The UTfit Collaboration Average of D meson mixing data: Spring 2012

We derive constraints on the parameters $M_{12}$, $\Gamma_{12}$ and $\Phi_{12}$ that describe $D$ meson mixing using all available data, allowing for CP violation. We also provide posterior distributions and predictions for observable parameters appearing in $D$ physics.

We derive constraints on the parameters M12, Γ12 and Φ12 that describe D meson mixing using all available data, allowing for CP violation. We also provide posterior distributions and predictions for observable parameters appearing in D physics.
Meson-antimeson mixing in the neutral D system has been established only in 2007 [1][2][3]. Early combinations of available data allowed to put stringent constraints on New Physics (NP) contributions, although the possibility of non-standard CP violation remained open [4][5][6][7][8]. More recently, CP violation in the D system received considerable attention after the measurement at hadron colliders of large direct CP violation in D → ππ and D → KK decays [9,10], which may signal the presence of NP [11][12][13][14][15][16]. It then becomes crucial to extract updated information on the mixing amplitude in order both to disentangle more precisely indirect and direct CP violation in D → ππ and D → KK, and to obtain up-to-date constraints on NP in ∆C = 2 transitions that can be used to constrain NP contributions to ∆C = 1 processes in any given model.
In this letter, we perform a fit to the experimental data in Table I following the statistical method described in ref. [39]. We assume that all Cabibbo allowed (and doubly Cabibbo suppressed) decay amplitudes in the phase convention CP|D = |D and CP|f = η f CP |f satisfy the relation A(D → f ) = η f CP A(D →f ), which is expected to hold in the SM (in the standard CKM phase convention) with an accuracy much better than present experimental errors. In the same approximation this implies Γ 12 real. For singly Cabibbo suppressed decays D 0 → K + K − and D 0 → π + π − we allow for direct CP violation to be present. We assume flat priors for x = ∆m D /Γ D , y = ∆Γ D /(2Γ D ) and |q/p|, with |D L,S = p|D 0 ± q|D 0 and |p| 2 + |q| 2 = 1. We can then express all mixing-related observables in terms of x, y and |q/p| using the following formulae [4,[40][41][42][43]: x . Asymmetric errors have been symmetrized. We do not use measurements that do not allow for CP violation in mixing, except for ref. [27] (as shown in ref. [3], the results for x and y from the Dalitz analysis of D → Ksππ are not sensitive to the assumptions about CP violation in mixing).
with δ f a strong phase and A D forced to vanish in the fit. In addition, for the CP asymmetries we have where D f (t) is the observed distribution of proper decay time and τ D 0 is the lifetime of the neutral D mesons.
For the purpose of constraining NP, it is useful to express the fit results in terms of the ∆C = 2 effective Hamiltonian matrix elements M 12 and Γ 12 : with Φ 12 = arg Γ 12 /M 12 . Consistently with the assumption A(D → f ) = A(D →f ), Γ 12 can be taken real with negligible NP contributions, and a nonvanishing Φ 12 can be interpreted as a signal of new sources of CP violation in M 12 . For the sake of completeness, we report here also the formulae to compute the observables x, y and δ from M 12 and Γ 12 : in agreement with [42] up to a factor of √ 2. The results of the fit are reported in Table II. The corresponding p.d.f are shown in Figs. 1 and 2. Some twodimensional correlations are displayed in Fig. 3.
A direct comparison with the HFAG results [38] is not straightforward, as our fit does not fall into any of the HFAG categories (no CPV, no direct CPV, direct CPV), since we allow for direct CP violation only in singly Cabibbo suppressed decays. However, our fit results should be close to the "no direct CPV" HFAG fit. Indeed, we find compatible results within errors. We notice, however, that HFAG performs a fit with four independent parameters (x, y, φ and |q/p|), while only three of these parameters are independent, as can be seen from eq. (1). In particular, φ should vanish for |q/p| = 1. This feature can be seen in Fig. 3 (up to the smoothing of the p.d.f) but not in the equivalent plot from HFAG, which displays completely different 2-dimensional contours. We can but recommend that in the future HFAG takes the relation φ = arg(y + iδx) always into account. The results in Table II can be used to constrain NP contributions to D −D mixing and decays. M.C. is associated to the Dipartimento di Fisica, Università di Roma Tre. E.F. and L.S. are associated to the Dipartimento di Fisica, Università di Roma "La Sapienza". We acknowledge partial support from ERC Ideas Starting Grant n. 279972 "NPFlavour" and ERC Ideas Advanced Grant n. 267985 "DaMeSyFla". We thank B. Golob and A. Schwartz for clarifications about the HFAG averages.