Implications of D-Mixing for New Physics

Meson mixing has historical significance– Charm quark (and mass) inferred from Kaon

mixing

– Top mass predicted from Bd mixing

– Strong constraints on New Physics (SUSY, LRM, …) that has affected collider searches

Each meson is different (x = m/):

And thus each measurement is important

J. Hewett SLAC 07

0.776,

The observation of D-mixing is exciting!

• 1st Observation of Flavor Changing Neutral Currents in the up-quark sector!

• 1st Glimpse of flavor physics in the up-quark sector

• 1st Constraints on flavor violation in up-quark sector

• Sparked much interest in the community• Catalogue of New Physics Contributions

– Golowich, JLH, Pakvasa, Petrov arXiv:0705.3650

Compilation of Predictions for D-Mixing

• D-Mixing provides important constraints for model building

– Flavor physics provides strong constraints on models

– Many models poorly tested in +2/3 quark sector

– Many models shove flavor violation into up-quark sector in order to satisfy K mixing large effects in D mixing

H. Nelson, Lepton-Photon 1999

D-Mixing in the Standard Model: Short Distance

• Box diagram is tiny– GIM is efficient!– b-quark contribution is CKM suppressed– s-quark contribution is suppressed by SU(3) breaking

• xbox ~ 10-5 , ybox ~ 10-7

• Higher orders in the OPE may give larger results

Georgi; Bigi

D Mixing in the Standard Model: Long Distance

• Charm is neither light or heavy, so well-developed theoretical techniques don’t apply.

• Sum over all possible, multi-particle, intermediate hadronic states

• yD is less model-dependent; calculate yD and use dispersion relations to obtain xD

• Can result in: yD ~ xD ~ 1%Possible that experimental result is explained by SM effects

Constraining New Physics

• Assume no interference between SM & NP• NP alone does not exceed measured value

of xD

Use 1 value:

xD < 11.7 x 10-3

Allow for 2 and for future exp’t improvements:

xD < 3, 5, 8, 15 x 10-3

New Physics in D-mixing: Formalism

Use the OPE to define an effective Hamiltonian

Complete set of independent operators:

Calculate Ci at NP scale

Evolve HNP to charm scale

New Physics in D-mixing: Formalism

Compute LO QCD corrections

Evolve matching conditions to the charm scale

Anomalous dimensions matrix

New Physics in D-mixing: Formalism

Evaluate hadronic matrix elements

with

We take BD = BD(S) = 0.82 (quenched

lattice) fD = 222.6 16.7-2.4

+2.3 MeV (CLEO-c)

Models Considered

1. Extra Fermions• Fourth Generation• Heavy Vector-like Quarks

• Q=-1/3 Singlet Quarks• Q=+2/3 Singlet Quarks

• Little Higgs Models

2. Extra Gauge Bosons• Generic Z’ Models• Family Symmetries• Left-Right Symmetric

Model

• Alternate LRSM from E6

GUTS• Vector Leptoquarks

3. Extra Scalars• Flavor Conserving 2 Higgs

Doublet Models

• Flavor Changing Neutral Higgs

• Scalar Leptoquarks• Higgsless Models

4. Extra Symmetries• Minimal Supersymmetric

SM• Quark-Squark Alignment• R-Parity Violation• Split Supersymmetry

5. Extra Dimensions• Universal Extra

Dimensions• Split Fermion Models• Warped Geometries

Heavy Q=-1/3 Quark

Present in, e.g.,

• E6 GUTS

• 4th generation

Removes strong GIM suppression Of SM

Constraints in mass-mixing plane

Unitarity of CKM matrix gives |Vub’Vcb’|< 0.02D-mixing improves this constraint by one order of magnitude!

3

5

8

11.7

15 x 10-3

Heavy Q=2/3 Singlet Quarks

• Induces FCNC couplings of the Z– Violation of Glashow-Weinberg-Paschos conditions

• Tree-level contribution to D mixing

Constraints on mixing improved over CKM unitarity bounds by TWO orders of magnitude!

Little Higgs Models

These models contain heavy vector-like T-quark

Strongest bounds on this sector!

Will affect T-quark decays and collider signatures

Arkani-Hamed, Cohen, Katz, Nelson

Sample particle spectrum

Little Higgs Models with T-parity

Buras etal

Scan over numerous parameters

Generic Z’ Models

• Many models have Z’ bosons with flavor changing couplings

• Induces tree-level FCNC

CL = CR = C

Either C is extraordinarily small, or FC Z’ is unobservable @ VLHC

Z’

Left-Right Symmetric Model

•Restores parity @ high energies•SU(2)L x SU(2)R x U(1)B-L •Seesaw mechanism for masses

Parameters:1. = gR/gL

2.Right-handed CKM

3.WR mass

Bounds from K mixing:MWR > 1.6 TeV w/ manifest LRS

=1

L,R

L,R

2-Higgs Doublet Model

• Model II: One doublet gives mass to down-type quarks, second to top-type quarks

• Model I: interesting region excluded by b s

• v2 = v12+v2

2 ; tan = v2/v1

2HDM: Negligible Effects in D Mixing

Flavor Changing Neutral Higgs

• Models w/ multiple Higgs doublets naturally lead to tree-level FCNC

• General discussion:• Severe constraints in d-quark sector from K-

mixing

Cheng-Sher Ansatz

• Specific flavor changing Higgs model, where couplings take the form

Tree-level t-h Box

Supersymmetry (MSSM)

Large contribution from squark-gluino exchange in box diagram

Super-CKM basis:

•squark and quark fields rotated by same matrices to get mass eigenstates

•Squark mass matrices non-diagonal

•Squark propagators expanded to include non-diagonal mass insertionsStrong constraints from K mixing has historically

lead to assumption of degenerate squarks in collider production

mass insertion

helicity index

MSSM: All 8 operators contribute

Constraints on up/charm-squark mass difference

LL,RR LL=RR

LR,RL

LR=RL

Compare to constraints on down/strange-squark mass difference from Kaon mixing (green curve)

LL,RR LL=RR

LR,RL

LR=RL

Bagger, Matchev, Zhang

Supersymmetry (MSSM)

• 1st two generations of squark masses now constrained to be degenerate to same level of precision in both Q=+2/3 and -1/3 sectors!

• Historically used as a theoretical assumption, now determined experimentally

• Degenerate squarks lead to large squark production cross section @ Tevatron/LHC

Other Supersymmetric Contributions are Negligible

Box diagram exchange:• 1 neutralino + 1 gluino with up/charm-

squarks mass insertions, subleading to 2 gluino graph by

(g/gs)2

• Neutralinos with up/charm-squarksmass insertions, suppressed by (g/gs)4

• Charginos with d/s/b-squarksdiagonal squark propagators, flavor violation from

CKM structure SUSY-GIM cancellation in effect as d/s/b-squarks are essentially degenerate

• Charged Higgssmall, as shown aboveThis is a very different situation than with Bd

and Bs mixing!

Supersymmetry with Alignment

• Quark & squark mass matrices are approximately aligned and diagonalized such that gluino interactions are flavor diagonal

• Squark mass differences are not constrained

• Bounds from Kaon mixing prevent generation of Cabibbo angle in the down-sector

Nir, Seiberg

Sets mq ≥ 2 TeV

Difficult @ LHC!

~

Supersymmetry with R-Parity Violation

Most general superpotential allows for B & L violating terms which also violate R-parity

Many constraints on these couplings from rare processes

RPV Contributions to D Mixing

L ≠ 0 terms:

B ≠ 0 given by slepton d-squark No tree-level contribution!

TakingFactor of 50 (250) stronger than previous bounds for i = 2 (3) !

Taking strengthens the bound by factor of ~ 4

Constraints on R-Parity Violation

Setting

Extra Dimensions: Split Fermion Scenario

• Gauge boson Kaluza Klein states couple via overlap of wavefunctions

• Generates FCNC by rotation to quark mass basis

•Fermions localized at specific locations in extra flat dimension•Suppresses proton decay•Generates fermion hierarchy

Arkani-Hamed, Schmaltz

Constraints on Split Fermion Scenario

Distance between u- & c-quarks in 5th dimension

Compactification scale

u- & c-quarks are localized very close or extra dimensions unobservable @ VLHC

Constraints from Other Meson Mixings

• D Mixing• K Mixing

• Bs Mixing

• Bd Mixing

• Each system constrains different quark spacings

• D Mixing gives strongest constraints!

Extra Dimensions: Universal Extra Dims

• All SM fields in TeV-1, 5d, S1/Z2 bulk

• No branes! translational invariance is

preserved tree-level conservation of

p5

• KK number conserved at tree-level: broken at higher order by boundary terms

• KK parity conserved to all orders, (-1)n

Appelquist, Cheng, Dobrescu

Spectrum looks like SUSYSizeable effects in B & K systems (Buras etal)

UED: Negligible Effects in D Mixing

KK mass spectrum:

Boundary terms: Primarily affects 3rd generation

UED GIM: exact cancellation level by level in KK tower!

n n

n

n

Extra Dimensions: Warped Geometries

Based on Randall-Sundrum modelsBulk = Slice of AdS5

•SM in the bulk•Induces tree-level FCNC

•Result dependent on fermion localization

Planck brane TeV brane

Constraints on Warped Geometries

1st gauge KK state M > 2-3 TeVRestricts LHC search range

3 popular scenarios for fermion placement in the bulk

Unparticle Physics

Based on nontrivial scale invariance in the IR– Scale invariant stuff cannot have definite mass

(masses can be rescaled by a scale transformation)

– A free massless particle is scale invariant – In QFT, fields can also be multiplied by fractional

powers of a rescaling parameter unparticles!– Related to formal work in conformal theory– Unparticles interact w/ SM fields and match onto

Banks-Zak operators at scale

• What do unparticles look like in the laboratory?

Banks, Zaks

Georgi

Unparticle stuff with scale dimension d looks like a non-integral number of invisible particles

Constraints on Unparticles from D Mixing

JLH, T Rizzo, in prep

Probes the Planck scale!

Operator for D mixing: (1/) (d-1) c( + r5)u + hc-

r = 1 LHr = 0 Vr = -1 RH

Summary of Model Constraints

Conclusions

• Observation of D-mixing yields stringent bounds on New Physics

• These bounds surpass or compete with other constraints

• These bounds affect collider(LHC) physics

• Look forward to future experimental refinements!

• Observation of CP Violation would be clear signal of New Physics…