We compute in order alpha_s the nonrelativistic QCD (NRQCD) short-distance coefficients that match quark-antiquark operators of all orders in the heavy-quark velocity v to the electromagnetic current. We employ a new method to compute the one-loop NRQCD contribution to the matching condition. The new method uses full-QCD expressions as a starting point to obtain the NRQCD contribution, thus greatly streamlining the calculation. Our results show that, under a mild constraint on the NRQCD operator matrix elements, the NRQCD velocity expansion for the quark-antiquark-operator contributions to the electromagnetic current converges. The velocity expansion converges rapidly for approximate J/psi operator matrix elements.
We calculate the O(alpha_s^3 ln(alpha_s)) contributions to the heavy-quarkonium production and annihilation rates. Our result sheds new light on the structure of the high-order perturbative corrections and opens a new perspective for a high-precision theoretical analysis. We also determine the three-loop anomalous dimensions of the nonrelativistic vector and pseudoscalar currents.
We calculate O(alpha_S^4 m) and O(alpha_S^4 m log(alpha_S)) corrections to the quarkonium 1S energy level analytically, which have been overlooked in recent studies. These are the contributions from one Coulomb-gluon exchange with the 1-loop vacuum polarization insertion. A part of the corrections was computed numerically some time ago; we correct its error.
Presently the quarkonium spectrum, written in terms of the quark MSbar-mass, is known at O(alpha_s^3 m) accuracy. We point out that in order to achieve O(alpha_s^4 m) accuracy it is sufficient to calculate further (I) the O(alpha_s^4 m) relation between the MSbar-mass and the pole-mass, and (II) the binding energy at O(alpha_s^5 m) in the large-beta_0 approximation. We calculate the latter correction analytically for the 1S-state and study its phenomenological implications.
In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.
A recent determination of the mass of the b quark, based exclusively on quantum chromodynamics (by avoiding strictly to introduce any phenomenological interaction potential of nonperturbative origin), may be improved by allowing for a merely numerical solution of the corresponding eigenvalue problem.
We compute S-wave and P-wave electromagnetic quarkonium decays at order v^7 in the heavy-quark velocity expansion. In the S-wave case, our calculation confirms and completes previous findings. In the P-wave case, our results are in disagreement with previous ones; in particular, we find that two matrix elements less are needed. The cancellation of infrared singularities in the matching procedure is discussed.
The decay $Z^{0}\rightarrow Q+ \ell^{+}\ell^{-}$, where $Q$ is a $J^{PC}=1^{--}$ quarkonium state, has a very clean final state, which should make it easy to detect. The branching ratio of this mode is greater than $10^{-6}$ for $ρ$, $ϕ$, and $ψ$, indicating that these processes may be detectable at LEP.
We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the $η_b$ decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.
We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We discuss the interplay of the scales arising in the Soft-Collinear Effective Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2. For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for 1-z << alpha_s^2. The S- and P-wave octet shape functions are calculated. W…
We show that perturbation theory may give reasonable numbers for the decays of the bottomonium and charmonium ground states to $e^+e^-$ and to $γγ$. To reach this conclusion it is important to perform the resummation of logs. In particular, we obtain the value $Γ(η_b (1S) \to γγ)=0.35 \pm 0.1 ({\rm th.}) \pm 0.05 (\lQ)$ KeV.
We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> T >> m alpha_s^2 >> m_D (m being the heavy-quark mass), at order m alpha_s^5. We first sequentially integrate out the scales m, m alpha_s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion …
We compute the energy levels of some of the lower-lying heavy quarkonium states perturbatively up to O(alpha_s^5*m) and O(alpha_s^5*m*log[alpha_s]). Stability of the predictions depends crucially on the unknown 4-loop pole-MSbar mass relation. We discuss the current status of the predictions with respect to the observed bottomonium spectrum.
We consider the exclusive pseudoscalar heavy-quarkonium (eta_{b,c}) production in association with a photon at future lepton colliders where the collider energies of O(10^2) GeV are far greater than the quarkonium mass. At these energies, the logarithm of mass to collision energy becomes increasingly large hence its resummation becomes particularly important. By making use of the light-cone-distribution factorization formula, we resum the logarithms up to next-to-leading-logarithmic accuracy (NLL) that corresponds to order-alpha_s accuracy. We combine the resummed result with a known fixed-ord…
In a recent paper, we included two loop, relativistic one loop and second order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, $O(α_s^4)$ and leading $\Lambdav^4/m^4$ terms. The results were obtained with, in particular, the value of the two loop static coefficient due to Peter; this been recently challenged by Schröder. In our previous paper we used Peter's result; in the present one we now give results with Schröder's, as this is likely to be the correc…
We report about a recent calculation of the heavy quarkonium mass and decay width in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> pi T >> m alpha_s^2 >> m_D, m being the heavy-quark mass, up to order m alpha_s^5. The calculation may be relevant to understand the behavior of the Y(1S) in a quark-gluon plasma at present-day colliders.
Here we would like to review recent progress on the resummation on logarithms of $α_s$ in heavy quarkonium. We will mainly focus on the phenomenological relevance of these achievements. Determinations of the $η_b(1S)$ mass, $B_c(1S)$ hyperfine splitting, inclusive electromagnetic decays and implications for $t$-$\bar t$ production near threshold.
Quarkonium production at a given large p_T is dominated by parton fragmentation: a parton which is produced with transverse momentum p_T/z fragments into a quarkonium state which carries a fraction z of the parton momentum. Since parton production cross sections fall steeply with p_T, high z fragmentation is favored. However, quantum number constraints may require the emission of gluons in the fragmentation process, and this softens the z dependence of the fragmentation function. We discuss the possibility that higher- order processes may enhance the large z part of fragmentation functions and…
We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/psi --> e^+e^- and eta_c --> gamma gamma. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-N_f limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguitie…
We compute the third-order correction to electromagnetic S-wave quarkonium production and annihilation rates due to the emission and absorption of an ultrasoft gluon. Our result completes the analysis of the non-relativistic quarkonium bound-state dynamics in the next-to-next-to-next-to-leading order. The impact of the ultrasoft correction on the Upsilon(1S) leptonic width and the top quark-antiquark threshold production cross section is estimated.
We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M^4 in the heavy-quark mass expansion, which includes center of mass operators, and at order alpha_s^2 in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order 1/M^6 and at order alpha_s^2 that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at order v^7 in the heavy-quark velocity expansion. If we count alpha_s(M) ~ v^2, the calculation provides the complete next-to-leading order corrections to the P-wave hadronic widths, and in …
The short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into heavy quarkonium states is calculated to order alpha_s^2. The gauge-invariant definition of the fragmentation function by Collins and Soper is employed. Ultraviolet divergences are removed using the MS-bar renormalization procedure. The longitudinal term in the fragmentation function agrees with a previous calculation by Beneke and Rothstein. The next-to-leading order correction to the transverse term disagrees with a previous calculation.
Nucleon electromagnetic form factors are considered in the framework of the generalized Skyrme model with dilaton-quarkonium field. In our recent publication we have got big discrepancies between calculated form factors and dipole approximation formula. Here we have reasonably good accordance between them in finite impulse region after vector meson dominance have been taken into account. Omega and Rho -meson have been included into only hadron structure of the photon.
We present an evaluation of heavy quarkonium states (bottomium and charmonium) from first principles. We use tree-level QCD (including relativistic corrections) and the full one-loop potential; nonperturbative effects are taken into account at the leading order through the contribution of the gluon condensate <alpha_strong G^2>. We use the values Lambda_QCD= 200 (+80/-60) MeV and <alpha_s G^2> = 0.042 +/- 0.020 GeV^4, but we trade the value of the quark mass by the masses of J/psi, Upsilon as input. We get good agreement in what is essentially a zero parameter evaluation for the masses of the …
We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual …
We study $O(α_sv^2)$ corrections to decays of $^1S_0$ heavy quarkonium into light hadrons and two photons within the framework of nonrelativistic QCD, and find these $O(α_sv^2)$ corrections to have significant contributions especially for the decay into light hadrons. With these new results, experimental measurements of the hadronic width and the $γγ$ width of $η_c$ can be described more consistently. By fitting experimental data, we find the long-distance matrix elements of $η_c$ to be $|\mathcal{R}_{η_c}(0)|^2=0.834^{+0.281}_{-0.197}\ \textrm{GeV}^3$ and $< \bm{v}^2 >_{η_c}=0.232^{+0.121}_{-…
We improve the pNRQCD approach to annihilation processes of heavy quarkonium and make first pNRQCD predictions for exclusive electromagnetic production of heavy quarkonium. We consider strongly coupled quarkonia, i.e., quarkonia that are not Coulombic bound states. Possible strongly coupled quarkonia include excited charmonium and bottomonium states. For these, pNRQCD provides expressions for the decay and exclusive electromagnetic production NRQCD matrix elements that depend on the wavefunctions at the origin and few universal gluon field correlators. We compute electromagnetic decay widths a…
We study the energy spectrum of bottomonium in perturbative QCD, taking alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar) and (b,cbar) states are also examined.
We compute $S$-wave quarkonium wavefunctions at the origin in the $\overline{\rm MS}$ scheme based on nonrelativistic effective field theories. We include the effects of nonperturbative long-distance behaviors of the potentials, while we determine the short-distance behaviors of the potentials in perturbative QCD. We obtain $\overline{\rm MS}$-renormalized quarkonium wavefunctions at the origin that have the correct scale dependences that are expected from perturbative QCD, so that the scale dependences cancel in physical quantities. Based on the calculation of the wavefunctions at the origin,…
The exclusive processes are considered, where a point-like source of heavy quark-antiquark pairs $Q \bar Q$, e.g. their electromagnetic current, produces a pair consisting of a heavy quarkoniumlike exotic meson (tetraquark) or baryon (pentaquark) and a light meson or an antibaryon. For a sufficiently large mass of the heavy quark $m_Q$ there is a range of the energy $E$ above the $Q \bar Q$ threshold, where $E \ll m_Q$ and still the energy is large compared to the strong interaction scale, $E \gg Λ_{QCD}$. It is shown that in this energy range, where the heavy quarks are nonrelelativistic, a s…
We study the spectra of the bottomonium and B_c states within perturbative QCD up to order alpha_s^4. The O(Lambda_QCD) renormalon cancellation between the static potential and the pole mass is performed in the epsilon-expansion scheme. We extend our previous analysis by including the (dominant) effects of non-zero charm-quark mass in loops up to the next-to-leading non-vanishing order epsilon^3. We fix the b-quark MSbar mass $\bar{m}_b \equiv m_b^{\bar{\rm MS}}(m_b^{\bar{\rm MS}})$ on Upsilon(1S) and compute the higher levels. The effect of the charm mass decreases $\bar{m}_b$ by about 11 MeV…
We study an effect of the off-shellness of the quark and antiquark inside a heavy quarkonium system on IR renormalons contained in the perturbative computations of the quarkonium energy levels. We demonstrate that, when the off-shellness p_Q^2 -m_Q^2 \sim alpha_S^2 m_Q^2 is larger than m_Q Lambda_QCD, renormalons in the energy levels as calculated in perturbative QCD are suppressed by a factor Lambda_QCD/alpha_S^2 m_Q as compared to those in 2 m_pole + V_QCD(r). In this case the residual O(Lambda_QCD^4) renormalon has the same dimension as that of the leading gluon-condensate contribution.
In the limit of a high temperature T and a large quark-mass M, implying a small gauge coupling g, the heavy quark contribution to the spectral function of the electromagnetic current can be computed systematically in the weak-coupling expansion. We argue that the scale hierarchy relevant for addressing the disappearance ("melting") of the resonance peak from the spectral function reads M >> T > g^2 M > gT >> g^4 M, and review how the heavy scales can be integrated out one-by-one, to construct a set of effective field theories describing the low-energy dynamics. The parametric behaviour of the …
By making use of the finite-temperature real-time static potential that was introduced and computed to leading non-trivial order in Hard Thermal Loop resummed perturbation theory in recent work, and solving numerically a Schrödinger-type equation, we estimate the quarkonium (in practice, bottomonium) contribution to the spectral function of the electromagnetic current in hot QCD. The spectral function shows a single resonance peak which becomes wider and then disappears as the temperature is increased beyond 450 MeV or so. This behaviour can be compared with recently attempted lattice reconstr…
We present a calculation of the rates for Higgs-boson decays to a vector heavy-quarkonium state plus a photon, where the heavy quarkonium states are the J/psi and the Upsilon(nS) states, with n=1, 2, or 3. The calculation is carried out in the light-cone formalism, combined with nonrelativistic QCD factorization, and is accurate at leading order in m_Q^2/m_H^2, where m_Q is the heavy-quark mass and m_H is the Higgs-boson mass. The calculation contains corrections through next-to-leading order in the strong-coupling constant alpha_s and the square of the heavy-quark velocity v, and includes a r…
We calculate the leading mass-suppressed two-loop contribution, proportional to alpha_s^3/(m_q r^2), to the potential of a heavy quark-antiquark system. This contribution originates in the nonabelian nature of quantum chromodynamics (QCD) and has no analogue in quantum electrodynamics (QED). For this purpose, we elaborate a technique based on the implementation of the threshold expansion within the effective theory of nonrelativistic QCD (NRQCD). We discuss phenomenological implications of our result for heavy-quarkonium physics. We also confirm a previous result for the two-loop O(alpha_s^2) …
An overview is given of the theoretical developments on heavy quarks and quarkonia in heavy-ion collisions as reported at the "Hard and EM Probes 2018" conference. Specifically, we address progress in the understanding of heavy-flavor diffusion and its hadronization, quarkonium transport and the extraction of quarkonium melting temperatures, energy loss of heavy quarks at high momentum, and their rescattering in small colliding systems.
We present a systematic study of the production of the heavy quarkonium, i.e., $|(c\bar{c})[n] \rangle$ , $|(b\bar{c})[n] \rangle$ (or $|(c\bar{b})[n] \rangle$), and $|(b\bar{b})[n] \rangle$ quarkonium [$|(Q\bar{Q'})[n]\rangle$ quarkonium for short], through $Z^0$ boson semi-exclusive decays with new parameters \cite{lx} for the heavy quarkonium under the framework of the NRQCD, where $[n]$ stands for $n^1S_0$, $n^3S_1$, $n^1P_0$, $n^3P_J$ ($n=1, \cdots, 6$; $J=(0, 1, 2)$). "Improved trace technology" is adopted to derive the simplified analytic expressions at the amplitude level, which shall …
We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential Non-Relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed and the necessary techniques, providing…
We review recent theoretical developments in heavy quarkonium physics from the point of view of Effective Field Theories of QCD. We discuss Non-Relativistic QCD and concentrate on potential Non-Relativistic QCD. Our main goal will be to derive QCD Schrödinger-like equations that govern the heavy quarkonium physics in the weak and strong coupling regime. We also discuss a selected set of applications, which include spectroscopy, inclusive decays and electromagnetic threshold production.
Recently the full O(alpha_S^5 m, alpha_S^5 m log(alpha_S)) correction to the heavy quarkonium 1S energy level has been computed (except the a_3-term in the QCD potential). We point out that the full correction (including the log(alpha_S)-term) is approximated well by the large-beta_0 approximation. Based on the assumption that this feature holds up to higher orders, we discuss why the top quark pole mass cannot be determined to better than O(Lambda_{QCD}) accuracy at a future e^+e^- collider, while the MS-bar mass can be determined to about 40 MeV accuracy (provided the 4-loop MSbar-pole mass …
A method to determine the running of alpha from a measurement of small-angle Bhabha scattering is proposed and worked out. The method is suited to high statistics experiments at e+e- colliders, which are equipped with luminometers in the appropriate angular region. A new simulation code predicting small-angle Bhabha scattering is also presented
We extend existing calculations of the electromagnetic dipole operator contribution to the total decay rate and the photon energy spectrum of the decay \bar{B} -> X_sγat O(α_s^2) by working out the exact dependence on the charm quark mass.
We study the Single-Parton-Scattering (SPS) production of double quarkonia (J/psi+J/psi, J/psi+Upsilon, and Upsilon+Upsilon) in pp and pp(bar) collisions at the LHC and the Tevatron as measured by the CMS, ATLAS, LHCb, and D0 experiments in the Colour-Evaporation Model (CEM), based on the quark-hadron-duality, including Next-to-Leading Order (NLO) QCD corrections up to alpha_s^5. To do so, we also perform the first true NLO --up to alpha_s^4-- study of the p_T-differential cross section for single-quarkonium production. This allows us to fix the non-perturbative CEM parameters at NLO accuracy …
We propose a method to determine the running of $α_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004).
Exclusive vector-quarkonium photoproduction at NLO in alpha_s in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation
The O(N_f alpha^2) electroweak radiative corrections to the Thomson scattering matrix element are calculated for a general renormalization scheme with massless fermions. All integrals can be evaluated exactly in dimensional regularization which in several cases yields new results that are remarkably simple in form. A number of stringent internal consistency checks are performed. The Z-gamma mixing complicates the calculation of 1-particle reducible diagrams considerably at this order and a general treatment of this problem is given. Conditions satisfied by O(N_f alpha^2) counterterms are deriv…
We analyze the relativistic corrections to annihilation rates of S-wave quarkonia within the framework of NRQCD. We show that order v^2 corrections can be expressed in terms of the heavy quark pole mass and the quarkonium mass. The ratio of hadronic to radiative annihilation rates for eta_b and eta_c can therefore be predicted accurately. The contributions of color-octet operators to the hadronic decay rates of spin-triplet quarkonia are shown to be significant, even though they arise at order v^4 in the velocity expansion. We provide a rough estimate of the color-octet contributions and extra…
We compute the relativistic corrections to the color-singlet contribution to gluon fragmentation into a J/psi at relative order v^4, making use of the nonrelativistic QCD (NRQCD) factorization approach. The corresponding full-QCD process exhibits infrared divergences that manifest themselves as single and double poles in epsilon in 4-2epsilon dimensions. We isolate the infrared-divergent contributions and treat them analytically. In the matching of full QCD to NRQCD, the pole contributions are absorbed into long-distance NRQCD matrix elements. The renormalizations of the ultraviolet divergence…
We compute the energy dependence of the P_T-integrated cross section of directly produced quarkonia in pp collisions at next-to-leading order (NLO), namely up to alpha_s^3, within nonrelativistic QCD (NRQCD). Our analysis is based on the idea that the P_T-integrated and the P_T-differential cross sections can be treated as two different observables. The colour-octet NRQCD parameters needed to predict the P_T-integrated yield can thus be extracted from the fits of the P_T-differential cross sections at mid and large P_T. For the first time, the total cross section is evaluated in NRQCD at full …
In this work we use the low-energy EFT called potential non-relativistic QCD (pNRQCD) to calculate the partial decay width of different $b\bar{b}$-states undergoing an electric dipole transition at next-to-next-to leading order (NNLO). Explicitly, the $χ_{b J}$, for $J=0,1,2$, and the $h_b$ are investigated by computing the processes $χ_{b J} \to Υ+ γ$ and $h_b \to η_b + γ$. Relativistic corrections of relative order $v^2$ to the leading electric dipole operator are included. The analysis separates those contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrang…
We compute the O(alpha_s^2) correction to the decay rate eta_c --> gamma gamma and discuss its implications for precision quarkonium physics. We study the suitability of the ratio Gamma(J/psi --> e+e-)/Gamma(eta_c --> gamma gamma), in which the non-perturbative or soft effects cancel at O(alpha_s^{0,1}), for extracting fundamental parameters of QCD at low energies. We show that the QCD-based theory of charmonia is not capable of predicting this ratio with any degree of confidence.
The rare decay channels of Higgs boson to heavy quarkonium offer vital opportunities to explore the coupling of Higgs to heavy quarks. We study the semi-exclusive decay channels of Higgs boson to heavy quarkonia, i.e., $H^0\to |(Q\bar{Q^{\prime}})[n]\rangle+\bar{Q}Q^{\prime}$ ($Q^{(\prime)}=c~\text{or}~b$ quark) within the NRQCD framework. In addition to the lower-level Fock states $|(Q\bar{Q'})[1S]\rangle$ continent, contributions of high excited states $|(Q\bar{Q'})[2S]\rangle$, $|(Q\bar{Q'})[3S]\rangle$, $|(Q\bar{Q'})[4S]\rangle$, $|(Q\bar{Q'})[1P]\rangle$, $|(Q\bar{Q'})[2P]\rangle$, $|(Q\b…
The flavor-changing electromagnetic dipole operator O_7 gives the dominant contribution to the B -> Xs gamma decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent t -> Xb W calculation. The complete result allows us to test the validity of the naive non-abelianization (NNA) approximation that has been previously applied to estimate the NNLO QCD correction to Gamma(B -> Xs gamma)/Gam…
In kaon decay, electromagnetic radiative corrections can generate shifts in the apparent Delta I = 3/2 amplitude of order alpha A_0/A_2 ~ 22 alpha. In order to know the true Delta I = 3/2 amplitude for comparison with lattice calculations and phenomenology, one needs to subtract off this electromagnetic effect. We provide a careful estimate of the electromagnetic shift in the amplitude, which shows that it is smaller than naive expectations, with a fractional shift of delta A_2/A_2 = -0.016 +- 0.01.
Due to larger mass and earlier production, heavy quark(quarkonium) can be sensitive probes to investigate the fast decaying electromagnetic and vortical fields produced in heavy-ion collisions. The non-relativistic Schroedinger-like equation for heavy quarks under strong electromagnetic fields in the rotating frame is deduced and used to construct the two-body equation for the charmonium system. The effective potential between charm and anti-charm becomes anisotropic in electromagnetic and vortical fields, especially along the direction of the Lorentz force. The vorticity will affect this asym…
In the framework of the Bethe-Salpeter formalism used in previous papers to evaluate the quarkonium spectrum, here we reverse the point of view to extract an ``experimental'' running coupling alpha_s(Q^2) in the infrared (IR) region from the data. The values so obtained agree within the errors with the Shirkov-Solovtsov analytic coupling for 200 MeV <Q< 1.2 GeV, thus giving a very satisfactory unifying description of high and low energy phenomena. Below 1 GeV however alpha_s(Q^2) seems to vanish as Q to 0. The paper is based on a work in progress in collaboration with D.V.Shirkov.
