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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Alexey A. Petrov Wayne State University Table of Contents: Introduction Mixing: current/future experimental constraints Mixing: theoretical expectations Standard Model New Physics Conclusions and outlook Charm mixing in the Standard Model and Beyond

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Charm transitions serve as excellent probes of New Physics 1.Processes forbidden in the Standard Model to all orders Examples: 2.Processes forbidden in the Standard Model at tree level Examples: 3.Processes allowed in the Standard Model Examples: relations, valid in the SM, but not necessarily in general 1. Introduction: charm and New Physics 30 CKM triangle relations

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) D-mixing is the last chance to see New Physics in meson oscillations!!! 29 With the recent measurement of D m s in B s -mixing…

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Introduction: mixing Q=2: only at one loop in the Standard Model: possible new physics particles in the loop Q=2 interaction couples dynamics of D 0 and D 0 Time-dependence: coupled Schrödinger equations Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: 28

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Introduction: mixing Q=2: only at one loop in the Standard Model: possible new physics particles in the loop Q=2 interaction couples dynamics of D 0 and D 0 Time-dependence: coupled Schrödinger equations Diagonalize: mass eigenstates flavor eigenstates Mass and lifetime differences of mass eigenstates: 28

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Introduction: why do we care? mixing intermediate down-type quarks SM: b-quark contribution is negligible due to V cd V ub * (zero in the SU(3) limit) intermediate up-type quarks SM: t-quark contribution is dominant (expected to be large) 1. Sensitive to long distance QCD 2. Small in the SM: New Physics! (must know SM x and y) 1. Computable in QCD (*) 2. Large in the SM: CKM! (*) up to matrix elements of 4-quark operators Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, , nd order effect!!! 27

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) How would new physics affect mixing? Real intermediate states, affect both x and y SM, D C=1 NP! 1. : signal for New Physics? : Standard Model? 2. CP violation in mixing/decay Look again at time development : Expand mass matrix: Local operator, affects x, possible D C=2 new physics new CP-violating phase 26

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) New Physics in x and y Local D C=2 piece of the mass matrix affects x: 25 Double insertion of D C=1 affects x and y: Example: Suppose Zero in the SU(3) limit Falk, Grossman, Ligeti, and A.A.P. Phys.Rev. D65, , nd order effect!!! Can be significant!!! Amplitude phase space

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) How would CP violation manifest itself in charm? Possible sources of NP in CP violation in charm transitions : CPV in decay amplitudes (“direct” CPV) CPV in mixing matrix CPV in the interference of decays with and without mixing 24 With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix At this point CP-violating signal is a “smoking gun” signature of New Physics

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) 2. Experimental constraints on mixing 1.Time-dependent or time-integrated semileptonic analysis 2.Time-dependent analysis (lifetime difference) 3.Time-dependent analysis Quadratic in x,y: not so sensitive Sensitive to DCS/CF strong phase Idea: look for a wrong-sign final state 23

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) What if time-dependent studies are not possible I? f3f3 f1f1 f2f2 -charm factory (BES/CLEO-c) f4f4 Time-integrated analysis: DCSD contribution cancels out for double-tagged decays! CFDCS Quadratic in x,y: not so sensitive wanted: linear in x or y H. Yamamoto; I. Bigi, A. Sanda 22

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) What if time-dependent studies are not possible II? If CP violation is neglected: mass eigenstates = CP eigenstates CP eigenstates do NOT evolve with time, so can be used for “tagging” KSKS 00 CP Eigenstate (-) f1f1 f2f2 t -charm factories have good CP-tagging capabilities CP anti-correlated (3770): CP(tag) (-1) L = [CP(K S ) CP( 0 )] (-1) = +1 CP correlated (4140) (-) -charm factory (BES/CLEO-c) Can still measure y: D. Atwood, A.A.P., hep-ph/ D. Asner, W. Sun, hep-ph/

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) 3. Mixing: theoretical estimates Theoretical predictions are all over the board… so: Can x,y ~ 0.5% be a SM signal? What is the relationship between x and y (x ~ y, x > y, x < y?) in the Standard Model? x from new physics y from Standard Model Δ x from Standard Model (papers from SPIRES ) Updated predictions A.A.P. hep-ph/

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical estimates I A. Short distance gives a tiny contribution … as can be seen from a “straightforward computation”… with m c IS large !!! 19 Notice, however, that at NLO in QCD (x NLO,y NLO ) >> (x LO, y LO ) : Similar for x (trust me!)Example of NLO contribution E. Golowich and A.A.P. Phys. Lett. B625 (2005) 53 … x LO >> y LO !!! x NLO ~ y NLO !

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical estimates I A. Short distance + “subleading corrections” (in {m s, 1/m c } expansion): …subleading effects? 4 unknown matrix elements 15 unknown matrix elements Twenty-something unknown matrix elements Guestimate: x ~ y ~ ? Leading contribution!!! H. Georgi, … I. Bigi, N. Uraltsev 18

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Resume: model-independent computation with model-dependent result 17

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical estimates II B. Long distance physics dominates the dynamics… If every Br is known up to O(1%) the result is expected to be O(1%)! m c is NOT large !!! … with n being all states to which D 0 and D 0 can decay. Consider K, KK intermediate states as an example… cancellation expected! The result here is a series of large numbers with alternating signs, SU(3) forces 0 x = ? Extremely hard… J. Donoghue et. al. P. Colangelo et. al. Need to “repackage” the analysis: look at the complete multiplet contribution 16

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) SU(3) and phase space “Repackage” the analysis: look at the complete multiplet contribution Does it help? If only phase space is taken into account: no (mild) model dependence Each is 0 in SU(3) y for each SU(3) multiplet if CP is conserved Can consistently compute 15

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Example: PP intermediate states n=PP transforms as, take 8 as an example: This gives a calculable effect! Numerator: 1.Repeat for other states 2.Multiply by Br Fr to get y Denominator: phase space function 14

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Results Product is naturally O(1%) No (symmetry-enforced) cancellations Disp relation: compute x (model-dependence) naturally implies that x,y ~ 1% is not excluded in the Standard Model 13 E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 A.F., Y.G., Z.L., Y.N. and A.A.P. Phys.Rev. D69, , 2004

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Resume: model-dependent computation with model-dependent result 12

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Summary of SM theoretical expectations 11

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) 10 Attacking New Physics Multitude of various models of New Physics can affect x

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) 10 Attacking New Physics “Four amigos” Multitude of various models of New Physics can affect x

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Global Analysis of New Physics in x 9 Let’s write the most general D C=2 Hamiltonian … with the following set of 9 independent operators… RG-running relate C i ( m ) at NP scale to the scale of m ~ 1 GeV, where ME are computed (on the lattice) E.Golowich, J. Hewett, S. Pakvasa and A.A.P. Each model of New Physics provides unique matching condition for C i ( L NP )

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) New Physics in x and y: lots of extras Extra gauge bosons 8 Extra scalars Extra fermions Extra dimensions Extra global symmetries Left-right models, horizontal symmetries, etc. Two-Higgs doublet models, leptoquarks, technicolor, etc. 4 th generation, vector-like quarks, little Higgs, etc. Universal extra dimensions, split fermions, warped ED, etc. SUSY: MSSM, alignment models, split SUSY, etc. Example: two-Higgs doublet model: E.Golowich, J. Hewett, S. Pakvasa and A.A.P.

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Summary of NP theoretical expectations 7

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) A bit more about CP violation in charm 6

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) CP violation: experimental constraints 1. Standard analysis: rate asymmetries ModeE791, %FOCUS, %CLEO, % D 0 → K + K ±4.9± ±2.2±1.50.0±2.2±0.8 D0 → +-D0 → +- -4.9±7.8±3.04.8±3.9±2.51.9±3.2±0.8 D 0 → K S 0 0.1±1.3 D0 → 0+K-D0 → 0+K- -3.1±8.6 … which is of the first order in CPV parameters, but requires tagging 2. Recall that CP of the states in are anti-correlated at (3770): a simple signal of CP violation: … which is of the second order in CPV parameters, i.e. tiny 5

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) CP violation: new experimental possibilities Look for CPV signals that are 1. first order in CPV 2. do not require flavor tagging Consider the final states that can be reached by both D 0 and D 0, but are not CP eigenstates ( , KK *, K , K , …) where A.A.P., PRD69, (R), 2004 hep-ph/

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) CP violation: untagged asymmetries Expect time-dependent asymmetry… … whose coefficients are computed to be This is true for any final state f … and time-integrated asymmetry 3

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) CP violation: untagged asymmetries (K + ) For a particular final state K , the time-integrated asymmetry is simple This asymmetry is 1. non-zero due to large SU(3) breaking 2. contains no model-dependent hadronic parameters (R and are experimental observables) 3. could be as large as 0.04% for NP Note: larger by O(100) for SCS decays ( , …) where R ~ 1 A.A.P., PRD69, (R), 2004 hep-ph/

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Conclusions Charm provides great opportunities for New Physics studies –large available statistics –mixing: x, y = 0 in the SU(3) limit (as V * cb V ub is very small) –mixing is a second order effect in SU(3) breaking –it is conceivable that y ~ x ~ 1% in the Standard Model –it is possible for y to be dominated by New Physics Quantum coherence will allow CLEO-c/BES to perform new measurements of strong phases in charm mixing studies –important inputs to time-dependent studies of mixing and f 1 / g Quantum coherence will allow BES/CLEO-c to perform new studies of mixing –no DCSD contamination in double-tag K studies –new mixing measurements unique to tau-charm factories Observation of CP-violation or FCNC transitions in the current round of experiments provide “smoking gun” signals for New Physics - untagged asymmetries are more sensitive to CPV 1

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Additional slides 0

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Questions: 1. Can any model-independent statements be made for x or y ? 2. Can one claim that y ~ 1% is natural? What is the order of SU(3) breaking? i.e. if what is n?

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical expectations At which order in SU(3) F breaking does the effect occur? Group theory? is a singlet with that belongs to 3 of SU(3) F (one light quark) Introduce SU(3) breaking via the quark mass operator All nonzero matrix elements built of must be SU(3) singlets The C=1 part of H W is -2

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical expectations note that D i D j is symmetric belongs to 6 of SU(3) F D mixing is prohibited by SU(3) symmetry Explicitly, 1. No in the decomposition of no SU(3) singlet can be formed 2. Consider a single insertion of transforms as still no SU(3) singlet can be formed NO D mixing at first order in SU(3) breaking 3. Consider double insertion of D mixing occurs only at the second order in SU(3) breaking A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, ,

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Quantum coherence: supporting measurements Time-dependent analysis A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019 Strong phase can be measured at CLEO-c! where and Strong phase is zero in the SU(3) limit and strongly model-dependent With 3 fb -1 of data cos can be determined to | cos | < 0.05! Silva, Soffer; Gronau, Grossman, Rosner

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) Theoretical expectations Most probably don’t exists… If SU(3) breaking enters perturbatively, it is a second order effect… Known counter-example: 1. Very narrow light quark resonance with m R ~m D What happens if part of the multiplet is kinematically forbidden? see E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998 Example: both are from the same multiplet, but the latter is kinematically forbidden see A.F., Y.G., Z.L., and A.A.P. Phys.Rev. D65, , 2002 A. Falk, Y. Grossman, Z. Ligeti, and A.A.P. Phys.Rev. D65, , 2002

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Charm 2006, June 5-7, Beijing Alexey Petrov (WSU) CP violation: new experimental possibilities 1 1.Time dependent (lifetime difference analysis): separate datasets for D 0 and D 0 This analysis requires 1. time-dependent studies 2. initial flavor tagging (“the D * trick”) Cuts statistics/sensitivity 5

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