INTERMEDIATE Vietmse 2
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This 67 page Class Notes was uploaded by Cassidy Kuvalis IV on Saturday September 12, 2015. The Class Notes belongs to Vietmse 2 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/201880/vietmse-2-university-of-california-irvine in Vietnamese at University of California - Irvine.
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Date Created: 09/12/15
SUSY06 June 16 2006 Determining the Unitarity Triangle from TwoBody Charmless Hadronic B Decays Cheng Wei Chiang National Central University amp Academia Sinica 2 work in progress with YuFeng Zhou KEK Outline gt Current status on constraining the unitarity triangle gt Flavor diagram approach to rare B decays gt Global 12 ts with different SU3F breaking schemes gt Fitting results and predictions particularly BS gt Summary CKM Mechanism gt The couplings between the uptype and downtype quarks are described by the CabibboKobayashiMaskawa CKM mechanism within the SM Vud V1quot Vub VCKM Vcd Vcs Vcb th Vts WI 2 1 A AA3p z1 A E AA AA3li ri77 AA22 1 gt Using the Wolfenstein parameterization CP Violation is encoded by the parameter 77 gt V b and Kd carry the largest weak phases but are the least known elements due to their smallness Unitarity Triangle gt Unitarity relation for V b and m Vudliib Vchcs Kthb 0 It can be Visualized as a triangle on a complex plane whose area characterizes CPV 77 77 5KgtACPlp7rgt7mgt7mm BRB XCYUI v AMBd and AMBS V V i V V vucjvgb pw 4 1 d VchCZ l ZV 00 10 ACADCPKa Km Acpw WKS My Man CKM tter Results gt FPCP06 update CKM tter httpckm tterjn2p3fr A 02272i00010 A 0809i0014 p ONTO02770031 4 7 0348400204m18 r 3 a 973 439575 0D 8 22 86 1000 759849411o 3 UTFit s Results UTFit thutfnroma1infnit gt FPCP06 Updates A 02258 r 00014 p 0198 i 0030 77 0364 i 0019 0 946 i 46 8 239i10 7 613 i 450 Questions gt Can we extract useful information for the unitarity triangle from purely charmless B decays also gt Will it be consistent with other methods gt Can the predictions of our theory perturbative nonperturbative for the rare decays agree with the data eg Bereke andNeuberL 2003 gt Can we get any hint of new physics from them Charmless Two Body B Decays gt Charmless twobody hadronic B decay modes are often sensitive to Kd andor Vub Thus they can play a more important role in the determination of the unitarity triangle gt With increasing precision on the branching ratios and CPAs it is possible to provide an additional constraint on the p 77 vertex andor some hints for new physics via a global t gt We distinguish two types of rare decays strangenessconserving AS 0 b 9q g d and strangenesschanging lASl l b a q g s gt The former type is dominated by the colorallowed tree amplitude whereas the latter type is dominated by the QCD penguin amplitudes Old Results of Global SU3F Fits cwc Gmnau Luo Rosner and Supruu PRD 69 034001 2004 PRD 70 034020 2004 gt Charmless VP modes y 57 N 69 charmless P P modes y 54 N 66 both consistent with constraints from other observables 39 cKMFine v 25 H I u 25 so 75 100 125 150 175 so 75 100 125 130 17s 7degreeg y degleesl Flavor Diagram Approach Zeppeufeld 1981 Chan Cheug198619871991Savage Wise 1989 Griusteiu Lebed 1996 Gronau et a1 1994 1995 1995 gt This approach is intended to rely to the greatest extent on model independent avor SU3 symmetry arguments rather than on speci c model calculations of amplitudes gt The avor diagram approach 0 only concerns with the avor aw nonperturbative in strong interactions 0 has a clearer weak phase structure unlike isospin analysis where different weak phases usually mix Tree Level Diagrams gt All these treelevel diagrams involve the same CKM factor a T T39 u as C C39 I altfr r VllLltu 1 q 71 I tree extemal W mission I I colorsuppressed internal W mission I a EE39 Loop Level Penguin Diagrams gt All these looplevel diagrams also have the same CKM factors with u 0 and t quark running in the loop gt Will use the unitarity condition to remove the topmediated loop diagrams c P P39 0 PA PA penguin annihilation neutral mesons Q CD strong penguin internal gluon emission external gluon emission I avor singl t Next to Leading Order Flavor Diagrams gt One also obtains one of the following diagrams whenever T C or P is seen in the amplitude list gt They are higher order in weak interactions PEW C q PEW Z t1 q i EW appear together with C appear together with T and S in decay amps and P in decay amps Flavor Amplitudes gt We use the following notation t E 141quot Y5 YibgtP W t E Ya tT Y lgwgw c E Y C Yogi lifQPEW c E Y jEcC Y p a 4543 Ya P ngw a p ltYb Ya app EPEW l 1 s 2 01 155 5 EFEW s39 s 4Y5 Ya 553 gPm where Yqbq V010 Vqrbquot gt We assume that the toppenguins dominate gt The CKM factors have been explicitly pulled out gt Unprimed amplitudes are used for AS 0 transitions and primed amplitudes for MS l ones Amplitude Decomposition m 176 1 gt Comparing pi from B K Ilt and BaKIlt with LUquot from BaK07r one gets Lizpquot 022 r 002 consistent with VCdVCSL paitly justifying our use of SU3F as the working assumption SU3 Breaking gt We use p and 77 as our tting parameters instead of weak phases gt We consider various SU3 breaking schemes and present the following four representatives 1 exact avor SU3 symmetry for all amplitudes including the factor fK t for m only including the factor fK j for both m and Cl only and including a universal SU3 breaking factor 5 for all amplitudes on top of scheme3 gt Including the factor fK j for lPl does not improve 1 2mquot gt Still keep exact SU3 symmetry for the strong phases WN Partial Fits 7239 7239 7239K and K gt There are 22 data points in this set including the BRs and CPAs along with qubl 0426r0036gtlt10394 and WM 4163i065gtlt 104 that help xA and p 2 2 WI gt Robust results against Parameter Scheme 1 911mm 1 said 3 slim 1 39 p 010 i UU5 010 003 Ul39 007 015 i 005 SU3 breaking n Mums 4 gt Prefer fK t for T and T C factorlzable to a 5 good approximation 1 5 gt 5 104 in 1511quot l gt More rellable because 5 1 xed 1 xed Zmui 1551l 11111 no uncertalntles from CL 91 23 28 I7and 77 UT from 7239 72 7Z39K and K K Only gt Scheme 3 only difference from others miniscule 72 ag92 1 a 67 5 a 5 102 95 CL 29335329 16 21 3 1 3 32 95 CL 640373750 1 LT 57 3 1g 81 95 CL gt Slightly higher p 77 vertex Large C Amplitude gt We observe a large colorsuppressed tree amplitude C with the ratio lCTl being about 068 r 008 and a sizeable relative strong phase ofabout 756 r l3 In our old ts the ratio and relative strong phase between C and T are 2 07 and N 110130 gt These are mainly driven by the facts that the 7r07r0 mode has a large branching ratio and that ACPK7r0 is very different from ACPK7r gt The large Cl and strong phase may be explained within SM by including NLO vertex corrections LL Mishima Sauda 2005 Electroweak Penguins gt Within the SM the colorallowed penguin can be related to the sum of colorallowed and suppressed tree amplitudes via a Fierz transformation Neuben and Rosner 1998 Gmnau Pirjol and Van 1999 PEW 5EWlT CIBMPEW 3 Ce 010 5 2 777 2 00135 i 00012 where EW 2 01 02 gt In our ts we treat FEW and the strong phase SPEW 40 wrt I as free parameters their values do not vary much in different schemes and agree with the SM expectation gt We ignore the colorsuppressed penguin amplitude because it will introduce one more free parameter but not improve the tting con dence level Predictions for BL101 Decays chnmm Srhevww 5 Ur Jrquot cxp ccf exp 145 a usazuwz awn m f gth r gtnnrquot IBR nun sof10B Predictions for BS Decays Cf 349X1075 Scheme 1 Scheme 2 Scheme 3 5mm 4 ODiUO UOiOJ 03i00 00i0 ODiUO OOiOJ 03i00 00i03 4 3i10 48il3 45i10 48il3 16i04 l iUA 15i04 15i04 71 3quot lSGilU 55il l86ill i88i45 Bar uKa 198i10 VE iHl 200il1 2C3i48 CPxn j 0 0 0 0 39 0 0 0 0 involvetp UJSiUOES 033i007 US iC UT USEiUL UMiUED 036i010 USEiUU US iUJB involve f p 70 lUiU U 70i0i002 70 iUiUUE 7 nilos direct CP 0 C 0 0 similar to U U 0 0 Bay 0 0 0 O 70304 i 0 254 70 332 i 0245 i U 244 70504 i 3947 012200 1quot 0150039 0W 9 0039 0194033F LINEN 70 044 i 0 004 70 044 i 0004 quot 44 i 0004 70 044 i 0004 Global Fits Very Preliminary gt There are totally 34 data points to t gt The singlet penguin S is required to explain large branching ratios of the 77 0K modes gt Fitting quality is a lot worse largely due to 5 le and to some extent ACP77 39Kt and B t 77 39 gt Call for the need of more theory parameters Pn Ya mum 08l i 0012 mm n m 013 i 0053 0077 033 0053 0015 i O 007 I 005 l 1006 UT from Global Fits gt Scheme 3 only difference from others miniscule 73 gags6 66 gag 94 21 g g 25 19563 27 74 7 83 67 31 3 87 gt The p 77 is further shifted toward larger 7 but smaller 8 1 0 y 95 CL 1 a 95 cu l U y 95 CL 12 All P P modes Summary gt We perform global 12 ts to charrnless B a P P decays and determine theoretical parameters in various SU3 conserving and breaking schemes gt The p 77 vertex obtained from the partial ts is higher than but consistent with the other ts global ts shifts it to a smaller p value These results are robust in the schemes we consider gt We observe a large C with a nontrivial strong phase and a PEW about the right size as in the SM gt We make predictions based upon the tting results particularly for the BS system to be observed in the next few years gt We will also look at the VP modes Matt Hansen Peng Oh UCSB Outline Lya transfer homogenous vs clumpy H Our work clumpy H as absorbing mirrors Your basic outflow scenario m i W chngwt LLKH Neutral Hydrogen n 2 gt n 1 Ionized Hll regions 68 of ionizing photons converted into Lya photons others Balmer Source SFR and AGN Line 7 EquivalentWidth Offset from systemic Overall pro le width amp shape Optically Thick Sphere Trapped in set 4 Doppler core NCO 10 Frequency random walks Cross section is frequency dependent mean free path changes h Bias to return to core Escapes on largest frequency excursion where mfp cloud size Vesc 400N211 kms Total number of scatters is huge NSCt N 370 N 108N21 so any dust will quench the Lya j 7 gt E i NCC 604 in Spiral Galaxy M33 Is the homogenous picture really tenable for star forming regions 153 IS NCC 604 in Spiral Galaxy M33 picture really tenable for star forming regions A study of low Z starburst ga correlation between UV absc absorption the conclusion Giavalisco et al 96 Apj 466HHC39R E Escaping photons solve the mazequot 0 scatters typical Clumps optically thick Reflection dominates transmission A natural way for Lya to escape when os Hl is thick and dusty 1 139 Li Malhotra amp Rhoads 2002 ApJ 565 Some Lyman Alpha Emitters zgt4 have EWgt240A Stellar max EW240A so not a stellar source Clumpy gas allows FUV absorb gt Lya absorb Requires gas rich amp LMC dusty Newsld lggl Apl 370 gtgt escaping EW larger than source EW quot39 3 39 l 39 7 r 1 egPettini atal OZApJ 569 Some z3 LBGs have broad Lya 800kms and narrower metal absorption lines 200kms Easily reproduced by clumpy outflowsVgas200kms k Each clump reflects gtgt transmits Treat each clump surface like an absorbing mirror Absorption Reflection Angles Frequency Redistribution Let Monte Carlo simulations do all the work found simple tting formulas D Multiphase Lya transfer Easy lanalytic line transfer in hand lfast multiphase transfer simulations for your favorite toy geometry clumps shells laments Itransfer through hydrodynamic simulation output now feasible eliminates the optically thick regions Monte Carlo Simulations Compute photon trajectories for an ensemble of photons Optical path length between each interaction 6 Each interaction results in one of the following Resonant Hl scattering Dust absorption Dust scattering Repeat until photon escapes the HI clump or is absorbed Outflows rc3 018 NCrit 3 X 1021cnr2 fesc 036 NCrit 8 x 1020cnr2 fesc Large widths don t nee large outflow speeds 2 00 l 1500 1900 50ll EW boost 3x plausible V kms quotVoumow for nonnegligible of LAEs Dennin Fluids Group UC Irvine I Flow in twodimensions novel uid behavior at interfaces M Dennin U C Irvine Department of Physics and Astronomy and Institute for Surface and Interfacial Science Dennin Fluids Group UC Irvine I Research Overview Fluid Instabilities Complex Fluids Interfacial Flows convection foams granular Langmuir Monolayers pattern formation 0 ow behavior 39 2D uids spatiotemporal chaos 39 jamming 39 interfaoial PhySiCS O domain growth effective T bio applications 0 controlstabilization micro vs meso tech applications Dennin Fluids Gmup UC Irvine I Outline Introduction to monolayers 0 Experimental Methods 0 Three outstanding issues Large changes in viscosity Nonlinear behavior Anomalous pressure dependence ELquot 1 Hmmdbg El g g fl Langme MfQ i H l Y H I I I I I I I I I I w c o E m 3 C co ltgt OH 03H3 OH ACID ESTER ALCOHOL Deunin Fluids Group UC Irvine Langmuir Monolayer History 1 18th century BC Babylonians spread oil for divination 2 1770 Benjamin Franklin experiments with damping of surface waves 3 1800 s Rayleigh works on surface tension 4 Turn of the century Agnes Pockels develops the Langmuir trough in her kitchen 5 Early 1900 s Langmuir provides detailed explanations of thickness of layers and orientation of molecules He develops the Langmuir lm balance to measure surface tension Dennin Fluids Gmup UC Irvine I Langmuir monolayers today Technology sprays emulsions foams etc direction we are exploring 0 Biology membranes direction we are exploring Rheology liquid crystals not simple Newtonian fluids area of focus Big Chahge Rich Phase Behavihr LIPl r thhhh hh hdh s A E 22 E LC 1 10 LELC LEG Hg 19 22 31 42 1300 Areamolecule AZmol hqmd i iv ceqry mah m 3y Dennin Fluids Group UC Irvine I Experimental Methods characterization of uid properties 0 Velocity pro les 0 Steady state viscosity 0 Complex shear modulus Dennin Fluids Group UC Irvine Denniri Fluids Group UC Irvine microscope Torsion pendulum Movable barrier 39 1 I Dennin Fluids Group UC Irvine Schematic of Apparatus A outer barrier or ngers B torsion pendulum C xed inner cylinder 39 511 j v6 Qro v x JIerLI K IE 7 j v 13 m i r vR 0 H 7 W a quot mfg 1 quotV I F x E gt El J xxx 4qu wg U K M J 1 HM 4F 91 E Q N m m r H M H y x 7 L quot A J p i s 6W 7rrL Q L 53 d I H quot g hr 0 F 5 2 R 7 5 Q B 3983 EVE D 17 5 ma ff 74 r3 F D i 431quot J F 1 kg W HQ 1 H H W M a D M 91 U U M g alr gkbti ig U J W 6211 xi Ev Ed I My 37 M lg IL Cl Dennin Fluids Gmup UC Irvine Track particles Brewster Angle Microscope Images Monolayer without Monolayer under shear shear go 39 2 a Velocity cmsec r c 68 73 Dwm m UC Emmi NQWN WTE HMH 016 Velocity cmsec O 39o 00 73 Dennin Fluids Gmup UC Irvine I Viscosity and Shear Modulus Rotate outer cylinder constant rate ofstrain 7quot 0 Angular displaoement of rotor provides a measurement of the stress 6 0 Oscillate inner rotor with known torque gt known sn ess measure strain response 7 Dennin Fluids Gmup UC Irvine I Measured Quantities O Steady state viscosity 1 039 39 Time dependent shear modulus Gt 01 71 0 Complex Shear modulus G 0 0a 7a G G iG Dennin Fluids Group UC Irvine I Interesting Questions 0 Long time scales kinetics at an interface 0 Nonlinear properties relation between viscosity and complex shear modulus Interesting pressure dependence L 1 Emma 31 g g Q g g 2 quotf 5 E E E 9 7f F 2 lt5 0 O 6 lt5 0 2 O O 3 O 2 o O 6 Q O m de a wamdg gm 10w EM Dennin Fluids Gmup UC Irvine I Top view of monolayer Monolayer is in a hexa c liquid crystal phase I 1 Deimiii Fluids Group UC Emilie Viscosity 95 01 001 n D I I 39 El I D I El I I o pH26 D o pH34 I pH41 u pH61 O O l o I 0 o 8 o o o o 3 0 I l I I I 2 4 6 8 10 timehr Viscosity as a function of time for different pH values GhaskadVi Carr and Dennin J Chem Phys 1999 G39 amp Gquot dynecm 01 I Iquot Dquot Pquot quot tan F39 43 pH 55 1 Lmear measurement 39 I I m Iquot 39I F I G39 El Gquot 00 02 04 06 08 I 10 12 time hr GhaskadVi Carr and Dennin J Chem Phys 1999 Dennin Fluids Group UC Irvine 39L39i r1 1 1 Viscosity for 3 different bulk concentrations a of Ca ions at 01 39 392 pH 55 gt Ca concentration 39 o 0001 mM 0 0015 mM 1 0040 mM 001 539 0 o I 0650 mM 39 0 2 4 6 8101214161820 time hr GhaskadVi Carr and Dennin J Chem Phys 1999 Dennin Fluids Gmup UC Irvine I Relations between T and G 0 COXMmtn7mljq a11 a39 my 0 G39 0 Simple Linear relation TIquot m 2 0 Amplitude dependence of G Ghaskadvi et al Langmuir 1997 Results for 20H TCA a H 32 dynecm b H 48 dynecm A Twardos and Dennin Langmuir 2003 01 39001 01 shear rate or frequency 8391 1000 100 l n and Gquoto gs n and Gquoto gs lt1 I W 0001 viscosity gs Results for C21 a H 10 dynecm T 18 OC L2 phase 3 r 001 b H 20 dynecm T 18 0C near transition H 3 c cH20 dynecmT14 OC g 3 L39Z 01 E 100 001 10 001 01 1 Twardos and Dennm Langmulr 2003 shear rate or frequency 51 n and Gquotm gs n and Gquotm gs n and Gquotm gs Dennin Fluids Group UC Irvine I Anomalous Pressure Behavior Peak in viscosity as a function of pressure Associated with ordering of the headgroups Ghaskadvi et al Langmuir 1997 and Ghaskadvi and Dennin Langmuir 2000 Associated with tilt angle Brooks et 31 Langmuir 1999 Dennin Fluids Group UC Irvine I De nition of Gt t O39 t G t t 39 dt 39 L dt Assume a model for Gt Gt 0023quotAv Ge Pressure dynecm 60 50 40 30 20 140 150 160 170 180 Trough Area cm2 190 Phase Transition around H 26 dynecm 1 Dennm Fluids Group UC Emma G0 dynecm Peak in Gt Pressuredynecm 5 0G0 Ix O O 6 u I I l O O I llll I 30 35 40 45 50 55 G39 dynecm 100 100 39 A 10 39 E 39 E 3 D C gt E in 1 A 39 I I I I I I n 0 0 1o 20 30 4o 50 60 Pressure dyneCm Pressuredynecm Different symbols correspond to different frequencies Dennin Fluids Group UC Irvine I Summary Langmuir monolayers exhibit a range of surprising behavior Interesting kinetics in interfacial systems Surface viscosity is not simple interesting shear rate equency dependence interesting surface pressme dependence
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