Theore cal developments in the physics ofcharm quarks

Alexey A. Petrov
Wayne State Universitytiti

The 20th Lomonosov Conference on Elementary Par cle Physics
LomCon20,
Moscow, August 19-25, 2021
Alexey A Petrov (WSU)
Moscow State University, August 19-25,
2021

Introduc on: charming results– Charm quark con nue to churn out surprises!
• spectroscopy: from X(3872) to X(6900) to pentaquark to Tcc+?
qc̄cq̄
cq̄cq̄
cc̄cc̄
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CP (KK⇡⇡) = ( 15.4 ± 2.9) ⇥ 10 4

• D-mixing: y > x?
y = 0.68+0.06
0.07
x = 0.37 ± 0.12%<latexit sha1_base64="13DjZ/0QhQShSfFxIBMEYtkXMSU=">AAACA3icbZDLSgMxFIYz9VbrbdSdboJFEMRhRktbF0LRjcsK9gLtOGTSTBuayQxJRihDwY2v4saFIm59CXe+jZm2iLcfQj7+cw7J+f2YUals+8PIzc0vLC7llwsrq2vrG+bmVlNGicCkgSMWibaPJGGUk4aiipF2LAgKfUZa/vAiq7duiZA04tdqFBM3RH1OA4qR0pZn7ozgGbStcvUmPbQtuzz20iN9V8aFgmcWNU0E/4IzgyKYqe6Z791ehJOQcIUZkrLj2LFyUyQUxYyMC91EkhjhIeqTjkaOQiLddLLDGO5rpweDSOjDFZy43ydSFEo5Cn3dGSI1kL9rmflfrZOooOqmlMeJIhxPHwoSBlUEs0BgjwqCFRtpQFhQ/VeIB0ggrHRs0xBOM5W/Vv4LzWPLObFKV6Vi7XwWRx7sgj1wABxQATVwCeqgATC4Aw/gCTwb98aj8WK8TltzxmxmG/yQ8fYJYbeUSw==</latexit><latexit sha1_base64="TEeQxZFmgsRug0kz0PN/ZEw+je8=">AAACAXicbVDLSsNAFJ3UV42vqBvBzWApuApJW6wuhKIblxXsA5pQJtNJO3TyYGYillA3/oobF4q49S/c+TdO2iBqPXC5h3PuZeYeL2ZUSMv61ApLyyura8V1fWNza3vH2N1riyjhmLRwxCLe9ZAgjIakJalkpBtzggKPkY43vsz8zi3hgkbhjZzExA3QMKQ+xUgqqW8c3MFzaJnVuhMHqtsV6JSh4+h63yhZpjUDXCR2TkogR7NvfDiDCCcBCSVmSIiebcXSTRGXFDMy1Z1EkBjhMRqSnqIhCohw09kFU1hWygD6EVcVSjhTf26kKBBiEnhqMkByJP56mfif10ukf+qmNIwTSUI8f8hPGJQRzOKAA8oJlmyiCMKcqr9CPEIcYalCm4dwluHk++RF0q6YdtWsXddKjYs8jiI4BEfgGNigDhrgCjRBC2BwDx7BM3jRHrQn7VV7m48WtHxnH/yC9v4Fg2qTNw==</latexit>– Maybe the rst signs of New Physics
will come from charm…

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Alexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Charming CP-viola on

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LomCon20, Moscow, August 19-25, 2021

Charming CP viola on• How can CP-viola on be observed in charm system?
– can be observed by comparing CP-conjugated decay rates invarious ways, both with and w/out me dependence– can manifest itself in charm ∆C=1 transi ons (direct CP-viola on)(D ! f ) 6= (CP [D] ! CP [f ])dCPV– or in ∆C=2 transi ons (indirect CP-viola on): mixing
2M12 i 12
2
Rm = |q/p| =⇥m (i/2)⇥
2

2= 1 + Am ⇥= 1

CPVmix– or in the interference b/w decays (∆C=1) and mixing (∆C=2)
CPVint19

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Alexey A Petrov (WSU)

Introduc on: nonleptonic charm decays?
★ Can be classi ed by SM CKM suppression of tree amplitude (Vus ~ )ud¯⇤Vcs Vud★ Cabibbo-favored (CF: 0) decays- originates from c → s ud
- examples: D0 →K-π+q̄⇤Vcs(d) Vus(d)

u
¯ s̄
d,

★ Singly Cabibbo-suppressed (SCS: 1) decayd, s- originates from c → q uq
- examples: D0 →ππ and D0 → KKq̄u⇤
Vcd Vuss̄d★ Doubly Cabibbo-suppressed (DCS: 2) decay- originates from c → d us
- examples: D0 →K+π-q̄★ We shall concentrate on SCS decays. Why is that?
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𝛌18Alexey A Petrov (WSU)

Direct CP-viola on in charm: reali es of life
★ IDEA: consider the DIFFERENCE of decay rate asymmetries: D →ππ vs D → KK!

For each nal state the asymmetry

D0: no neutrals in
the final state!

directmixinginterference★ A reason: amKK=amππ and aiKK=aiππ (for CP-eigenstate final states), so, ideally,
mixing asymmetries cancel (rf=Pf/Af)!

★ ... and the resulting DCPV asymmetry is

aCP = adKK

ad⇡⇡ ⇡ 2adKK (double!)⇤
GF ⇥(T + E + Psd ) + a 4 e i Pbd
AKK = p2⇤
GF ⇥( (T + E) + Psd ) + a 4 e i Pbd
A⇡⇡ = p2

★ ... so it is doubled in the limit of SU(3)F symmetry

SU(3) is badly broken in D-decays
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Afrtermath• Experimental results– note that while the new result does cons tute an observa on ofCP-viola on in the di erence…
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CP = aCP (K K )aCP (⇡ ⇡ + ) = ( 0.156 ± 0.029)%

LHCb 2019– … it is not yet so for the individual decay asymmetries
LHCb 2017• Need con rma on from other experiments (Belle II)• What does this result mean? New Physics? Standard Model?
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Theore cal troublestiAlexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Calcula ng CP-asymmetries?
• E ec ve Hamiltonian for singly Cabibbo-suppressed (SCS) decays– drop all “penguin” operators (Qi for i ≥ 3) as Ci are small,– recall that

andwithout QCD
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Alexey A Petrov (WSU)

with QCD
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CP-asymmetry: topological avor ow• Topological avor- ow diagrams could be used to deal
Recent: B. Bhattacharya, A.
with hadronic uncertain es
Datta, AAP, J. Waite, 2107.13564
T and CA and ESE
• Fit many decay modes, assume SM weak phase!
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Alexey A Petrov (WSU)• All SCS decays can be wri en in terms of the set of avor
ow diagrams

H.-Y. Cheng, C.W. Chiang
Phys.Rev.D 100 (2019) 9, 093002

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CP-asymmetry: topological avor ow

CP-asymmetry: topological avor ow• Fits to experimental data in SCS and CF results in
H.-Y. Cheng, C.W. Chiang
Phys.Rev.D 100 (2019) 9, 093002
but see also:
B. Bhattacharya, A. Datta, AAP,
J. Waite, 2107.13564• Individual asymmetries:• Asymmetry di erences

Consistent with Standard Model?
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Theore cal troubles★ But these asymmetries are notoriously di cult to compute★ In the Standard Model- need to estimate size of penguin/penguin contractions vs. tree
- unknown penguin contributions- SU(3) analysis: some ME are enhanced?
Golden & Grinstein PLB 222 (1989) 501; Pirtshalava & Uttayarat 1112.5451- could expect large 1/mc corrections (E/PE/PA/…)
Isidori et al PLB 711 (2012) 46; Brod et al 1111.5000- flavor-flow diagrams
Broad et al 1203.6659; Bhattacharya et al PRD 85 (2012) 054014;
Cheng & Chiang 1205.0580; 1909.03063; Gronau, Rosner★ General comments on SU(3)/flavor flow — type analyses- fit both SM and (possible) NP parts of the amplitudes: can one claim SM-only?
- many parameters: can one claim O(10-4) precision if rates are known to O(10-2)?

★ Need direct calculations of amplitudes/CPV-asymmetries- QCD sum rule calculations of aCP- SU(3) breaking analyses of D → PV, VV

Khodjamirian, AAP- constant (but slow) lattice QCD progress in D →Hansen, Sharpe

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Alexey A Petrov (WSU),CP-asymmetry: LCSR evalua on• Recipe for calcula on of CPV asymmetry– prepare decay amplitudes (and using– add and subtract), put in a new form

– de ne things we cannot compute (extract from branching ra os)– … and things we can

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Alexey A Petrov (WSU)dCPV: calcula ng matrix elements• Evaluate (leading) diagrams contribu ng to the correla on func on– calculate OPE in terms of known LC DAs

Khodjamirian, AAP: PLB774 (2017) 235– extract A⇡⇡ and AKK amplitudes from measured branch. frac ons

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Alexey A Petrov (WSU)LCSR: predic ons• As a result…

• Thus,and with

adir
CP =

2rb sin (rK sin K + r⇡ sin ⇡ )s(d)• Phases of r⇡⇡(KK) are given by the phases of P⇡⇡(KK) ?
Yes:

No:

Khodjamirian, AAP: PLB774 (2017) 235• Again, experiment:tiAlexey A Petrov (WSU)<latexit sha1_base64="ixEIIHv/gAQWaE0qP1+LI7iQlvU=">AAACFHicbZDLSsNAFIYnXmu9RV26GSyFiliSel8IxbpwWcFeoIlhMp20QycXZiZCCXkIN76KGxeKuHXhzrdx2mahrT8MfPznHM6c340YFdIwvrW5+YXFpeXcSn51bX1jU9/aboow5pg0cMhC3naRIIwGpCGpZKQdcYJ8l5GWO6iN6q0HwgUNgzs5jIjto15APYqRVJajH1jXhEkEkZPU6ul90qU8hZewdGiUzZNTaEU+NMpG5WLfKkJHLygeC86CmUEBZKo7+pfVDXHsk0BihoTomEYk7QRxSTEjad6KBYkQHqAe6SgMkE+EnYyPSmFROV3ohVy9QMKx+3siQb4QQ99VnT6SfTFdG5n/1Tqx9M7thAZRLEmAJ4u8mEEZwlFCUEVAsGRDBQhzqv4KcR9xhKXKMa9CMKdPnoVmpWwelSu3x4XqVRZHDuyCPVACJjgDVXAD6qABMHgEz+AVvGlP2ov2rn1MWue0bGYH/JH2+QONLZqr</latexit>adir
CP = ( 0.156 ± 0.029)%
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LomCon20, Moscow, August 19-25, 2021

Charming mixing

Alexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Charming mixing★ How can one tell that a process is dominated by long-distance or short-distance?

★ To start thing off, mass and lifetime differences of mass eigenstates...
xD =

M2

M1
D

, yD =

21

2 D★ ...can be calculated as real and imaginary parts of a correlation function
Z
n
o
1
4
| C|=1| C|=10yD =Im hD | i d x T Hw(x) Hw(0) |D0 i
2MD D
bi-local time-ordered product


Z
n
o
1
| C|=20
4| C|=1| C|=100xD =Re 2hD |H|D i + hD | i d x T Hw(x) Hw(0) |D0 i
2MD D
bi-local time-ordered productlocal operator(b-quark, NP): small?

★ … or can be written in terms of hadronic degrees of freedom…
1y=2
Alexey A Petrov (WSU)

n
n

⇥

0
D |HWC=1 |n⇥ n|HWC=1 |D ⇥ +
0

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⇤

D |HWC=1 |n⇥ n|HWC=1 |D0 ⇥LomCon20, Moscow, August 19-25, 2021

Mixing: short-distance computa on★ SD calculation: expand the operator product in 1/mc, e.g.

★ Note that 1/mc is not small, while factors of ms make the result small- keep Vub ≠ 0, so the leading SU(3)-breaking contribution is suppressed by b2 ~ 10
- ... but it is tiny, so look for SU(3)-breaking effects that come from mass insertions
and quark condensates
12 =

LO:
NLO:

2
s

ss
12

2 sd
12 +

H. Georgi, …
I. Bigi, N. Uraltsev

dd
12+2 s bO(ms4)
O(ms3)

sd
12

dd
12

2
b

O(ms2)
O(ms1)

dd
12

O(1)
O(1)

M. Bobrowski et al
JHEP 1003 (2010) 009
E. Golowich and A.A.P.
Phys. Lett. B625 (2005) 53- ... main contribution comes from dim-12 operators!!!

Guestimate:
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LomCon20, Moscow, August 19-25, 2021
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Alexey A Petrov (WSU)x ~ y ~ 10-3 ?

Scale-se ng in charm mixing?
★ SD calculation: non-universal perturbative scales?

★ Recall:★ Why should the contributions to dd-, sd-, and ss- be evaluated at
the same scale?
Lenz, Piscopo, Vlahos
arXiv:2007.03022

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LomCon20, Moscow, August 19-25, 2021

Scale-se ng in charm mixing?
• Scale uncertainty: varia on of scale from M/2 to 2M– Try varying scales in dd-, sd-, and ss- independently– Try phase-space modulated:

µss
1 =µ

2✏

µsd
1 =µ

✏

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µsd
1 =µ
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LomCon20, Moscow, August 19-25, 2021

Things to take home
Ø Philosophy: does exclusive approach to mixing constitute a prediction?
Ø Computation of charm mixing amplitudes is a difficult task
– no dominant heavy dof, as in beauty decays– light dofs give no contribution in the flavor SU(3) limit

Ø Charm quark is neither heavy nor light enough for a clean application ofwell-established techniques– “heavy-quark-expansion” techniques miss threshold effects– “heavy-quark” techniques give numerically leading contribution that isparametrically suppressed by 1/m6
– “hadronic” techniques need to sum over large number of intermediate states,
AND cannot use current experimental data on D-decays– “hadronic” techniques currently neglect some sources of SU(3) breaking– “quark-level” computation needs to be revisited!

Alexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Things to take home
Ø Theory/Experiment relation:❌

Theory❌

Experiment ❌

Experiment✔

Not a very interesting case…

SM wins again?

TheoryTheory✔

Theory✔

Experiment❌

Experiment✔

SM wins again!

New Physics!

Ø Observation of CP-violation in the current round of experiments could have provided
a “smoking gun” signals for New Physics- But latest LHCb observation seem to be broadly consistent (?) with SM<latexit sha1_base64="ixEIIHv/gAQWaE0qP1+LI7iQlvU=">AAACFHicbZDLSsNAFIYnXmu9RV26GSyFiliSel8IxbpwWcFeoIlhMp20QycXZiZCCXkIN76KGxeKuHXhzrdx2mahrT8MfPznHM6c340YFdIwvrW5+YXFpeXcSn51bX1jU9/aboow5pg0cMhC3naRIIwGpCGpZKQdcYJ8l5GWO6iN6q0HwgUNgzs5jIjto15APYqRVJajH1jXhEkEkZPU6ul90qU8hZewdGiUzZNTaEU+NMpG5WLfKkJHLygeC86CmUEBZKo7+pfVDXHsk0BihoTomEYk7QRxSTEjad6KBYkQHqAe6SgMkE+EnYyPSmFROV3ohVy9QMKx+3siQb4QQ99VnT6SfTFdG5n/1Tqx9M7thAZRLEmAJ4u8mEEZwlFCUEVAsGRDBQhzqv4KcR9xhKXKMa9CMKdPnoVmpWwelSu3x4XqVRZHDuyCPVACJjgDVXAD6qABMHgEz+AVvGlP2ov2rn1MWue0bGYH/JH2+QONLZqr</latexit>adir
CP = ( 0.156 ± 0.029)%

LHCB-PAPER-2019-006- Maybe if we only have a reliable calculation of the SM effects…
Khodjamirian, AAP: PLB774 (2017) 235
Chala, Lenz, Rusov, Scholtz: JHEP 1907 (2019) 161
Alexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Alexey A Petrov (WSU)

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LomCon20, Moscow, August 19-25, 2021

Experimental analysis from LHCb
★ Since we are comparing rates for D0 and anti-D0: need to tag the flavor at
production

D⇤+ ! D0 ⇡s+“D*-trick” -- tag the charge of the slow pion(or muon for D’s produced in B-decays)★ The difference ∆aCP is also preferable experimentally, as
detect, ⇡sdetect, D
prod
CP
araw
=
a
+
a
+
a
+
a
f
f
D
D⇤
f

detection
asymmetryof D0

physics

detection
asymmetry ofsoft pion

production
asymmetryof D*+★ D* production asymmetry and soft pion asymmetries are the same for
KK and ππ final states-- they cancel in ∆aCP!

★ Integrate over time,
aCP, f =Z 1
0★ Viola! Report observation!
Alexey A Petrov (WSU)

aCP (f ; t)D(t)dt = adf +hti inda⌧ f

distribution of proper decay time

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LomCon20, Moscow, August 19-25, 2021

dCPV: calcula ng matrix elements
Khodjamirian, NPB 605 (2001) 558• Use modi ed light-cone QCD Sum Rule (LCSR) method– start with the correla on func on (and)– use dispersion rela on in (p-k) and (p-q), perform Borel transform,
Khodjamirian, Mannel, Melic, PLB571 (2003) 75
extract matrix element:s– perform LC expansion of F(s, s’ mD2) to get P⇡⇡– note that

with

thus
5
ti

ti

ti

ti

fi

Alexey A Petrov (WSU)

LomCon20, Moscow, August 19-25, 2021

Error budget: parameter uncertain es

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LomCon20, Moscow, August 19-25, 2021
ti

Alexey A Petrov (WSU)