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Register a new userVector Leptoquarks Beyond Tree Level II: $mathcal{O}(alpha_s)$ Corrections and Radial Modes
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We clarify open issues in relating low- and high-energy observables, at next-to-leading order accuracy, in models with a massive leptoquark embedded in a flavor non-universal $SU(4) times SU(3) times SU(2) times U(1)$ gauge group. Extending previous work on this subject, we present a complete analysis of the $mathcal{O}(alpha_s)$ corrections to the matching conditions of semileptonic operators at the high scale. These corrections are not negligible, but they do not exceed the 10% level and are subleading compared to the $mathcal{O}(alpha_4)$ corrections proportional to the leading leptoquark coupling, which is expected to be much larger than the QCD coupling in the parameter space region of phenomenological interest. We further analyze the impact of radial modes, both at $mathcal{O}(alpha_4)$ and at $mathcal{O}(alpha_s)$ accuracy, highlighting their role in the renormalization of the theory.
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Models with massive vector leptoquarks, resulting from an $SU(4)$ gauge symmetry spontaneously broken at the TeV scale, are of great phenomenological interest given the current anomalies in semileptonic $B$ decays. We analyze the relations between low- and high-energy observables in such class of models to next-to-leading order accuracy in the $SU(4)$ gauge coupling $g_4$. For large values of $g_4$, motivated by recent $B$-physics data, one-loop corrections are sizeable. The main effect is an enhanced contribution at low-energy, at fixed on-shell couplings. This result has important implications for current and future high-energy searches of vector leptoquark models.
Extending previous work on this subject, we evaluate the impact of vector-like fermions at next-to-leading order accuracy in models with a massive vector leptoquark embedded in the $SU(4)times SU(3)^primetimes SU(2)_Ltimes U(1)_X$ gauge group. Vector-like fermions induce new sources of flavor symmetry breaking, resulting in tree-level flavor-changing couplings for the leptoquark not present in the minimal version of the model. These, in turn, lead to a series of non-vanishing flavor-changing neutral-current amplitudes at the loop level. We systematically analyze these effects in semileptonic, dipole and $Delta F=2$ operators. The impact of these corrections in $bto s u u$ and $bto ctau u$ observables are discussed in detail. In particular, we show that, in the parameter region providing a good fit to the $B$-physics anomalies, the model predicts a $10%$ to $50%$ enhancement of $mathcal{B}(Bto K^{(*)} u u)$.
We analyze the minimal supersymmetric Higgs self-couplings at O(alpha_t alpha_s) within the effective potential approach. The two-loop corrections turn out to be of moderate size in the DRbar scheme if the central scale is chosen as half the SUSY scale. The inclusion of the two-loop corrections reduces the renormalization scale dependence to the per-cent level. These results have a significant impact on measurements of the trilinear Higgs self-couplings at the LHC and a future e^+e^- collider.
Inclusive $chi_{cJ}$ $(J=0,1,2)$ production from $Upsilon(1S)$ decay is studied within the framework of nonrelativistic QCD (NRQCD) factorization at leading order in $v_Q^2$, which includes the contributions of $bbar{b}({}^3S_1^{[1]})to cbar{c}(^3P_J^{[1]})+X$ and $bbar{b}({}^3S_1^{[1]})to cbar{c}(^3S_1^{[8]})+X$. For both channels, the short-distance coefficients are calculated through ${cal O}(alpha_s^5)$, which is next-to-leading order for the second one. By fitting to the measured $Upsilon(1S)$ branching fractions to $chi_{c1}$ and $chi_{c2}$, we obtain the color-octet long-distance matrix element (LDME) $langlemathcal{O}^{chi_{c0}}({}^3S_1^{[8]})rangle =(4.04pm0.47_{-0.34}^{+0.67})times10^{-3}$ GeV$^3$, where the first error is experimental and the second one due to the renormalization scale dependence, if we use as input $langlemathcal{O}^{chi_{c0}}({}^3P_0^{[1]})rangle=0.107$ GeV$^5$ as obtained via potential-model analysis. Previous LDME sets, extracted from data of prompt $chi_{cJ}$ hadroproduction, yield theoretical predictions that systematically undershoot or mildly overshoot the experimental values of $mathcal{B}(Upsilonto chi_{cJ}+X)$.
In the paper, we study the properties of the $Z$-boson hadronic decay width by using the $mathcal{O}(alpha_s^4)$-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the $Z$-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $mathcal{O}(alpha_s^5)$-order terms are highly suppressed, e.g. conservatively, we have $Delta Gamma_{rm Z}^{rm had}|^{{cal O}(alpha_s^5)}_{rm PMC}simeq pm 0.004$ MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW-QCD mixed corrections, and QED-QCD mixed corrections, our final prediction of the hadronic $Z$ decay width is $Gamma_{rm Z}^{rm had}=1744.439^{+1.390}_{-1.433}$ MeV, which agrees with the PDG global fit of experimental measurements, $1744.4pm 2.0$ MeV.
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