Heavy Quarks with Domain Wall fermions

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1 Heavy Quarks with Domain Wall fermions Justus Tobias Tsang RBC-UKQCD Collaborations University of Southampton 1 August / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

2 RBC-UKQCD Collaborations BNL and RBRC Mattia Bruno Tomomi Ishikawa Taku Izubuchi Chulwoo Jung Christoph Lehner Meifeng Lin Taichi Kawanai Hiroshi Ohki Shigemi Ohta (KEK) Amarjit Soni Sergey Syritsyn CERN Marina Marinkovic Columbia University Ziyuan Bai Norman Christ Luchang Jin Christopher Kelly Bob Mawhinney Greg McGlynn David Murphy Daiqian Zhang Jiqun Tu University of Connecticut Tom Blum Edinburgh University Peter Boyle Guido Cossu Luigi Del Debbio Richard Kenway Julia Kettle Ava Khamseh Brian Pendleton Antonin Portelli Oliver Witzel Azusa Yamaguchi K.E.K. Julien Frison Peking University Xu Feng Plymouth University Nicolas Garron University of Southampton Jonathan Flynn Vera Gülpers James Harrison Andreas Jüttner Andrew Lawson Edwin Lizarazo Chris Sachrajda Francesco Sanfilippo Matthew Spraggs Tobias Tsang* York University (Toronto) Renwick Hudspith 2 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

3 Outline Motivation 1 Motivation / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

4 Motivation - Flavour Physics η excluded area has CL > 0.95 sin 2β ε K α CKM f i t t e r EPS 15 V ub γ γ α γ excluded at CL > 0.95 ρ β α & m s m d m d ε K sol. w/ cos 2β < 0 (excl. at CL > 0.95) Experiment Theory Belle, BaBar, CLEO-c LHCb, Belle II K, D and B physics to test unitarity of the CKM matrix. Place tight bounds on SM predictions CKMfitter Group (J. Charles et al.), Eur. Phys. J. C41, (2005) [hep-ph/ ], updated results and plots available at: 4 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

D and B physics Motivation = + + = + = FLAG average for = + + FNAL/MILC 14A ETM 14E ETM 13F FNAL/MILC 13 FNAL/MILC 12B FLAG average for = + QCD 14 HPQCD 12A FNAL/MILC 11 PACS-CS 11 HPQCD 10A

5 D and B physics Motivation = + + = + = FLAG average for = + + FNAL/MILC 14A ETM 14E ETM 13F FNAL/MILC 13 FNAL/MILC 12B FLAG average for = + QCD 14 HPQCD 12A FNAL/MILC 11 PACS-CS 11 HPQCD 10A HPQCD/UKQCD 07 FNAL/MILC 05 FLAG average for = TWQCD 14 ALPHA 13B ETM 13B ETM 11A ETM MeV FLAG 2016 (arxiv: ) Goal: D (s) and B (s) phenomenology masses decay constants semi-leptonics Outcome: Test of SM Reduce systematic errors by direct computation 5 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

6 Charm physics in the RBC/UKQCD program Charm phenomenology: f D, f Ds, semi-leptonics Bottom phenomenology via the ratio method (arxiv: ): f B, f Bs, Bag, ξ, semi-leptonics 2+1+1f ensemble generation GIM mechanism for Rare Kaons ( need same action for charm and light) Charm contribution to the HVP Semi-leptonic B decays in RHQ e.g. B D 6 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

7 Motivation: Domain Wall Fermions DWFs provide a method to simulate (approximately) chiral fermions on the lattice PROS: CONS: Used for light and strange sea quarks (N f = 2 + 1) Automatic O(a) improvement No operator mixing: easier renormalisation More expensive due to fifth dimension Introduces additional tunable parameters: L s, M 5 7 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

8 DWF - a (very) brief introduction Introduce a finite fifth dimension of length L s. Choose the Domain Wall Height M 5 LH and RH massless modes exponentially localised at boundaries. A measure of the residual chiral symmetry breaking is given by m res : J 5q (x)p(0) x am res (t) = P(x)P(0) (where J 5q is the pseudoscalar density in 5 th dimension) x 8 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

9 Quenched Pilot Study IDEA Map out parameter space of DWF suitable for heavy quarks Interested in cut-off effects keep L const Test continuum scaling of basic observables Expect similar behaviour in the dynamical case β L/a a 1 (GeV) L(fm) tree-level Symanzik improved gauge action Over-relaxation heat bath JHEP 05 (2015) 072 (arxiv: [hep-lat]) JHEP 04 (2016) 037 (arxiv: [hep-lat]) 9 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

10 M 5 -Scan Motivation β = M5=1.2 M5=1.3 M5=1.4 M5=1.5 M5=1.6 M5=1.7 M5=1.8 M5=1.9 f hh /f hh ref /m ηhh [GeV 1 ] 10 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

11 M 5 -Scan Motivation β = 4.41 β = 4.41, 4.66 f hh /f hh ref M5=1.2 M5=1.3 M5=1.4 M5=1.5 M5=1.6 M5=1.7 M5=1.8 M5=1.9 f hh /f hh ref β =4.41, M 5 =1.4 β =4.41, M 5 =1.6 β =4.41, M 5 =1.8 β =4.66, M 5 =1.4 β =4.66, M 5 =1.6 β =4.66, M 5 = /m ηhh [GeV 1 ] /m ηhh [GeV 1 ] 10 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

12 M 5 -Scan Motivation β = 4.41 β = 4.41, 4.66 f hh /f hh ref M5=1.2 M5=1.3 M5=1.4 M5=1.5 M5=1.6 M5=1.7 M5=1.8 M5=1.9 f hh /f hh ref β =4.41, M 5 =1.4 β =4.41, M 5 =1.6 β =4.41, M 5 =1.8 β =4.66, M 5 =1.4 β =4.66, M 5 =1.6 β =4.66, M 5 = /m ηhh [GeV 1 ] /m ηhh [GeV 1 ] Expect flat continuum limit for M 5 = / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

13 Residual mass behaviour β = 4.41, M 5 = 1.6 am res eff (at) am h =0.10 am h =0.15 am h =0.20 am h =0.25 am h =0.30 am h =0.35 am h =0.40 am h = at 11 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

14 Residual mass behaviour β = 4.41 am res eff (at) am h =0.10 am h =0.15 am h =0.20 am h =0.25 am h =0.30 am h =0.35 am h =0.40 am h =0.45 am res eff (at/2) M 5 =1.2 M 5 =1.3 M 5 =1.4 M 5 =1.5 M 5 =1.6 M 5 =1.7 M 5 =1.8 M 5 = at am h Limitation of am h / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

15 Continuum Limit of decay constants R sh msh ref =1.3GeV msh ref =1.6GeV msh ref =m Ds msh ref =2.4GeV Consider R sh = f norm sh f sh msh m norm sh with msh norm = 1.0GeV Very flat continuum limit can simulate charm even on the coarsest ensemble, a 2 [GeV 2 ] 12 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

16 Continuum Limit of dispersion relation E 2 [GeV 2 ] Example Continuum Limit E 2 [GeV 2 ] Comparison to Continuum msh ref =2.4GeV msh ref =m Ds msh ref =1.6GeV msh ref =1.3GeV a 2 [GeV 2 ] p = 2π L (1, 1, 1) and m sh = m Ds p 2 [GeV 2 ] 13 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

17 Summary of quenched pilot study Can simulate charm quarks with Moebius DWFs: Found sweet-spot in DWF parameter space to be M 5 = 1.6 Limitation: am h 0.4 Exponentially localised Flat CL for decay constants and dispersion relation Expect same features in dynamical case: Set up charm program on RBC/UKQCD s dynamical 2+1f ensembles 14 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

18 Dynamical Ensembles (N f = 2 + 1) 2 ensembles with physical pion masses m π [MeV] C0 M0 F1 C1 C2 M1 M2 L 3 T /a 4 a 1 /GeV m π /MeV a 2 [GeV 2 ] (C0 + M0: arxiv: ) 15 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

19 Set up of Simulation Valence Quarks: light and strange: unitary (M 5 = 1.8) heavy from quenched study: am h 0.4, M 5 = 1.6, L s = 12 Expect same qualitative features in N f = Mixed action between the (light+strange) and the heavy quark sector. Computational Details: Volume averaging by using Z 2 -Wall sources. HDCG (arxiv: ) for light and strange. CG for heavy Monitored time-slice residual (arxiv: ): r t = max t Dψ η t ψ t Many source position per configuration 16 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

20 Check bound on am h in dynamical case (C0) Residual mass (N f = 2 + 1) am res (t) t/a am h =0.45 am h =0.40 am h =0.35 am h =0.30 reach in m h m eff (t) [GeV] D s (PDG) am h = am h =0.40 am h =0.35 am h = t/a Restriction am h 0.4 in agreement with quenched Cannot reach physical charm on the coarsest ensembles 17 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

21 Decay Constant Data Φ D [GeV 3/2 ] Masses and MEs from combined fit to AP and PP including 1st excited states: O(a, m l, m s, m h ) phys C0 C1 C2 Φ D M0 M1 M2 F1 PRELIMINARY /m ηc [GeV 1 ] Φ P = f P mp Φ Ds [GeV 3/2 ] Φ Ds 0.32 phys M0 C0 M C1 M2 C2 F /m ηc [GeV 1 ] PRELIMINARY 1 so far: Z A from conserved light-light current 18 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

22 Ratio of Bag parameters ξ PLAN: ξ B P = P0 O VV +AA P f 2 P m2 P charm bottom C0 C1 C2 M0 M1 M2 F1, ξ = f hs Bhs f hl Bhl PRELIMINARY /m Ds [GeV 1 ] Renormalisation of mixed action for Bag parameters. Extrapolate to B via ratio method. arxiv: / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

23 Analysis Motivation O(a, m l, m s, m h ) O(a = 0, m phys l, ms phys, mc phys ) Extrapolate to ms phys (from global fit arxiv: ). Global fit: CL+heavy quark mass + light quark mass O(a, m l, m h ) = O(0, m phys l, m phys h ) + CCL 0 ( a2 ) + Cχ 0 mπ 2 mπ 2 phys where m 1 P h = m 1 P h + C 0 P h m 1 P h m phys 1 P h with Ph = D, D s, η c (1) 20 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

24 Analysis Motivation O(a, m l, m s, m h ) O(a = 0, m phys l, ms phys, mc phys ) Extrapolate to ms phys (from global fit arxiv: ). Global fit: CL+heavy quark mass + light quark mass O(a, m l, m h ) = O(0, m phys l, m phys h ) [ where m 1 P h = m 1 P h + + CCL 0 + C1 CL m 1 [ ] Cχ 0 + C 1 χ m 1 P h (mπ 2 mπ 2 + [ C 0 P h ] m 1 P h ] P h a 2 m phys 1 P h with Ph = D, D s, η c phys ) (1) 20 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

25 Strange Quark Mass Correction Slight mistuning between unitary and physical strange quark mass. ensemble mismatch coarse (16) -1.1% medium (17) -4.8% fine (17) -0.6% am unitary s am physical s Parameterise mistuning in terms of dimensionless α: ( ) O phys = O uni ms phys ms uni 1 + α O m phys s Find α O from subset of ensembles and apply to others. 21 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

26 Strange Quark Mass Correction ( O phys = O uni ms phys 1 + α O m uni s m phys s ) Calculate 2 values of m s on C1 and M1 O =m α O values C1 M1 O =f O =Φ m 1 [GeV η c ] 22 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

27 Strange Quark Mass Correction ( O phys = O uni ms phys 1 + α O m uni s m phys s ) Calculate 2 values of m s on C1 and M1 Extrapolate to F1 masses O =m O =f O =Φ α O values m 1 [GeV η c ] C1 M1 22 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

28 Strange Quark Mass Correction ( O phys = O uni ms phys 1 + α O m uni s m phys s ) Calculate 2 values of m s on C1 and M1 Extrapolate to F1 masses Extrapolate to F1 lattice spacing O =m O =f O =Φ α O values C1 M1 F m 1 [GeV η c ] 22 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

29 f Ds /f D Global Fit Motivation O(a, m l, m h ) = O(0, m phys l, m phys h )+CCL 0 a2 +Cχ 0 mπ 2 +CP 0 h m 1 P h f Ds /f D mη phys c C0 C1 C2 PRELIMINARY /m ηc [GeV 1 ] M0 M1 M2 F1 f Ds /f D = 1.167(8) stat 23 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

30 f Ds /f D Systematics Motivation m π and m h, dependence f Ds /f D mπ max =450MeV PRELIMINARY π =400MeV mπ max =350MeV m max (CL,χ) m c fixed with 1/m Ph ( f Ds /f D = 1.167(8) +4 ) stat 2 fit where P h = D( ), D s ( ), ηc connected ( ) 24 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

31 Φ D O(a, m l, m h ) = O(0, m phys l, m phys h ) + CCL 0 ( ) a2 + Cχ 0 + Cχ 1 m 1 P h mπ 2 + CP 0 h m 1 (2) P h Φ D [GeV 3/2 ] mη phys c C0 C1 C2 PRELIMINARY /m ηc [GeV 1 ] Φ D = (44) stat GeV 3/2 M0 M1 M2 F1 25 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

32 Φ Ds ( ) O(a, m l, m h ) = O(0, m phys l, m phys h ) + CCL 0 + C CL 1 m 1 P h a 2 (3) + Cχ 0 mπ 2 + CP 0 h m 1 P h Φ Ds [GeV 3/2 ] mη phys c C0 C1 C2 PRELIMINARY /m ηc [GeV 1 ] M0 M1 M2 F1 Φ Ds = (26) stat GeV 3/2 26 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

33 comparison with FLAG (decay constants) adapted from FLAG 2016 (arxiv: ) / = + + = + = FLAG average for = + + FNAL/MILC 14A ETM 14E ETM 13F FNAL/MILC 13 FNAL/MILC 12B FLAG average for = + THIS WORK (stat only) QCD 14 HPQCD 12A FNAL/MILC 11 PACS-CS 11 HPQCD 10A HPQCD/UKQCD 07 FNAL/MILC 05 FLAG average for = TWQCD 14 ALPHA 13B ETM 13B ETM 11A ETM MeV = + + = + = FLAG average for = + + FNAL/MILC 14A ETM 14E ETM 13F FNAL/MILC 13 FNAL/MILC 12B FLAG average for = + THIS WORK (stat only) HPQCD 12A FNAL/MILC 11 PACS-CS 11 HPQCD/UKQCD 07 FNAL/MILC 05 FLAG average for = TWQCD 14 ALPHA 13B ETM 13B ETM 11A ETM 09 PRELIMINARY and STATISTICAL ERROR ONLY 27 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

34 V cd and V cs comparison with literature = + + = + = adapted from FLAG 2016 (arxiv: ) using data from arxiv: FLAG average for = + + ETM 14E FNAL/MILC 14A FLAG average for = + HPQCD 11/10B HPQCD 12A/10A FNAL/MILC 11 QCD 14 THIS WORK (stat only) FLAG average for = ETM 13B neutrino scattering CKM unitarity PRELIM, STAT ERROR ONLY Fit systematics: m cuts π ways to set m c mass-dependent chiral and CL coeffs. Not finalised yet Take all correlation into account FV Isospin sea-charm effects renormalisation 28 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

35 Limitations and how to reach further Problems am max h < am phys c on Coarse Poor Signal-to-noise for m π = 139MeV and m h m phys c Solutions? Stout Smeared charm Gaussian Smearing for source + sink Noise growth m eff [GeV] dc(t)/c(t) D mesons on M am h =0.22 am h = am h =0.34 am h = t/a 29 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

36 Smeared Runs : Tests Smearing Found sweetspot for M 5 = hits of stout smearing Standard Stout parameter ρ = 0.1 hit comparison am res t/a 1 hit 2 hit 3 hit Conclusion Gaussian smearing of light and strange Stout smearing of heavy quarks am h / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

37 Smeared Runs Motivation WORK IN PROGRESS: First Data (Limited statistic) f Ds /f D C0 C1 C2 M1 M2 PRELIMINARY /m ηc [GeV 1 ] am h reach Sweetspot: M 5 = hits of stout smearing (ρ = 0.1) am h 0.7 Can reach charm on all ensembles Physical program: f D, f Ds, semi-leptonics, bag parameters, ξ, HVP Ratio Method to reach b. 31 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

38 Smeared Runs - residual mass am res (t) am h =0.69 am h =0.63 am h =0.57 am h = t/a 32 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

39 Summary Motivation What we have done: Established heavy Moebius DWFs: M 5 = 1.6, am h 0.4 D and D s decay constants at Physical Pion Masses (2 + 1f simulation) in an automatically O(a)-improved setting. Continuum Limit with 3 lattice spacings. Global fit with control of systematics Current work: Finalising systematic error budget Produce smeared data on other ensembles semi-leptonics, ratio method, combined analysis of all data 33 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

40 ADDITIONAL SLIDES 33 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

41 Definitions Motivation Decay constants: 0 A µ cq D q (p) = f Dq p µ D q Extraction of V cd and V cs Bag Parameters: B P = P 0 OVV +AA P 0 8/3f 2 P m2 P where O VV +AA = ( hγ µ q)( hγ µ q) + ( hγ 5 γ µ q)( hγ 5 γ µ q) ξ: Extraction of V td /V ts ξ = f hs Bhs f hl Bhl 34 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

42 f Ds Motivation and f D Systematics Φ D Φ D [GeV 3/2 ] (CL,χ) mπ max =450MeV PRELIMINARY mπ max =400MeV mπ max =350MeV Can resolve C 1 χ Φ Ds Φ Ds [GeV 3/2 ] (CL,χ) mπ max =450MeV PRELIMINARY mπ max =400MeV mπ max =350MeV Can resolve C 1 CL To Do: Renormalisation FV Isospin Fully correlated fits m ηc -disconnected sea-charm 34 / 34 Justus Tobias Tsang Heavy Quarks with Domain Wall fermions

Kaon Physics in the Standard Model

Kaon Physics in the Standard Model RBC and UKQCD Collaborations USQCD All Hands Meeting April 28, 2017 Norman H. Christ Columbia University Five Topics 2 nd order weak with charm Long distance contribution