Flavour in the

era of the LHC 

A Model-Independent Analysis

of New Physics Contributions

in |F| = 2 transitions J. CHARLES (CPT Marseille), H. LACKER (Dresden University),

A. ROBERT, S. MONTEIL (LPC IN2P3 – University Blaise Pascal)

on behalf the CKMfitter group

November 7-10th 2005

Outline – New Physics in |F|=2 transitions1

Part I. Introduction. Part II. Exploring New Physics in Bd mixing. Basic inputs. Adding and measurements. Adding aSL contribution.

Part III. Exploring New Physics in K mixing.

Part IV. Prospective for New Physics in the Bs mixing.

Quality of CKM Standard fit

Standard Model accommodates successfully

all the present flavour data.

2

There is no need a priori for NP contributions in tree-mediated flavour changing processes.

00

0022

BSMeffHB

BfulleffHB

diedr

Modelling New Physics in |B|=2

Assumption no NP in tree-mediated decay amplitudes: |Vub|/|Vcb| and are the main inputs constraining the CKM parameters.

Introduce NP inB=2 transitions accounted for model-independently through two additional parameters.

Is there still room for new physics ?Follow the strategy developed in the paper: The CKMfitter group, Eur. Phys. J. C41 (2005)

Past & present attempts (a selection of)Soares, Wolfenstein, Phys. Rev. D47 (1993)

Grossman, Nir, Worah, Phys. Lett. B407 (1996)Laplace, Ligeti, Nir, Perez, Phys. Rev. D65 (2002)

Ciuchini et al., hep-ph/0307195Bona et al., hep-ph/0509219

3

NP in Bd-Bd mixing (I)

)22cos(

)22sin(

,2

d

d

dd

cbub

mr

VV

• The SM value on 2d=0 is at the border of the CLMax region.

• Shows slight disagreement between Vub and sin(2.

Remove b-> scomponent from the inclusive Vub average Vub=(4.15 ±0.12 ±0.23).10-3

• Any region with 2d > /2 is discarded.

4

NP in Bd-Bd mixing (II)

)(

)22cos(

)22sin(

/2

GGSZGLWADS

mr

VV

d

d

dd

cbub

Adding measurements.

• Two solutions for NP parameters emerge.

• Vub and constrain the CKM parameters.

5

NP in Bd-Bd mixing (III)

Adding measurements.

)222sin(

)22cos(

)22sin(

/2

d

d

d

dd

cbub

mr

VV

The constraint (w/o ) displays also four solutions.

Reinforce the SM region but the preferred NP region is not the one defined by .

6

NP in Bd-Bd mixing (IV)

)222sin(

)(

)22cos(

)22sin(

/2

d

d

d

dd

cbub

GGSZGLWADS

mr

VV

and are of major importance in constraining the NP parameters.

NB: sin(d) is not included. (almost no influence.)

7

NP in Bd-Bd mixing aSL in the game

212

122

12

12SL

2cosIm

2sinRe

d

dSM

d

dSM

rMrMa

Though the experimental precision is far from the prediction, aSL is a crucial input for constraining NP parameters. Only observable depending on both rd

2 and 2d.

(12/M12 is considered here at Leading Order)

aSL= -0.0026 ± 0.0067(HFAG 2005)

8

deg3.52

92.0

2.38.8

73.023.0

2

d

dr

NP parameters extraction

SL

)(

2

)222sin(

)22cos(

)22sin(

/

a

mr

VV

d

GGSZGLWADS

d

d

dd

cbub

The NP solution at has 1-CL < 3%.

9

(Uncertainties are given at 1)

2/BdBd ff 10/

BdBd ff

10/dd BB

Influence of non-pert. hadronic parameters in md

2*22

2

2

)(6

dtbtdtWdBBBF

d rVVxSmBfmG

mdd

• As far as the lattice uncertainties are considered, fBd is the relevant parameter to improve. • A factor 2 has important impact. A factor 10 is not decisive with the current experimental uncertainties of the observables.

10

2/dd BB 10/dd BB

Alternative parametrization of NP in |B|=2

))1(

Im(

)1(22

1

212

12

2

2

d

d

d

id

SM

SM

SL

id

SMd

idd

ehMa

ehArg

mehm

)1( 21212

didSM ehMM

Without and aSL constraints

Isolate the pure NP contributionfrom (SM+NP) terms:

11

With and aSL constraints

Agashe et al. hep-ph/0509117

65.006.008.0

dh

Allowing in addition NP in K-K mixing (I)

00

00

Im

Im

KSMeffHK

KfulleffHK

rK

KK

d

d

d

dd

cbub

r

a

GGSZGLWADS

mr

VV

SL

2

)222sin(

)(

)22cos(

)22sin(

/

45.046.0

09.1

deg1.41.9

8.42

76.025.0

92.02

K

d

d

r

r

12

(1)

Allowing in addition NP in K-K mixing (II)

13

The NP region at 2d=/2 in Bd mixing implies also NP in K mixing corresponding to K< 0

14 NP in Bs mixing Prospective study (I)

s~ can be extracted from

the global Standard Model fit.

The angle governing the mixing in the Bs system is already known to good precision in the SM

sins =

*

*

argtstb

cscbs

VV

VV

15 NP in Bs mixing Prospective study (I)

NP in Bs mixing (B=2 and S=2) is accounted for model-independently through two additional parameters, akin to the Bd system :

00

00

SM

full22

ss

ss

BeffHB

BeffHBs

iesr

KDB

KDB

BJBJB

A

DBm

d

sss

csss

smix

sss

(*)

-1

fromdeg859

fromdeg14572

and / ,/ combinedfrom

028.0036.0)2sin(

fromps 011.0000.20

)22sin(

)22sin(

2

ss

ss

ss mr

• LHCb expected sensitivities correspond to 2 fb-1 (See Talks of O.Schneider & L.Fernandez):

NP in Bs mixing Prospective study (II)16

deg6.17.1

1.02

11.009.0

01.12

s

sr

(1)

)22sin(

)22sin(

)222sin(

ysensitivit LHCb Adding

)(

)22cos(

)22sin(

/

2

2

SL

2

ss

ss

ss

KK

d

d

d

dd

cbub

mr

r

a

GGSZGLWADS

mr

VV

10s

CONCLUSIONS17

• Bd mixing: which room for new physics ? ... Not much.

• K mixing: the only constraint is from k under constrained pb as far as specific NP phase & modulus are considered.

• Bs mixing: LHCb will immediately see NP if O(10°).

APPENDIX

I Main inputs to the fit

|Vub| (average) = (4.15 ± 0.12 ± 0.23).10-3

|Vcb| (incl) = (41.58 ± 0.45 ± 0.58).10-3

|Vcb| (excl) = (41.4 ± 2.1).10-3

|K| = (2.282 ± 0.017).10-3

md = (0.509 ± 0.004) ps-1

sin(2) = 0.687 ± 0.032

S+-= -0.50 ± 0.12

C+- = -0.37 ± 0.10

C00 = -0.28 ± 0.39

B,all charge Inputs to isospin analysisS+-

L = -0.22 ± 0.22C+-

L = -0.02 ± 0.17BL,all charge Inputs to isospin analysisB3 Time dependent Dalits analysis

BD(*) K(*)(-) Inputs to GLW,ADS & GGSZ analysis

mK = (3.490 ± 0.006).10-12 MeV

BK = 0.79 ± 0.04 ± 0.09

mK+ =(493.677 ± 0.016) MeV

fK= 159.8 ± 1.5 MeV

tt= 0.5765 ± 0.0065

ct= 0.47 ± 0.04

B(MS) = 0.551 ± 0.007

fBd√Bd =(223 ± 33 ± 12) MeV

aSL= - 0.0026 ± 0.0067

II measurements

Adding B

22

2

2

22

2

18

)( ubB

B

BBF Vfm

mm

mGBBR

• Powerful in the future for constraining the SM region.• Potential annihilation by means of H+ prevents for considering this input in the analysis.

With md, removethe fB dependence

III