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The Hadron Collider Physics Summer Schools, Fermilab August 9-18, 2006 1 Heavy Flavors Sheldon Stone, Syracuse University

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Heavy Flavors. Sheldon Stone, Syracuse University. Introduction. “Heavy” flavors, defined as b & c quarks, not t, which is heavier, as the top doesn’t live long enough to form a meson and just decays ~100% directly to b quarks (In England we have “Heavy” flavo u rs) - PowerPoint PPT Presentation

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• IntroductionHeavy flavors, defined as b & c quarks, not t, which is heavier, as the top doesnt live long enough to form a meson and just decays ~100% directly to b quarks (In England we have Heavy flavours) Charm is interesting in several special areas, but I will concentrate on bsFirst I will discuss some specific b phenomenology and then point out why these studies are extremely important and interesting

• Some B Meson Decay Diagramsa) is dominant b) is color suppresseda) & b) are called tree level diagrams

• The Standard ModelTheoretical BackgroundPhysical States in the Standard Model

The gauge bosons: W, g & Zo and the Higgs HoLagrangian for charged current weak decays

Where

• The CKM Matrix

Unitary with 9*2 numbers 4 independent parametersMany ways to write down matrix in terms of these parameters

• The Basics: Quark Mixing & the CKM MatrixA, l, r and h are in the Standard Model fundamental constants of nature like G, or aEMh multiplies i and is responsible for CP violationWe know l=0.22 (Vus), A~0.8; constraints on r & h d s buctmassmass

• The 6 CKM TrianglesFrom Unitarityds - indicates rows or columns usedThere are 4 independent phases: b, g, c, c (a can be substituted for g or b, as a+b+g=p)ccgbaArea of each = A2l6h, the Jarlskog Invariant

• |Vcb| Both Vcb & Vub can be determined using diagram (a) when W--nCan use either inclusive decays BX-n, with B~10%or exclusive BD*-n with B~6%|Vcb|=(41.960.230.350.59)x10-3 inclusive (see Kowalewski ICHEP 2006) Very well based theoretically (HQET)Note difference is 2.6x10-3, much larger than quoted theoretical errors!

• |Vub| This is much more difficult because the bu rate is so much smaller than bcInclusive decays are studied with severe cuts to reduce bu background|Vub|=(4.490.190.27)x10-3For exclusive decays use Bp-n (in principle also r -n)

Again differencebetween inclusive & exclusive

• Measurements of Bo & BS mixing

• Bo-Bo MixingBo can transform to Bo, like neutral Ks

The eigenstates of flavor, degenerate in pure QCD mix under the weak interactions. Let QM basis be {|1>,|2>} {|Bo>,|Bo>}, then

• Mixing Measurements Diagonalizing we have Dm= mBH-mBL=2|M12|, DG~0R= prob BoBo/ prob BoBoFirst seen by ARGUSP(BoBo)= 0.5Ge-Gt[1+cos(Dmt)]Must tag the flavor of the of the decaying B at t=0 using the other B

• Dmd MeasurementsDmd average 0.5070.004 ps-1Accuracy better than 1%

• Bd Mixing in the Standard ModelRelation between B mixing & CKM elements:

F is a known function, hQCD~0.8BB and fB are currently determined only theoreticallyin principle, fB can be measured, but its very difficult, need to measure B- l-nCurrent best hope is Lattice QCD

• Bs Mixing in the Standard ModelMeasurement of Bs mixing provides the ratio of Vtd/Vts which gives the same essential information as Bd mixing alone, but with much better control of theory parameters|Vtd|2=A2l4[(1-r)2+h2]|Vtd|2/ |Vts|2=[(1-r)2+h2]Circle in (r,h) plane centered at (1,0)To relate constraints on CKM matrix in terms of say r & h need to use theoretical estimates of x=fBs2BBs/ fBd2BBd

• CDF Measurement of DmsP(BSBS)=0.5X GSe-GSt[1+cos(DmSt)]It is useful to analyze the data as a function of a test frequency wg(t)=0.5 GS e-GSt[1+Acos(wt)]CDF:

D0 90% cl bounds21>DmS>17 ps-1

• Constraint on r - h planeNeed to use theory value forUsing both Vub/Vcb & B mixing

In principle, could measure fB|Vub| using B-t-n, but difficult: Belle discovery was corrected & Vub error is significant, so use D decaysSeehttp://ckmfitter.in2p3.fr/

• Leptonic Decays: D(s) +n c and q can annihilate, probability is to wave function overlap Diagram:

_

(s)or cs

• Measuring Charm at ThresholdDD production at threshold: used by Mark III, and more recently by CLEO-c and BES-II.Unique event propertiesOnly DD not DDx producedEase of B measurements using "double tags BA = # of A/# of D'sBeam Constrained Mass

• Measurement of fD+ To find signal, look for events consistent with one m+ track opposite a D- tag with a missing n Compute

Find

• DS+m+n + t+n, t p+n DS+m+n + t+n, t p+n Sum contains 100 m+n + t+n events for MM2
• Comparisons with TheoryCLEO-c data are consistent with most models, more precision needed, for both

• Measurements of CP Violating Angles

• Formalism of CP ViolationCP Eigenstates:

Because of mixing mass eigenstates are a superposition of a|Bo>+b|Bo> that obey the Schrdinger equation

• Bo CP Formalism IIFor CP not being conserved, instead of B1 & B2

CP is violated if q/p 1

Time dependence is given by

• Bo CP Formalism IIIThis leads to the time evolution of flavor amplitudes as

Dm=mH-mL, G GL GH (true for Bd, not necessarily for Bs)Probability of a Bo decay is given by & is pure exponential in the absence of CP violation

• CP violation using CP eigenstatesCPV requires the interference of two amplitudes. We use the direct decay for one amplitude and mixing for the other oneDefineA=A=|A/A|1 is evidence of CP violation in the decay amplitude (direct CPV)With mixing included, we have CPV if

• CP V using CP eigenstates IICP asymmetry

for |q/p| = 1

When there is only one decay amplitude, l=1 thenTime integrated

good luck, maximum is 0.5

• CPV using CP eigenstates IIIFor Bd,

Now need to add A/Afor J/y Ks:

• AmbiguitiesSuppose we measure sin(2b) using yKs, what does that tell us about b? Ans: 4 fold ambiguity- b, p/2-b, p+b, 3p/2-bOnly reason h>0, is Bk>0 from theory, and related theoretical interpretation of e

• B Kinematics at the Y(4S) (Babar & Belle)From AbeAsymmetric e+e-machines at Y(4S)

• Fit to Dt DistributionsB0 tag resolution, wrong tagsB0 tag

• 2006: BaBar + BelleFrom Hazumi ICHEP 2006

• b (not sin2b) measurementsB0gD*+D*-KsTime-dependent Dalitz analysis (T.Browder, A. Datta et al. 2000) cos2b > 0(94%CL, model-dependent) B0gDh0 (h0 = p0 etc.)Time-dependent Dalitz analysis cos2b > 0Belle: 98.3%CL(hep-ex/0605023, accepted by PRL)BaBar 87% CL (BABAR-CONF06/017)

• CPV in Charmless B DecaysCan have both tree & loop diagrams in p+p- (or r+r-)

The weak phase in the tree graph is g. The weak phase in the Penguin is different. Therefore, the Penguin can (and does) mess up CP via mixing in p+p-Penguin is unmasked by evidence of popo TreePenguin

• CPV in Br+r-First done by BaBar confirmed by BelleNot a CP eigenstate, but final state is almost fully longitudinally polarizedfL=0.978+0.024+0.015 (BaBar)However, Penguin pollution revealed at 3s level (BaBar):B(roro)=( 1.20.40.3)x10-6B(r+r-)=(23.52.24.1)x10-6

-0.013

• CPV in Br+r- IIConstraints on a

• Results on a

• g: BDoK decays, Do Ksp+p-Can have CPV in B decays Just need two interfering amplitudesFor the B- decay: A(B-DoK-) AB A(B-DoK-) ABrBei(dB-g)Use modes where the Do is indistinguishable from the Do. Then use Daltiz plot analysis to find g see A. Giri et al., [hep-ph/0303187]

• g from BDoK-, Do Ksp+p-d2 ln L/d2sensitivityBelle first saw aclear differenceNow data show a smaller effect

• Poor Constraints on gSeehttp://www.utfit.org/

• Putting It All Together: StatusGlobal fit using all available inputs eK is from CP violation in Ko system

• Reasons for Further B Physics StudiesThere is New Physics out there: Standard Model is violated by the Baryon Asymmetry of Universe & by Dark MatterI will show that B physics will be crucial towards interpreting New Physics found at the LHC

• The Enigma of BaryogenesisWhen the Universe began, the Big Bang, there was an equal amount of matter & antimatterNow we have most matter. How did it happen?Sakharov criteriaBaryon (B) number violationDeparture from thermal equilibriumC & CP violation

• Sakharov Criteria All SatisfiedB is violated in Electroweak theory at high temperature, B-L is conserved (need quantum tunneling, powerfully suppressed at low T)Non-thermal equilibrium is provided by electroweak phase transitionC & CP are violated by weak interactions. However the violation is too small!nB-nB/ng = ~6x10-10, while SM can provide only ~10-20Therefore, there must be new physics

• Dark MatterDiscovered by Zwicky in 1933 by measuring rotation curves of galaxies in the Coma clusterAlso gravitational lensing of galaxy clustersIs dark matter composed ofSupersymmetric particles?

• The Hierarchy ProblemPhysics at the Planck scale ~1019 GeV is much larger than at the ~100-1000 TeV electroweak scale, requires delicate cancellations between fundamental quantities and quantum corrections.New Physics is needed to solve this problem

• Loop Diagrams - PenguinsEffects of New Particles on B DecaysThese decays are suppressed, so New Particles can show enhanced effects

• MSSM Measurements, from Hinchcliff & Kersting (hep-ph/0003090)Contributions to Bs mixingCP asymmetry 0.1sinfmcosfAsin(Dmst), ~10 x SM

• SupersymmetrySupersymmetry contains squarks and sleptons. Squark mass matrixes contain information on SUSY breaking mechanisms &/or GUT scale interactions.Quark flavor changing neutral current processes, e.g. BS or D0 mixing, are sensitive to the off-diagonal elements of the squark mass matrix.

• ExamplesT.Goto,Y.O.Y.Shimizu,Y.Shindou,and M.Tanaka,2003SMBS mixing CP Violation in BSFrom Okada ICHEP 2006SUSY GUT & BS Mixing

• SO(10)ala Chang, Masiero & Murayama hep-ph/0205111Large mixing between nt and nm (from atmospheric n oscillations) can lead to large mixing between bR and sR. This does not violate any known measurementsLeads to large CPV in Bs mixing, deviations from sin(2b) in Bof Ks and changes in the phase g ~~

• New Physics Effects in Some Different ModelsDifferent models give different patterns (2003 SLAC WS Proceedings)

• Possible Size of New Physics EffectsFrom Hiller hep-ph/0207121

• bs Transitions (Penguins)In SM t in loop dominates and CP asymmetry should be equal to that in J/yKs Other objects in loop, new virtual particles, could interfere So this process is sensitive to new physics

• CPV Measurements In bs We cannot just average these modes, but ....=sin2b =0.500.06DS=.52.05-.68.03 = -0.16 0.06Does u & c parts of Penguin contribute? Yes but DS >0, ~0.1New Physics???

• Electroweak penguins BK(*)l+l- With l+l- pair, can have either pseudoscalar or vector mesons New physics can affect both rates and kinematic distributions.

• BK(*)l+l-: Lepton F-B Asymmetry Lepton angular distribution in l+ l- rest framehep-ex/0508009Belle: lepton 386 M BBSMNP scenariosBut large errors &somewhatcontradictorydata from BaBar

• Constraints on New PhysicsNext to Minimal Flavor Violation constructionAssume NP in tree decays is negligibleIs there NP in Bo-Bo mixing?

Use Vub, ADK, SyK, Srr, Dmd, ASL = semileptonic asymmetry Fit to h, r, rd, qd (or h, s)

Agashe, Papucci, Perez, & Pirjol hep-ph/0509117

• New Physics ConstraintsAmplitudes ~20% of SM still allowed in any region, more near 0oStill a lot of room for New Physics in Bd systemhs

• BS SystemNew Physics almost unconstrained

• DG in BS DecaysDG = GL- GH, where G=1/t of light vs heavy In Bd system DG is small, driven by common channels for Bo & Bo (i.e. p+p-)BSDS+(*) DS-(*), where CP+ outweighs CP- BS (recall CDF measured DmS), CDF & D0 have measurements, order of B(BD(*)DS(*))~10%Recall

DG =2|G12|cosfS, where fS is the CP violating phase in BS mixing, expected to be tiny in SM ~-2l2h=-.04 rad but effected by NPCan measure DG using t measurements

• Measuring f Phase of BS mixingCP violation in BS mixing

hf = 1, depending on f= CP+ or CP -Contrast with Bo G(Bof)~e-t/t[1+AdircosDmt+sinfDmt]

• Measuring f Without Flavor TaggingSum

Some sensitivity to f without flavor tagging

• Measuring f with BSJ/y h (or f)BSJ/y h (where h gg or p+p-po) is a CP eigenstate similar to BoJ/y KS. However, detecting the h is difficult for some hadron collider detectorsJ/y f is not a CP eigenstate, but is very useful in all experiments. Must take into account different spins: S, P, D.use Transversity analysisMost sensitivity expected using flavor tagged analysis

• D0 Untagged AnalysisD0 has 97845 eventsfS=-0.790.560.01 (rad)DGS=0.170.090.04 ps-1DG/G~0.250.13

• Future Experiments

• B experiments at the LHCLHCb: first dedicated b experiment at a hadron collider, the LHCExcellent vertexingExcellent particle idSuper B? Two efforts, one at Frascati and SuperBelle in JapanLHCbCMSATLAS

• LHCb Projections