$ are near its maximum, consistent with the global fit.

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arXiv2011

Chiral Anomaly Effects and the BaBar Measurements of the $γγ^{*}\to π^{0}$ Transition Form Factor

The recent BaBar measurements of the $γγ^{*}\to π^{0}$ transition form factor show spectacular deviation from perturbative QCD prediction for large space-like $Q^{2}$ up to $34\,\rm GeV^{2}$. When plotted against $Q^{2}$, $Q^{2}F(Q^{2})$ shows steady increase with $Q^{2}$ in contrast with the flat $Q^{2}$ behavior predicted by perturbative QCD, and at $34\,\rm GeV^{2}$ is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes $Z^{0}\to π^{0}γ$, $e^{+}e^{-}\to π^{0}γ$ and apply our results to the $γ^{*}γ\to π^{0}$ transition form factor measured in the $e^{+}e^{-}\to e^{+}e^{-}π^{0}$ process with one highly virtual photon. We find that, the transition form factor $F(Q^{2})$ behaves as $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ and produces a striking agreement with the BaBar data for $Q^{2}F(Q^{2})$ with $m=132\,\rm MeV$ which also reproduces very well the CLEO data at lower $Q^{2}$.

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arXiv2011

$η-η^{\prime}$ Mixing Angle from Vector Meson Radiative Decays

The octet-singlet $η-η^{\prime}$ mixing mass term could have a derivative $O(p^{2})$ term as found in recent analysis of the $η-η^{\prime}$ system. This term gives rise to an additional momentum-dependent pole contribution which is suppressed by a factor $m_η^{2}/m_{η^{\prime}}^{2}$ for $η$ relative to the $η^{\prime}$ amplitude. The processes with $η$ meson can then be described, to a good approximation, by the momentum-independent mixing mass term which gives rise to a new $η-η^{\prime}$ mixing angle $θ_{P}$, like the old $η-η^{\prime}$ mixing angle used in the past, but a momentum-dependent mixing term $d$, like $\sin(θ_{0}-θ_{8})$ in the two-angle mixing scheme used in the parametrization of the pseudo-scalar meson decay constants in the current literature, is needed to describe the amplitudes with $η^{\prime}$. In this paper, we obtain sum rules relating $θ_{P}$ and $d$ to the physical vector meson radiative decays with $η$ and $η^{\prime}$, as done in our previous work for $η$ meson two-photon decay, and with nonet symmetry for the $η^{\prime}$ amplitude, we obtain a mixing angle $θ_{P}=-(18.76\pm 3.4)^{\circ}$, $d=0.10\pm 0.03$ from $ρ\toηγ$ and $η^{\prime}\toργ$ decays, for $ω$, $θ_{P}=-(15.81\pm 3.1)^{\circ}$, $d=0.02\pm 0.03$, and for $ϕ$, $θ_{P}=-(13.83\pm 2.1)^{\circ}$, $d=0.08\pm 0.03$. A larger value of $0.06\pm 0.02$ for $d$ is obtained directly from the nonet symmetry expression for the $η^{\prime}\toωγ$ amplitude. This indicates that more precise vector meson radiative decay measured branching ratios and higher order SU(3) breaking effects could bring these values for $θ_{P}$ closer and allows a better determination of $d$.

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arXiv2011

Chiral anomaly, triangle loop and the the $γγ^{*}\to π^{0}$ form factor

The recent BaBar measurements of the $γγ^{*}\to π^{0}$ form factor show spectacular deviation from perturbative QCD computations for large space-like $Q^{2}$. At $34\,\rm GeV^{2}$ the data are more than 50% larger than theoretical predictions. Stimulated by these new experimental results, we revisit our previous paper on triangle loop effects related to chiral anomaly, and apply our method to the $γ+ γ^* \to π^0$ form factor measured in the single tag mode $e^{+} + e^{-}\to e^{+} + e^{-} + π^{0}$ with one highly virtual photon. The resultant form factor $F(Q^{2})$ - which depends on only one parameter (the mass $m$ of up, down quark circulating in the triangle loop) behaves like $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ - shows a striking agreement with BaBar data for $m \approx 132\,\rm MeV$. The rising logarithm squared form factor, surprisingly unnoticed in the literature, is in sharp contrast with the rather flat ones derived from perturbative QCD approaches.

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arXiv2010

Two-Photon and Two-gluon Decays of $0^{++}$ and $2^{++}$ P-wave Heavy Quarkonium States

By neglecting the relative quark momenta in the propagator term, the two-photon and two-gluon decay amplitude of heavy quarkonia states can be written as a local heavy quark field operator matrix element which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation, as shown in a recent work on $η_{c,b}$ two-photon decays. In this talk, I would like to discuss a similar calculation on $P$-wave $χ_{c0,2}$ and $χ_{b0,2}$ two-photon decays. We show that the effective Lagrangian for the two-photon decays of the $P$-wave $χ_{c0,2}$ and $χ_{b0,2}$ is given by the heavy quark energy-momentum tensor local operator and its trace, the $\bar{Q}Q$ scalar density. A simple expression for $χ_{c0}$ two-photon and two-gluon decay rate in terms of the $f_{χ_{c0}}$ decay constant, similar to that of $η_{c}$ is obtained. From the existing QCD sum rules value for $f_{χ_{c0}}$, we get $5\rm\,keV$ for the $χ_{c0}$ two-photon width, somewhat larger than measurement.

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arXiv2009

${\mathcal A}_{\rm CP}$ Puzzle: Possible Evidence for Large Strong Phase in $B\to Kπ$ Color-Suppressed Tree Amplitude

In QCD Factorization(QCDF), the suppression of the color-suppressed tree amplitude relative to the color-allowed one in $B\to Kπ$ decay implies a direct CP asymmetry in $B^{-}\to K^{-}π^{0}$ to be of the same sign and comparable in magnitude to that in ${\bar B}^{0}\to K^{+}π^{-}$, in contradiction with experiment. This is the $A_{\rm CP}$ $B\to Kπ$ puzzle. One of the current proposal to solve this puzzle is the existence of a large color-suppressed amplitude with large strong phase which implies also a large negative ${\bar B}^{0}\to {\bar K}^{0}π^{0}$ CP asymmetry. In this paper, by an essentially model-independent calculation, we show clearly that the large negative direct CP asymmetry in ${\bar B}^{0}\to {\bar K}^{0}π^{0}$ implies a large $C/T$, the ratio of the color-suppressed to the color-allowed tree amplitude and a large negative strong phase for $C$. By adding to the QCDF amplitude an additional color-suppressed term to generate a large $C/T$ and a large strong phase for $C$ and an additional penguin-like contribution, we obtain branching ratios for all $B\to Kπ$ modes and CP asymmetry for ${\bar B}^{0}\to K^{+}π^{-}$ and $B^{-}\to K^{-}π^{0}$ in agreement with experiment, and a large and negative CP asymmetry in ${\bar B}^{0}\to {\bar K}^{0}π^{0}$ which could be checked with more precise measurements.

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arXiv2009

$B\to Kπ$ decays

Though QCD Factorization(QCDF) could produce sufficiently large $B\to Kπ$ branching ratios close to experiments, the predicted direct CP asymmetry in ${\bar B}^{0}\to K^{+}π^{-}$ decay is however still quite below experiment, even with a large negative phase in the annihilation term, according to existing calculations. This suggests the presence of an additional strong phase in the decay amplitude which could come from the long-distance final state interactions(FSI) like charming penguin. In this paper, we show that, by adding to the $B\to Kπ$ decay QCDF amplitude, a real part and an absorptive part with a strength 10% and 30% of the penguin amplitude, respectively, we could bring the $B\to Kπ$ branching ratios and the ${\bar B}^{0}\to K^{-}π^{+}$ CP asymmetry close to the measured values. We also find that the color-allowed electroweak penguin is appreciable and that from the QCDF electroweak-strong penguin interference terms and the measured $B^{-}\to {\bar K}^{0}π^{-}$ we obtain $(9.0\pm 0.3)\times 10^{-6}$ for the ${\bar B}^{0}\to {\bar K}^{0}π^{0}$ branching ratio, a bit lower than experiment. Similarly, the predicted value for $B^{-}\to K^{-}π^{0}$ in terms of the ${\bar B}^{0}\to K^{-}π^{+}$ branching ratio agrees well with experiment. This suggests that the measured value for ${\bar B}^{0}\to {\bar K}^{0}π^{0}$ in fact should be lower than the current measured value.

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arXiv2009

Effective Lagrangian for Two-photon and Two-gluon Decays of $P$-wave Heavy Quarkonium $χ_{c0,2}$ and $χ_{b0,2}$ states

In the traditional non-relativistic bound state calculation, the two-photon decay amplitudes of the $P$-wave $χ_{c0,2}$ and $χ_{b0,2}$ states depend on the derivative of the wave function at the origin which can only be obtained from potential models. However by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation. Following the same line as in recent work for the two-photon decays of the $S$-wave $η_{c}$ and $η_{b}$ quarkonia, we show that the effective Lagrangian for the two-photon decays of the $P$-wave $χ_{c0,2}$ and $χ_{b0,2}$ is given by the heavy quark energy-momentum tensor local operator or its trace, the $\bar{Q}Q$ scalar density and that the expression for $χ_{c0}$ two-photon and two-gluon decay rate is given by the $f_{χ_{c0}}$ decay constant and is similar to that of $η_{c}$ which is given by $f_{η_{c}}$. From the existing QCD sum rules value for $f_{χ_{c0}}$, we get $5\rm keV$ for the $χ_{c0}$ two-photon width, somewhat larger than measurement, but possibly with large uncertainties.

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arXiv2008

$B\to Kη,Kη^{\prime}$ Decays

The nonet symmetry scheme seems to describe rather well the masses and $η-η^{\prime}$ mixing angle of the ground state pseudo-scalar mesons and is thus expected to be also a good approximation for the matrix elements of the pseudo-scalar density operators which play an important role in charmless two-body B decays with $η$ or $η^{\prime}$ in the final state. In this talk, I would like to report on a recent work on the $B^{-}\to K^{-}η, K^{-}η^{\prime}$ decay using nonet symmetry for the matrix elements of pseudo-scalar density operators. We find that the branching ratio $B\to PP$, with an $η$ meson in the final state agrees well with data, while those with an $η^{\prime}$ meson are underestimated by $20-30%$. This could be considered as a more or less successful prediction for QCDF, considering the theoretical uncertainties involved. This could also indicate that an additional power-suppressed terms could bring the branching ratio close to experiment, as with the $B\to K^{*}π$ and $B\to K^{*}η$ decay for which the measured branching ratios are much bigger than the QCDF predictions.

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arXiv2008

Two-photon decay of pseudoscalar quarkonia

We report on our recent evaluation of the two-photon width of the pseudoscalar quarkonia, eta_c(nS) and eta_b(nS) in an approach based on Heavy-Quark Spin Symmetry (HQSS). To what concerns the 1S state eta_c, our parameter-free computation agrees with experiments, as well as most of other theoretical works. On the other hand, our computation for the 2S-state looks 2S like a confirmation that there may exist an anomaly related to the decay of eta_c(2S), especially in the light of the new preliminary result of the Belle collaboration. We also point out that the essentially model-independent ratio of eta_b two-photon width to the Upsilon leptonic width and the eta_b two-photon width could be used to extract the strong coupling constant alpha_s.

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arXiv2008

FCNC $B_s$ and $Λ_b$ transitions: Standard Model versus a single Universal Extra Dimension scenario

We study the FCNC $B_s \to ϕγ, ϕν\bar ν$ and $Λ_b \to Λγ, Λν\bar ν$ transitions in the Standard Model and in a scenario with a single Universal Extra Dimension. In particular, we focus on the present knowledge of the hadronic uncertainties and on possible improvements. We discuss how the measurements of these modes can be used to constrain the new parameter involved in the extra dimensional scenario, the radius $R$ of the extra dimension, completing the information available from B-factories. The rates of these $b \to s$ induced decays are within the reach of new experiments, such as LHCb.

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arXiv2008

Nonet symmetry in η, η^{\prime} and B\to Kη,Kη^{\prime} decays

The nonet symmetry scheme seems to describe rather well the masses and $η-η^{\prime}$ mixing angle of the ground state pseudo-scalar mesons. It is expected that nonet symmetry should also be valid for the matrix elements of the pseudo-scalar densitty operators which play an important role in charmless two-body B decays with $η$ or $η^{\prime}$ in the final state. Starting from the divergences of the SU(3) octet and singlet axial vector currents, we show that nonet symmetry for the pseudo-scalar mass term implies nonet symmetry for the pseudo-scalar density operators. In this nonet symmetry scheme, we find that the branching ratio $B\to PP,PV$, with $η$ in the final state agrees well with data, while those with $η'$ are underestimated, but by increasing the $B\to η'$ form factor by $40-50%$, one could explain the tree-dominated $B^{-}\to π^{-}η'$ and $B^{-}\to ρ^{-}η'$ measured branching ratios. With this increased form factor and with only a moderate annihilation contribution, we are able to obtain $62\times 10^{-6}$ for the penguin-dominated $B^{-}\to K^{-}η'$ branching ratios, quite close to the measured value. This supports the predicted value for the $B\to η'$ form factor in PQCD and light-cone sum rules approach. A possible increase by 15% of $<0|\bar{s} iγ_5 s|s\bar{s}>$ for $η_{0} $ would bring the predicted $B^{-}\to K^{-}η'$ branching ratio to $69.375\times 10^{-6}$, very close to experiment.

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