Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master integrals are calculated exactly in d dimensions; their epsilon expansions are also obtained.
The one-loop HQET heavy-heavy vertex diagram with arbitrary powers of all three denominators and arbitrary residual energies is investigated. Various particular cases in which the result becomes simpler are considered.
We calculate the HQET quark-gluon vertex at one loop, for arbitrary external momenta, in an arbitrary covariant gauge and space-time dimension. Relevant results and algorithms for the three-point HQET integrals are presented. We also show how one can obtain the HQET limit directly from QCD results for the quark-gluon vertex.
Differential equations for the one-loop HQET vertex diagram with arbitrary self-energy insertions and arbitrary residual energies are reduced to the $\varepsilon$ form and used to obtain the $\varepsilon$ expansion in terms of Goncharov polylogarithms.
We compute perturbative matching coefficients to the Heavy Quark Effective Theory representation for the QCD effective local $ΔB=2$ Hamiltonian that determines the mass difference in $B^0-\bar{B}^0$ system of states. We report on the results at NNLO in the strong coupling constant for matching coefficients of two physical operators in HQET. Our results provide the firm confirmation that the recent NLO sum rules analysis of the bag parameter $B_q$ is stable with regard of inclusion of higher order radiative corrections. As a by-product of our calculation we give a fully analytical solution for …
I review recent developments in Heavy Quark Effective Theory (HQET) that lead to an almost model--independent determination of the $|\Vcb|$ element of the Cabibbo--Kobayashi--Maskawa matrix from exclusive semileptonic $B\ra D^{(*)}$ decays. In particular, I compare the theoretical uncertainties in the $B\ra D^*\ell\,\barν$ and the $B\ra D\,\ell\,\barν$ decay modes. I discuss the applications of QCD sum rules within HQET to semileptonic heavy meson decays and give predictions for the form factors measurable in $B\ra D^{(*)}\ell\,\barν$ decays.
We combine the resummations for radiative corrections and for the heavy quark expansion to study the inclusive radiative decay $B \to X_sγ$. The infrared renormalon ambiguity is also taken into account. Including both theoretical and experimental uncertainties, we determine the allowed domain for the HQET parameters ${\bar Λ}$ and $λ_1$ centered at ${\bar Λ}=0.65$ GeV and $λ_1=-0.71$ GeV$^2$.
The radiative decays of heavy baryons and lowest three doublets of heavy mesons are studied with the light cone QCD sum rules in the leading order of heavy quark effective theory.
We examine the measured rates for the decays $D\to K^{(*)}\ellν$, $B\to K^{(*)}ψ^{(\prime)}$ and $B\to K^*γ$ in a number of scenarios, in the framework of the heavy quark effective theory. We attempt to find a scenario in which all of these decays are described by a single set of form factors. Once such a scenario is found, we make predictions for the rare decays $B\to K^{(*)}\ell^+\ell^-$. While we find that many scenarios can provide adequate descriptions of all the data, somewhat surprisingly, we observe that two popular choices of form factors, namely monopolar forms and exponential forms,…
In this paper we discuss the Standard Model and new physics sensitivity of the $Λ_b\toΛ^\ast(1520)(\to N\!\bar{K})\ell^+\ell^-$ decay at low-recoil, where $\ell^\pm$ are massive leptons and $N\!\bar{K}=\{pK^-, n\bar{K}^0 \}$. We provide a full angular distribution with a set of operators that includes the Standard Model operators and their chirality flipped counterparts, and new scalar and pseudo-scalar operators. The resulting angular distribution allows us to construct observables that we study in the Standard Model and in model-independent new physics scenarios. To reduce the hadronic effec…
The relation between the heavy-quark field in QCD and the corresponding field in HQET is derived up to three loops, and to all orders in the large-$β_0$ limit. The corresponding relation between the QED electron field and the Bloch--Nordsieck one is gauge invariant to all orders. We also prove that the $\bar{\text{MS}}$ anomalous dimension of the QED electron field depends on the gauge parameter only at one loop.
We examine the rates for the exclusive decays $B\to K^{(*)}\ell^+\ell^-$. We use the scaling predictions of the heavy quark effective theory to extract the necessary form factors from fits to various combinations of data. These data include the $D\to K^{(*)}\ellν$ semileptonic decays, as well as the nonleptonic decays $B\to K^{(*)}ψ^{(\prime)}$ and the rare decay $B\to K^*γ$. We use different parametrizations of form factors, and find that integrated decay rates are not very sensitive to the forms chosen. However, the decay spectra and the forward-backward asymmetry in $B\to K^*\ell^+\ell^-$ a…
We determine to order alpha^3 the so-called residual mass in the lattice regularisation of the Heavy Quark Effective Theory for Nf=2. Our (gauge-invariant) strategy makes use of Numerical Stochastic Perturbation Theory to compute the static interquark potential where the above mentioned mass term appears as an additive contribution. We discuss how the new coefficient we compute in the expansion of the residual mass can improve the determination of the (MS bar) mass of the b-quark from lattice simulations of the Heavy Quark Effective Theory.
We compute perturbative corrections to matching coefficients of QCD to HQET for the matrix element of the $ΔB=2$ operator that determines the mass difference in $B^0-\bar{B}^0$ system of states. This involves the technical point of choosing the operator basis in HQET, separating physical operators from evanescent ones. We obtain an analytical result for some of the two-loop corrections at order $α_s^2$.
We postulate a supplemental power counting within the heavy quark effective theory, that results in a small, highly-constrained set of second-order power corrections, compared to the standard approach. We determine all $\bar{B} \to D^{(*)}$ form factors, both within and beyond the standard model to $\mathcal{O}(α_s/m_{c,b}, 1/m_{c,b}^2)$, under truncation by this power counting. We show that the second-order power corrections to the zero-recoil normalization of the $\bar{B} \to D^{(*)} l ν$ matrix elements ($l = e$, $μ$, $τ$) are fully determined by hadron mass parameters, and are in good agre…
We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents $J=(q^TCΓτq)Γ'Q$ with arbitrary Dirac matrices $Γ$ and $Γ'$. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons $Λ_Q$, $Σ_Q$ and $Σ_Q^*$. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents $(J=\bar qΓq)$ in massless QCD as well as in HQET.
We derive a new parton-like formula, which establishes a simple connection between the electroweak decay rate $Γ(\bar B \to X_sγ$) and the rate of a free b-quark decay. The main features of our approach are the treatment of the b-quark as an on-mass-shell particle and the inclusion of the effects arising from the b-quark transverse motion in the $\bar B$-meson. Using various b-quark light-front (LF) distribution functions, both phenomenological one and the ones derived from current constituent quark models, and neglecting perturbative corrections we compute the photon energy spectra and the mo…
We apply Heavy Quark Effective Theory to the production of $0^-$ and $1^-$ $Q\bar{q}$ states in $e^+ e^-$ annihilation. We show that HQET implies that the electric quadrupole amplitudes vanish and we propose tests for this theory. We also show how HQET can be applied to distinguish the $^3D_1$ and $^3S_1$ $Q\bar{Q}$ states.
In this work, we find the expressions of continuum HQET four-fermion operators in terms of lattice operators in perturbation theory. To do so, we calculate the one--loop continuum--lattice HQET matching for the complete basis of $ΔB=2$ and $ΔB=0$ operators (excluding penguin diagrams), extending and completing previous studies. We have also corrected some errors in previous evaluations of the matching for the operator $O_{LL}$. Our results are relevant to the lattice computation of the values of unknown hadronic matrix elements which enter in many very important theoretical predictions in $B$-…
We investigate the structure of the $D_{1}^0(2420[2430]) (J^P=1^+)$ mesons via analyzing the semileptonic $B_{c}\to D_{1}^0 lν$ transition in the frame work of the three--point QCD sum rules and the heavy quark effective theory. We consider the $D_{1}^0$ meson in three ways; the pure $|c\bar{u}\rangle$ state, a mixture of two $|^3P_1\rangle$ and $|^1P_1\rangle$ states with a mixing angle $θ$ and a combination of two mentioned states with mixing angle $θ=35.3^\circ$ in the heavy quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the t…
We compute the leading order (in $α_s$) perturbative QCD and power ($1/m_b^2)$ corrections to the hadronic invariant mass and hadron energy spectra in the decay $B \to X_s \ell^+ \ell^-$ in standard model. This is done both by using the heavy quark expansion technique (HQET) and a perturbative-QCD improved Fermi motion (FM) model which takes into account $B$-meson wave-function effects. The corrections in the hadron energy ($E_H$) spectrum are found to be small over a good part of this spectrum in both the methods. However, the expansion in $1/m_b$ in HQET fails near the lower kinematic end-po…
We present a high statistics, quenched lattice calculation of the B-parameters $B_{B_d}$ and $B_{B_s}$, computed at lowest order in the HQET. The results were obtained using a sample of 600 quenched gauge field configurations, generated by Monte Carlo simulation at $β=6.0$ on a $24^{3}\times 40$ lattice. For the light quarks the SW-Clover action was used; the propagator of the lattice HQET was also tree-level improved. Our best estimate of the renormalization scale independent B-parameter is $\hat{B}_{B_d} = 1.03 \pm 0.06 \pm 0.18$. $\hat{B}_{B_d}$ has been obtained by using ``boosted'' pertur…
Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}γ^{[μ_1}\ldotsγ^{μ_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $γ_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2α_{\rm s}(m_b)/3…
The CKM matrix element $|V_{cb}|$ can be extracted by combining data from experiments with lattice QCD results for the semileptonic form factors for the $\bar{B}\to D^{(*)} \ell \barν$ decays. The Oktay-Kronfeld (OK) action was designed to reduce heavy-quark discretization errors to below $1\%$, or through $\mathcal{O}(λ^3)$ in HQET power counting. Here we describe recent progress on bottom-to-charm currents improved to the same order in HQET as the OK action, and correct formerly reported results of our matching calculations, in which the operator basis was incomplete.
In the framework of heavy quark effective theory we use QCD sum rules to calculate the masses of the $\bar c s$ $(0^+, 1^+)$ and $(1^+, 2^+)$ excited states. The results are consistent with that the states $D_{sJ}(2317)$ and $D_{sJ}(2460)$ observed by BABAR and CLEO are the $0^+$ and $1^+$ states in the $j_l={1\over 2}^+$ doublet.
$|V_{cb}|$ determinations from $\bar{B} \to D^{(*)} \ell \barν$ decays within the SM and beyond
Central China Normal University(华中师范大学);Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University(粒子物理与夸克轻子物理重点实验室(教育部),华中师范大学);Nagoya University(名古屋大学);Institute for Advanced Research (IAR), Nagoya University(名古屋大学高等研究院);Kobayashi-Maskawa Institute (KMI) for the Origin of Particles and the Universe, Nagoya University(名古屋大学小林-益川粒子起源宇宙研究所)
Within the framework of HQET, $Λ_{b}\rightarrowΛ_{c}τ\barν_τ$ and $Ω_{b}\rightarrowΩ_{c}^{(*)}τ\barν_τ$ weak decays are studied to the order of $1/m_c$ and $1/m_b$. Helicity amplitudes are written down. Relevant Isgur-Wise functions given by QCD sum rule and large $N_c$ methods are applied in the numerical analysis. The baryonic R-ratios $R(Λ_c)$ and $R(Ω_c^{(*)})$ are obtained.
We investigate the semi-leptonic decays of $\bar B \to D^{(*)} \ell\barν$ in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for the form factors, which is described with the heavy quark expansion up to $\mathcal O(1/m_c^2)$ beyond the simple approximation considered in the original CLN parameterization. An analysis with this setup was first given in the literature, and then we extend it to the comprehensive analyses including (i) simultaneous fit of $|V_{cb}|$ and the HQET parameters to available experimental full distribution data and theory constraints, and (ii) New Physic…
We study the renormalization of operators of the type ${\bar h_{v'}} ΓG^{μν} h_v$ in the heavy-quark effective theory (HQET). We construct the combinations of such operators that are renormalized multiplicatively, and calculate their velocity-dependent anomalous dimensions at the one-loop order. We then show that the virial theorem of the HQET is not renormalized, and that in the limit of equal velocities the anomalous dimension of the chromo-electric operator vanishes to all orders in perturbation theory. This implies an exact relation between renormalization constants, which may help in a fu…
We analyse matrix elements of Delta B=2 operators by combining QCD results with the ones obtained in the static limit of HQET. The matching of all the QCD operators to HQET is made at NLO order. To do that we have to include the anomalous dimension matrix up to two loops, both in QCD and HQET, and the one loop matching for all the Delta B=2 operators. The matrix elements of these operators are relevant for the prediction of the B-\bar B mixing, B_s meson width difference and supersymmetric effects in Delta B=2 transitions.
We study the $B^0_s-\bar{B^0_s}$ mixing amplitude in Standard Model by computing the relevant hadronic matrix element in the static limit of lattice HQET with the Neuberger light quark action. In the quenched approximation, and after matching to the $\bar{\rm MS}$ scheme in QCD, we obtain $\hat{B}^{\bar{\rm MS},{\rm NLO}}_{B_s}(m_b)=0.940(16)(22)$.
We compute the perturbative corrections to the HQET sum rules for the matrix element of the ΔB=2 operator that determines the mass shift of $B^0$, $\bar{B}^0$ states. Technically, we obtain analytically the non-factorizable contributions at order $α_s$ to the bag parameter that first appear at the three-loop level. Together with the known non-perturbative corrections due to vacuum condensates and $1/m_b$ corrections, the full next-to-leading order result is now available. We present a numerical value for the renormalization group invariant bag parameter that is phenomenologically relevant and …
By combining the first unquenched lattice computation of the B-meson binding energy and the two-loop contribution to the lattice HQET residual mass, we determine the (\bar{MS}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The inclusion of the two-loop corrections is essential to extract (\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal O}(Λ^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon singularities in the perturbative series of the residual mass. Our best estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we have combined the different errors in q…
A slowly running technicolor coupling will affect the size of non-oblique corrections to the $Zb\bar b$ vertex from extended technicolor dynamics. We show that while ``walking technicolor'' reduces the magnitude of the corrections, they generally remain large enough to be seen at LEP.
We compute the last missing piece of the two-loop ${\cal O}(αα_s)$ corrections to $γt \bar{t}$ vertex at the $t \bar{t}$ threshold due to the exchange of a $W$ boson and a gluon. This contribution constitutes a building block of the top quark threshold production cross section at electron positron colliders.
In this paper, we present the exact calculations for the vertex $\bar{s}γb$ and $\bar{s} Z b$ in the unitary gauge. We found that (a) the divergent- and $μ$-dependent terms are left in the effective vertex function $Γ^γ_μ(p,k)$ for $b \to s γ$ transition even after we sum up the contributions from four related Feynman diagrams; (b) for an on-shell photon, such terms do not contribute et al; (c) for off-shell photon, these terms will be canceled when the contributions from both vertex $\bar{s}γb$ and $\bar{s} Z b$ are taken into account simultaneously, and therefore the finite and gauge indepen…
It is shown that the longitudinal double spin asymmetry $A_{ll}$ in polarized diffractive $l p \to l p+Q \bar Q$ reaction depends strongly on the spin structure of quark-pomeron vertex. The SMC spin facilities may be one of the best place to perform such experiment.
We apply HQET to semi-leptonic $B$ and $B_{s}$ meson decays into the observed charmed $P$ wave states. In order to examine the sensitivity of the results to the choice of a specific model, we perform all calculations using several different meson models, and find that uncertainty introduced by the choice of a particular model is about 30\%. Specifically, assuming $τ_{B}=1.50ps$ and $V_{cb}= 0.040$, we obtain branching ratios of $(0.27\pm 0.08)\%$ and $(0.45\pm 0.14)\%$ for $B\rar D_{1}l\barν_{l}$ and $B\rar D_{2}^{*}l\barν_{l}$ decays, respectively.
Using effective field theory techniques we discuss the QCD corrections to the large-$m_t$ contributions to the process $Z\rightarrow b \bar b$. In particular we obtain the $\a$ correction to the non-universal $\log m_t$ contribution to the $Zb\bar b$ vertex.
We present a model--independent analysis of the $Z b \bar b$ vertex, with the aim of constraining contributions of new physics to the left- and right--handed couplings of the $b$. We find that the left--handed coupling of the $b$ is quite narrowly constrained by present data, but that the right--handed coupling is still largely unconstrained.
I stress the fact that a complete study of possible New Physics effects in the $Z \rightarrow b\bar{b}$ vertex requires a combined analysis of the ratio $R_b= Γ(Z \rightarrow b\bar{b})/ Γ(Z \rightarrow hadrons)$ and the longitudinally polarized forward backward asymmetry, $A_b$. This is illustrated with a number of models such as the two Higgs-doublet model, the MSSM, Technicolour and models with an extra $Z'$. The use of effective lagrangean techniques is briefly discussed.
LEP precision measurements of the $Zb\bar{b}$ vertex coupling are sufficiently accurate to see the non-oblique corrections from the heavy gauge boson responsible for the large top mass in standard extended tecnicolour models. If the ETC couplings are strong the techni-fermion condensate may be enhanced by several orders of magnitude allowing a top mass of order 150GeV to be obtained for large values of the ETC breaking scale sufficient to supress the ETC contribution to the $Zb{\bar b}$ vertex. In this letter we investigate the degree of fine tuning of the ETC coupling required in a realistic …
Triple gauge boson vertex, which is inherent to the model of a dynamical breaking of the electroweak symmetry, leads to an effective four-fermion interaction of quarks. Calculation of the effective coupling constant in the framework of the model results in agreement with recent information on enhancement of inclusive high E_T jet cross section at \sqrt{s} = 1.8 TeV. Thus this effect may be connected with triple gauge boson vertex with coupling constant λ\approx 0.7, which will clearly manifest itself at the soon forthcoming LEP II.
As a first step towards the computation of the NLO corrections to the photon impact factor in the $γ^*γ^* \to γ^* γ^*$ scattering process, we calculate the one loop corrections to the coupling of the reggeized gluon to the $γ^*\to q\bar{q}$ vertex. We list the results for the Feynman diagrams which contribute: all loop integrations are carried out, and the results are presented in the helicity basis of photon, quark, and antiquark.
Dynamical mass generation in a three-dimensional version of finite-temperature QED is studied with the help of Schwinger-Dyson equations in the real-time formalism. We go beyond the bare-vertex approximation and include wave-function renormalization effects. This introduces a system of two integral equations which are solved numerically. In order to increase the reliability of the results, fermion and photon self-energies varying independently with energy and momentum are used. The method applied enables a detailed study of the behaviour of the theory with increasing temperature and number of …
The light axial vector mesons can couple to $K^*\bar{K}+c.c.$ in an $S$ wave at the tree level. Due to the near-threshold $S$-wave interactions the couplings can be affected by the final state interactions. It is of peculiar interest that the pion exchange between $K^*\bar{K}+c.c.$ can go through a triangle diagram which is within the kinematics of the triangle singularity (TS). This mechanism will introduce energy dependence and a $D$-wave amplitude to the vertex couplings. Hence, it should be necessary to investigate the role played by the $K^*\bar{K}+c.c.$ threshold in order to have a bette…
The reactions e+e- -> t bar-c nu_e bar-nu_e, t bar-c e+ e- are very sensitive probes of the flavor-changing-scalar couplings which can occur in a model with one extra Higgs doublet. At the Next Linear Collider, with a center of mass energy of sqrt{s}=0.5--2 TeV, several hundreds and up to thousands of such events may be produced if the mass of the light neutral Higgs is a few hundred GeV. We also briefly comment on the decays t -> c W+ W-, t -> c Z Z. All of these reactions are severely suppressed in the Standard Model
We estimate the correction to the Zbb-bar vertex arising from the exchanges of the sideways extended technicolor (ETC) boson and the flavor-diagonal ETC boson in the multiscale walking technicolor model. The obtained result is too large to explain the present data. However, if we introduce a new self- interaction for the top quark to induce the top quark condensate serving as the origin of the large top quark mass, the corrected R_b=Gamma_b/Gamma_h can be consistent with the recent LEP data. The corresponding correction to R_c=Gamma_c/Gamma_h is shown to be negligibly small.
In this paper we calculate the corrections to zt\bar {t} couplings induced by non-commuting ETC interactions. The extra parameters \delgbl, s^2 and {1\over x} of non-commuting ETC models and the usual SM parameters will be be assumed to be determined from a global fit to the LEP 1 EW data. We find that in the heavy (light) case F^t_L is modified by at most 4% (2.8%) relative to its SM value provided \delrb < .0088. This implies that it will be very difficult to disentangle the ETC corrections from SM corrections to zt\bar {t} vertex or to probe the effects of non-commuting ETC on zt\bar {t} co…
We study the one-loop corrections to the $Zb\bar{b}$ vertex in extensions of the Standard Model with arbitrary numbers of scalar doublets, neutral scalar singlets, and charged scalar singlets. Starting with a general parameterization of theories with neutral and singly-charged scalar particles, we derive the conditions that, in a renormalizable model, must be obeyed by the couplings in order for the divergent contributions to cancel. Then, we show that those conditions are indeed obeyed by the models that we are interested in, and we write down the full finite expression for the vertex in thos…
We investigate the new contributions to the parameters $g_L$ and $g_R$ of the $Z b \bar b$ vertex in a multi-Higgs-doublet model (MHDM). We emphasize that those contributions generally worsen the fit of those parameters to the experimental data. We propose a solution to this problem, wherein $g_R$ has the opposite sign from the one predicted by the Standard Model; this solution, though, necessitates light scalars and large Yukawa couplings in the MHDM.
We consider the leading one-loop Yukawa-coupling corrections to the h^0 b b-bar coupling at O(m_t^2)in the MSSM in the decoupling limit. The decoupling behavior of the corrections from the various MSSM sectors is analyzed in the case of having some or all of the supersymmetric mass parameters and/or the CP-odd Higgs mass large as compared to the electroweak scale.
Next-to-leading order QCD corrections to the $γ^{*} \longrightarrow Q\bar{Q}-Reggeon$ vertex are calculated, where $Q\bar{Q}$ denotes a heavy quark pair $c\bar c$ or $b\bar b$. The heavy quark mass effects on the photon impact factor are found to be significant, and hence may influence the results of high energy photon-photon scattering and heavy quark pair leptoproduction. In our NLO calculation, similar to the massless case, the ultraviolate(UV) divergences are fully renormalized in the standard procedure, while the infrared (IR) divergences are regulated by the parameter $ε_{IR}$ in dimensi…
Hadron diffraction dissociation is considered in the dipole Pomeron model where the Pomeron is represented by a double pole in the J-plane. We find that unitarity is satisfied without decoupling of the triple Pomeron vertex. The reaction bar{p}+p --> bar{p}+X is analysed.
We explore corrections to electroweak parameters in the context of Extended Technicolor (ETC) models in which the ETC gauge-boson which generates the top-quark mass carries weak $SU(2)$ charge. For $m_t \sim 150$ GeV there exist potentially large corrections to the $Z$ decay width to $b$-quarks. Interestingly, in contrast to the situation in ETC models where the gauge-boson which generates the top-quark mass is a weak $SU(2)$ singlet, the corrections may {\it increase} the $Z \to b \bar{b}$ branching ratio.