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In this paper, the resulting photon emission rate in the collision ug → sgγ is studied and calculated using Spectral Function simulation methods to understand the quark-gluon plasma. The Spectral Function and photon emission rate of the ug → sgγ reaction are analyzed at a critical temperature of 157 MeV with a flavor number of n f =5. To calculate the spectral function with low statistical uncertainty, the quantum chromodynamics theory of quark-gluon collisions is used to investigate the accuracy of thermal photon emission in determining photon emission rates. The Spectral Function analysis utilized multi-lattice space and extrapolation correlation factors at nf =5 for the ug → sgγ collision to extract the behavior of the spectral function and its effects on the photon rate from the QCD lattice correlations. The photon emission rate from the ug → sgγ interaction at 157 MeV offers insights into collision dynamics through spatial transverse vector correlations and lattice QCD. The Spectral Function analysis was performed in a multi-lattice space based on the extrapolation correlation factors with the flavor number 5 of the ug → sgγ collision. The QCD correlations, combining non-perturbative and perturbative effects at finite coupling, show an agreement within 10%.

A bstract We compute the 1-jettiness soft function for the decay of a heavy quark into a light quark jet plus colorless particles at three-loop order in soft-collinear effective theory. The 1-jettiness measurement fixes the total small light-cone momentum component of the soft radiation with respect to the jet direction. This soft function is a universal ingredient to the factorization of heavy-to-light quark decays in the limit of small 1-jettiness. Our three-loop result is required for resummation at the N 3 LL′ level, e.g. near the endpoint in the photon energy spectrum of the B → X s γ decay. It is also a necessary ingredient for future calculations of fully-differential heavy-to-light quark decay rates at N 3 LO using the N -jettiness subtraction method, e.g. for semileptonic top decays. Using our result for the soft anomalous dimension we confirm predictions on the universal infrared structure of QCD scattering amplitudes with a massive external quark at three loops.

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum (qT) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-x logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding MS¯\\[ \\overline{\\mathrm{MS}} \\]-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the qT spectrum for color-singlet production, for which we compute the complete qT2/Q2 suppressed power corrections at Oαs\\[ \\mathcal{O}\\left({\\alpha}_s\\right) \\], including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.

We consider the effects of a non-vanishing strange-quark mass in the determination of the full basis of dimension six matrix elements for Bs mixing, in particular we get for the ratio of the V − A Bag parameter in the Bs and Bd system: B¯Q1s/B¯Q1d=0.987−0.009+0.007\\[ {\\overline{B}}_{Q_1}^s/{\\overline{B}}_{Q_1}^d={0.987}_{-0.009}^{+0.007} \\]. Combining these results with the most recent lattice values for the ratio of decay constants fBs/fBd\\[ {f}_{B_s}/{f}_{B_d} \\] we obtain the most precise determination of the ratio ξ=fBsB¯Q1s/fBdB¯Q1d=1.2014−0.0072+0.0065\\[ \\xi ={f}_{B_s}\\sqrt{{\\overline{B}}_{Q_1}^s}/{f}_{B_d}\\sqrt{{\\overline{B}}_{Q_1}^d}={1.2014}_{-0.0072}^{+0.0065} \\] in agreement with recent lattice determinations. We find ΔMs = (18.5− 1.5+ 1.2)ps− 1 and ΔMd = (0.547− 0.046+ 0.035)ps− 1 to be consistent with experiments at below one sigma. Assuming the validity of the SM, our calculation can be used to directly determine the ratio of CKM elements |Vtd/Vts| = 0.2045− 0.0013+ 0.0012, which is compatible with the results from the CKM fitting groups, but again more precise.

Abstract We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee’s method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-β 0 approximation. Here, we introduce an “ ambiguity function,” which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-β 0 approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.

Abstract We present results for SCET and bHQET matching coefficients and jet functions in the large-β 0 limit. Our computations exactly predict all terms of the form α s n + 1 n f n $$ {\\alpha}_s^{n+1}{n}_f^n $$ for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to O α s 4 $$ \\mathcal{O}\\left({\\alpha}_s^4\\right) $$ . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of α s using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor H m that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β 0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

A bstract We focus on a non-abelian gauge field coupled to a single (but general) representation of a family of N f fermions. By using the same machinery that had allowed us to evaluate the sub-leading large- N f term of the five-loop Beta function earlier, we here report on a confirmation of the all- N f result that has in the meantime been published by another group. Furthermore, in order to push forward the 5-loop renormalization program regarding gauge parameter dependence, we present the linear terms of the complete set of anomalous dimensions, in an expansion in the covariant gauge parameter around the Feynman gauge.

A bstract We present the complete formula for the cusp anomalous dimension at four loops in QCD and in maximally supersymmetric Yang-Mills. In the latter theory it is given by Γ cusp , A α s 4 = − α s N π 4 73 π 6 20160 + ζ 3 2 8 + 1 N 2 31 π 6 5040 + 9 ζ 3 2 4 . Our approach is based on computing the correlation function of a rectangular light-like Wilson loop with a Lagrangian insertion, normalized by the expectation value of the Wilson loop. In maximally supersymmetric Yang-Mills theory, this ratio is a finite function of a cross-ratio and the coupling constant. We compute it to three loops, including the full colour dependence. Integrating over the position of the Lagrangian insertion gives the four-loop Wilson loop. We extract its leading divergence, which determines the four-loop cusp anomalous dimension. Finally, we employ a supersymmetric decomposition to derive the last missing ingredient in the corresponding QCD result.