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Bernd A. Kniehl

Publications and source records attributed to Bernd A. Kniehl.

At least 55 records · Page 3Linked to original sources
arXiv2015

Two-loop electroweak threshold corrections to the bottom and top Yukawa couplings

We study the relationship between the $\overline{\mathrm{MS}}$ Yukawa coupling and the pole mass for the bottom and top quarks at the two-loop electroweak order ${\cal O}(α^2)$ in the gaugeless limit of the standard model. We also consider the $\overline{\mathrm{MS}}$ to pole mass relationships at this order, which include tadpole contributions to ensure the gauge independence of the $\overline{\mathrm{MS}}$ masses. In order to suppress numerically large tadpole contributions, we propose a redefinition of the running heavy-quark mass in terms of the $\overline{\mathrm{MS}}$ Yukawa coupling. We also present $Δr$ in the $\overline{\mathrm{MS}}$ scheme at ${\cal O}(α^2)$ in the gaugeless limit. As an aside, we also list the exact two-loop expression for the mass counterterms of the bottom and top quarks.

hep-ph↗
arXiv2015

Two-loop electroweak threshold corrections in the Standard Model

We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the $\overline{\mathrm{MS}}$ scheme at full order ${\cal O}(α^2)$ in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the $\overline{\mathrm{MS}}$ masses, we work in $R_ξ$ gauge and systematically include tadpole contributions. We also consider the gaugeless-limit approximation and compare it with the full two-loop electroweak calculation.

hep-ph↗
arXiv2015

$η_c$ production at the LHC challenges nonrelativistic-QCD factorization

We analyze the first measurement of $η_c$ production, performed by the LHCb Collaboration, in the nonrelativistic-QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant $α_s$ and the relative velocity $v$ of the bound quarks including the feeddown from $h_c$ mesons. Converting the long-distance matrix elements (LDMEs) extracted by various groups from $J/ψ$ yield and polarization data to the $η_c$ case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.

hep-ph↗
arXiv2014

Considerations concerning the generalization of the Dirac equations to unstable fermions

We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.

hep-ph↗
arXiv2014

Propagator mixing renormalization for Majorana fermions

We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.

hep-th↗
arXiv2013

All-order renormalization of propagator matrix for fermionic system with flavor mixing

We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions and their expansions through two loops for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.

hep-ph↗
arXiv2013

Inclusive J/psi and psi(2S) production from b-hadron decay in p anti-p and pp collisions

We study the inclusive production of J/psi and psi(2S) mesons originating from the decays of bottom-flavored hadrons produced in p anti-p collisions at the Fermilab Tevatron and in pp collisions at the CERN LHC. We work at next-to-leading order in the general-mass variable-flavor-number scheme (GM-VFNS) implemented with nonperturbative fragmentation functions fitted to e^+e^- data of inclusive b-hadron production exploiting their universality. The three-momentum distributions of the charmonia used were extracted from B-decay data in the framework of nonrelativistic-QCD factorization. Comparing the theoretical predictions thus obtained with transverse-momentum distributions measured by the CDF II, ALICE, ATLAS, CMS, and LHCb Collaborations, we find excellent overall agreement as for both absolute normalization and lineshape, which provides a nontrivial test of the GM-VFNS over wide ranges of center-of-mass energy, transverse momentum, and rapidity.

hep-ph↗
arXiv2013

About the EW contribution to the relation between pole and MS-masses of the top-quark in the Standard Model

Results of our recent re-analysis of the electroweak contribution to the relation between pole and running masses of top-quark within the Standard Model is reviewed. We argue, that if vacuum of SM is stable, then there exists an optimal value of renormalization group scale (IR-point), at which the radiative corrections to the matching condition between parameters of Higgs sector and pole masses is minimal or equal to zero. Within the available accuracy, we find the IR-point to lie in an interval between value of Z-boson mass and twice the value of W-boson mass. The value of scale is relevant for extraction of Higgs self-coupling from cross-section as well as for construction of effective Lagrangian.

hep-ph↗
arXiv2013

NLO NRQCD disfavors the interpretation of X(3872) as $χ_{c1}(2P)$

We study $χ_{c1}(2P)$ inclusive hadroproduction at next-to-leading order (NLO), both in $α_s$ and $v^2$, within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the color-singlet $^3P_1^{[1]}$ and color-octet $^3S_1^{[8]}$ $c\bar c$ Fock states as well as the mixing of the latter with the $^3D_1^{[8]}$ state. Assuming the recently discovered X(3872) hadron to be the $J^{PC}=1^{++}$ charmonium state $χ_{c1}(2P)$, we perform a fit to the cross sections measured by the CDF, CMS, and LHCb Collaborations. We either obtain an unacceptably high value of $χ^2$, a value of $|R_{2P}^\prime(0)|$ incompatible with well-established potential models, or an intolerable violation of the NRQCD velocity rules. We thus conclude that NLO NRQCD is inconsistent with the hypothesis $X(3872)\equivχ_{c1}(2P)$.

hep-ph↗
arXiv2013

Average gluon and quark jet multiplicities at higher orders

We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS-bar factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstandig problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain alpha_s^(5)(M_Z)=0.1199 +- 0.0026 in the MS-bar scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln(x) terms through the NNLL level and of ln(Q^2) terms by the renormalization group, in excellent agreement with the present world average.

hep-ph↗
arXiv2013

HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4

HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: one, pfq, is relevant for manipulations of hypergeometric functions_{p+1}F_p, and the second one, AppellF1F4, for manipulations with Appell hypergeometric functions F_1,F_2,F_3,F_4 of two variables.

math-ph↗
arXiv2013

On the difference between the pole and the MSbar masses of the top quark at the electroweak scale

We argue that for a Higgs boson mass M_H ~125 GeV, as suggested by recent Higgs searches at the LHC, the inclusion of electroweak radiative corrections in the relationship between the pole and MS-bar masses of the top quark reduces the difference to about 1 GeV. This is relevant for the scheme dependence of electroweak observables, such as the rho parameter, as well as for the extraction of the top quark mass from experimental data. In fact, the value currently extracted by reconstructing the invariant mass of the top quark decay products is expected to be close to the pole mass, while the analysis of the total cross section of top quark pair production yields a clean determination of the MS-bar mass.

hep-ph↗
arXiv2013

Next-to-leading-order tests of nonrelativistic-QCD factorization with $J/ψ$ yield and polarization

We report on recent progress in testing the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) at next-to-leading order (NLO) for $J/ψ$ yield and polarization. We demonstrate that it is possible to unambiguously determine the leading color-octet long-distance matrix elements (LDMEs) in compliance with the velocity scaling rules through a global fit to experimental data of unpolarized $J/ψ$ production in $pp$, $p\bar{p}$, $ep$, $γγ$, and $e^+e^-$ collisions.Three data sets not included in the fit, from hadroproduction and from photoproduction in the fixed-target and colliding-beam modes, are nicely reproduced. The polarization observables measured in different frames at DESY HERA and CERN LHC reasonably agree with NLO NRQCD predictions obtained using the LDMEs extracted from the global fit, while measurements from the FNAL Tevatron exhibit severe disagreement. We demonstrate that alternative LDME sets recently obtained in two other NLO NRQCD analyses of $J/ψ$ yield and polarization, with different philosophies, also fail to reconcile the Tevatron polarization data with the other available world data.

hep-ph↗
arXiv2013

Color-kinematic Duality for Form Factors

Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two- and three-loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.

hep-th↗
arXiv2012

Higgs boson mass and new physics

We discuss the lower Higgs boson mass bounds which come from the absolute stability of the Standard Model (SM) vacuum and from the Higgs inflation, as well as the prediction of the Higgs boson mass coming from asymptotic safety of the SM. We account for the 3-loop renormalization group evolution of the couplings of the Standard Model and for a part of two-loop corrections that involve the QCD coupling alpha_s to initial conditions for their running. This is one step above the current state of the art procedure ("one-loop matching--two-loop running"). This results in reduction of the theoretical uncertainties in the Higgs boson mass bounds and predictions, associated with the Standard Model physics, to 1-2 GeV. We find that with the account of existing experimental uncertainties in the mass of the top quark and alpha_s (taken at 2sigma level) the bound reads M_H>=M_min (equality corresponds to the asymptotic safety prediction), where M_min=129+-6 GeV. We argue that the discovery of the SM Higgs boson in this range would be in agreement with the hypothesis of the absence of new energy scales between the Fermi and Planck scales, whereas the coincidence of M_H with M_min would suggest that the electroweak scale is determined by Planck physics. In order to clarify the relation between the Fermi and Planck scale a construction of an electron-positron or muon collider with a center of mass energy ~200+200 GeV (Higgs and t-quark factory) would be needed.

hep-ph↗
arXiv2012

Low-mass Higgs decays to four leptons at one loop and beyond

The ongoing searches for Higgs-boson signals in data taken at the CERN LHC and the Fermilab Tevatron crucially rely on the decay channels H -> Z l l and H -> W l nu. We present a precision study of the partial widths of these decay channels including the full one-loop electroweak corrections and the dominant contributions at two and three loops, of O(G_F^2 m_t^4), O(G_F m_t^2 alpha_s), and O(G_F m_t^2 alpha_s^2). Since the invariant mass of the off-shell intermediate boson is relatively low in the mass window 115 GeV < m_H < 129 GeV of current interest, lepton mass effects are relevant, especially for the tau lepton.

hep-ph↗