Twisted mass QCD for weak matrix elements

Peña, Carlos

doi:10.22323/1.032.0019

Cited by 6 publications

(6 citation statements)

References 31 publications

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“…This new B K analysis has also been presented in Ref. [6]. All computational details are identical to those of Ref.…”

Section: Four-fermion Operatorsmentioning

confidence: 83%

“…Those of Ref. [12], as well as the one provided to us by the ZeRo Collaboration, 6 are the result of a direct computation of the PCAC Ward identity at the corresponding bare coupling, using O(a) improved (untwisted) Wilson fermions, whereas the estimates from Ref. [3] are the result of an interpolation in β of the data of Ref.…”

Section: Cutoff Effects Of the Twist Anglementioning

confidence: 99%

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Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

et al. 2007

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We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking effects, which are at most 5%, decrease as we approach the continuum limit. We also compute the pseudoscalar decay constant in the continuum limit, with reduced systematics. As a consequence of improved tuning of the mass parameters at β = 6.1, we reanalyze our previous B K results. Our main phenomenological findings are r 0 f K = 0.421(7) andB K = 0.735(71).

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“…This new B K analysis has also been presented in Ref. [6]. All computational details are identical to those of Ref.…”

Section: Four-fermion Operatorsmentioning

confidence: 83%

Section: Cutoff Effects Of the Twist Anglementioning

confidence: 99%

Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

et al. 2007

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“…This yields a much greater flexibility and allows for a complete elimination of lattice specific mixings and subtractions, even including O(a) improvement. Finally, similar considerations apply to QCD with static b-quarks, where the mixing of four-quark operators is considerably simplified by twisting the light quarks (see 28 for a recent review and further references).…”

Section: Further Applicationsmentioning

confidence: 99%

Lattice QCD With a Chiral Twist

Sint

2007

Perspectives in Lattice QCD

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In these lectures I explain how chiral symmetry of continuum QCD naturally leads to a class of lattice regularisations known as twisted mass QCD (tmQCD). As compared to standard Wilson quarks, its advantages are the absence of unphysical zero modes, the possibility to circumvent lattice renormalisation problems and automatic O(a) improvement. On the other hand, the physical parity and flavour symmetries are explicitly broken. I discuss these aspects and then turn to the theory in a finite space-time volume with Schrödinger functional boundary conditions. Again, chiral transformations of the continuum theory may be used as a guide to formulate an alternative lattice regularisation of the Schrödinger functional, with interesting applications to renormalization problems in QCD. 10:50 Proceedings Trim Size: 9in x 6in ms 2 cepts. This includes in particular a discussion of O(a) improvement and the question whether it is compromised by currently used non-perturbative renormalization procedures based on the QCD Schrödinger functional (SFschemes). In fact, the standard Schrödinger functional boundary conditions turn out to be difficult to reconcile with automatic O(a) improvement and the construction of an alternative set-up for the Schrödinger functional may therefore be advantageous.This writeup is organised as follows: I start with the interplay between the choice of the quark mass term and the form taken by parity, flavour and chiral symmetry transformations (sect. 2). After a reminder of standard Wilson quarks and the problem of unphysical zero modes (section 3), lattice tmQCD is introduced in sect. 4. Based on the formal continuum theory a dictionary between tmQCD and QCD correlation functions is readily established, which is expected to hold between properly renormalised correlation functions. It then becomes clear how to by-pass certain renormalization problems of standard Wilson quarks (sect. 5), and the computation of B K is discussed in some detail. In sect. 6 automatic O(a) improvement of tmQCD is analysed using Symanzik's effective theory. Potential problems of tmQCD associated with flavour and parity breaking are shortly mentioned in sect. 7. In sect. 8, the properties of Schrödinger functional renormalisation schemes (SF schemes) are discussed. Motivated by the clash of the standard set-up with automatic O(a) improvement and by the slow decoupling of heavy quarks in mass-dependent SF schemes, a modified definition of the Schrödinger functional is proposed, and its effectiveness regarding O(a) improvement is illustrated in an example taken from perturbation theory. Section 9 contains some conclusions. Continuum QCD and chiral transformationsLet us consider the continuum action of QCD with N f = 2 massless quarks b . Decomposing the action into a pure gauge and a fermionic part, S = S g +S f , we here focus on the fermionic part,The quark and antiquark fields ψ,ψ are flavour doublets, interacting minimally with the gluon field A µ via the covariant derivative D µ = ∂ µ + A µ .b Conventions used for Euclidean...

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“…An interesting demonstration of the progress in B K calculations is that the value of B K calculated using the TM Wilson fermions ends up being in agreement with other B K calculations using different fermion formulations [17]. The calculation of B K with TM Wilson fermions has been discussed in great detail in the plenary talk by Pena [22] so we skip all the details here. The values of B K calculated by CP-PACS [18] and by RBC [19] using domain wall fermions are in good agreement with those of other fermion formulations.…”

Section: B K In Quenched Qcdmentioning

confidence: 64%