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C. T. Sachrajda

Publications and source records attributed to C. T. Sachrajda.

At least 91 records · Page 5Linked to original sources
arXiv2002

Factorization, the light-cone distribution amplitude of the B-meson and the radiative decay B -> gamma l nu_l

We study the radiative decay B -> gamma l nu_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.

hep-ph↗
arXiv2002

K^+ -> pi^+ pi^0 Decays on Finite Volumes and at Next-to-Leading Order in the Chiral Expansion

We present the ingredients necessary for the determination of physical K->pi pi decay amplitudes for Delta I=3/2 transitions, from lattice simulations at unphysical kinematics and the use of chiral perturbation theory at next-to-leading order. In particular we derive the expressions for the matrix elements , where O_W is one of the operators appearing in the Delta S=1 weak Hamiltonian, in terms of low-energy constants at next-to-leading order in the chiral expansion. The one-loop chiral corrections are evaluated for arbitrary masses and momenta, both in full QCD and in the quenched approximation. We also investigate the finite-volume effects in this procedure.

hep-lat↗
arXiv2002

Kaon Weak Matrix Elements with Wilson Fermions

We present results of several numerical studies with Wilson fermions relevant for kaon physics. We compute the B_K parameter by using two different methods and extrapolate to the continuum limit. Our preliminary result is B_K(2 GeV)=0.66(7). Delta I=3/2 K->pi pi matrix elements are obtained by using the next-to-leading order expressions derived in chiral perturbation theory in which the low energy constants are determined by the lattice results computed at unphysical kinematics. From the simulation at beta=6.0 our (preliminary) results read: _{I=2}=0.14(1)(1) GeV^3 and _{I=2}=0.69(6)(6) GeV^3.

hep-lat↗
arXiv2002

Effects of Quenching in ΔI=1/2 Kaon Decays

We present the inconsistencies which arise in quenched QCD in $ΔI=1/2$ non-leptonic kaon decays using chiral perturbation theory (ChPT) to one loop. In particular we discuss how the lack of unitarity of the quenched theory invalidates the usual methods for the extraction of matrix elements from correlation functions.

hep-lat↗
arXiv2002

$K^{+}\toπ^{+}π^{0}$ decays at next-to-leading order in the chiral expansion on finite volumes

We present the ingredients for determining $K^{+}\toπ^{+}π^{0}$ matrix elements via the combination of lattice QCD and chiral perturbation theory ($χ$PT). By simulating these matrix elements at unphysical kinematics, it is possible to determine all the low-energy constants (LECs) for constructing the physical $K^{+}\toπ^{+}π^{0}$ amplitudes at next-to-leading order (NLO) in the chiral expansion. In this work, the one-loop chiral corrections are calculated for arbitrary meson four-momenta, in both $χ$PT and quenched $χ$PT (q$χ$PT), and the finite-volume effects are studied.

hep-lat↗
arXiv2001

Finite Volume Effects in Weak Hadronic Decays

In this talk we discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\toππ$ decays). In particular we show how the relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and Lüscher, can be extended to all elastic states under the inelastic threshold. We also provide a derivation of the Lüscher quantization condition directly in quantum field theory.

hep-lat↗
arXiv2001

Extraction of K-->pipi Matrix Elements with Wilson Fermions

We present the status of a lattice calculation for the K-->pipi matrix elements of the (delta S=1) effective weak Hamiltonian, directly with two pion in the final state. We study the energy shift of two pion in a finite volume both in the I=0 and I=2 channels. We explain a method to avoid the Goldstone pole contamination in the computation of renormalization constants for (delta I=3/2) operators. Finally we show some preliminary results for the matrix elements of (delta I=1/2) operators. Our quenched simulation is done at beta=6.0, with Wilson fermions, on a (24^3 X 64) lattice.

hep-lat↗
arXiv2001

$K \to ππ$ Decays in a Finite Volume

We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\toππ$ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and Lüscher, is extended to all elastic states under the inelastic threshold. We present a detailed comparison of our approach with that of Lellouch and Lüscher and discuss the possible limitations of the method which could arise due to the presence of inelastic thresholds. We also examine a standard alternative method which can be used to extract the real part of the decay amplitude from correlators of the form $< 0 |T[ππ{\cal H}_WK ]| 0 >$. We show that in this case there are finite-volume corrections which vanish as inverse powers of the volume, which cannot be removed by a multiplicative factor.

hep-lat↗
arXiv2001

Sudakov effects in B -> pi l nu form factors

In order to obtain information about the Standard Model from exclusive hadronic two-body B-decays, we have to quantify non-perturbative QCD effects. Approaches based on the factorization of mass singularities into hadronic distribution amplitudes and form factors provide a rigorous theoretical framework for the evaluation of these effects in the heavy quark limit. But it is not possible to calculate power corrections in a model-independent way, because of non-factorizing long-distance contributions. It has been argued that Sudakov effects suppress these contributions and render the corresponding corrections perturbatively calculable. In this paper we examine this claim for the related example of semileptonic B -> pi decays and conclude that it is not justified. The uncertainties in our knowledge of the mesons' distribution amplitudes imply that the calculations of the form factors are not sufficiently precise to be useful phenomenologically. Moreover, a significant contribution comes from the non-perturbative region of large impact parameters, and is therefore uncalculable. We also raise a number of theoretical issues in the derivation of the underlying formalism. For B-decays it is thus not possible to invoke Sudakov effects to calculate amplitudes for decays which have long-distance divergences (end-point singularities) in the standard hard-scattering approach.

hep-ph↗
arXiv2001

Non-perturbative improvement of lattice QCD at large momenta

We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass. It requires off-shell improvement of quark fields and composite operators, which is achieved by studying the behaviour of quark and gluon correlation functions at large momenta.

hep-lat↗
arXiv2001

QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters

In the heavy-quark limit, the hadronic matrix elements entering nonleptonic $B$-meson decays into two light mesons can be calculated from first principles including ``nonfactorizable'' strong-interaction corrections. The $B\toπK,ππ$ decay amplitudes are computed including electroweak penguin contributions, SU(3) violation in the light-cone distribution amplitudes, and an estimate of power corrections from chirally-enhanced terms and annihilation graphs. The results are then used to reduce the theoretical uncertainties in determinations of the weak phases $γ$ and $α$. In that way, new constraints in the $(\barρ,\barη)$ plane are derived. Predictions for the $B\toπK, ππ$ branching ratios and CP asymmetries are also presented. A good global fit to the (in part preliminary) experimental data on the branching fractions is obtained without taking recourse to phenomenological models.

hep-ph↗
arXiv2001

Lattice B-Physics

I review the status of lattice simulations relevant for phenomenological studies of B-physics. Results for much-studied quantities such as f_B, B_B and form-factors for semileptonic decays are presented as well as those for quantities which have begun to be studied only recently (such as B-lifetimes). The improvement in the precision of the determinations of the mass of the b-quark, which has been made possible by new results for perturbative coefficients, is discussed. Finally I describe new ideas being developed with the aim of making computations of two-body non-leptonic decays possible.

hep-lat↗
arXiv2000

QCD factorization for $B\toπK$ decays

We examine some consequences of the QCD factorization approach to non-leptonic B decays into $πK$ and $ππ$ final states, including a set of enhanced power corrections. Among the robust predictions of the approach we find small strong-interaction phases (with one notable exception) and a pattern of CP-averaged branching fractions, which in some cases differ significantly from the current central values reported by the CLEO Collaboration.

hep-ph↗
arXiv2000

QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states

We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, but allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as $B\to Dπ$ and $B\to ππ$. We discuss the factorization formula for a general final state from a general point of view. We then consider factorization for decays into heavy-light final states (such as $B\to Dπ$) in more detail, including a proof of the factorization formula at two-loop order. Explicit results for the leading QCD corrections to factorization are presented and compared to existing measurements of branching fractions and final-state interaction phases.

hep-ph↗
arXiv1999

Future Perspectives in Lattice Field Theory

I review some of the contributions which lattice simulations are likely to make during the next five years or so to the development of our understanding of particle physics. Particular emphasis is given to the evaluation of non-perturbative QCD effects in experimentally measurable amplitudes, and the corresponding extraction of fundamental parameters.

hep-lat↗
arXiv1999

QCD Factorization for $B\toππ$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit

We show that, in the heavy quark limit, the hadronic matrix elements that enter $B$ meson decays into two light mesons can be computed from first principles, including `non-factorizable' strong interaction corrections, and expressed in terms of form factors and meson light-cone distribution amplitudes. The conventional factorization result follows in the limit when both power corrections in $1/m_b$ and radiative corrections in $α_s$ are neglected. We compute the order-$α_s$ corrections to the decays $B_d\toπ^+π^-$, $B_d\toπ^0π^0$ and $B^+\toπ^+π^0$ in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.

hep-ph↗
arXiv1998

Computation of the b-quark Mass with Perturbative Matching at the Next-to-Next-to-Leading Order

We compute the two-loop term in the perturbation series for the quark-mass in the lattice Heavy Quark Effective Theory. This is an ingredient in the matching factor required to obtain the $b$-quark mass from lattice simulations of the HQET. Combining our calculations with numerical results from the APE collaboration, we find, at two-loop order, $\bar m_b \equiv m_b^{\bar{MS}}(m_b^{\bar{MS}}) =4.41\pm 0.05\pm 0.10 $GeV. It was expected that the two-loop term would have a significant effect and this is indeed what we find. Depending on the choice of "reasonable" coupling constant in the one-loop estimates the result for $\bar m_b$ can change by several hundred MeV when the two-loop terms are included.

hep-lat↗