Heavy Quark Effective Theory Research Articles

Combined analysis of semileptonic B decays to D and D* : R(D(*)) , |Vcb| , and new physics

The measured $\bar{B}\to D^{(*)} l \bar\nu$ decay rates for light leptons ($l=e,\mu$) constrain all $\bar{B}\to D^{(*)}$ semileptonic form factors, by including both the leading and ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\bar{B}\to D^{(*)} l \bar\nu$ decay distributions to predict the $\bar{B} \to D^{(*)} \tau\bar\nu$ rates and determine the CKM matrix element $|V_{cb}|$. Most theoretical and experimental papers have neglected uncertainties in the predictions for form factor ratios at order $\Lambda_{\text{QCD}}/m_{c,b}$, which we include. We also calculate ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$ and ${\cal O}(\alpha_s)$ contributions to semileptonic $\bar{B}\to D^{(*)} \ell \bar\nu$ decays for all possible $b \to c$ currents. This result has not been available for the tensor current form factors, and for two of those, which are ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$, the corrections are of the same order as approximations used in the literature. These results allow us to determine with improved precision how new physics may affect the $\bar{B}\to D^{(*)} \tau\bar\nu$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.

Relativistic corrections to the form factors of Bc into S -wave charmonium

We investigate the form factors of $B_c$ meson into $S$-wave charmonium within the nonrelativistic QCD effective theory and obtain the next-to-leading order relativistic corrections to the form factors, where both the $B_c$ meson and the charmonium are treated as the nonrelativistic bound states. Treating the charm quark as a light quark in the limit \ $m_c/m_b\to 0$, some form factors are identical at the maximum recoil point, which are consistent with the predictions in the heavy-quark effective theory and the large-energy effective theory. Considering that the branching ratios of $B^+_c \to J/\psi D_s^+$ and $B^+_c \to J/\psi D_s^{*+}$ have been measured by the LHCb and ATLAS Collaborations recently, we employ the form factors of $B_c$ meson into $S$-wave charmonium at the next-to-leading order accuracy to these two decay channels and obtain more precise predictions of their decay rates. Numerical results indicate that the factorizable diagrams dominate the contribution in these two channels, while the colour-suppressed and the annihilation diagrams contribute less than 10 percent. Our results are consistent with the LHCb and ATLAS data.

Λc semileptonic decays in a quark model

Hadronic form factors for semileptonic decay of the $\Lambda_c$ are calculated in a nonrelativistic quark model. The full quark model wave functions are employed to numerically calculate the form factors to all relevant orders in ($1/m_c$, $1/m_s$). The form factors obtained satisfy relationships expected from the heavy quark effective theory (HQET). The differential decay rates and branching fractions are calculated for transitions to the ground state and a number of excited states of $\Lambda$. The branching fraction of the semileptonic decay width to the total width of $\Lambda_c$ has been calculated and compared with other theoretical estimates and experimental results. The branching fractions for $\Lambda_c\to\Lambda^{*} l^{+}\nu_l\to\Sigma\pi l^{+}\nu_l$ and $\Lambda_c\to\Lambda^{*} l^{+}\nu_l\to N\bar{K} l^{+}\nu_l$ are also calculated. Apart from decays to the ground state $\Lambda$(1115), it is found that decays through the $\Lambda(1405)$ provide a significant portion of the branching fraction $\Lambda_c\to X_s l\nu_l$. A new estimate for $f=B(\Lambda_c^{+}\to\Lambda l^{+}\nu_l)/B(\Lambda_c^{+}\to X_s l^{+}\nu_l)$ is obtained.

Supersymmetry across the light and heavy-light hadronic spectrum. II.

We extend our analysis of the implications of hadronic supersymmetry for heavy-light hadrons in light-front holographic QCD. Although conformal symmetry is strongly broken by the heavy quark mass, supersymmetry and the holographic embedding of semiclassical light-front dynamics derived from five-dimensional anti-de Sitter (AdS) space nevertheless determines the form of the confining potential in the light-front Hamiltonian to be harmonic. The resulting light-front bound-state equations lead to a heavy-light Regge-like spectrum for both mesons and baryons. The confinement hadron mass scale and their Regge slopes depend, however, on the mass of the heavy quark in the meson or baryon as expected from Heavy Quark Effective Theory (HQET). This procedure reproduces the observed spectra of heavy-light hadrons with good precision and makes predictions for yet unobserved states.

Measurement of the shape of the $\Lambda^0_b \to \Lambda^+_c\mu^-\overline{ν}_{\mu}$ differential decay rate

A measurement of the shape of the differential decay rate and the associated Isgur-Wise function for the decay $\Lambda^0_b \to \Lambda^+_c\mu^-\overline{ν}_{\mu}$ is reported, using data corresponding to 3 fb$^{−1}$ collected with the LHCb detector in proton-proton collisions. The $\Lambda^+_c \mu^-\overline{ν}_{\mu} (+ anything)$ final states are reconstructed through the detection of a muon and a $\Lambda^+_c$ baryon decaying into $pK^-\pi^+$, and the decays $\Lambda^0_b \to \Lambda^+_c\pi^+\pi^-\mu^-\overline{ν}_{\mu}$ are used to determine contributions from $\Lambda^0_b \to \Lambda^{*+}_c\mu^-\overline{ν}_{\mu}$ decays. The measured dependence of the differential decay rate upon the squared four-momentum transfer between the heavy baryons, $q^2$, is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions.

D -wave charmed and bottomed baryons from QCD sum rules

We study the $D$-wave charmed baryons of $SU(3)$ flavor $\mathbf{\bar3}_F$ using the method of QCD sum rule in the framework of heavy quark effective theory (HQET). We find that the $\Lambda_c(2880)$, $\Xi_c(3055)$ and $\Xi_c(3080)$ can be well described by the $D$-wave $SU(3)$ $\mathbf{\bar 3}_F$ charmed baryon multiplets of $J^P=3/2^+$ and $5/2^+$, which contain two $\lambda$-mode orbital excitations, i.e., the $\Lambda_c(2880)$ has $J^P=5/2^+$, and the $\Xi_c(3055)$ and $\Xi_c(3080)$ have $J^P = 3/2^+$ and $5/2^+$, respectively. Our results also suggest that the $\Lambda_c(2880)$ has a partner state, the $\Lambda_c(3/2^+)$ of $J^P=3/2^+$. Its mass is around $2.81 ^{+0.33}_{-0.18}$ GeV, and the mass difference between it and the $\Lambda_c(2880)$ is $28^{+45}_{-24}$ MeV. We also evaluate the masses of their bottom partners.

Effective Field Theory approach to heavy quark fragmentation

Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the $b$-quark fragmentation function from electron-positron annihilation data at the $Z$-boson peak at next-to-next-to leading order, with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the $b$-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. While the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the $b$-quark fragmentation function at smaller values of momentum fraction.

Density distributions in the B meson

We report on a two-flavor lattice QCD study of the axial, charge and matter distributions of the $B$ meson and its first radial excitation. As our framework is the static limit of Heavy Quark Effective Theory (HQET), taking their Fourier transform gives access to several form factors at the kinematical point $q^2=0$. Moreover they provide some useful information on the nature of an excited state, i.e. a radial excitation of a quark-antiquark bound state or a multihadron state.

Heavy–light charm mesons spectroscopy and decay widths

We present the mass formula for heavy-light charm meson for one loop, using heavy quark effective theory. Formulating an effective Lagrangian, the masses of the ground state heavy mesons have been studied in the heavy quark limit including leading corrections from finite heavy quark masses and nonzero light quark masses using a constrained fit for the eight equation having eleven parameters including three coupling constants g, h and g'. Masses determined from this approach is fitted to the experimentally known decay widths to estimate the strong coupling constants, showing a better match with available theoretical and experimental data

Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

We study the heavy quark mass dependence of selected observables constructed from heavy-light meson correlation functions in small-volume two-flavour lattice QCD after taking the continuum limit. The light quark mass is tuned to zero, whereas the range of available heavy quark masses $m_h$ covers a region extending from around the charm to beyond the bottom quark mass scale. This allows entering the asymptotic mass-scaling regime as $1/m_h \to 0$ and performing well-controlled extrapolations to the infinite-mass limit. Our results are then compared to predictions obtained in the static limit of continuum Heavy Quark Effective Theory (HQET), in order to verify non-perturbatively that HQET is an effective theory of QCD. While in general we observe a nice agreement at the few-% level, we find it to be less convincing for the small-volume pseudoscalar decay constant when perturbative matching is involved.

Study of1DStrange Charmed Meson Family Using HQET

Recently LHCb predicted spin 1 and spin 3 statesDs1⁎(2860)andDs3⁎(2860)which are studied through their strong decays and are assigned to fit the13D1and13D3states in the charm spectroscopy. In this paper, using the heavy quark effective theory, we state that assigningDs1⁎(2860)as the mixing of13D1-23S1states is rather a better justification to its observed experimental values than a pure state. We study its decay modes variation with hadronic coupling constantgxhand the mixing angleθ. We appoint spin 3 stateDs3⁎(2860)as the missing1D 3-JPstate and also study its decay channel behavior with coupling constantgyh. To appreciate the above results, we check the variation of decay modes for their spin partners states, that is,1D2and1D2′, with their masses and strong coupling constant, that is,gxhandgyh. Our calculation using HQET approach gives mixing angle of the13D1-23S1state forDs1⁎(2860)to lie in the range (-1.6radians≤θ≤-1.2radians). Our calculation for coupling constant values givesgxhto lie within value range of0.17–0.20andgyhto be 0.40. We expect from experiments to observe this mixing angle to verify our results.

Decay Constants of Heavy-Light Mesons from QCD

We summarize our recently improved results for the pseudoscalar [S. Narison, Phys.Lett. B718 (2013) 132; S. Narison, Nucl. Phys. Proc. Suppl. 234 (2013) 187; S. Narison, Phys.Lett. B721 (2013) 269], vector and Bc [S. Narison, Int. J. Mod. Phys. A30 (2015) 20, 1550116] meson decay constants from QCD spectral sum rules where N2LO⊕ estimate of the N3LO PT⊕d≤6 condensates have been included in the SVZ expansion. The “optimal results” based on stability criteria with respect to the variations of the Laplace/Moments sum rule variables, QCD continuum threshold and subtraction constant μ are compared with recent sum rules and lattice calculations. To understand the “apparent tension” between some recent results, we present in Section 8 a novel extraction of forfB⁎/fBfrom heavy quark effective theory (HQET) sum rules by including the normalization factor (Mb/MB)2 relating the pseudoscalar to the universal HQET correlators for finite b-quark and B-meson masses. We obtain fB⁎/fB=1.025(16) in good agreement with 1.016(16) from spectral sum rules (SR) in full QCD [3]. We complete the paper by including new improved estimates of the scalar, axial andBc⁎meson decay constants (Sections 11–13). For further phenomenological uses, we attempt to extract a Global Average of the sum rules and lattice determinations which are summarized in Tables 2–6. We do not found any deviation of these SM results from the present data.

F-wave heavy-light meson spectroscopy in QCD sum rules and heavy quark effective theory

We study the $F$-wave $\overline{c}s$ heavy meson doublets $({2}^{+},{3}^{+})$ and $({3}^{+},{4}^{+})$. They have large orbital excitations $L=3$, and may be good challenges (tests) for theoretical studies. To study them we use the method of QCD sum rule in the framework of heavy quark effective theory. Their masses are predicted to be ${m}_{({2}^{+},{3}^{+})}=(3.45\ifmmode\pm\else\textpm\fi{}0.25,3.50\ifmmode\pm\else\textpm\fi{}0.26)\text{ }\text{ }\mathrm{GeV}$ and ${m}_{({3}^{+},{4}^{+})}=(3.20\ifmmode\pm\else\textpm\fi{}0.22,3.26\ifmmode\pm\else\textpm\fi{}0.23)\text{ }\text{ }\mathrm{GeV}$, with mass splittings $\mathrm{\ensuremath{\Delta}}{m}_{({2}^{+},{3}^{+})}={m}_{{3}^{+}}\ensuremath{-}{m}_{{2}^{+}}=0.046\ifmmode\pm\else\textpm\fi{}0.030\text{ }\text{ }\mathrm{GeV}$ and $\mathrm{\ensuremath{\Delta}}{m}_{({3}^{+},{4}^{+})}=0.053\ifmmode\pm\else\textpm\fi{}0.044\text{ }\text{ }\mathrm{GeV}$, respectively. We note that this is a pioneering work and these results are provisional.

QCD sum rule calculation forP-wave bottom baryons

We study the P-wave bottom baryons using the method of QCD sum rule and heavy quark effective theory. Our results suggest that Lambda_b(5912) and Lambda_b(5920) can be well described by the baryon doublet [3F_bar, 1, 1, rho], and they belong to the SU(3) 3F_bar multiplets of J(P)=1/2(-) and 3/2(-). Their SU(3) flavor partners, Xi_b(1/2-) and Xi_b(3/2-), have masses 6.06 \pm 0.13 GeV and 6.07 \pm 0.13 GeV, respectively, with mass splitting 9 \pm 4 MeV. The results obtained using baryon doublet [3F_bar, 1, 0, lambda] are similar and also consistent with the experimental data. We also study the SU(3) 6F multiplets by using the baryon multiplets [6F, 0, 1, lambda], [6_F, 1, 0, rho] and [6F, 2, 1, lambda], and our results suggest that the P-wave bottom baryons Sigma_b, Xi'_b and Omega_b have (averaged) masses about 6.0 GeV, 6.2 GeV and 6.4 GeV, respectively.

Baryonic matter onset in two-color QCD with heavy quarks

We study the cold and dense regime in the phase diagram of two-color QCD with heavy quarks within a three-dimensional effective theory for Polyakov loops. This theory is derived from two-color QCD in a combined strong-coupling and hopping expansion. In particular, we study the onset of diquark density as the finite-density transition of the bosonic baryons in the two-color world. In contrast to previous studies of heavy dense QCD, our zero-temperature extrapolations are consistent with a continuous transition without binding energy. They thus provide evidence that the effective theory for heavy quarks is capable of describing the characteristic differences between diquark condensation in two-color QCD and the liquid-gas transition of nuclear matter in QCD.

B-meson spectroscopy in HQET at order1/m

We present a study of the B spectrum performed in the framework of heavy quark effective theory expanded to next-to-leading order in $1/{m}_{\mathrm{b}}$ and nonperturbative in the strong coupling. Our analyses have been performed on ${N}_{\mathrm{f}}=2$ lattice gauge field ensembles corresponding to three different lattice spacings and a wide range of pion masses. We obtain the ${\mathrm{B}}_{\mathrm{s}}$-meson mass and hyperfine splittings of the B- and ${\mathrm{B}}_{\mathrm{s}}$-mesons that are in good agreement with the experimental values and examine the mass difference ${m}_{{\mathrm{B}}_{\mathrm{s}}}\ensuremath{-}{m}_{\mathrm{B}}$ as a further cross-check of our previous estimate of the b-quark mass. We also report on the mass splitting between the first excited state and the ground state in the B and ${\mathrm{B}}_{\mathrm{s}}$ systems.

Heavy baryons with strangeness in a soliton model

We present results from a chiral soliton model calculation for the spectrum of baryons with a single heavy quark (charm or bottom) and non-zero strangeness. We treat the strange components within a three flavor collective coordinate quantization of the soliton that fully accounts for light flavor symmetry breaking. Heavy baryons emerge by binding a heavy meson to the soliton. The dynamics of this heavy meson is described by the heavy quark effective theory with finite mass effects included.

Renormalization of quasiparton distribution

Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasi parton distributions. Like a light-cone parton distribution, a quasi parton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of non-local operators in general is not well understood. However, in the case of quasi quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizable by the quark wave function renormalization in the axial gauge. We first show that the renormalization of the self energy correction to the quasi quark distribution is equivalent to that of the heavy-light quark vector current in heavy quark effective theory at one-loop order. Assuming this equivalence at two-loop order, we then show that the multiplicative renormalizability of the quasi quark distribution is true at two-loop order.

Non-perturbative Heavy Quark Effective Theory: Introduction and Status

We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.

Analysis of the semileptonic $$B_c\rightarrow D_1^0$$ B c → D 1 0 transition in QCD sum rules and HQET

We investigate the structure of the $$D_{1}^0(2420[2430])(J^P=1^+)$$ mesons via analyzing the semileptonic $$B_{c}\rightarrow D_{1}^0 l\nu $$ 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: as a pure $$|c\bar{u}\rangle $$ state, as a mixture of the two $$|^3P_1\rangle $$ and $$|^1P_1\rangle $$ states with a mixing angle $$\theta $$ , and as a combination of the two mentioned states with mixing angle $$\theta =35.3^\circ $$ in the heavy-quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the three above conditions. These form factors are numerically calculated for $$|c\bar{u}\rangle $$ and the heavy-quark limit cases. The obtained results for the form factors are used to evaluate the decay rates and the branching ratios. Also for mixed states, all of the mentioned physical quantities are plotted with respect to the unknown mixing angle $$\theta $$ .