PRECISION FORM FACTORS OF PIONS , KAONS & PROTONS at the highest timelike momentum transfers & FIRST MEASUREMENTS OF HYPERONS

Electromagnetic form factors of hadrons for timelike momentum transfers can be measured by particle-antiparticle annihilation into hadron-antihadron pairs. We have made the world’s first high precision measurements of timelike form factors of π and K mesons, and ground states of the baryons, protons, and the hyperons Λ0 , Σ0 , Σ+ , Ξ0 , Ξ– , Ω– at the high momentum transfers of 14.2 and 17.4 GeV2 . Limitations of perturbative QCD are revealed, and evidence is presented for the effects of diquark correlations in Λ0 and Σ0 .


Timelike Momentum Transfers -Preliminary
• For baryons, there are two form factors, the Pauli and Dirac form factors, or more familiarly, the magnetic   () and the electric   () form factors.
• For  +  − →  the differential cross section is   (, )   =          𝟐  + cos   + /    ()  sin • At large squared momentum transfers, s, the quantity  = 4  2 / becomes small, the contribution of    becomes small, and it becomes difficult to determine it.
• According to the dimensional counting rule of QCD, the above cross section decreases as s -5 , making it extremely difficult, if not impossible, to measure baryon form factors for | 2 | ≡  > 20.
• For pseudoscalar mesons,  and K, with zero spin, there is only one form factor,   (), and the differential cross section is   (, )   =      |   |  sin   Further, the cross sections decrease only as s - 3 , making life at large |Q 2 | easier!

Timelike Form Factors of the Proton
• Spacelike form factors of the proton have been measured since the 1980's, and precision measurements have existed for Q 2 up to 31 GeV 2 .
• Prior to 1993, measurements of the timelike form factors of the proton by the reaction  +  − →  were sparse, had large errors, and were confined to |Q 2 | < 5.7 GeV 2 .
•  1.The quark distribution in the proton is not like a Mercedes star , with the three quarks having identical distributions but diquark-quark , with a preferential pairing of the two identical u-quarks.
2. |Q 2 | = 13 GeV 2 is not large enough for pQCD to be valid.
• Although no alternate explanations have been offered, the diquark-quark model did not acquire acceptance.More about this later.
• To test the second possibility, the validity of pQCD at large |Q 2 |, we have made high precision measurements of   () to timelike   = 14.2 and 17.4 GeV 2 .using data taken at the  +  − CESR collider at Cornell, and the detector CLEO-c.

PREJUDICES & OBSTACLES
• In trying to measure form factors at a collider like CESR at Cornell, one has to overcome two big obstacles.
1.The first is the prejudice that only weak interaction flavor physics is important, the rest has little priority.It is an uphill battle to get the required beam time allocated for form factor measurements.
2. The second obstacle is more generic.Everybody loves resonances, and they want to love to run on peaks of resonances.
• Unfortunately, hadron form factors are not weak interaction physics and you do not want to measure on the peaks of vector resonances which directly decay into e + e -.
• Unless, of course, you can show that the resonances at which you want to run have negligibly small cross sections for decay into the hadron pairs of your interest, i.e., () ⟶  +  − .Our measurements are based on just this fact being true for resonances above  threshold at 3.73 GeV, so that we are able to use data taken at (3770) and (4160) to measure form factors.
• An important pQCD prediction is that since both leptonic and hadronic decays of charmonium resonances depend on wave functions at the origin, the ratios of their branching fractions are identical, (  ′ ) / (()) to hadrons = (  ′ ) / (()) to leptons • This simple prediction allows us to estimate branching fractions for a specific hadronic decay of a resonance (n') if that same decay has been measured at another resonance (n).Since, ℬ  3770 ,  4170 →  +  − / ℬ  3686 →  +  − = 0.36,1.04× 10 −3 , we conclude that the branching fractions for the hadronic decays of (3770) and (4160) are more than three orders of magnitude smaller than the corresponding measured decays of (3686).
• With nearly 5 million (3772) and (4160) each, formed in the present measurements, and our detection efficiencies, we estimate resonance events The observed counts for each decay turn out to be about 100 times larger than these resonance contributions.Therefore, all observed  +  − → , ,  , and hyperon yields we observe can be attributed to form factors.
The CLEO-c detector is a cylindrical general purpose detector.The detector components important for the present measurements are the CsI electromagnetic calorimeter, the drift chamber for charged particle detection, and the RICH detector, all of which are located in a 1 Tesla solenoidal magnetic field.The acceptance for photons and charged particles in the central detector is | cos | < 0.8.Charged particle resolution is   / = 0.6% @ 1 GeV/c.Photon resolution is   / = 2.2% @1 GeV, and 5% @ 100 MeV.
• Despite > 300 observed counts, we are not able to determine   /   .

FORM FACTORS OF PIONS AND KAONS
I now turn to the form factors of pions and kaons 1.The first thing to notice is that for spin zero pseudoscalars like  ± , K ± there is no magnetic form factor*, and there is just one form factor.  • As you will see, excellent timelike form factor data for  and K at large Q 2 now exist.It is a pity that the corresponding spacelike data do not exist to allow us to determine if the ratio F ,K (timelike)/F ,K (spacelike) ≈ 2, as it is for protons.
• Timelike form factors of any hadron can be determined by measuring ( +  − →  +  − ),  = , , , hyperons, but one has to reject 3 to 4 orders of magnitude larger background of QED-produced e + e − and μ + μ − pairs, and substantial tails of lighter hadrons.
• Cabibbo anecdote!Theoretical Implications (cont'd) • This leads to the serious problem that even the ratio, which is supposed to remove the dependence on the assumed identity of pion and kaon wave functions, is predicted to be   /   =   2 /   2 = 0.67 ± 0.01 This is (36±1)% smaller than our measurement of 1.09±0.04for |Q 2 |=17.4GeV 2 .

Measurements of Pion and Kaon Form Factors
• With the precision of our measurements, it is quite obvious that something is very wrong.
Kamal K. Seth, 10/28/2013 21 Could it be the assumed identity of the  and K wave functions ?Could it be that pQCD is not valid even for   = . GeV  ?
Theoretical Implications (cont'd) • Since the relation    2 /    2 =   2 /   2 is based on assuming identical wave functions for pions and kaons, Lepage and Brodsky (1980) conjectured that because the s-quark in the kaon is ∼27 times heavier than the ,  quarks in the pion, and the SU(3) flavor symmetry is broken, the kaon wave function may differ from the pion wave function by acquiring an asymmetric component, and account for the observed violation of the above relation.

Estimating SU(3) Breaking in the Kaon
• Lepage and Brodsky (1980) suggested that a large violation of the   /  =   2 /  2 identity can arise if there is a substantial SU(3) breaking effect in the kaon wave function.They predicted that a large SU(3) breaking effect would lead to a large form factor for the neutral kaon, and      /   +  − of the order one, and suggested that      should be measured.
• Following this suggestion, we have made the first ever measurement of the form factor      (|  |) at |Q 2 | = 17.4 GeV 2 .
• Since the cross section for  +  − →     is expected to be small, and we do not attempt to detect K L= , careful criteria for event identification had to be developed, and their efficacy tested.We have done so by measuring (2) →     for |Q 2 | = 13.6 GeV 2 using the same event selection criteria as for |Q 2 | = 17.4 GeV 2 , and confirmed that we obtain ℬ((2) →     ) in agreement with its known value.
• For  +  − →     at  = 4.17 • In other words, the SU(3) breaking effect on the ratio is found to be small, certainly much less than of "the order of one".
• To come back to the original problem of   /  (expt.) ≠   2 /   2 , it is now apparent that it can not be attributed to SU(3) breaking alone.The problem remains unresolved.
• Here is a challenge worthy of the best theoretical attempts.

Form Factors of Hyperons
• I already told you that in 1960, before quarks were even proposed, but strangeness and strange baryons, the hyperons, were known, Cabibbo and Gatto wrote the classic papers on the measurement of timelike form factors by e + e - hadron-antihadron.They discussed the proton and neutron, and pion and kaon, and went on to say that it would be very interesting to measure hyperon form factors.But they noted that the cross sections are likely to be very small, and despaired whether they could be measured.
• And now we have measured hyperon form factors for the first time* with good precision at the large momentum transfer of |Q 2 | = 14.2 GeV 2 .
• We identify the hyperons by their dominant decays.These (and their branching fractions) are: *Recently BaBar [PRD 76, 092006 (2007)] reported form factor measurements for ΛΛ and Σ 0 Σ 0 using the ISR method.While they have good statistical precision near threshold, the number of observed events decreases rapidly, and for  2 > 9 GeV 2 they are only able to obtain upper limits.

Form factor events
Form Factors of Hyperons -Results • The numbers of events ( ) in the signal region leads to the Born cross section ο = ( )/(ℒ), where ε is the MC-determined efficiency, ℒ = 802 pb -1 is the  +  − luminosity, and C = 0.76 -0.78 is the correction factor for initial state radiation.The cross section is related to the form factors as   =     /     + /     .
• In the table we quote our results for   14.2 GeV 2 assuming    =    for both charged and neutral hyperons, because at  ≡  2 = 14.2 GeV 2 , finite values of    are possible even for the neutral hyperons.

F
,K (spacelike) Data limited to Q 2 < 2.5 GeV 2 for  Q 2 < 0.12 GeV 2 for K Spacelike Form Factors of Pions and Kaons • Spacelike form factors of mesons are very difficult to measure, because meson targets do not exist.Two different methods have been used.1. F  and F K from Elastic Scattering of pions/kaons off atomic electrons, (K)e − → (K)e − .Unfortunately, in this approach the momentum transfer is very small.At CERN for 200 GeV pions, Q 2 () ≤ 0.25 GeV 2 and Q 2 (K) ≤ 0.11 GeV 2 were realized.2. F  from Electroproduction of pions, e − p → e −  + n, has serious theoretical problems and uncertainties.The good precision data are confined to Q 2 < 2.45 GeV 2 (JLab).F K from Electroproduction of kaons -No data exist.

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I will not bore you with the nitty-gritty of how using all the detector components of CLEO-c, the drift chambers, the central calorimeter, the RICH detector, and muon detector, we were able to identify , K, and p cleanly, in presence of the monstrous backgrounds of electrons and muons.Here is how clean!  ≡   + +   − /  3.77 GeV -MC 3.77 GeV -Data 4.17 GeV -Data • The angular distributions for both pions and kaons at both  = 3772 MeV and 4170 MeV fit very well the sin 2  distribution for electric form factors.There is little evidence for 1 + cos 2  distribution contribution expected for a magnetic form factor.The important experimental results are: 1.There is a remarkable agreement of the form factors for both pions and kaons with the dimensional counting rule prediction of QCD, that |Q 2 |F ,K are nearly constant, varying with |Q 2 | only weakly as  S (|Q 2 |). 2. The existing theoretical predictions for pions underpredict the magnitude of F  (|Q 2 |) at large |Q 2 | by large factors, ≥ 2. 3. The big surprise is that while pQCD predicts that F  /F K =(f  /f K ) 2 =0.67±0.01,we find: F  / F K = 1.21 ± 0.03, at |Q 2 | = 14.2 GeV 2 , F  / F K = 1.09 ± 0.04, at |Q 2 | = 17.4 GeV 2 .Theoretical Implications Lattice lives in Euclidean time, and is not capable of addressing timelike form factors.So we expect no lattice-based predictions for form factors, and have to live with predictions based on QCD-based models for timelike form factor predictions.• The starting point of the existing calculations is factorization, with    =  in ×   ×  out The meson wave functions  in,out represent soft components, not calculable perturbatively.T H represents the hard interaction, "hopefully calculable in perturbative QCD." • Since ab initio the quark wave functions are not known, various empirical wave functions have been used.Lepage and Brodsky used the asymptotic wave function    ∝   ( − ) where the  and  share momenta equally.Chernyak and Zhitnitsky used the QCD sum-rule-inspired wave function ()  ∝ ( −   )    which produces a two humped distribution.

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While large differences in pion and kaon wave functions were proposed by Chernyak & Zhitnitsky (1984), recent quenched lattice calculations (Braun et al., PRD 74, 074501 (2006)), and AdS/CFT light-front QCD model calculations (Brodsky and de Teremond, arXiv:0802.0514[hep-ph](2008)), predict a much smaller asymmetric component in the kaon wave function, and a much smaller effect of SU(3)-breaking than CZ proposed.• It has been suggested that an experimental determination of the effect of SU(3)-breaking can be made by measuring the form factor of the neutral kaon, and we are making such a measurement CZ kaon wave functions Lattice  and K wave functions GeV, we obtain 4 events in the signal region, and a Monte Carlo background estimate of 2 counts.This leads for |Q 2 | = 17.4 GeV 2 to:        = . ×  − , 90% CL of  − . ×  −        /   +  −   = ., 90% CL of  − ..

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We have developed very successful event selection criteria to measure branching fractions for () → hyperons.The figure shows the extremely clean hyperon event distributions as a function of  = ( ℎ + (ℎ ))/ .• Using the same event selections we have analyzed our data of L = 805 pb -1 at  = 3.772 GeV, or |Q 2 | = 14.2 GeV 2 for form factor decays of hyperons.

the momentum transfer is large enough for perturbative QCD to be valid.
+  − →  +  − ,  +  − =     | ,  | At that time, the discussion could only use the small amount of small Q 2 data for F  with larger errors which was available then.

and at large |Q 2 | one could, in principle, have magnetic form factors! Form Factors of Pions and Kaons (pre-1990)
F ,K (timelike) For |Q 2 | > 5 GeV 2 Up to ±100% errors

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As we go from protons to hyperons, serially replacing one, two, or three up/down quarks with strange quarks, what do we expect to learn at |Q 2 | = 14.2 GeV 2 ?•

Do we see SU(3) breaking effects? Do we see diquark correlation effects?
2re    for hyperons proportional to   , as for nucleons?Do neutral hyperons have finite   (2