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

TLDR: In this article, two variants of quenched twisted mass QCD (tmQCD) with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass were simulated.

About: This article is published in Nuclear Physics.The article was published on 2007-07-30 and is currently open access. It has received 25 citations till now. The article focuses on the topics: Quantum chromodynamics & Quark.

Figures

Table 1 The parameters of the run at twist angle α = π/2. The dataset at β = 6.1 is a new run, while all other data are those of Ref. [1]

Table 2 The parameters of the run at twist angle α = π/4. The dataset at β = 6.1 is a new run, while all other data are those of Ref. [1]

Fig. 2 the ratio (Msd/Msc)2, plotted against (Msd/M phys K ) 2 with MphysK = 495 MeV, is compared to (Mud/Msc)2. Note that the statistical errors of these ratios turn out to be very small, due to the strong correlations between numerator and denominator. We see that at β = 6.0 the two ratios are incompatible; their deviation from unity (which quantifies flavour breaking) is at most a 5% effect. As we approach the continuum limit at β = 6.3, the two ratios become compatible and their deviation from unity reduces to 1–2%. Our conclusion is that flavour symmetry breaking effects at the mass ranges we are considering appear to be under control, diminishing fast as the continuum limit is approached. Besides this general conclusion, there are a couple of observations to be made: (i) At β = 6.0 we find that Mud < Msd , in agreement to the findings of [14] (see Fig. 13 of that work)8; (ii) at fixed reference mass (Msc/M phys

Table 13 Pseudoscalar effective masses and decay constants, for the π/2 case, computed with the offset critical hopping parameter κ ′cr(β = 6.1)

Table 12 Twist angles, computed with an offset critical hopping parameter κ ′cr(β = 6.1) and from two different procedures, indicated by the corresponding equations. The upper (lower) part of the table corresponds to the π/2 (π/4) case

Table 14 Comparison of the flavour breaking effects in the pseudoscalar masses, computed with the offset κ ′cr(β = 6.1). In the last column, we also show the results of the “prediction” based on Eq. (A.13)

Frequently asked questions

Q1. What are the contributions in "Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass qcd" ?

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, the authors confirm that flavour symmetry breaking effects, which are at most 5 %, decrease as they approach the continuum limit. As a consequence of improved tuning of the mass parameters at β = 6. 1, the authors reanalyze their previous BK results. 

Q2. What are the future works in "Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass qcd" ?

Thus, if Wilson fermions are to be used in the future in the determination of weak matrix elements, the use of tmQCD variants that embody automatic O ( a ) improvement [ 31 ] may prove essential. As the authors are entering the era of tmQCD simulations with dynamical quarks [ 32 ], it will be important to explore these issues in future unquenched studies. 

Q3. What are the values of the Schrödinger functional computations used in this work?

The (re)normalization constants (ZA, ZP, etc.) as well as the improvement coefficients (cA, bA, etc.) used in this work are also taken from previous Schrödinger functional computations. 

Q4. What is the corresponding lattice correlation function to use in Eq. (4.1?

The corresponding lattice correlation function to be used in Eq. (4.1) is:• f(AR)sd (x0) → 1√ 2[ f(AR)sd (x0) − if(VR)sd (x0) ] ,where now flavours s, d are both twisted. 

Q5. What is the effect of the fluctuations on the twisted mass?

In any case, these fluctuations are only a small effect, reflecting the overall uncertainty of the tuning of the twist angle to a constant target value (which amounts to a condition of constant physics as the authors approach the continuum limit). 

Q6. What is the effect of the LANL group on BK?

For instance, using either the values for ZA,ZV, cA determined by the ALPHA Collaboration or those obtained by the LANL group [22] results in sizeable effects on BK at β = 6.0. 

Q7. What is the fit for FK in the continuum limit?

The best result for FK in the continuum limit is obtained with a constrained fit of F̃ud (for the π/2 case) and F̃sd (for the π/4 case). 

Q8. What is the requirement that all quark masses be measured at a reference pseudoscalar?

together with the requirement that all quark masses be degenerate and phenomenological quantities be measured at a reference pseudoscalar meson mass, constitute their constant physics requirement. 

Q9. What is the main reason why the tmQCD approach is important?

if Wilson fermions are to be used in the future in the determination of weak matrix elements, the use of tmQCD variants that embody automatic O(a) improvement [31] may prove essential.