End User's View of Lattice QCD Cheng-Wei Chiang National Central University & Academia Sinica Lattice QCD Journal Club March 9, NTU

C.W. ChiangEnd User of LQCD2 Outline  Why I am here  Quantities of particular interest to me  What I hope to learn about LQCD  Concluding remarks

C.W. ChiangEnd User of LQCD3 Why Am I Here?  I should be the last person to speak here… … and indeed I am.  I know next to nothing about lattice QCD calculations… … except that I quote lattice results from time to time.  To be honest, the reason I keep using the lattice results whenever necessary is… … I do not know what numbers to put into my calculations and papers.  So I am not here to tell you anything new… … rather, I come here to learn, just like a graduate student…  And hopefully one day I can possibly give a talk with a title like… “An unquenched lattice QCD analysis with staggered quarks”

C.W. ChiangEnd User of LQCD4 What Do I Care About?  I am more interested in: Weak interactions; CP violation; Flavor structure of elementary particles; and New physics.  These issues are likely to be all related.  Currently, a lot of research activities (th + exp) focus on the study of bottom physics because: It helps us fixing important parameters in the SM and testing QCD (perturbative and non-perturbative) calculations; and It may lead us to discrepancies and thus physics beyond SM.

C.W. ChiangEnd User of LQCD5 CKM Mechanism  The couplings between the up-type and down-type quarks are described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism within the SM.  Using the Wolfenstein parameterization, CP violation is encoded by the parameter .  V ub and V td carry the largest weak phases, but are the least known elements due to their smallness.

C.W. ChiangEnd User of LQCD6 Unitarity Triangle  Unitarity relation for V ub and V td : V ud V ub * + V cd V cb * + V td V tb * = 0. It can be visualized as a triangle on a complex plane whose area characterizes CPV. (2)(2) (3)(3) (1)(1) (0,0) (1,0) A CP (t)[(cc)K L,S,  ’K S,  K S,…]A CP [D CP K , K ,…]  M B d and  M B s BR(B  X c,u l )  , A CP [ , ,  …]

C.W. ChiangEnd User of LQCD7 CKMfitter Results  FPCP06 update: =  A =   = –0.031  = –  = – 5.0  =  1.00  = – 4.1 [CKMfitter:

C.W. ChiangEnd User of LQCD8 Quantities of Interest  In order to reach the ultimate goal of fixing the ( ,  ) vertex, we need the input of hadronic matrix elements (ME’s): Decay constants; Weak decay form factors; Bag parameters.  Being low-energy parameters, they are the same within or beyond the SM, making their applications wider.  Unfortunately, these ME’s cannot be computed perturbatively or extracted from experiments if one does not assume knowledge of CKM matrix elements.  Lattice QCD is the only known first-principle calculating tool for such quantities.

C.W. ChiangEnd User of LQCD9 Example: B s Mixing  Within the SM, the value of  M B is given by  Here S 0 (x t ) = and the NLO short-distance QCD correction  2B ' and J 5 ' Experimental parameters M B s =  GeV.  This quantity is suggested to be used to determine |V ts |, which is otherwise difficult to extract from current experiments.  However, it requires the input of f B s  B B s =  [Hashimoto 2005]

C.W. ChiangEnd User of LQCD10 Example: B s Mixing  If what one cares the |V td /V ts |, the error on the hadronic factor can be further reduced by considering the ratio:  Here  = 1.23  [Hashimoto 2005]

C.W. ChiangEnd User of LQCD11 Results from D0 & CDF  The FCNC effect in b-s sector of the SM was recently confirmed in the B s meson mixing observed by both CDF and D0:  Within the SM, this implies: |V td /V t s | =  In comparison, the latest Belle results for b → d  and b → s  give a 95% CL range of ~ [0.201  0.030] for the above ratio.

C.W. ChiangEnd User of LQCD12 B s Mixing With New Physics Contributions  New physics with significant b → s FCNC will add to SM (or even induce new) |  B| = |  S| = 2 operators that affect B S mixing.  In that case,  M B s will not be suitable for extracting |V ts |. Instead, it can be used to constrain new physics parameters.  For example, for Z 0 models with tree-level FCNC in LH sector one has  Here we still assume no new operators. But in general, there can be [Barger, CWC, Jiang, Langacker 2004]

C.W. ChiangEnd User of LQCD13 Constraint on Z 0 Model Parameters  Now the effect of LH FCNC induced by the Z’ boson is:  For  L sb = 0 or 180 o,  L sb < 6.20 £ 10 –4 (most conservative).  Part of the errors comes from the lattice number of the hadronic parameters f B s  B Bs. Smaller errors can impose more stringent bounds on the parameter space.  A more comprehensive analysis should also include contributions from new operators. [Cheung, CWC, Deshpande, Jiang 2006]

C.W. ChiangEnd User of LQCD14 Form Factors  To extract |V ub /V cb | (or individually) from exclusive semileptonic or radiative B decays, it is important to minimize the uncertainty in the ratio (or individually) of B  X u and B  X c form factors.  In two-body hadronic B decays, if the decay amplitude can be factorized: amp ~ (CKM factor) (WC) (decay const) (form factor) then an accurate determination of the decay rate also relies on, in particular, the form factor.  Usually, the form factors are computed or parameterized in various models (BSW, LCSR, Light-Front, ISGW, etc).  Better determination from LQCD will improve the above analysis and our understanding of model calculations.

C.W. ChiangEnd User of LQCD15 Form Factors  In certain decays, penguin annihilation diagrams are claimed to be non-negligible because of no helicity suppression for such operators and may lead to interesting phenomena (e.g., the B  VV polarization anomaly: f L ~ 0.5 for  K * and  K * ).  For two-body charmless decays, they involve light-to-light form factors that are less familiar to us. In addition to PQCD calculations, it will be very useful if we also have LQCD numbers.  Also, once we go beyond the SM, there will generally be ME’s of new operators to be needed. [Keum, Li, Sanda 2000; Kagan 2004]

C.W. ChiangEnd User of LQCD16 Decay Constants  Although the decay constants of light mesons are easier to extract from experiments, it is not the story for heavy mesons.  For example, the purely leptonic decay B    is recently observed. But  Therefore, we need lattice calculation of f B. So is the case of f D.

C.W. ChiangEnd User of LQCD17 What Do I Want to Learn?  What are the approaches of different LQCD groups? How do they differ from one another?  What are the advantages and disadvantages of those approaches?  How can I learn to do LQCD calculations (e.g., starting from some toy or classic exercises), and is it possible to do it on a desktop (laptop) computer?  What are current major activities and technical issues in the field and what are the future directions?  Understand the jargons and be able to read in more depth lattice papers.

C.W. ChiangEnd User of LQCD18  The knowledge of certain hadronic matrix elements is crucial in extracting information of the CKM parameters from experiments, directly affecting the precision of them.  For physics beyond the SM, there generally will be matrix elements involving new operators that contribute to experimental observables. They also need to be evaluated to a good accuracy in order for people to discuss effects / constrain parameters of new physics.  We hope TWQCD will make more contributions in these and other important directions. Concluding Remarks

Thank You