Toward a coherent picture

of diphoton and flavour anomalies

Dario Buttazzo

Physik-Institut - Universitat Zurich

LNF Frascati, 28 - 4 - 2016

based on arXiv:1604.03940 in collaboration with A. Greljo, G. Isidori, D. Marzocca

Motivation 1(a): LFU in charged currents

Violation of lepton flavour universality in b c decays:

RD() =B(B D() )B(B D()`)

R(D)0.2 0.3 0.4 0.5 0.6

R(D

*)

0.2

0.25

0.3

0.35

0.4

0.45

0.5BaBar, PRL109,101802(2012)Belle, PRD92,072014(2015)LHCb, PRL115,111803(2015)Belle, arXiv:1603.06711

) = 67%2HFAG Average, P(SM prediction

= 1.02

R(D), PRD92,054510(2015)R(D*), PRD85,094025(2012)

HFAGPrel. Winter 2016

4 excess over the SMprediction

Good agreement between3 different experiments

15% enhancement oftree-level LL amplitude(bLcL)(L )

Motivation 1(b): LFU in neutral currents /e universality in b s transitions

RK =B(B K+)B(B Ke+e)

q2[1,6] GeV

= 0.745+0.0900.074 0.036

LHCb 1406.6482

B K+ angular distribution (P 5)LHCb-PAPER-2015-051

Altmannshofer and Straub, 1411.3161

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2-1.0

-0.5

0.0

0.5

1.0

C9

=-C10

C9e

=-

C10e LF

U

Combined fit: 3.9over the SM prediction

15% contribution tothe LL operator(bLsL)(LL)

Motivation 1: LFU in B decays

I Dynamical assumption: New Physics in Left-handed currents.

I Flavour structure: approximate U(2)5 symmetry.

Specific realisations involve heavy vectors:

Vector triplets Greljo, Isidori, Marzocca 1506.01705

Vector leptoquarks Barbieri, Isidori, Pattori, Senia 1512.01560

Motivation 2: the diphoton excess

Searches for resonances inpp at the LHC:excess of events atm = 750 GeV in bothATLAS and CMS

For narrow resonance, localsignificance 3.6 (ATLAS)and 3.4 (CMS).

() []

Data consistent with a (pseudo)-scalar particle gg X .

13 TeV(pp ) B( ) = 4.7+1.21.1 fbsee e.g. B, Greljo, Marzocca 1512.04929

5

Motivation (2): Diphoton resonance excess

! " # $

Figure 7: Combination of the diphoton cross section from ATLAS [1] and CMS [2] with both 8 and13 TeV data, interpreting the resonance as a narrow-width pseudoscalar produced in gluon fusion.

Acknowledgments

This research was supported in part by the Swiss National Science Foundation (SNF) undercontract 200021-159720. We thank Jonas Lindert and Jernej F. Kamenik for useful discussions.

A Updated diphoton signal-strength combination

Our combination of the most recent analysis of the diphoton excess performed by ATLAS [1]and CMS [2], is shown in Fig. 7. We use the published CMS combination of the 8 TeV and13 TeV data (red solid line), while the ATLAS 8 TeV (dotted blue) and 13 TeV (dashed blue)constraints are extracted from the available information by assuming they follow a Poissondistribution, as already done in Ref. [24]. The 13 TeV distribution is obtained by imposing thata 3.5 significance (for the narrow-width case) and an observed excluded cross section at 95%CLof excl95%CL = 10/acc fb are reproduced, where acc 0.6 is our estimate of the acceptance in thefiducial region [24]. The 8 TeV distribution is instead obtained imposing a 1.9 significance anda compatibility with the 13 TeV data of 1.2 assuming production via gluon-fusion. The finalcombination is shown in Fig. 7 (black solid line), and corresponds approximately to

13 TeV(pp ) B( ) = 4.7+1.21.1 fb . (65)

27

Figure 7: Combination of the diphoton cross section from ATLAS [1] and CMS [2] with both 8 and13 TeV data, interpreting the resonance as a narrow-width pseudoscalar produced in gluon fusion.

Acknowledgments

This research was supported in part by the Swiss National Science Foundation (SNF) undercontract 200021-159720. We thank Jonas Lindert and Jernej F. Kamenik for useful discussions.

A Updated diphoton signal-strength combination

Our combination of the most recent analysis of the diphoton excess performed by ATLAS [1]and CMS [2], is shown in Fig. 7. We use the published CMS combination of the 8 TeV and13 TeV data (red solid line), while the ATLAS 8 TeV (dotted blue) and 13 TeV (dashed blue)constraints are extracted from the available information by assuming they follow a Poissondistribution, as already done in Ref. [24]. The 13 TeV distribution is obtained by imposing thata 3.5 significance (for the narrow-width case) and an observed excluded cross section at 95%CLof excl95%CL = 10/acc fb are reproduced, where acc 0.6 is our estimate of the acceptance in thefiducial region [24]. The 8 TeV distribution is instead obtained imposing a 1.9 significance anda compatibility with the 13 TeV data of 1.2 assuming production via gluon-fusion. The finalcombination is shown in Fig. 7 (black solid line), and corresponds approximately to

13 TeV(pp ) B( ) = 4.7+1.21.1 fb . (65)

27

Why diphoton searches? Clean signal over smooth and well known background (e.g. H(125)!) Several extensions of the Standard Model predict high-mass states

decaying to two photons Benchmark models

Marco Delmastro Diphoton searches in ATLAS 2

Spin-2 analysise.g. Randall-Sundrum graviton

Spin-0 analysise.g. extended Higgs sector

2HDM" 5 physical states h0, H0, A0, H

" Under certain conditions, scalar and/or pseudo-scalar states can have sizable branching ratio to diphoton

Model predicts tower of Kaluza-Klein graviton states with TeV mass scale

Phenomenology" mG* = mass of lightest KK excitation" /MPl = dimensionless coupling to SM

fields

X

?

Diphoton resonance searches at ATLAS and CMS:Excess of events at m ~ 750 GeV

Local significance (narrow width):ATLAS: 3.6CMS: 3.4

All data consistent with (pseudo)scalar resonance signal: g g X ! !

ATLAS-CONF-2016-018 CMS-PAS-EXO-16-018

See for example: [Buttazzo, AG, Marzocca]

WARNING

The following content is based on the assumption that the abovehits for new physics are not a statistical fluctuation. No warranty is

given about the correctness of this assumption. Any reference toreal phenomena is (probably) purely accidental. The authorsdecline any liability or responsibility for taking the following

speculations too seriously.

Is there a way to fit all these anomaliesin a single, coherent picture?

The model

A new strongly-interacting sector, with vector-like fermions ,and a confined gauge group SU(NTC)

Approximate global symmetry SU(NF )L SU(NF )R U(1)

SM

confines at ~ TeV

elementary TC fermions

SU(NTC)L, R

pNGB: , , 0, F pp

Vector mesons: , 0, , RD() , RK

Greljo, Isidori, Marzocca 1506.01705

The model

A new strongly-interacting sector, with vector-like fermions ,and a confined gauge group SU(NTC)

Approximate global symmetry SU(NF )L SU(NF )R U(1)

SU(NF)L x SU(NF)R x U(1)V

SU(NF)V x U(1)V

SM

confines at ~ TeV

elementary TC fermions

SU(NTC)L, R

pNGB: , , 0, F pp

Vector mesons: , 0, , RD() , RK

Greljo, Isidori, Marzocca 1506.01705

The model

A new strongly-interacting sector, with vector-like fermions ,and a confined gauge group SU(NTC)

Approximate global symmetry SU(NF )L SU(NF )R U(1)

SU(NF)L x SU(NF)R x U(1)V

SU(NF)V x U(1)V

SM

confines at ~ TeV

elementary TC fermions

SM gauging SU(NTC)L, R

pNGB: , , 0, F pp

Vector mesons: , 0, , RD() , RK

Greljo, Isidori, Marzocca 1506.01705

The model

A new strongly-interacting sector, with vector-like fermions ,and a confined gauge group SU(NTC)

Approximate global symmetry SU(NF )L SU(NF )R U(1)

SU(NF)L x SU(NF)R x U(1)V

SU(NF)V x U(1)V

SM

confines at ~ TeV

elementary TC fermions

SM gauging

mixingqL, L TC

baryons

SU(NTC)L, R

pNGB: , , 0, F pp

Vector mesons: , 0, , RD() , RK

Greljo, Isidori, Marzocca 1506.01705

Pseudo Nambu-Goldstone bosons

The theory condenses at a scale f :

ij = f2B0ij

SU(NF )L SU(NF )R SU(NF )V : N2F 1 Goldstone bosons.

The global symmetry SU(NF )V is explicitly broken by the massterms M and by SM gauge interactions D.

LPT =f2

4

(Tr[(D)

(D)]

+ 2B0(Tr[M] + Tr[M]))

= exp(

2if taa)

is the pNGB matrix;

M = diag(mi) is the TC-quark mass matrix;B0 20 f in QCD

Example: for (1,2, Y ), |a = 12|LaL, m = 2B0mL.

Chiral anomalyCoupling to SM gauge fields through anomaly. For a singlet :

LWZW

162f

(g21A

BBBB

+ g22AWWW

iW

i + g

23A

GGG

AG

A

)

Agg = 2NTCTr[tTaT a], AWW = 2NTCTr[t

i i], ABB = 2NTCTr[tY2].

(no coupling to gluons for a non-singlet neutral state, e.g. 0)

Decay widths:

=2

643A

m3f2,

gg =2s

643Agg

m3f2.

Fitting the diphoton signal

f (70 80 GeV)NTC(assuming gg gg, , V V )

- - -

-+

[]

(

)[]

Coupling to SM fermions

Assumption

The 3rd generation of SM fermions couple to the compositesector through mixing with a suitable set of TC baryons.

Lmix q qLBq + ` LB`

L = g (aq BqBq + a` B`B`)

(gq qLqL + g` L`L

)

B

B

V

SM

SM

The couplings of vector mesonsto different TC-baryons are notuniversal (depend on the flavourstructure of the baryons andmesons)

An explicit example: minimal model SU(5)

coupling to quarks & gg anomaly coloured TC-fermions coupling to doublets qL, `L at least a SU(2)L-doublet TC-quark

Minimal field content: {Q (3,1, YQ), L (1,2, YL)} 5 + 5.

SU(5)L SU(5)R SU(5)V : 24 pNGBFlavour structure GSM irrep pNGB Mass m2

V (QQ) (8,1, 0) 2B0mQU (LQ) (3,2, YQYL) B0(mL +mQ) (LL) (1,3, 0) 2B0mL

3(LL) 2(QQ) (1,1, 0) 25B0(3mL + 2mQ)

Plus gauge corrections m2 ' 32

162

i g

2iC

(i)2 (

a) (0.1 0.3m)2

An explicit example: minimal model SU(5)NTC = 3: two choices of YQ,L that give baryons with quantum n. of q, `

|B`(B`)(1,2,1/2) |LLL, |Bq(3,2,1/6) |QQL,

for {YQ, YL} = { 16 , 16} or {YQ, YL} = {0, 16}.No other mixing with SM states possible.

ABB = 2

3

5NTC

(Y 2L Y 2Q

), AWW =

1

2

3

5NTC , A

gg =

3

5NTC .

Assuming only decays through anomalies: f = 71 (79) NTC GeV.

(YQ, YL) RZ RZZ RWW

A: ( 16, 1

6) 6.7 11 37

B: (0, 16) 5.0 9.1 34

Experimental bounds:

RZ . 5.6, RZZ . 11, RWW . 36.

(see e.g. B, Greljo, Marzocca 1512.04929)

- - -

-+

[]

(

)[]

Vector resonances

|a(1,3,0) =12|LaL, |(1,1,0) =

12|LL, |(1,1,0) =

13|QQ.

(+ coloured states)Mass of vector mesons: m2Vij = c

20(4f)

2 + c21B0(mi +mj). (c0,1 . 1)

L = g (aq BqBq + a` B`B`)

and (LL) couple to both Bq andB`, a

q,` 2aq,` O(1).

(QQ) can couple via connecteddiagrams only to Bq, a

` 1,

aq

2/3 aq .

B

B

V

SM

SM

I Assuming similar coupling g for vector mesons and pNGB with thesame flavour composition (e.g. and ), g g/

15.

tt (3.3 GeV) m2

m2B

gBB2t2 B( tt) . 19%.

Another example: two doublets SU(8)

Next-to-minimal field content: {Q (3,2, YQ), L (1,2, YL)}

SU(8)L SU(8)R SU(8)V : 63 pnGBFlavour structure GSM irrep pNGB Mass m2

V, V, (QQ) (8,1, 0), (8,3, 0), (1,3, 0) 2B0mQU , U (LQ) (3,3,Y ), (3,1,Y ) B0(mL +mQ) (LL) (1,3, 0) 2B0mL

3(LL) (QQ) (1,1, 0) 12B0(3mL +mQ)

Many choices of YQ,L that give baryons with quantum numbers of q, `,but only two reproduce the signal: {YQ, YL} = { 12 , 16}, or { 16 , 12}.

A : |B`(1,2,1/2) |LLL, |Bq(3,2,+1/6) |QLL,B : |B`(1,2,+1/2) |QQQ, |Bq(3,2,1/6) |QQL.

RZ RZZ RWW

A, B 0.6 0.09 0 In both cases f = 70 NTC GeV.

Interlude: a U(2)5 flavour symmetry

An approximate symmetry of the SM quark Yukawa couplings:

VCKM

mu

md

Under U(2)q U(2)u U(2)d, the 3rd generation quarkstransform as a singlets, while the first two as doublets,

qL =

(qLq3L

), uR =

(uRtR

), dR =

(dRbR

).

If extended to the lepton sector, U(2)5.

Weakly broken by the spurions Vq 2q and V` 2`, plus lightfermion masses (e.g. yu (2q,2u)).

Barbieri et al. 1105.2296Barbieri, B, Sala, Straub 1203.4218

Vector resonances and flavour

I. The interactions between heavy vectors and SM fermions arise onlyfrom mixing between SM fermions and techni-baryons.

II. The mixing respects an approximate U(2)5 flavor symmetry: sizablemixing only with 3rd generation.

III. The leading corrections to the exact U(2)5 limit are obtained fromthe U(2)qL and U(2)`L spurion doublets.

B` ``i`iL , (` q), `(q)i =(`(q)1 ,

`(q)2 , 1

).

In the down-quark mass basis, (q1q2) = (Vtd, Vts) ( = 0: exact alignment).

Coupling to vector mesons

L g[aq

2q

qij

(qiL

qjL)

+ a` 2`

`ij

(iL

`jL)],

with `(q)ij

`(q)i

`(q)j .

Example: a colorless triplet

|a = 12

(LaL) (1,3, 0)

SU(2)L-triplet current:

Ja = gqijq

(qiL

aqjL)

+ g`ij`

(iL

a`jL), a = a/2.

L aJa L()4f = 1

2m2JaJ

a

Lc.c. = gqg`

2m2(V q)ij

`ab

(uiLd

jL

)(aL

bL

)+ h.c.,

LFCNC = gqg`

`ab

4m2

[qij(diLd

jL

) (V qV )ij

(uiLu

jL

)] [(aL`

bL

)(aL

bL

)],

LF=2 = g2q

8m2

[(qij)

2(diLd

jL

)2+ (V qV )2ij

(uiLu

jL

)2],

LLFV = g2`

8m2`ab

`cd(

aL`

bL)(

cL`

dL) ,

LLFU = 1

2m2

[g

2`

2`ab

`cd + g

2``ad

`cb

](aL`

bL)(

cL

dL) .

Parameters: `, qbs

Low-energy data fit Input data and . Parameters: q,` = gq,`mWgm , qbs, `.

Obs. Oi Prediction Oi(x) Experimental valueb c R0 `q 0.13 0.03b s C9 (/em)`(`q + 0` 0q) c

qbs/|V tbVts| 0.58 0.16

Bs mix RF=2Bs

(2q + (

0q)

2)|qbs|2 (|V tbVts|2R

loopSM )

1 0.10 0.07b c` Rebc 2`q` < 0.01

` R/e1 + 2``+ (0` )22`2 |`|22+ 2`+(0` )22 `2 1.0040 0.0032

3 2 (GF /

2)(2` + (

0` )

2)`

`h < 4.1 109 GeV2

D mix 2uc (GF /

2)(2q + (

0q)

2)|VubV cb|2 < 5.6 1014 GeV2

b s RK() 23 +13

1 + em (`q 0` 0q) qbs|V tbVts|CSM2 < 2.6

Color octet contribution to meson mixing: (0q)2 22O/3L gO2

qijVAqiLTAq

jL

Leptoquarks in the extended SU(8) model can also contributesee also Barbieri, Isidori, Pattori, Senia 1512.01560

Low-energy fit: results

!" #

!!"# !#"$ #"# #"$ !"#!!"#

!#"$

#"#

#"$

!"#

!

!"#$%&"'%()* !

!

"

#

!!"#!!"$ !"! !"$ !"#!!"!%!

!!"!!&

!"!!!

!"!!&

!"!%!

!"#

!"#$%&"'%()* !

!

"#

$%

!"! !"# !"$ !"%!!"&

!!"'

!!"(

!!"$

!"!

!"$

!! "!"!! !"#$#

!!

!"#$%&"'%()* !

Fit driven by R0(D) = q`. Small values of qbs Vts. Good fit to b c. Somewhat

smaller b s due to Bs mixingand /e constraints.

Only contribution from and

Low-energy fit: results

Including QQ and LL mesons

Excellent fit to b c andb s Size of qbs as expected Somewhat tuned

cancellation in Bs mixing

!" #

!!"# !!"$ !"! !"$ !"#!"!!

!"!%

!"$!

!"$%

!"#

!"#$%&"'%()* !

!

"

#

$%

!!"# !"! !"# !"$ !"%!#"$!#"!!!"&!!"'!!"(!!"$!"!!"$

!! "!"!! !"#$#

!!

!"#$%&"'%()* !

! " #

!!"!#!!"!$ !"!! !"!$ !"!#!"%

!"#

!"&

!"'

!"(

!")

!"*

+"!

" !! ! " #$!

!!!!

""#!

!"#$%&"'%()* !

LHC phenomenology: mesonsDue to large coupling, vector mesons decay mainly into 3rd gen. fermions.

0+ ( ) =g2`

96m , 0bb (tt) =

g2q32

m.

I is expected to be a broad resonance

0.01

0.2

0.5

0.01

0.2

0.5

R0

m = 1.7 TeV

-5 0 5-50

5

gq

g

0 / mDecays to pairs of pNGB through TCinteraction can also be sizable:

=g2192

m

(1 4m

2

m2

),

(L = g2

abca

bc)

I Main production channel: bb 0 single production.For gq = 5, m = 1.7 TeV, one finds bb/uu 7.

LHC phenomenology: 0 ATLAS search for Z decaying into +, 1502.07177

JHEP07(2015)157

hadhad channel

Z/ Multijet W/Z/+jets Top + diboson Z SSMPreselection 276(18) 611(5) 64(1) 24(2) 10.1(2)

OS 270(18) 316(4) 53(1) 21(2) 9.5(2)

(1, 2) > 2.7 117(2) 209(3) 35(1) 11(2) 9.2(2)

lephad channel

Z/ Jet fake Z/ $$ Top + diboson Z SSMPreselection 46 800(300) 154 670(130) 17 340(250) 12 330(70) 14.3(2)

OS 46 300(300) 111 270(120) 16 180(240) 11 830(70) 13.9(2)

($, ) > 2.7 32 200(300) 47 650(80) 12 490(210) 3530(40) 13.5(2)

mT < 50 GeV 29 490(230) 22 660(60) 11 240(210) 808(16) 8.5(2)

Table 3. Number of expected signal (mZSSM = 1750 GeV) and background events in the hadhadand lephad channels after successively applying each selection criterion. The statistical uncertaintyin the least significant digit(s) is shown in parentheses.

Eve

nts

1

10

210

310ATLAS

-1 = 8 TeV, 19.5 fbsData

*/Z

Multijet

*+jets/Z/W

Top + diboson

Uncertainty

(750)Z'

(1250)Z'(1750)Z'

) [GeV]missTE, had-vis, had-vis(totTm

200 300 400 500 1000Obs.

/ e

xp.

0.5

1

1.5 stat. sys.

Eve

nts

-110

1

10

210

310

410

510 ATLAS -1 = 8 TeV, 20.3 fbsData

*/Z

fakeJetll*/Z

Top + dibosonUncertainty

(750)Z'

(1250)Z'(1750)Z'

) [GeV]missTE, had-vis, l(totTm

70 100 200 300 1000Obs.

/ e

xp.

0.5

1

1.5 stat. sys.

Figure 6. The mtotT distribution after event selection in the (left) hadhad and (right) lephadchannels. The estimated contributions from SM processes are stacked and appear in the same orderas in the legend. The expected contributions from three Z SSM signals with masses of 750, 1250and 1750 GeV are shown, stacked on the total SM expectation. The events observed in data areoverlaid. The hatched area indicates the uncertainty on the total estimated background. The binshave a constant width of (left) 0.153 and (right) 0.184 in log(mtotT ). The last bin includes overflowevents. The inset shows the ratio of the observed events over the total expected SM contribution.The statistical uncertainty from the observed events and the expected SM contribution are shownon the points and by the yellow band, respectively. The red band depicts the total systematic andstatistical uncertainties on the SM contribution added in quadrature.

18

For large masses (above 1.5 TeV), basically one bin in totaltransverse mass: mTtot > 850 GeV.

95% C.L. exclusion above 1.5 TeV: < 4 fb (7 fb) for a narrowwidth (20% width).

LHC phenomenology: 0 Recast the exclusion approximating mTtot m :

0 / m0.010.20.5

m = 1.7 TeV pp @ 8 TeV

500 1000 1500 2000 2500 300010-810-610-410-2

m (GeV)

-1 d/dm

(GeV

-1 )+- invariant mass

8 4 2

1

0.4

R0 (gq=g)

pp @ 8 TeV1600 1800 2000 2200 24000

2

4

6

8

10

m (GeV)g q

=g

pp(m>850 GeV) (fb)

Cross-section (pp ), for m > 850 GeV

ATLAS bound: & 4 7 fb. The relevant region above 1.5 TeV stillallowed, but will be probed soon!

LHC phenomenology: 0 bb

Large coupling to t, b: bb is another relevant channel.CMS search for heavy resonances pp X jj/jb/bb, 1501.4198.

At present, limits notcomparable with channel,if gq g`. If gq & g`, it could also

become an interestingchannel soon!

(ATLAS results similar)

LHC phenomenology: Leptoquarks

The signal in pp (and pp bb) is a rather generic predictionin this framework, whatever the specific realisation.

Flavour anomalies at low pT High pT signatures at LHC

I The exchange ofLeptoquarks in the t-channelgives a very similar signaturein .

Summary

There are several intriguing experimental hints of newphenomena, both at low and high pT :

Lepton flavour universality violation in B decays,

Diphoton resonance at LHC.

They can be described by a single coherent picture, involvinga new strongly interacting sector and vectorlike confinement:

Singlet pNGB pp

Flavour effects due to exchange of vector resonances , , . . .

U(2) flavour symmetry: couplings mostly to 3rd generation, aspecific pattern of flavour violation in light generations.

A generic prediction: new resonances should be seen soon in , bb final states at the LHC!

A few comments

The models presented here are a sketch: many differentrealisations are possible: more states, different symmetrygroups, . . .

Many predictions qualitative, due to strong interactions.

Many experimental searches not optimized for this scenario.

Higgs not (yet) included in the picture: if new physics at theTeV, should be natural.

Is the embedding in SU(5) of the minimal scenario accidental?