## Periodic Reporting for period 1 - HEAVYDWF (Charm and Bottom flavour physics with chiral lattice fermions)

**Reporting period:**2015-10-01

**to**2017-09-30

## Summary of the context and overall objectives of the project

According to our current understanding of nature, there are four fundamental forces: gravitation, electro-magnetism, weak and strong force. The Standard Model (SM) of elementary particle physics provides a very successfully description of electro-magnetism, weak, and strong interactions. It contains elementary particles (leptons and quarks) and the force carriers (W/Z boson, photons, and gluons) as well as the 2012 discovered Higgs particle, which plays a key role in the generation of mass. The strong interactions are responsible for confining quarks into bound states either formed of quark-antiquark pairs (mesons) or three quark bound states (baryons). The theory of the strong interactions is named quantum chromodynamics (QCD) and is, unlike the electro-magnetism or the weak force, of nonperturbative nature. Thus to calculate strong interactions contributing to SM processes special concepts, like lattice field theory simulations, have to be used.

Out of the six known quarks, the b-quarks play a special role: due to their large mass of 4.18 GeV [PDG] they allow to explore processes at otherwise not accessible energies and couple more strongly to the Higgs boson than the lighter quarks. Of particular interest are weak decays of b-quarks to another lighter quark where in addition a pair of leptons (electron, muon, tau or neutrino) is emitted. If the b-quark is bound as a quark-antiquark pair, the particle is named B-meson and such decays are classified as semileptonic. Lately, such semileptonic B decays have received much attention because several experiments (BaBar, Belle, and LHCb) see indications for violations of lepton flavor universality i.e. results exhibit an unexpected dependence whether the lepton is e.g. an electron or a tau. When combined these results amount to the strongest indications of new physics seen so far. However, improvements of the SM predictions are highly desirable which include predictions for so called form factors based on lattice field theory calculations. These form factors parametrize contributions from the strong force and the calculation faces the challenge to simulate b-quarks carrying a mass larger than the lattice cut-off currently possible to simulate.

The emphasis of this project is to improve simulations involving such heavy quarks and calculate quantities relevant to the experimental research program. First we explored using so called domain-wall fermions for simulations of heavy quarks and found them suitable for quark masses in the range of c-quarks (1.28 GeV [PDG]). With a modification (link smearing), up to half the mass of b-quarks can be simulated and the results extrapolated to the physical b-quark mass. In addition concepts to nonperturbatively renormalize heavy-light operators have been investigated. While such extrapolations are promising to determine simple quantities (decay constants, neutral meson mixing parameters), the application to a form factor calculations is more difficult. To explore improvements for the most timely form factor calculations involving the decay of a b-quark to a c-quark, we therefore chose to study B_(s) -> D_(s)^(*) l nu semileptonic decays using a different, effective action to simulate b-quarks at their physical mass but use the newly established concept of heavy domain-wall fermions to simulate c-quarks. We have completed the massive scale numerical simulations and implemented all parts of the analysis required for the different projects. Preliminary results have been presented at workshops and conferences and work is in progress to prepare a manuscript for submission to a peer-reviewed journal.

Out of the six known quarks, the b-quarks play a special role: due to their large mass of 4.18 GeV [PDG] they allow to explore processes at otherwise not accessible energies and couple more strongly to the Higgs boson than the lighter quarks. Of particular interest are weak decays of b-quarks to another lighter quark where in addition a pair of leptons (electron, muon, tau or neutrino) is emitted. If the b-quark is bound as a quark-antiquark pair, the particle is named B-meson and such decays are classified as semileptonic. Lately, such semileptonic B decays have received much attention because several experiments (BaBar, Belle, and LHCb) see indications for violations of lepton flavor universality i.e. results exhibit an unexpected dependence whether the lepton is e.g. an electron or a tau. When combined these results amount to the strongest indications of new physics seen so far. However, improvements of the SM predictions are highly desirable which include predictions for so called form factors based on lattice field theory calculations. These form factors parametrize contributions from the strong force and the calculation faces the challenge to simulate b-quarks carrying a mass larger than the lattice cut-off currently possible to simulate.

The emphasis of this project is to improve simulations involving such heavy quarks and calculate quantities relevant to the experimental research program. First we explored using so called domain-wall fermions for simulations of heavy quarks and found them suitable for quark masses in the range of c-quarks (1.28 GeV [PDG]). With a modification (link smearing), up to half the mass of b-quarks can be simulated and the results extrapolated to the physical b-quark mass. In addition concepts to nonperturbatively renormalize heavy-light operators have been investigated. While such extrapolations are promising to determine simple quantities (decay constants, neutral meson mixing parameters), the application to a form factor calculations is more difficult. To explore improvements for the most timely form factor calculations involving the decay of a b-quark to a c-quark, we therefore chose to study B_(s) -> D_(s)^(*) l nu semileptonic decays using a different, effective action to simulate b-quarks at their physical mass but use the newly established concept of heavy domain-wall fermions to simulate c-quarks. We have completed the massive scale numerical simulations and implemented all parts of the analysis required for the different projects. Preliminary results have been presented at workshops and conferences and work is in progress to prepare a manuscript for submission to a peer-reviewed journal.

## Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

"The use of domain-wall fermions for the simulation of charm-like quarks has been established and also applied to the calculation of semileptonic form factors at zero and non-zero momentum. It has been shown that by using link smearing quarks heavier than charm can be simulated reaching as far as half the bottom mass on RBC-UKQCD's currently available gauge field configurations.

To test domain-wall fermions for simulating heavy quarks, several nonperturbative quantities have been calculated. Each calculation requires to implement required matrix elements describing the processes of interest. Next nonperturbative simulations using super-computers are carried out. These simulations are based on using Monte Carlo methods to statistically integrate the phase space using Feynman's path integral. Subsequently a statistical analysis is performed leading to quantities at fixed quark masses and values of the lattice spacing. After repeating the simulations for different quark masses and values of the lattice spacing, the results have to be renormalized before all data are analyzed together by carrying out a fit to extrapolate the quantities to the physical values of the quarks masses and the continuum limit. At this point systematic effects originating from the simulation or the analysis need to be estimated in order to obtain results with full error budget and suitable for comparison or combination with experimental results.

We have completed such simulations for quantities including decay constants for D, D_s, B, and B_s mesons, parameters for neutral meson mixing for D, B, and Bs_mesons as well as their ratio xi. Furthermore, form factors for semileptonic decays of B and Bs-mesons have been calculated. We have established the different parts of the analysis and are currently finalizing nonperturbative determinations of the renormalization factors as well as estimates for the systematic uncertainties. The project will be completed by preparing manuscripts for submission to peer-reviewed journals. In case of the semileptonic form factor calculation we are focusing at the determination of Bs -> Ds l nu and Bs -> K l nu decays because these will enable LHCb to obtain an independent determination of the ratio of CKM matrix elements |V_cb|/|V_ub|. Afterwards we will analyze B->D^(*) l nu decays and obtain theoretical predictions for the ratios R_D and R_D^* to address LFUV.

Preliminary results have been presented at the annual Lattice conferences in Southampton (2016) and Granada (2017), as well as at the major phenomenological conferences ICHEP 2016 in Chicago, and the EPS-HEP 2017 in Venice with summaries written up as proceedings. In addition OW was invited to report on this work at the LHCb UK meeting in Oxford in January 2017 as well as the LHCb workshop ""Implications of LHCb measurements and future prospects"" at CERN, Geneva, Switzerland in November 2017. Moreover, he has been invited to present his work at several seminars and other workshops.

PB and OW organized very successfully 9th International workshop on QCD and numerical algorithms workshop (QCDNA) in Edinburgh in 2016. Given the success, OW was invited to help organize the follow-up workshop QCDNA X in Coimbra (2017)."

To test domain-wall fermions for simulating heavy quarks, several nonperturbative quantities have been calculated. Each calculation requires to implement required matrix elements describing the processes of interest. Next nonperturbative simulations using super-computers are carried out. These simulations are based on using Monte Carlo methods to statistically integrate the phase space using Feynman's path integral. Subsequently a statistical analysis is performed leading to quantities at fixed quark masses and values of the lattice spacing. After repeating the simulations for different quark masses and values of the lattice spacing, the results have to be renormalized before all data are analyzed together by carrying out a fit to extrapolate the quantities to the physical values of the quarks masses and the continuum limit. At this point systematic effects originating from the simulation or the analysis need to be estimated in order to obtain results with full error budget and suitable for comparison or combination with experimental results.

We have completed such simulations for quantities including decay constants for D, D_s, B, and B_s mesons, parameters for neutral meson mixing for D, B, and Bs_mesons as well as their ratio xi. Furthermore, form factors for semileptonic decays of B and Bs-mesons have been calculated. We have established the different parts of the analysis and are currently finalizing nonperturbative determinations of the renormalization factors as well as estimates for the systematic uncertainties. The project will be completed by preparing manuscripts for submission to peer-reviewed journals. In case of the semileptonic form factor calculation we are focusing at the determination of Bs -> Ds l nu and Bs -> K l nu decays because these will enable LHCb to obtain an independent determination of the ratio of CKM matrix elements |V_cb|/|V_ub|. Afterwards we will analyze B->D^(*) l nu decays and obtain theoretical predictions for the ratios R_D and R_D^* to address LFUV.

Preliminary results have been presented at the annual Lattice conferences in Southampton (2016) and Granada (2017), as well as at the major phenomenological conferences ICHEP 2016 in Chicago, and the EPS-HEP 2017 in Venice with summaries written up as proceedings. In addition OW was invited to report on this work at the LHCb UK meeting in Oxford in January 2017 as well as the LHCb workshop ""Implications of LHCb measurements and future prospects"" at CERN, Geneva, Switzerland in November 2017. Moreover, he has been invited to present his work at several seminars and other workshops.

PB and OW organized very successfully 9th International workshop on QCD and numerical algorithms workshop (QCDNA) in Edinburgh in 2016. Given the success, OW was invited to help organize the follow-up workshop QCDNA X in Coimbra (2017)."

## Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Given indications of LFUV in semileptonic B-decays, it is of utmost importance to improve the theoretical predictions. Given the numerical data we already collected, we expect to obtain nonperturbative determinations of form factors not only for B_(s) -> D_(s)^(*) l nu but also e.g. for B->K^(*) l^+ l^- or Bs -> phi l^+ l^-. These will complement sum-rule calculations and improve the theoretical predictions. Not only questions of lepton flavor universality violations will be addressed by our results but also deviations seen in the angular observables, like P'_5, for B->K^* l^+l^-.