Rare Charm Decays

0.1 MB·English

by  Sandip Pakvasa

Rare Charm Decays
5
S. Pakvasaa
0
0
aDepartment of Physics and Astronomy
2
University of Hawaii, Honolulu, HI 96822
n
a
J Rare FCNC decay modes of charmed mesons are reviewed. The standard model predictions, including both
short distance and long distance contributions, are summarized. Several new physics options that can give
4
detectable signals are described.

1
v
4
1
1. INTRODUCTION after several surprising enhancements. However,
0
even this is very small compared to the long dis-
1 ThemainreasonthatD0 D¯0 mixingandrare
0 − tance contributions from s and u channel poles
(FCNC)decaysofcharmmesonsareinterestingis
5 from nearby states and VMD contributions from
0 theexcitingpossibilityofnewphysicsbeyondthe ρ,w,φ..Theseestimatessufferfromuncertainties
/ Standard Model(SM) being visible. In turn this
h fromseveralsources. Themassmcistoolargefor
is the case since the GIM mechanism suppress-
p the chiral symmetry approximation and it is too
- ingFCNCtransitionsissonearlyperfectandthe small for the HQET approximation. Hence, one
p contribution of b quarks is suppressed. There is
e hastoresorttoinspiredguesswork[1,2,3]. Inany
potentially a large window for new physics. The
h case, the end results seem reasonable and vindi-
: major obstacle in this endeavor is the fact that cated by recent measurements. The are in the
v
i thelongdistanceeffectscanbelargeandfurther- range of 10−5 to 10−7. The recent mBeasurement
X more are not always reliably calculable. of (D0 φ0γ) 2.6 10−5 by BELLE [4] is
r What one can do is calculate both short and welBl withi→n the ex∼pected×range.
a
longdistancecontributionsasreliablyaspossible
The bottomlineisthatitisextremelyunlikely
inSMandconsiderpossiblenewphysicsscenarios
that new physics in the short distance c uγ
with potentially large effects. →
can be separated from the much larger SM long
distance(LD) contributions.
2. STANDARD MODEL
2.1. Radiative Decay Modes 2.2. Really Rare Decay Modes
FirstconsiderradiativemodesofthekindD We now turn to rare decay modes which have
→
Vγ D Vγ. The short distance effective a better chance for new physics to show up [5,6].
, s
Hamiltoni→an for c u+γ is given by The decay mode D0 γγ is also long distance
→ dominated, the larges→t contribution coming from
4G 10 the on-shell KK, KK∗ and K∗K∗ intermediate
F
Heff =− √2 XCi(µ)Oi(µ) (1) states,withanestimateof(1 3) 10−8forthe ,
i=1 tobecomparedto3 10−11f−rom×ashortdistanBce
×
where c are the Wilson Coefficients that carry estimate. The current bound is 3 10−5.
i
×
the content of the short distance physics inside The mode D0 µ+µ− has a short distance
→
the loop and O are the relevant operators. Ma- contribution to of 10−18; the LD contribution
i
B
trix elements will contain long distance physics. is dominated by on-shell γγ states and with the
New physics can affect the matching conditions aboveestimateforγγ,onefindsaBRintherange
at µ = M. In the SM the predicted branch- (3 8) 10−13. The e+e− mode in the SM is
− ×
ing ratio ( ) for c uγ is found to be 10−8 suppressed by (m /m )4.
e µ
B → ∼
1
2
The dilepton modes of the kind D Xℓ+ℓ− If one works in a basis which diagonalizes the
→
are very interesting. The SD component can be fermionmassmatrices,thensfermionmassmatri-
calculated and LD component is estimated with ces(andthussfermionpropagators)willgenerally
the dominant contribution coming from specific be nondiagonal. As a result, flavorchangingpro-
hadronicstates. Intermediatevectormesonstates cesses can occur. One can use phenomenology to
give rise to sharp peaks. The estimates for the restrict these FCNC phenomena. The Q= 1/3
−
branching ratios are 10−6 for D+ π+ℓ+ℓ− sector has yielded fairly strong constraints but
and 10−5 for D πℓ∼+ℓ−. → thusfaronlyD0-D¯0mixinghasbeenusedtolimit
s
→
Otherdilepton modes whichare relativelyrare the Q = +2/3 sector. In our analysis, we have
are D+ e+ν ,D e+ν , and D0 l+l−γ taken charm FCNCs to be as large as allowedby
e s e
→ → →
with expected of3 10−9,1.6 10−7 and10−9 the D-mixing upper bounds.
B × ×
repectively. For the decays D X ℓ+ℓ−, the gluino con-
u
→
tributions will occur additively relative to those
3. NEW PHYSICS ANALYSIS from the SM and so we can write for the Wilson
coefficients,
Onecanconsidera widevarietyofnew physics
scenarios which can contribute to rare D decays C =C(SM)+Cg˜. (3)
i i i
[5,6,7,8]. For example (i) Supersymmetry, either
MSSM or R-parity violating, (ii) new degrees of Togetsomefeelingfordependenceonthe(δ1u2)λλ′
freedomsuchas(a)extrascalars,(b)extragauge parameters, we display the examples
bosons, (c) extra fermions, (d) extra dimensions, Cg˜ (δu ) and(δu ) , Cg˜ (δu ) ,(4)
(iii) new strong dynamics such as varieties of 7 ∝ 12 LL 12 LR 9 ∝ 12 LL
Technicolor, top condensates etc., (iv) others. whereas for quark helicities opposite to those in
Someofthesegiverisetopotentiallyobservable the operators of Eq. (4), one finds
ratesforsomeoftherarecharmdecaymodes. We
review these below. Cˆ7g˜ ∝ (δ1u2)RRand(δ1u2)LR, Cˆ9g˜ ∝ (δ1u2)RR.(5)
3.1. MSSM Moreover,the termin Cˆg˜ whichcontains (δu )
7 12 LR
In MSSM there are new Flavor Changing cou- experiences the enhancement factor Mg˜/mc.
plings and there are possible large contributions For some modes in D Xuℓ+ℓ−, the effect
→
to some rare decay modes. of the squark-gluino contributions can be large
To calculate R-parity conserving SUSY contri- relative to the SM component, both in the total
butions,oneemploystheso-calledmass insertion branching ratioandfor certainkinematic regions
approximation. of the dilepton mass. The mode D0 ρ0e+e− is
→
Inthisapproach,asquarkpropagatorbecomes especiallyinterestingsincethe canbeashighas
B
modified by a mass insertion that changes the 1.3 10−5 (only a factor of 10 below the current
×
squark flavor. For convenience, one expands the bound) and the enhancement is in the low m2
ee
squarkpropagatorinpowersofthe dimensionless region.
quantity (δiuj)λλ′, 3.2. R-parity violating SUSY
(Mu)2 The effect of assuming that R-parity can be
(δiuj)λλ′ = Mij2λλ′ , (2) violated is to allow additional interactions be-
q˜ tween particles and sparticles. Ignoring bilinear
where i = j are generation indices, λ,λ′ denote terms which are not relevant to our discussion of
thechira6lity,(Mu)2 aretheoff-diagonalelements FCNC effects, we introduce the R-parity violat-
ij
of the up-type squark mass matrix and M rep- ing (RPV) super-potential of trilinear couplings,
q˜
resents the average squark mass. The exchange
= ǫ [1/2λ LaLbE¯ +λ′ LaQbD¯ (6)
of squarks in loops thus leads to FCNC through W6Rp ab ijk i j k ijk i j k
loop diagrams. + 1/2ǫ λ′′ U¯αD¯βD¯γ]
αβγ ijk i j k
3
where L, Q, E¯, U¯ and D¯ are the standard chiral Table 1
super-fieldsoftheMSSMandi,j,karegeneration fortheSMandRPVSUSY(Seereferences5-8).
B
indices. The quantities λijk, λ′ijk and λ′i′jk are a Decay Mode B SM B 6RP
prioriarbitrarycouplingswhichtotal9+27+9= D+ π+e+e− 2 10−6 2.3 10−6
→ × ×
45 unknown parameters in the theory. Presence D+ π+µ+µ− 1.9 10−6 1.5 10−5
→ × ×
of leptoquarks is phenomenologically identical to D0 ρ0e+e− 1.8 10−6 5 10−6
→ × ×
RPV SUSY. D0 π0e+e− 0.8 10−6
→ ×
For our purposes, the presence of RPV means D0 π+νν¯ 5 10−16
that tree-level amplitudes become possible in D0 →K¯0νν¯ 2.×4 10−16
→ ×
which a virtual sparticle propagates from one of Ds π+νν¯ 8 10−15
→ ×
thetrilinearverticesinEq.(7)toanother. Inpar- D0 γγ (1 3)10−8
→ −
ticular,theFCNCsectorprobedbycharmdecays D0 µ+µ− (3 8)10−13 3 10−6
→ − ×
involvesthe λ′ . Introducingmatrices , D0 e+e− 10−23 10−10
to rotate lef{t-hiajkn}ded up-quark fields andULrigDhtR- D0 →µ±e∓ 0 10−6
→
handed down-quark fields to the mass basis, we D+ π+µ±e∓ 0 3 10−5
→ ×
obtain for the relevantpart of the superpotential D0 ρ0µ+e− 0 1.4 10−5
→ ×
D0 e+e−γ 10−9 5 10−9
Wλ′ = λ˜′ijk[−e˜iLd¯kRujL−u˜jLd¯kReiL (7) D0 →µ+µ−γ 10−9 5×10−8
(d˜k)∗(e¯i )cuj +...] , D+→ e+ν 3 10−9 10×−3
− R L L D →e+ν 10×−7 10−2
s
whereneutrinointeractionsarenotshownandwe →
define
λ˜′ λ′ L ∗R . (8)
ijk ≡ irsUrjDsk Forexample, (D eν )canbeaslargeas10−4
τ
Somebounds onthe{λ˜′ijk}arealreadyavailable and B(Ds →Beντ)→can be as large as 5×10−3;
from data on such diverse sources as charged- these are to be compared to the SM rates for
current universality, the ratio Γπ→eνe/Γπ→µνµ, D →eνe of3×10−9 andDs →eνe of1.6×10−7.
the semileptonic decay D Kℓν , etc. There are also enhancements in D e+e−γ and
ForthedecayD+ π+→e+e−,tℓheeffectispro- D0 µ+µ−γ, this time at high q2→and the BR
portional to λ˜′ λ˜→′ . Although the effect on can→beenhancedbyasmuchas20fortheµ+µ−γ
11k · 12k
thebranchingratioisnotlarge,thedileptonspec- mode.
trumawayfromresonancepolesissensitivetothe
3.3. Extra Scalars and Fermions
RPV contributions.
Another interesting mode is D0 µ+µ−. With extra scalarbosons which couple to both
→ quarks and leptons, decay modes such as D0
Upon using the bound, we obtain →
µ+µ− andD0 µ−e++µ+e− canbe enhanced.
6Rp <3.5 10−6 . (9) Thisisalsotru→eofnewgaugebosons(e.g. gauged
BD0→µ+µ− ×
family symmetry). Extra quarks of charge -1/3
A modest improvement in the existing limit on
and extra leptons can also perform the same
BD0→µ+µ− will be very interesting. function. In all these, as high as 10−10 for
Lepton flavor violating processes are allowed B
D0 µ+µ− and 10−13 for D0 µ−e++µ+e−
by the RPV lagrangian. One example is the → →
can be reached.
mode D0 e+µ−, for which existing parameter
→
bounds predict 3.4. Large Extra Dimensions
For several years, the study of large extra di-
6Rp <0.5 10−6 (10) mensions (‘large’ means much greater than the
BD0→µ+e− × Planck scale) has been an area of intense study.
In RPV SUSY, there are also potentially large This approach might hold the solution of the hi-
contributions to several other dilepton modes. erarchy problem while having verifiable conse-
4
quences at the TeV scale or less. Regarding the 4. SUMMARY AND CONCLUSIONS
subjectofrarecharmdecays,one’sreactionmight
I wouldliketo think thatI haveconvincedyou
be to ask, “How could extra dimensions possibly
that there are opportunities in the Q=+2/3 sec-
affect the decays of ordinary hadrons?” We pro-
tor. There are large windows of opportunities
vide a few examples in the following.
for newphysics toappearinmanymodes despite
Supposethespacetimeofourworldamountsto
large long distance effects.
a 3+1 brane which together with a manifold of
In the near term it will be very interesting
additional dimensions (the bulk) is part of some
to improve bounds on modes such as D0
higher-dimensional space. A field Θ which can →
µ+µ−, D ρℓ+ℓ−, D πℓ+ℓ− and search
propagate in a large extra dimension will exhibit → →
for D/D eν and study D ℓ+ℓ−γ.
aKaluza-Klein(KK)towerofstates Θn ,detec- s → →
{ }
tion of which would signal existence of the extra
5. ACKNOWLEDGEMENT
dimension. Given our ignorance regarding prop-
erties ofthe bulk orofwhichfieldsareallowedto I would like to thank the organizers, and es-
propagate in it, one naturally considers a variety
pecially Nick Solomey, for outstanding hospital-
of different models. ity and a stimulating meeting. I thank my col-
Assume, for example, the existence of an extra
laborators Gustavo Burdman, Gene Golowich,
dimension of scale 1/R 10−4 eV such that the JoAnne Hewett, and also Svetlana Fajfer and
∼
gravitational field (denote it simply as G) alone PaulSinger for many enjoyable discussions. This
can propagate in the extra dimension. There are
work was supported in part by US.D.O.E under
then bulk-gravitonKK states Gn which couple Grant #DE-FG02-04ER41291.
{ }
to matter. In principle there will be the FCNC
c u Gn transitions and since the Gn remain REFERENCES
→ { }
undetected, there will be apparent missing en-
ergy. However this mechanism leads to too small 1. G. Burdman, E. Golowich, J. Hewett and S.
a rate to be observable. Pakvasa,Phys. Rev. D52, 6383 (1995).
Another possibility which has been studied is 2. C. Greub, T. Hurth, M. Misiak, and D.
that the scale of the extra dimension is 1/R Wyler, Phys. Lett. B382, 415 (1996).
∼
1 TeV and that SM gaugefields propagatein the 3. C. Bajc, S. Fajfer and R. Oakes, Phys. Rev.
bulk. However, precision electroweak data con- D54, 5883 (1996); S. Fajfer, S. Prevlosekand
strain the mass of the first gauge KK excitation P. Singer, Eur. Phys. J. C6, 47 (1999).
to be in excess of 4 TeV, and hence their contri- 4. O. Tajima et. al. (the Belle Collaboration),
butions to rare decays are small. Phys. Rev. Lett. 92, 101803 (2004).
More elaborate constructions,such as allowing 5. G. Burdman, E. Golowich, J. Hewett, and S.
fermionfieldstopropagateinthefive-dimensional Pakvasa,Phys. Rev. D66, 014009(2002).
bulk of the Randall-Sundrum localized-gravity 6. S. Fajfer, S. Prevlosek and P. Singer, Phys.
model, are currently being actively explored. Rev. D64, 11409 (2001); S. Fajfer, P. Singer
andJ.Zupan,Phys.Rev.D64,074008(2001).
7. S. Fajfer, P. Singer and J. Zupan, Eur. Phys.
J. C27, 2001 (2003).
3.5. Strong Dynamics 8. A. G. Akeroydand S. Recksiegel,Phys. Lett.
New strong interactions can be responsible B554, 38 (2003).
for electro-weak symmetry breaking and/or the
fermion masses. Some examples are top conden-
sates, extended technicolor etc. In general these
canleadtoFCNCcouplingsofZ cuandhence
→
to decay modes such as D0 µ+µ− at a level of
→
10−10.