Christopher T C Sachrajda

Higher-order effects in asymptotically free gauge theories : the anomalous dimensions of Wilson operators

We calculate the anomalous dimensions of the lowest twist, flavour non-singlet operators in the Wilson expansion to two loops. The calculation is performed using dimensional regularization and the minimal subtraction renormalization scheme. The physical relevance of our results in deep inelastic scattering is discussed.

Higher Order Effects in Asymptotically Free Gauge Theories. 2. Flavor Singlet Wilson Operators and Coefficient Functions

Abstract We complete the calculation of all parameters needed to discuss deep inelastic scattering in QCD to subleading order by calculating the anomalous dimensions of the twist-two flavour singlet operators in the Wilson expansion to two loops and the coefficient functions to order g 2 . The calculation is performed in the dimensional regularization scheme with the minimal subtraction renormalization prescription. The application of the results to deep inelastic scattering is discussed.

Hadronic Wave Functions at Short Distances and the Operator Product Expansion

Abstract The operator product expansion, of appropriate products of quark fields, is used to find the anomalous dimensions which control the short distance behavior of hadronic wave functions. This behavior in turn controls the high- Q 2 limit of hadronic form factors. In particular, we relate each anomalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal α S ( Q 2 )/ Q 2 fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements.

Is the Mass of the Higgs Boson About 10-GeV?

Abstract Grand unified models of strong, weak and electromagnetic interactions improve the motivation for weak symmetry breaking by radiative corrections, which would imply that mH ∼ 10 GeV for sin2 θW ∼ 0.20. We make a systematic study of the phenomenology of a Higgs boson in this mass range, and find that it may be observable in ϒ decays and pp collisions, as well as in toponium decays.

Spectator effects in inclusive decays of beauty hadrons

Abstract We present a model-independent study of spectator effects, which are responsible for the lifetime differences between beauty hadrons. These effects can be parametrized in terms of hadronic matrix elements of four four-quark operators. For B mesons, the coefficients of the non-factorizable operators turn out to be much larger than those of the factorizable ones, limiting considerably the usefulness of the vacuum insertion approximation. Non-factorizable contributions to the lifetime ratio τ(B − ) τ(B d ) could naturally be of order 10–20%, and not even the sign of these contributions can be predicted at present. In the case of the Λb baryon, heavy-quark symmetry is used to reduce the number of independent matrix elements from four to two. In order to explain the large deviation from unity in the experimental result for τ(Λ b ) τ(B d ) , it is necessary that these baryon matrix elements be much larger than those estimated in quark models. We have also reexamined the theoretical predictions for the semileptonic branching ratio of B mesons and charm counting, finding that, given the present theoretical and experimental uncertainties, there is no significant discrepancy with experiment.

Asymptotic freedom beyond the leading order

We make a quantitative analysis of the full g2 interaction corrections to the leading Q2 dependence of νW2 at x ⩾ 0.4, as given by an asymptotically free gauge theory. It turns out that due to partial cancellations between various contributions the g2 corrections are small. The best fit with the SLAC ep data after including the g2 corrections is almost identical to that without these corrections, the only effect being a change in Λ, the one free parameter, which sets the scale of the theory. On the other hand the effect of including target mass corrections is to improve the agreement of the prediction for νW2ep with data for large values of x. We study the implications of g2 and target mass corrections for R = σL/σL and conclude, in agreement with other authors, that although both types of corrections are vital they do not account for values of R for x ⩾ 0.5 as measured at SLAC.

Lepton Pair Production and the Drell-Yan Formula in QCD

Abstract The Drell-Yan formula is found to be valid in low order perturbation theory calculations in QCD. The formula is only reproduced when quark-antiquark annihilation and bremsstrahlung diagrams are all taken into account. These calculations suggest that when the experimentally extracted quark and antiquark distribution functions (which slowly violate Bjorken scaling) are used in the Drell-Yan formula, subprocesses such as those involving the bremsstrahlung of the massive lepton pair, or ones with gluons in the initial state, should not be calculated independently, as they are already included in the formula.

Flavour symmetry breaking in antiquark distributions

We show that knowledge of the valence quark distribution of a proton at one value of q2, enables one to calculate a contribution to the difference between the distribution of anti-up quarks (up) and anti-down quarks (dp) in the sea of the proton at higher values of q2. This difference can be expressed as a linear combination of the structure functions F1, for νp → νX and e−p → e−p (for which one knows the q2 behaviour of the moments) and for νp → μ−X and νp → μ+X (for which one knows the q2 behaviour of the odd moments). The calculable contribution involves a non-trivial continuation of the even (odd) moments of the neutral (charged) current structure functions to odd (even) moments. We calculate this contribution and although we find that its sign is negative we point out that this cannot be interpreted as a consequences of the Pauli exclusion principle. We discuss the constraints our results impose on antiquark distributions.

Factorization, the light-cone distribution amplitude of the B-meson and the radiative decay B→γℓνℓ

Abstract We study the radiative decay B → γ l ν l in the framework of QCD factorization . We demonstrate explicitly that, in the heavy-quark limit and at one-loop order in perturbation theory, the amplitude does factorize, i.e., that it can be written as a convolution of a perturbatively calculable hard-scattering amplitude with the (non-perturbative) light-cone distribution amplitude of the B -meson. We evaluate the hard-scattering amplitude at one-loop order and verify that the large logarithms are those expected from a study of the b → u transition in the Soft-Collinear Effective Theory. Assuming that this is also the case at higher orders, we resum the large logarithms and perform an exploratory phenomenological analysis. The questions addressed in this study are also relevant for the applications of the QCD factorization formalism to two-body non-leptonic B -decays, in particular, to the component of the amplitude arising from hard spectator interactions.

On the difficulty of computing higher-twist corrections

Abstract We discuss the evaluation of power corrections to hard scattering and decay processes for which an operator product expansion is applicable. The Wilson coefficient of the leading-twist operator is the difference of two perturbative series, each of which has a renirmalon ambiguity of the same order as the power corrections themselves, but which cancel in the difference. We stress the necessity of calculating this coefficient function to sufficiently high orders in perturbation theory so as to make the uncertainty of the same order of or smaller than the relevant power corrections. We investigate in some simple examples whether this can be achieved. Our conclusion is that in most of the theoretical calculations which include power corrections, the uncertainties are at least comparable to the power corrections themselves, and that it will be a very difficult task to improve the situation.We discuss the evaluation of power corrections to hard scattering and decay processes for which an operator product expansion is applicable. The Wilson coefficient of the leading-twist operator is the difference of two perturbative series, each of which has a renormalon ambiguity of the same order as the power corrections themselves, but which cancel in the difference. We stress the necessity of calculating this coefficient function to sufficiently high orders in perturbation theory so as to make the uncertainty of the same order or smaller than the relevant power corrections. We investigate in some simple examples whether this can be achieved. Our conclusion is that in most of the theoretical calculations which include power corrections, the uncertainties are at least comparable to the power corrections themselves, and that it will be a very difficult task to improve the situation.