Λc→Λl+νl Form Factors and Decay Rates from Lattice QCD with Physical Quark Masses

Abstract

The first lattice QCD calculation of the form factors governing Λc → Λ + ν decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the Λc → Λe + νe and Λc → Λµ + νµ decay rates divided by |Vcs| 2 are 0.2007(71)(74) ps −1 and 0.1945(69)(72) ps −1 , respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa matrix element |Vcs| from a global fit and the Λc lifetime from experiments, this translates to branching fractions of B(Λc → Λe + νe) = 0.0380(19)LQCD(11)τ Λc and B(Λc → Λµ + νµ) = 0.0369(19)LQCD(11)τ Λc . These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives |Vcs| = 0.949(24)LQCD(14)τ Λc (49)B.Precision studies of processes in which heavy bottom or charm quarks decay to lighter quarks play an important role in testing the Standard Model of elementary particle physics. While most of these analyses are being performed using B and D mesons, decays of Λ b and Λ c baryons can provide valuable additional information. Two examples that shed new light on puzzles posed by mesonic decays are the determination of the ratio of CKM matrix elements, and an analysis of the. Both studies rely on nonperturbative lattice QCD calculations of form factors describing the baryonic matrix elements of the underlying quark currents [3,4].This letter focuses on the charmed-baryon decays Λ c → Λ + ν ( = e, µ), whose rates are proportional to |V cs | 2 in the Standard Model. Previous determinations of this CKM matrix element are(1)The motivations for studying Λ c → Λ + ν include the following:1. Taking the precisely determined value of |V cs | from CKM unitarity, a comparison between calculated and measured Λ c → Λ + ν decay rates provides a stringent test of the methods used to compute the heavy-baryon decay form factors.2. Combining the Λ c → Λ + ν decay rates from experiment with a lattice QCD calculation of the Λ c → Λ form factors gives a new direct determination of |V cs | and new constraints on physics beyond the Standard Model (see, e.g., Ref.[9] for a recent discussion of new physics in c → s + ν transitions).3. If the Λ c → Λ + ν decay rates are known precisely, from experiment or lattice QCD, these modes can be used as normalization modes in measurements of a wide range of other charm and bottom baryon decays [10].The most precise measurements of the Λ c → Λ + ν branching fractions (decay rates times the Λ c lifetime) to date have recently been reported by the BESIII Collaboration [11,12],In the Standard Model, the decay rates depend on six form factors that parametrize the matrix elements Λ(p )|sγ µ c|Λ c (p) and Λ(p )|sγ µ γ 5 c|Λ c (p) as functions of q 2 = (p−p ) 2 . These form factors have previously been estimated using quark models and sum rules [13]...

Overview of Λc decays

“…In parallel with the lattice QCD calculations mentioned earlier for Λ c → Λl þ ν l [21], there appeared recently one for the Cabibbo-suppressed ΔS ¼ 0 processes Λ c → nl þ ν l [14]. The corresponding branching fractions are displayed in the right-hand column of Table IX. …”

“…With ðm c ;m s ;m u;d Þ ¼ ð1710;536;364Þ MeV [20], a slightly higher branching fraction is obtained (see the Appendix), again indicating that semileptonic Λ c decays are not saturated by the Λl þ ν l final state. A calculation in lattice QCD [21] finds BðΛ c → Λe þ ν e Þ¼ð3.80 AE 0.19 AE 0.11Þ% and BðΛ c → Λμ þ ν μ Þ ¼ ð3.69 AE 0.19 AE 0.11Þ%, where the first error comes from lattice QCD and the second from the uncertainty in the Λ c lifetime. The agreement with experiment further confirms the need for a form factor and, indirectly, hints at a role for excited final states in Λ c semileptonic decays.…”

Λc→N form factors from lattice QCD and phenomenology of Λc→Meinel1 2018Phys. Rev. DSelf Cite665592View full textAdd to dashboardCite

“…As in Refs. [22,29,31], the systematic uncertainty in fðjp 0 jÞ for a given momentum jp 0 j and data set was estimated as the larger of the following two: (i) the shift in fðjp 0 jÞ at the given momentum, and (ii) the average of the shifts in fðjp 0 jÞ over all momenta. These systematic uncertainties were added to the statistical uncertainties in quadrature.…”

“…[29], while the a f 3 were constrained to be 0 AE 30 as in Ref. [31]. In the higher-order fit, additional sources of systematic uncertainties were simultaneously incorporated as follows:…”

Testing the W -exchange mechanism with two-body baryonic B decays

“…Note that the calculation used N c = 3 in the naive factorization and n = 2 for baryon form factors with dipole behavior, whereas C Λ + cp f,g are not clearly given. However, being sensitive to the color number, a 2 with N c = 3 has been shown to fail to accommodate the non-factorizable effects [29]; besides, while it is poorly understood whether n = 1 or n = 2 is preferred [21], n = 1 is most often used in recent QCD models [28,36,37]. In the generalized factorization, together with n = 1 for the monople-type form factors, we obtain…”