Precision determination of the charm quark mass Christine Davies University of Glasgow HPQCD collaboration. CHARM2013, August 2013

Transcription

1 Precision determination of the charm quark mass Christine Davies University of Glasgow HPQCD collaboration CHARM2013, August 2013

2 Quark masses are CDF fundamental parameters of the SM but cannot be directly determined from experiment. Well-defined masses are scheme and scale-dependent. Convention to use MS Compare results from multiple approaches for strong test of QCD. Masses are input to theoretical expressions for SM crosssections e.g. (but Higgs WG inflate errors -why?) H cc Higgs X- Section WG PDG lattice Karlsruhe (e + e -) world non-lattice!!s ! mc (GeV) ! mb (GeV) P. Mackenzie, Snowmass 2013

3 Lattice QCD works directly with the QCD Lagrangian. Can tune bare mass parameters very accurately using experimentally very well-determined hadron masses ' b b '' ' h b (2P) h b (1P) b2 b1 (2P) b0 b2 b0 b1 (1P) (1D) expt fix params postdcns predcns MESON MASS (GeV/c 2 ) ' ' c2 c h c1 c J/ c0 c ' B c B c B s B B c *' B c * B s * B * * B c0 R. Dowdall et al, HPQCD, D s D 0 K

4 Conversion of lattice quark masses to Direct methods: Determine m q,latt m MS (µ) =Z(µa)m latt MS scheme in lattice QCD. Calculate Z in lattice QCD pert. th. or use nonpert lattice matching. Error dominated by that of Z and continuum extrapolation. Note: Z cancels in mass ratios. Indirect methods: (after tuning m latt ) match a quantity calculated in lattice QCD to continuum pert. th. in terms of MS quark mass e.g. Current-current correlators for J J heavy quarks known through. α 3 s Chetyrkin et al, Maier et al

5 Issues with handling heavy quarks on the lattice: L q = ψ(d/ + m)ψ ψ(γ + ma)ψ is a finite difference on the lattice - leads to discretisation errors. What sets the scale for these? For light hadrons the scale is Λ QCD = few hundred MeV For heavy hadrons the scale can be m Q E(a) =E(a = 0) (1 + A(m Q a) 2 + B(m Q a) ) m c a 0.4,m b a 2 for a 0.1fm need good discretisation of Dirac equation and multiple values of for accurate continuum extrapolation. Highly Improved Staggered Quarks (HISQ) formalism has errors improved to α s (am) 2, (am) 4 a Follana et al, HPQCD, hep-lat/

6 R(s) R(s) Current-current correlator method for mc Continuum: extract charm piece of: C k R e + e (s) =σ(e+ e hadrons) 4πα 2 /(3s) pqcd! BES (2001) J/!!, " MD-1 # CLEO $ BES (2006) "# s (GeV) Π4.5 5 c (q 2 )= π 2 e2 V c k 0 α 1.5 2!, s (µ) Use k=1: m c (m c )=1.279(13)GeV from experiment, then a power series in, known through for first few values of k C k q 2 4(m c (µ)) 2 k α 3 s M k = 12π2 n! J errors: expt + α s e.g. Kuhn et al, hep-ph/ ds s k+1 R e + e (s) k d dq 2 Π c (q 2 ) 2 q =0 c c J vector coupling to photon Chetyrkin et al,

7 Current-current correlator method for lattice mc HPQCD + Chetyrkin et al, , C. Mcneile et al, HPQCD, Substitute time-moment of lattice charmonium correlator for experiment. In principle can use any current J now. For HISQ quarks pseudoscalar η c correlator is most accurate. J is absolutely normalised. step 1: calculate η c correlators by combining lattice charm quark propagators step 2: large time - fit to exponential, gives η c mass step 3: tune lattice quark mass so η c mass correct. step 4: calculate time moments to compare to QCD pert. theory. Emphasises short-time contribns. correlator(t) e-06 1e-08 1e-10 1e-12 1e-14 J J J PC any current now t

8 Correlator time-moments: G(t) =a 6 x G n = t (am c ) 2 < 0 j 5 (x, t)j 5 (0, 0) 0 > (t/a) n G(t) R n,latt = G 4 /G (0) 4 n =4 ratio to results with no gluon field improves disc. errors = am η c (G n /G (0) n ) 1/(n 4) n =6, 8, am c J (match k = 2, 3, 4...) extrapolate to a=0 and compare to contnm pert. th. R n,cont = m η c Ck P 2m c (µ) C P,0 k C P k C P,0 K =1+ c i α i s(µ) t J n = 2k +2

9 Fit first 4 moments simultaneously, gives Result: m c (m c )=1.273(6)GeV error dominated by unknown higher orders in pert. th. C. McNeile et al, HPQCD, Further check: compare vector moments (after normalising current) to those extracted from R e+ e Agreement is a 1% test of (lattice ) QCD m ηc 2m c (µ) expt (n th moment) 1/(n 2) (GeV 1 ) AND α s (µ) lattice and expt errors similar size n = 10 n = 8 n = 6 n = (am c ) 2 G. Donald et al, HPQCD,

10 m c /m s Mass ratio can be obtained directly from lattice QCD if same quark formalism is used for both quarks. Ratio is at same scale and for same nf. mq1,latt m q2,latt 14 a=0 = m q1,ms (µ) m q2,ms (µ) HISQ Not possible with any other method... mc/ms a 2 (in fm 2 ) m c = 11.85(16) n m f =3 s C. Davies et al,hpqcd, (1.3) MeV allows 1% accuracy in ms

11 Current-current correlator method -HISQ HPQCD, Repeat calcln for m q m c inc. ultrafine lattices 11 mηh /(2m h(µ)) mηh /(2m h(µ)) mηh /(2m h(µ)) (4) (4) (5) (5) (6) (7) (7) (8) (7) (8) (7) (7) (9) (9) log W 11 log W 12 log W BR log W CC log W 13 log W 14 log W 22 log W 23 R 6 /r 6 µ =3m h (µ) R 8 /r 8 µ =3m h (µ) log W 13 /W 22 log W 11 W 22 /W12 2 log W CC W BR /W R 10 /r log W CC /W BR µ =3m h (µ) log W 14 /W 23 log W 11 W 23 /W 12 W 13 m ηc m ηb (5) logm W ηh 12 (GeV) /u (8) log W BR /u 6 0 Agrees well with contnm. 1: Function (7) z(µ/m h log =3,m W CC ηh )/u m 6 0 ηh /(2m h ) as a funcof m ηh (6) results using The solid line, Rlog e + plus We 13 gray /u 8 0error envelope, shows a Saturday, = 0 extrapolation (6) August 2013 obtained log W from our fit. This is com- 14 /u 10 mηh /(2m h(µ)) c Can determine m ηh µ = 3m h m h m h /2 FIG. 6: z(µ/m h,m ηh ) versus m ηh for three different values of µ/m h. The curve for µ =3m h comes from the best fit heavy quarks - extrapolate to the moments. The other curves are obtained by evolving perturbatively from µ=3m h. (slightly) to b. m, mηh ) n f =5 b m h /m ηh b for (m b )=4.164(23)GeV key error is now extrapoln in a

12 mb/mc from lattice QCD m0hmηc/(m0cmηh ) mq1,latt m q2,latt a=0 = m q1,ms (µ) m q2,ms (µ) m ηc m ηb m ηh (GeV) completely nonperturbative determination of ratio gives: m b m c =4.49(4) Agrees with that from current-current correlator method - test of pert. th.

13 Ongoing work Existing lattice QCD results include u, d, s sea quarks with u/d quark masses heavier than their real values. NOW have gluon configurations including flavours of sea quarks and u/d quark masses at their physical values. M c /(2m c (m c )) , result a 2 (GeV -2 ) n=10 n=8 n=6 HPQCD preliminary results (HISQ quarks) show very little effect of c in sea (as expected) ETMC also working on mc with quarks in sea.

14 Improved accuracy on ratio mc/ms on nf = configs with physical u/d quarks: MILC/Fermilab result@lat13 m c m s = 11.75(6) will allow improved ms from improved mc determination

15 PDG compilation of results WEIGHTED AVERAGE 1.275±0.004 (Error scaled by 1.0) c-quark MASS (GeV) mc(mc)! 2 ALEKHIN 13 THEO 0.6 NARISON 13 THEO ALEKHIN 12 THEO NARISON 12A THEO 0.7 BODENSTEIN 11 THEO 0.1 LASCHKA 11 THEO AUBERT 10A BABR BLOSSIER 10 LATT 0.0 MCNEILE 10 LATT 0.1 CHETYRKIN 09 THEO 0.1 SIGNER 09 THEO 0.4 BOUGHEZAL 06 THEO 1.8 BUCHMULLER 06 THEO HOANG 06 THEO 3.9 (Confidence Level = 0.792) Their evaluation: 1.275(25) GeV good agreement between most precise lattice and non-lattice results NB new result from joint H1+ZEUS charm prodn cross-section: mc=1.26(6) GeV arxiv;

16 Conclusions m c (m c ) m b (m b ) is determined to 1% and to 0.5% from continuum and lattice methods. Will be hard to improve mc further directly. mb can be improved from lattice QCD with finer lattices reducing/removing extrapolation to b. Then determine mb/mc ratio nonperturbatively to improve mc Improved mc will give improved ms from 0.5% accurate mc/ms New lattice QCD determinations in progress using a variety of formalisms and now with u, d, s and c quarks in sea and physical u/d quarks. Watch this space... NOTE: errors are ~a factor of 3 better than Higgs WG assume

17 Error budget for HISQ current-current method m c ð3þ m b ð10þ m b =m c MS ðm Z Þ a 2 extrapolation 0.2% 0.6% 0.5% 0.2% Perturbation theory Statistical errors m h extrapolation Errors in r Errors in r 1 =a Errors in m c, m b prior Gluon condensate Total 0.6% 0.7% 0.8% 0.6%