Let's share together in a word of prayer. Father, we thank You for the great day we've already had. I thank You because my own heart is so full; I feel overwhelmed with all of the events of today, yesterday, and the past week. I pray, Lord, that I may somehow be able to be faithful to fulfill the expectation of these people who are so gracious to me and to my wife and family. Thank You, Father, for the high calling that You have given to all of us, and to me, especially to teach and present Your Word. Bless us tonight with Your Word; fill our hearts with joy as we share together, and also with conviction and insight, that we might understand what it really means to be salt and light in the world. May we really hear You speak.
Let's look at Matthew 5:13-16. Here, our Lord, in the Sermon on the Mount, directs His attention away from the multitudes to the group of disciples gathered closest to Him. He says to them, "You are the salt of the earth; but if the salt loses its flavor, how shall it be seasoned? It is then good for nothing but to be thrown out and trampled underfoot by men. You are the light of the world. A city that is set on a hill cannot be hidden. Nor do they light a lamp and put it under a basket, but on a lampstand, and it gives light to all who are in the house. Let your light so shine before men that they may see your good works and glorify your Father in heaven."
A magazine once carried a series of pictures that depicted one of the saddest stories imaginable. The first picture was of a vast wheat field in Kansas; it was a farm in Western Kansas. From horizon to horizon, all you could see was the wheat waving in the wind. The second picture was of a mother in distress inside her farmhouse in the middle of that wheat field. She had a small boy who had somehow wandered away from the house into that wheat field. The little fellow was so small that he couldn't be seen; she couldn't find him. She had called for her husband, and the two of them had searched all day long for that little boy, and they finally decided that they should call the neighbors, who began to search frantically all over the wheat field with no success. They knew the boy was too little to see above the wheat and find his own way out, so the picture showed her in great distress. The third photo depicted all the people who had heard of the little boy being lost. They gathered in the morning, joining their hands, hand-to-hand, and in a great, long line of humanity, linked only by their hands, swept from one end of that wheat field to the next. The last picture was a heartbreaker; it was a picture of the father standing over the body of his little son. They had finally found him, but he was dead. It was too late. A cold, cold night had claimed its victim. Underneath the final picture of a weeping father were these words, "Oh, God, if we had only joined hands sooner."
What a heart-searching story that is. Listen, people, Jesus said, as He looked out over the fields, "The field is white unto harvest, but the laborers are few." I really believe there is a world of lost men, lost women, lost boys and girls, way out in the field of the world. They can't find home, they can't find the Father's house, they can't see above the wheat of the world. They are perishing in the night of sin, and when the cold morning dawns, it will be too late. I believe the Lord Jesus Christ, here in Matthew 5:13-16, is saying to us, "Join hands. Be salt and light; sweep through the field of the world to find all of those who are desperately in need of your influence and your message." I don't think one or two can do it, I don't even think a handful can do it. I think the whole church has to join hands and be collective salt. Salt is useless as far as one grain is concerned, and light is a combination of fluorescence. We've got to take hands and sweep through the world, and that's the message that Jesus is giving us right here. We are salt and light to reach the lost with the Gospel of Jesus Christ, and this is the vital message contained in our Lord's words. He has followed up the Beatitudes. In the Beatitudes, He says, "Here is the character I expect you to have, and if you have this kind of character, then you are a child of My Kingdom. If you have this character, and are a child of my Kingdom, here is your job: sweep through the world as salt and light and make a difference." Jesus is calling on us, as we saw in our last study, to influence the world for His glory, to find the lost before it's too late. The key is what has gone on in the verses before. Having magnificently come to know the principles and the qualities that render us effective for God, that bring us into His Kingdom, that make us distinct from the world, He now tells us, "Move out into the world with that marvelous distinctiveness, find those that are lost, and bring them to Christ." The supreme matter in the Kingdom is character; character is the issue. The character described in the Beatitudes makes it possible for us to affect the world. You know, I really worry a lot in my own heart about Grace Community Church in this regard. I think we can get to the place where we are so in love with each other, if you will, where we are so thrilled about everything that goes on here. We can be so happy about it all, and sit in little groups and disciple each other, pray with each other, counsel each other, talk to each other, but the fact is, we're always in danger that we won't link hands and sweep through the world. We are in danger of never crawling out of our ivory tower of the bliss of our Christian fellowship. The Lord is saying that's something that we have to do. The emphatic is here - we are the only salt and we are the only light the world will ever know. Notice that the final Beatitude is transitional. The final Beatitude is in verse 10. "Blessed are they who are persecuted for righteousness' sake." Verse 11. "Blessed are you when men revile you, persecute you, say all manner of evil against you falsely." In other words, the world is going to hate us, and persecute us. We expect that to happen; we don't expect it to be easy. I believe it will get harder and harder all the time. It isn't going to get easier.
There is a little house next door to our church, and we had our special people in our house, handicapped people. They'd go in there for a few hours on a Sunday morning. But some judge somewhere ruled that a house cannot be used for religious purposes without a permit, even if you own the house. Sam Erickson, on our staff, called the city to find out about that and he said this, "You mean, if I want to have some people over to my house to study the Bible, we have to have a permit?" They said, "Yes." He said, "What if I want people to come over to my house to drink beer and watch pornographic movies, that's fine? But if we decided to talk about the Bible, we have to have a permit?" They said, "That's right." I don't know what that means for the future, but I don't think it's going to get any easier. I think the price will be paid.
I think God wants us to confront the world. Just because the world persecutes us, reviles us, and says all manner of evil against us falsely, just because it seems impossible that, in a country where the Constitution says no law could ever be passed that takes away any of the freedom of religion at all from anybody, we're facing the fact that you can't have a Bible study in your house without a permit. I really don't think that it will get any easier. I don't think that just because the world makes it tough on us that we should crawl in a hole or keep our mouths shut or hide. We should be like verse 13, salt and light in the world.
To better understand this concept, I told you last time that there are four great truths that you need to grip. First, the presupposition, then the plan, then the problem, then the purpose. I want to give you these quickly tonight; I know you heart is already full from so many other things today, and we've already had such a wonderful time, I don't want to just drag it out. I'm going to fire them at you quick, and I want you to get them.
The presupposition in this text is the decay and darkness of the world. The very text presupposes decay and darkness. Where you need salt, you have decay, and where you need light, there is darkness. Our Lord is saying, "Here is the presupposition: we are living in a decadent, dark world." That's what I was trying to say to you this morning - we've got to be different. We can't affect the world unless we are different. Our lives and relationships and homes have to be different. God could look at our world as He looked at that antediluvian, that pre-flood world. It says, "God saw that the wickedness of man was great in the earth, and every imagination of the thoughts of his heart was only evil continually." We live in a dark and decadent world; that is the presupposition to what Jesus says. Our world is a desperate world, and just because they make it hard on us, we can't stop preaching, because there is someone lost out in that field, and we have to sweep through the world no matter what the price.
The second thing we talked about last time was the plan. The presupposition is the darkness and decay of the world; the plan is the dominion of the disciples. We've got to move in the world and dominate it. Notice in verse 13 that we are the salt, in verse 14, we are the light. In verse 16, "Let your light so shine." What is God's plan to deal with this darkened, decaying world? His plan is us! It's us. There is no one else. It isn't going to be given to anyone else. It doesn't belong to famous evangelists. They'll never touch the people you touch. It doesn't belong to great preachers, or people on the radio or television, or people who write books. It belongs to all of us. This is God's divine plan.
The pronouns in verses 13-14 are emphatic: "You only are the salt. You only are the light. If you don't do it, there is nobody to do it." Look closely at the symbols. Last time, we studied salt. Salt speaks of influence. Salt is the silent testimony, it is our moving through the world and affecting it with our very life. We said that salt has five basic functions: purity, flavor, sting (in a wound), thirst (it creates thirst), and preservation. We are to be pure, glistening white against the darkness of the world. We are to flavor life with the wonder of God's presence among us. We are to sting and convict the sinful wound of the world. We are to create a thirst for Christ by the very way we live, as Israel is to be provoked to jealousy by the church. We are to be a preservative, we are an antiseptic in the world to retard the spread of its corruption. If it weren't for Christians in the world, it would be far more corrupt that it is now; we preserve it. By the way, notice that it says in verse 13, "You are the salt of the earth." This covers the whole earth; we are the only salt the whole earth will ever know. Jesus is saying, "The earth is like a carcass, slowly but relentlessly deteriorating, rotting and in great need of some power to restrain that corruption, to create a thirst for God, to sting sin's wound, to flavor life, and to bring purity to some dark and decaying soul." We are that salt. This is our witness as the silent impact of a godly life. Listen, the way to change the world isn't to change it politically, it isn't to rewrite the laws, or march, or to try and use technical paraphernalia for altering society. The way to change the world is to infiltrate it with godliness, righteousness, and holiness, and affect it from the inside out. Those other things aren't wrong, but they will be powerless unless our lives are what they ought to be. Think about it this way: never has the church been more involved in social action in recent history in our country. Never have we been so preoccupied with endeavoring to see Christianity in government, and what is the result? A society that is more immoral than it has ever been, because that's not the way to do it. The way to do it is the influence of a godly life. Martin Lloyd-Jones says this, "Most competent historians are agreed in saying that what undoubtedly saved England from a revolution such as was experienced in France at the end of the 18th Century was nothing but the evangelical revival. This was not done because anything was done directly, but because masses of individuals had become Christians and they were living this better life. They had this higher outlook. The whole political situation was affected, and the great acts of Parliament which were passed in the last century were mostly due to the fact that there were such large numbers of individual Christians found in the land." What he's saying is that they dominated the land by the power of their testimony.
It's wonderful to think of the fact that God can turn around a whole nation, a whole world, by using us. God uses simple things, you know that. He uses simple, mundane, everyday, routine, common things for the most amazing purposes. When He made man in the Garden, He didn't use gold, silver, or even iron; He used dirt. That ought to give you an idea of how He works right from the start. When He called David to deliver Israel from the Philistines, He didn't want Saul, the great king, and He didn't want Saul's massive armor. He used a shepherd and a couple of stones, that's all. When He came into the world, He didn't enter the family of the wealthy and noble, He didn't find Himself born in a castle; He simply chose a peasant girl and a stable. When He chose the Twelve, He didn't choose the elite, educated, and affluent. He just chose a group of ignorant Galileans. The Bible says, "Not many mighty, and not many noble." That's the way it always has been, because God gets the greater glory in the humbleness of the one that He uses. So He uses us, grains of sand, to influence a corrupting world. But it doesn't stop with influence. We now come to the second thing, light. Verse 14. "You are the light of the world." We're moving to another thought here. Salt and light balance each other in this sense. Salt is hidden; you don't see it at all. It just melts away into whatever it flavors or preserves. It works secretly to preserve from the inside, but light shines on the outside, and light is open and working visibly. In other words, salt is the influence of Christian character; it is quiet but powerful. Light is the communication of the content of the Gospel. So there are two sides; on one hand, we live it, on the other hand, we preach it. On one hand, from the inside, we affect society's thinking and living by the power of our lives. On the other hand, we turn on the light so that everyone can see the message we want to give. It isn't just in our words, but in our very overt, open godly conduct. We are not to be just a subtle influence like salt, but we are to be a very open and blatant influence like light. You see, salt can't change corruption into incorruption. Salt can only retard the corruption. That's only a negative function. Salt only holds back the corruption; we have to turn on the light of the Gospel to transform that corruption into incorruption. Of course, our light is primarily indicated in verse 16, "Let your light so shine before men that they will see your good works and glorify your Father who is in heaven." That implies, first of all, that they see our good works. Secondly, they glorify our Father in Heaven; that means they've heard something about our Father in Heaven. It implies both a life and a message lived and spoken.
So here we are as salt, retarding the things of corruption in the world. But at the same time, as light, we speak the truth of the light and live the truth of the light, so there is an overt and positive testimony as well.
You'll remember that in Acts 1:1, where Luke writes, "The former letter have I made unto you, O Theophilus, of all that Jesus began to do and to teach." Ever and always, those two things go together - the living and the speaking. Our light is a matter of living the righteous life and uttering the righteous content, the truth. If you study the Bible, you'll find that light is related to the true knowledge of God. Just a couple of Scriptures for an example, Psalm 36:9 says, "For with You is the fountain of life; in Your light we see light." So the first thing we need to realize is that God is light (I John 1). In Him is the fountain of life, and in His light will we see light; God is light. So if we are to be light, then we must manifest God. Psalm 119:105 says, "Your word is a lamp to my feet and a light to my path." God is light; the Word is light. In the New Testament, our Lord Jesus Christ says, "I am the light of the world. He that follows Me shall not walk in darkness but shall have the light of life." So we see that God is light. The Bible, the Word of God, is light. Christ is light, and that is the light that we are to shine on the world. We are to tell them about God, God's Word, and God's Christ. That's letting the light shine. It has to be spoken and then supported by a life that is consistent, right?
Remember I read to you Psalm 27:1, "The Lord is my light and my salvation." So the fact is, if you want to know what light is in the Bible, it's the comprehensive term referring to all of God's revelation; the revelation of Himself, His Word, and His Son. That's light. So we are to proclaim the message of light in a dark world, as well as to be salt in a decaying one.
In Luke 1:77, it says the purpose for which Christ came was, "To give knowledge of salvation to His people by the remission of their sins through the tender mercy of our God, whereby the dayspring from on high has visited us to give light to them that sit in darkness and in the shadow of death." That's why He came, to give light to them in darkness. So what our Lord is saying here is that, collectively, we manifest the light. He's the sun, we're just moons. He is the real light, the essence of light; we're reflectors. That's all. John 1:9 says that Christ is the light that lights every man that comes into the world. He's the only true light, but we are reflectors of that light. He is the sun, and we're the moons. Beloved, I think this is the primary duty of the church, to be light in the world. We are to spread the message of salvation, not just to sit around talking to each other. That is wonderful, and having fellowship is wonderful, and it's rich and exciting. But sooner or later, we have to be light in the world and salt in the earth. We've got to get out from being wrapped up in ourselves. Let me give you a free rendering of II Corinthians 4:6. God, who first ordered the light to shine in the darkness has flooded our hearts with His light. We now can enlighten men only because we can give them knowledge of the glory of God as we have seen it in the face of Jesus Christ. Let me read it again. God, who first ordered the light to shine in the darkness has flooded our hearts with His light. We now can enlighten men only because God has given us the knowledge of His glory as we have seen it in the face of Christ. So God passes the light all the way down through us. It's so important.
The Jews in Romans 2 claimed to be light. The Apostle Paul denies that. Their light had gone out. They weren't lights anymore. The Jews used to say that Jerusalem was a light to the Gentiles. In fact, a famous rabbi once called the city of Jerusalem 'the lamp of Israel.' But it wasn't true anymore when Jesus spoke these words that day on the hillside; Jerusalem wasn't any light. God's light wasn't there anymore, it was no lamp. The world was in darkness, so Jesus says, "It isn't Jerusalem that is the light anymore, it isn't Israel anymore. It isn't the Jewish people anymore that are light, but you only are the light." The church would be the light, the ones who followed Jesus Christ would be the light. So it has been all along: we're the light. Philippians 2:14 puts it this way. "Do all things without complaining and disputing, that you may become blameless and harmless children of God without rebuke." That's it folks. You have to live the life. The life has to be there; a blameless life. A life that is harmless, blameless, and without rebuke. If they're going to criticize us, let them have to make up something because there is nothing they can use. If we have to be hated, let us be like Christ - hated without a cause. Why? Because we are to be blameless, harmless children of God without rebuke in the midst of a crooked and perverse nation, among whom we shine as lights in the world. We are the lights, holding forth the Word of Life. Jesus illustrates this thought right here in Matthew 5; He says we've got to be visible, folks. We can't just be secret influences, we have to be visible. The light has to shine openly. Verse 14. "A city that is set on a hill cannot be hidden." If you had traveled in the Holy Land during Jesus' time, or perhaps even today, you would be impressed with the fact that the villages are built on the tops of the hills. I'll never forget going through Galilee and it seemed like every village I saw kind of sat up on a little hill. I remember going to Caana, and seeing Caana against a hill. Further up a little ways, to the north, I saw Nazareth up on a hill. All the villages were up on hills, and could be cooled by the breezes that blew in the day. They could be more easily defended, and when night came, it was a very common custom for them to light a lamp in the house. It just made the little village sparkle, and anyone who was walking through the night could easily find his way to the village because he could see the lights sparkling on the hill. So the point is a city couldn't be hidden. Everyone knew that light was for the purpose of manifesting. It's amazing to think about the fact that a Christian would say, "I know God's light has shined in my heart, but I don't see that I have any need to shine anywhere else." You're light, my friend, and light isn't supposed to be hidden. You're a city on a hill. The point is conspicuousness. We're not just subtle salt; we're very conspicuous light. Every traveler knew where the refuge was; every traveler knew where the little village was, because the lights sparkled like diamonds in the sky. We're not Masons in a secret society. We're not pagans, with mysteries only for the initiated. We don't have a cult known only to the few; we're a city set on a hill. The whole world ought to see us. By the way, that's why I love these doors that you can see through. I just love people to drive up and down Roscoe Boulevard and say, "Look at all those people. What are they doing?" We're a city set on a hill. We've got to be salt before we can be light; we have to have the character and the influence before we have a message that is believable. So that's the divine plan. The presupposition: a dark and decaying world. The plan: the dominion of the disciples as the dominate the world by their influence as salt, and by their message and content as light. Thirdly, the presupposition and plan also include a problem. There is a problem, folks. If the presupposition is the darkness and decay of the world; if the plan is the dominion of the disciples, then the problem is the danger of failure. There is that danger. With this tremendous responsibility, there is an attendant danger. We are salt and light, but we need to be warned because if sin enters our lives, and if we don't walk in the Spirit, then we will stop being effective as salt and we will be useless as light. Look again at verse 13. "You are the salt of the earth, but if the salt has lost its saltiness, what good is it?" Non-salty salt has absolutely no use. "It is thereafter good for nothing, but to be cast out and trampled under men's feet. Neither do men light a lamp and put it under a bushel, but on a lampstand, and it gives light to all in the house." The point is this: salt is only good when it has saltiness. Light is only good when it is conscious. There is no place for a secret disciple; there is no place for a secret Christian.
Let's look at the concept of salt. Our Lord said that the danger is that salt can lose its saltiness. Moraino in the Greek, it means 'flat and tasteless,' if you become flat and tasteless. There have been many explanations of this. Some say that the salt we have today doesn't lose its saltiness, and that, for the most part, is true. But in that day, it wasn't nearly as refined. The Dead Sea was and still is a tremendous repository for salt. You can go to the Dead Sea and lay flat on your back and just bob - it's incredible. I've done that. The salt from the marshes, lagoons, and the rocks around the Dead Sea is in abundance. But it easily acquired, in that time, and still, because of its impurity, a stale or alkaline taste, because it was mixed with gypsum, which was also there. So that kind of salt would lose its capability to salt and would become very alkaline and stale, and the only thing it was good for was to throw out on the road where people walked. They didn't want to throw it in the field, because it would kill everything growing there. So they threw it on the road, where all that would happen is that it would be trampled.
By the way, natural salt is impure in many cases, and mixed with other chemicals, can become unsalty. William Thompson, in his classic book The Land and the Book, which deals with the nation of Israel, tells about a merchant who rented several homes in which he stored salt. The merchant, however, forgot to cover the dirt floor before he put the salt down, and simply unloaded the salt on the dirt. When he returned later, he discovered that his salt had lost its flavor from being next to the earth. The whole supply he threw into the street, where men walked on it.
So we know that the kind of salt that they had at that time had the capacity to lose its saltiness, and that is to what our Lord is alluding. Something that they would no doubt understand, that salt could lose its saltiness. I just want you to understand that. In Luke 14:34, it says, "Salt is good. But if the salt has lost its savor, with what shall it be seasoned? It is neither fit for the land, nor for the dung hill, but men throw it out." So it is the same statement there in Luke.
We don't need to argue, and it's amazing how many commentators argue, that Jesus was wrong here because salt can't lose its saltiness. But if anyone knows about salt, He does. Just like He knows about everything else. So we just find another explanation, as I've just given to you, which is very simple. What He's saying is not that you lose your salvation; He's not saying that, if you're not careful, you'll lose your saltiness. No, what He's saying is that you'll lose your influence. If sin enters a Christian's life, he will lose his influence. If sin is in your life, you have no influence; you can't retard the corruption of the world because you're in it. You can't be purity against an impure background because you're impure too. You can't be stinging in the wounds of other people's sin because you have your own. You're not going to create in someone a thirst for God, because there is nothing there to make them thirsty for what you have. You are just like them in behavior.
The point here is not that you lose your salvation, but like I Corinthians 9:27, you become a castaway; you forfeit your influence and lose your impact. When a Christian loses his saltiness, it's a sad situation. You can lose it; just be sinful at work and you'll lose your reputation. If you're sinful at school, listen to the things that people say that aren't right, go along with the dirty talk, be involved with the things they do that you know aren't right. You'll lose your saltiness, and make no contribution to retard their corruption. You'll make no pure statement against an impure background. You'll create no thirst in anyone for God. The point is, God needs your influence and you are to be salt. But to be salt, you have to stay away from that which corrupts you. They say that perfectly pure salt never loses its flavor. I like that. You want to know something? None of us is perfectly pure salt; we won't be until we get to glory. As long as we're in this life, we will have impurities and the potential for losing our saltiness is always there. God help us to so live the kind of life that will influence the world!
Let's talk about light for a minute. He says a light is something set on a hill, put on a lampstand. It gives light to everyone in the house. You certainly don't light a lamp and stick it under a peck, which is literally a shaped basket. He says, "You don't stick it under a basket. You don't take a lamp and put it under a basket, that's absurd." The little lamps they used were terracotta. I don't know if you've seen one, but they have a spout on one end and a little handle on the other end, with a little floating wick in the middle. The would fill them up with oil and it would burn, three to four inches wide, two inches high, six inches long. They would leave it to light all night. In fact, in Proverbs 31, the lady who gets up and doesn't let her lamp go out by night is probably the kind of lady who makes sure there is always a lamp in the house, so that anyone who needs to find his way around can. She has enough oil to make sure that is done, and she is conscientious enough to get up in the middle of the night to relight the lamp so that there will always be a light in the house. Jesus is saying, "How foolish it would be to get your lamp trimmed, the wick clipped, fill it up with oil, and stick a basket on top of it so no one could see it." It would be silly. Christians, you know what is amazing? Some of us have within us the treasure in earthen vessels, the Gospel of Jesus Christ, only no one knows. Someone has said that most Christians are like an Arctic river - frozen at the mouth. I don't know if that's totally true, but there are a lot of us who haven't shared Jesus Christ with anyone in a year, five years, ten or fifteen years. We have a light alright, but we've just got a modios over it, a peck basket. Listen, if you're going to light, you have to get your light where people can see it. It's kind of interesting to look at verse 15 and see that it says, "Neither do men light a lamp and put it under a bushel, but put it on a lampstand, and it gives light to all who are in the house." Some feel that is a reference to Israel, that it specifically refers to them. The statement 'all that enter in' would refer to the Gentiles. I don't know that we can push that too far, but the point is that whoever it is, whether it's Israel, the Gentiles, or whoever it is, we want to make sure that the light is lit and visible. That's what Jesus is saying.
To the people He was saying it to, He was really calling for something new. He was saying, "You're a part of a religious system that is fouled up. If you live according to Kingdom character in the Beatitudes, then you really have to be different. You have to be light so that they can all see it, and that isn't easy, because they're not going to like what they see." It's always the fear of persecution that makes us hesitant; we're always a little afraid. So after the Beatitude 'blessed are the persecuted,' He has to reinforce that we not put our lights under bushels. He wants us to put it where everyone can see it, so that the whole world will know the truth of God. Verse 16 personalizes it. "Let your light so shine before me that they will see your good works." He's saying, "Let it shine." That's all; it's a simple message. Let your good deeds, kalos, good in terms of beauty, the manifest beauty. It is not that they are just good in and of themselves, but they have a beauty and attractiveness about them, they are winsome. In other words, "Let men see your winsomeness; let them see your beauty and attractiveness, your quality." It isn't just the good deed itself, it's the beauty that it manifests. I want to add a little footnote. The beginning of verse 16 says, "Let your light shine." You don't have to trump it up; you don't have to light it, crank it up, worry about getting it started, all you have to do is let it go. You can't stop the light, and you can't light the light, you can just stick a bushel on it. The light is there. If Christ lives in you, He is the light and you can't change that. Remember the song? Nobody can blow it out. That's right! There isn't anybody who will blow it out, because the light is there. But you can put a bushel basket on top of it so nobody will ever know. It may be the basket of fear, or wanting to be acceptable, not wanting to offend or make waves, or whatever. But whatever it is, it needs to come off. You don't have to light it and you can't put it out, you just have to let it shine by the way you live and the things you say.
Let it shine before men, in the presence of those who hate you and would kill you, reject you, and deny you. Let it shine and let them see the beauty of your works. You know, when you hide your testimony, you're not doing anything but preventing someone from seeing the beauty of God Himself. When you don't testify, you're just withholding from someone that which they desperately need to see if they're ever going to come to God.
What do we see, then? The presupposition our Lord gives is the decay and darkness of the world. The plan that He gives is the dominion of the disciples, the dominion of the Christians. The problem that He talks about is the danger of failure. We can hide that light and lose that saltiness, and if we do, we are losing our hands. And when we go through that field, we aren't going to find anyone that is lost. We've seen the presupposition, the plan, the problem, and now the purpose. If the presupposition is the decay of the world, and the plan is the dominion of the Christians, and the problem is the danger of failure, then the purpose is the dignity of God. It's at the end of verse 16, and I don't need to say much about it because I've preached on it so many times. The reason for all of this, the one single reason that over arches the whole universe. There is one single reason why you should be salt that is salty and light that is manifest, and it is this: that you might glorify your Father who is in Heaven. If you don't do it, then you are more concerned with your reputation than His glory. That's always the issue. "I don't know if I should stick my neck out. I might lose my job or reputation." Then you have just ascended the scale and what you have and attain and get is more important than the glory of God. You see?
"Not unto us, O Lord, not unto us but unto Thy name give glory," said the psalmist. Can you lose yourself? Can you be salt that is salty? Can you be light that is lit and manifest? You can if you only care about the glory of God, but if you let your own personality and popularity, and prestige, and reputation get in the way, then the glory of God is dragged down, your flag goes up, and you say, "I reign. I'll do what appeals to me." "Glorify your Father who is in Heaven." Notice that He uses the word 'Father,' I think because He wants to emphasize the beautiful tenderness and intimacy of God. Yet He says, "In Heaven," and there, He speaks of the majesty. On the one hand, God is a tender, loving Father. On the other hand, He is a majestic, sovereign God in Heaven. So He says we are to glorify God.
That is good news. That is the reason we live; there is no other reason but to glorify God. That's all. Dr. Robert Murray McShane was one of the saints of the last century. His face, they used to say, was sometimes lit up with a hallowed expression, so that people who came to see him fell on their knees to accept Jesus Christ when they saw his face. Others were so attracted to the indescribable beauty of holiness manifested on his countenance that Jesus became, to them, irresistible. Isn't that fantastic? Influence.
It is said of Fenelon, the great Christian of ages past, that his, "Communion with God was such that his face shown. Lord Peterborough, a skeptic, was once compelled to spend a night with him in an inn. In the morning, he hurried away saying, 'If I spend another night with that man, I'll be a Christian in spite of myself.' Fenelon's manner, his voice, and his face reflected so perfectly the glory of Christ that he was irresistibly attractive to even the worldliest and vilest of humanity." What about you? Are you the kind of salt that retards corruption and the kind of light that attracts in the beauty of holiness, as the shining of your goodness and beauty, the power of God released in you, touches the people around you? Do you never mitigate it, cover it, do you let it shine so that God can be glorified? Let's pray.
Salt and light, Father, a simple message. It needed to be, because this was just part of the first sermon You gave. They needed to hear the basics, and so do we, 2,000 years later. We who know the Bible so well need to hear again the same old story. There is a wheat field out there and the wheat is too tall for the people who are lost to see the Father's house. We have to join our hands and go from one end of the field to the other before it's too late and we come to one whom the cold of the night has taken to a Christless grave. God, help us to join hands before its too late for some. We know that, even today, some passed into eternity. Tomorrow, more will pass to eternity. You've told us to take the Gospel to every creature. Help us to be willing to influence the world like Helen Ewing did, wherever we walk, may we leave Christ behind. Help us to change conversations so that, when we show up, they say, "Shhh, he's coming," or, "She's coming." If we were to die tomorrow, would it be said that we made a difference in the world? Oh, Lord, may we be salt that is salty and light that is manifest. May we be a city set on a hill, may we let our lights so shine that men will see our good works and glorify the Father in Heaven. Deliver us from the sins that would render us tasteless and useless but to be thrown on the road and walked on. Deliver us from the fear and pride and exaltation of self that make us put our lights under a bushel. Help us to live the way that You want us to live, to make a difference in the world. We expect that the world won't like it, but even though there may be a reaction against it, there will be some who will come to Jesus Christ through our lives. May we be useful in the world's wheat field, to find those that are lost. We think of our Lord Jesus, as He looked over the city of Jerusalem and wept and said, "You will not come to Me that you might have life." Father, help us not to cause even more tears because we too have been unfaithful. May we so live to fulfill this marvelous command of our Lord Jesus Christ. We who have Kingdom character, may we let it influence the world in which we live. Make us different, Lord, that the world may be different because You are.
While your heads are bowed, let me say this. I think God is going to call on us in days ahead to stand up and be counted for His cause. I think we had a little taste of it in recent days, but that was nothing. I think of Hebrews 12, "We have not yet suffered unto blood." We certainly haven't been martyred yet. I don't know what the future has for us, but I think we need to come to grips with our lives right now. Where are you investing your time? Where are you investing your life, your money; where are you placing these things? You only have this one life, that's all, just one shot. You've claimed Christ, you love Christ; are you salt that is salty and light that is manifest? Let's make a difference in the world; the world really needs us. We're the only salt and light. Let's be different and make a difference. Will you covenant in your heart with me before God that that is what you want to do? Father, we thank You tonight, for how, again, in the simplicity and beauty of Your Word, You have penetrated our hearts. Make us different. We know there is a price to pay, and that's OK. You payed the supreme price for us, You bore the blows that should have been borne by us. Surely we can take the blows that the world means for You. Help us to be faithful, and may this community of believers make a difference in the world, not for our sake, and not for the sake of Grace Church, John MacArthur, or any individual, but for the glory of God the Father who is in Heaven. It's His glory alone that we seek. In the name of Jesus Christ, Amen.


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text:
\section{Introduction}
\hspace*{\parindent}
Large transverse momentum phenomena in deep inelastic scattering reactions have been extensively studied by the H1 and ZEUS collaborations at HERA. Large-$p_\bot$ particle and jet spectra have been measured and compared to next-to-leading order (NLO) QCD calculations. Large-$p_\bot$ photons have also been observed, in an inclusive way \cite{a,b} or in correlation with a hadronic jet \cite{a,c}. This latter reaction has been the subject of theoretical studies some ten years ago \cite{d,e}. The recent data from ZEUS~\cite{c} lead us to extend these studies and to compare the complete NLO QCD results with the $\gamma$-jet cross sections.

In principle, prompt photon production in deep-inelastic scattering (DIS) is a very simple process~: it goes via the Compton scattering of a virtual photon on a quark: $\gamma^* + q \to \gamma + q$ and requires only the knowledge of the distribution function of a quark in the proton. Including higher-order (HO) corrections considerably complicates the picture and new objects have to be introduced.
For example, in the scattering $\gamma^*+ g \rightarrow q + \bar q + \gamma$, the $q\bar q$ pair may be produced quasi-collinearly to the virtual photon, one of the parton in the pair being then scattered at large $p_\perp$: this configuration generates the virtual photon structure function (resolved photon) at lowest order associated to a large logarithm. It is then necessary to resum such large logarithms and introduce the all order photon structure function.
Furthermore, in the above process or in $\gamma^*+ q \rightarrow q +  g + \gamma$, the final photon may be produced collinearly to a final state quark or antiquark (bremsstrahlung) leading to a large logarithmic enhancement, thus generating the photon fragmentation fonction. Thus one is lead to distinguish four types of processes, all contributing already at leading order (LO): the direct-direct (d-d) one where both the virtual photon and the final real photon couple directly to the hard sub-process; the resolved-direct (r-d) where the virtual photon couples to the hard subprocess through its hadronic (perturbative or non perturbative) components; the direct-fragmented (d-f) and the resolved-fragmented (r-f) ones where the final photon appears as a fragment of a jet unlike in the previous two cases where it is isolated.  At HERA, all four processes corresponding to four topologies have essentially the same order of magnitude \cite{g}. However when dealing with isolated photon, the isolation criteria necessary to suppress the background from $\pi^0 \to \gamma\gamma$, considerably reduces the fragmentation components d-f and r-f.

The above discussion on the four topologies is valid as long as we can define a virtual photon structure function resumming all the large logarithms $\ln \left ( {p_\bot^2 + Q^2 \over Q^2} \right )$ \cite{f} where $p_\bot$ is a characteristic transverse momentum of the reaction (for instance that of the observed photon in the proton virtual-photon center-of-mass frame) and $Q^2$ the initial photon virtuality. These terms appear in the calculation of HO  corrections to the Born direct cross sections. If $p_\bot$ is not large enough ($p_\bot^2 \ \raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}\ Q^2$) it is of course not useful to subtract these logarithms from the direct HO corrections in order to resum them in the virtual photon structure function. On the other hand for $p_\bot^2 \gg Q^2$ this approach is useful~: indeed in this case the resolved cross sections have the same structure as a hadronic cross section involving two parton distributions convoluted with hard subprocesses. HO corrections are known, they are large and can be easily implemented.

The natural frame to observe large-$p_\bot$ phenomena and to calculate the corresponding NLO cross section in deep-inelastic scattering (DIS) is the proton virtual-photon center-of-mass system (hadronic frame or CM$^*$). The large $p_\bot^*$ of the final photon provides the scale which can be compared with the photon virtuality; a large ratio $p_\bot^{*2}/Q^2$ defines the kinematical range in which the photon structure function formalism is useful. Such an approach, but without the introduction of the virtual photon structure function, can be found in \cite{d}. It contains detailed studies on the jet algorithms and the scale choice dependence of the cross sections.

As the kinematical conditions are often specified in the laboratory frame and as a large-$p_\bot$ in the laboratory does not necessarily implies a large $p_\bot^*$ in the CM$^*$, a lower limit $p_\bot ^* > E_{\bot cut}^*$ can also be imposed by the experiments. This condition will preserve the validity of a perturbative calculation and the possibility to define a virtual photon structure function. The production of jets and of forward $\pi^0$ has been measured with this convention by H1 \cite{7,8} and ZEUS \cite{9}. On the other hand, several experiments have also used the laboratory frame (LAB frame) to present their results \cite{a,b,c} without imposing the requirement $p_\bot^* > E_{\bot cut}^*$. As we shall see, the approach involving the definition of the resolved cross section is not always under control, and we have to content ourselves with the calculations of unsubtracted direct contribution. Thus we loose the possibility to supplement them with HO corrections.

In this paper we consider DIS reactions in which an isolated photon and a jet are observed in the final state, extending the approach used in the inclusive case \cite{g} with only a photon observed in the final state. We discuss both cases, when the transverse momenta are defined in the CM$^*$ or in the LAB frames. This study is triggered by recent detailed ZEUS results \cite{c}. Unfortunately no $p_\bot^*$ constraint has been introduced by this collaboration, thus forbidding, in some kinematical domains, direct comparisons with complete NLO predictions.

The comparison with inclusive isolated cross section done in our previous paper was favored by the H1 kinematics \cite{a} having a large
domain where the condition $p_\bot ^{*2} > E_{\bot cut}^{*2}$ with $p_\bot ^{*2} /Q^2 \ \raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}} \ 1$ was verified. The situation is less
favorable with the ZEUS kinematics having a larger range in $Q^2$. The observation of a photon and a jet in the laboratory does not necessarily
imply a large invariant mass squared $s_{\gamma j}$ of this system (when the photon and the jet are almost parallel). Therefore the addition of a
jet is not sufficient to prevent configuration with $p_\bot ^* < E_{\bot cut}^*$. This fact leads us to introduce a cut-off $E_{\bot cut}^*$ in our calculations and to study the stability of our results when $E_{\bot cut}^*$ goes to zero. If, in some kinematical domains, the results are not sensitive to $E_{\bot cut}^*$ we will compare them with ZEUS data.

The plan of this paper is the following. The next section is devoted to the calculation of the gamma-jet cross section in the CM$^*$. By this we mean that the isolation algorithm for the photon and jet algorithm are defined in this frame. The jet algorithm also contains conditions such as ``jet of highest $p_\bot$'' in the CM$^*$. As we fix the kinematical variable $p_\gamma$ and $p_{jet}$ in the laboratory we require the condition $p_{\bot \gamma}^* > E_{\bot cut}^*$. We discuss in detail the introduction of the resolved component. The four contributions (d-d, d-f, r-d and r-f) are calculated and their respective importance is discussed. Then, in section 3, we discuss calculations performed in the laboratory frame. By this we mean that the isolation algorithm and jet algorithm are now defined in the laboratory where the kinematical boundaries are also fixed.  We furthermore study the differences between the standard cone algorithm and the democratic one for the photon isolation and for the jet definition. We have to introduce a cut-off $E_{\bot cut}^*$ in order to avoid possible instability of the cross section. Finally section 4 is devoted to the comparison with the recent ZEUS data~\cite{c}.

\section{Proton Virtual-photon Center of Mass Frame}
\hspace*{\parindent}
In this section, devoted to calculations in the CM$^*$, we study the four contributions to the $\gamma$-jet cross section discussed in the introduction. Such a frame looks like the laboratory frame of a hadronic collider; the colliding particles have collinear trajectories and the large transverse momentum $p_\bot^*$ of the observed final particle fixes the large scale appearing in the distribution functions and in the strong coupling constant. \par

However to be close to the experimental conditions we impose constraints on the observed kinematical variables, transverse momenta and rapidity, in the laboratory frame. The particle momenta are transformed to the CM$^*$ frame in which we define the isolation algorithm and the jet algorithm. As discussed in the introduction we impose a cut on the photon momentum $p_{\bot \gamma}^* > E_{\bot cut}^*$ in order to avoid instabilities of the cross section and to guarantee the validity of the perturbative regime. In this section we use the cone algorithm \cite{a)} for the isolation and the longitudinal $k_\bot$-algorithm \cite{b)} to define a jet. When two jets are present, we observe the jet of higher $p_\bot ^*$. For the photon the radius of the isolation cone is $R^* = 1.$ and we require a ratio ${E_\bot^{*had} \over E_\bot^{*\gamma} + E_\bot^{*had}}  \leq .1$ where $E_\bot^{*had}$ is the hadronic energy contained in the isolation cone. For the jet the radius $R_{jet}^*$ of the $k_\bot$-algorithm is set equal to $R_{jet}^* = 1$. Another algorithm, the so-called democratic algorithm will be discussed in section 3.\par

We use the CTEQ6M proton structure \cite{c)} and the virtual photon structure function presented in ref. \cite{f} and used in refs. \cite{g} and \cite{e)}.  The fragmentation function is that of the BFG collaboration (set II) \cite{h)}. Details on the NLO calculation can be found in ref. \cite{g,e),i),j)}. We work in the $\overline{\rm MS}$ scheme for factorization and renormalization with $\Lambda_{\overline{MS}}(4) = 236$~MeV and $N_f = 4$. The factorization and the renormalization scales are taken equal to $p_{\bot\gamma}^{*2} + Q^2$. The kinematical constraints are defined in the laboratory. We adopt those of ref.~\cite{c}. The colliding electron and proton have energies $E_e = 27.6$~GeV and $E_p = 920$~GeV corresponding to the center-of-mass energy $\sqrt{s} = 319$~GeV. The photon momentum has to lie within the ranges $4 < E_\bot^\gamma < 15$~GeV and $-.7 < \eta^\gamma < .9$. The jet momentum is required to have  2.5~GeV $< E_\bot^{jet} < $ 35~GeV and $-1.5 < \eta^{jet} < 1.8$. Constraints on the final electron are~: $E{'}_e > 10$~GeV, $\theta_e > 140^\circ$ (the $z$ axis is pointing toward the proton direction). Finally the photon virtuality is $10 < Q^2 < 350$~GeV$^2$. The numerical calculations are carried out using the adaptative Monte Carlo code BASIS~\cite{basis}.

\subsection{Direct-direct contribution}
\label{sec:dir-dir-CM}
\hspace*{\parindent}
In the d-d contribution the real and virtual photons are directly coupled to the hard subprocess and the Born term, $\gamma^*\,q \rightarrow \gamma\,q$, is particularly simple: it consists of the Compton scattering diagrams.  The cross section has a ${1 / \widehat{t}}$ behavior\footnote{Mandelstam variables with a hat are those of the subprocess.} when the photon is emitted close to the forward direction (collinear to the initial quark) and a ${1 / \widehat{s}}$ behavior when it is emitted collinear to the final quark. In the CM$^*$ the divergent configurations, in $ \widehat{s}$ or $\widehat{t}$, are forbidden by the requirement $p_{\bot\gamma}^* > E_{\bot cut}^*$. \par

Real HO corrections to the Born term are given by amplitudes involving an extra gluon coupled to the quark line. When this gluon is collinear to the initial quark the cross section is divergent. This divergence is subtracted and absorbed in the quark distribution. When this gluon is emitted at large $p_\bot^*$, the initial virtual photon can produce a collinear quark-antiquark pair. This is the origin of the virtual photon structure function. After integration on the final quark phase space one gets the expression $\sigma_{q\bar{q} \to \gamma g}^B (Q^2, p_{\bot\gamma}^*, y_\gamma^*) \otimes P_{\bar{q}\gamma} \ln \left (  {p_{\bot\gamma}^{*2} + Q^2 \over Q^2}\right )$ where the symbol $\otimes$ indicates a convolution between the Born cross section and the antiquark distribution in the virtual photon\footnote{$z$-dependent factors in the logarithm argument are not indicated. They are discussed in ref. \cite{f}.}. $P_{\bar{q}\gamma}$ is the DGLAP branching function $P_{\bar{q}\gamma}(z) = {3 \alpha \over 2\pi}\ e^2 [(1-z)^2 + z^2]$. In the large-$p_\bot^{*}$ regime, ${p_{\bot\gamma}^{*2} \over Q^2} \gg 1$, we can neglect $Q^2$ in the Born cross section. In order to resum the structure function we subtract $\sigma^B(0, p_{\bot\gamma}^* , y_\gamma^*) \otimes P_{\bar{q}\gamma}  \ln \left({M_\gamma^2 \over Q^2}\right)$ from the d-d HO term thus defining the HO$_s$ corrections. The subtracted term builds, through the inhomogeneous DGLAP evolution equation, the resummed structure function $G_{\gamma^{*}}^{q} (z, Q^2, M_\gamma^2)$ \cite{f}, the basis of the resolved contributions. We choose $M_\gamma^2 = p_{\bot\gamma}^{*2} + Q^2$ so that the structure function vanishes when $p_{\bot\gamma}^{*2} \ll Q^2$, and is proportional to $\ln {p_{\bot\gamma}^{*2} \over Q^2}$ for ${p_{\bot\gamma}^{*2} \over Q^2} \gg 1$.\par

Some numerical results are displayed in Fig.~\ref{fig:ygam-dir-CM} for the cross section $d\sigma^{d-d}/dy_\gamma$ with the cut $E_{\bot cut}^* = 2.5$~GeV. The kinematics has been
\begin{figure}[t]
\centering
\null\vspace{-0.2cm}
\includegraphics[scale=.75]{ygam-dir-CM.eps}
\caption{\it The photon rapidity distribution for the direct-direct (upper two curves, black) and direct-fragmented (lower two curves, colored) terms at the leading order and the next-to-leading order. The NLO cross sections are understood with the $P_{\bar{q}\gamma}  \ln \left( {M_\gamma^2 \over Q^2}\right)$ term subtracted and the cut $E_{\bot cut}^* = 2.5~\mbox{GeV}$ is implemented (see text).}
\label{fig:ygam-dir-CM}
\end{figure}
given at the beginning of section 2; $y_\gamma$ is the rapidity in the laboratory. As expected the cross section is largest in the forward direction due to the dominance of the $\widehat t$ term in the scattering amplitude. \par

We notice that the HO$_{s}$ corrections are negative, as already
observed in the inclusive case \cite{g}. On the contrary, the unsubtracted HO corrections are close to zero, the difference HO - HO$_{s}$ being the contribution of the lowest order resolved term that will be discussed in the next subsection. In fact, the NLO unsubtracted result cannot be distinguished from the d-d LO curve in Fig.~\ref{fig:ygam-dir-CM}.  The results in that figure strongly depend on the value of the cut-off $E_{\bot cut}^*$. This point is illustrated in table 1 where the total $\overline{\rm MS}$ cross section is displayed. We consider two domains in $Q^2$.
We see that for low value of $Q^2$ the NLO cross section is stable with respect to the $E_{\bot cut}^*$ value while it is not the case when considering the whole $Q^2$ range. In the former case, the Lorentz boost between the laboratory and the CM$^*$ frames, $q_\perp = \sqrt{Q^2(1-y)}$ with $y$ the usual DIS variable (scaled virtual-photon energy in the laboratory), is small and  $p_{\perp\gamma}^*$ remains relatively large, and close to its $p_{\perp\gamma}$ value in the laboratory, so that the cross section is insensitive to the cut-off. On the contrary for large values of $Q^2$,   $p_{\perp\gamma}^*$ may reach small values where perturbation theory is not reliable (very large HO corrections) and where the theoretical predictions become sensitive to the cut-off. The errors associated to the NLO cross sections are the values resulting from the Monte-Carlo integration procedure (for the Born cross sections the errors are at the per-mil level).

\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
 &\multicolumn{2}{|c|}{} &\multicolumn{2}{|c|}{}  \\
&\multicolumn{2}{|c|}{10 $< Q^2< $ 350 GeV$^2$} &\multicolumn{2}{|l|}{\qquad 10 $< Q^2< $ 50 GeV$^2$}  \\
&\multicolumn{2}{|c|}{} &\multicolumn{2}{|l|}{}  \\
\hline
&&&&\\
$E_{\bot cut}^*$ &{Born}  &{NLO}&{Born} &{NLO} \\
&&&&\\
\hline
&&&&\\
1.5 GeV  &7.50 &$2.16 \pm  .05$ &3.51 & $2.99 \pm .03$\\
&&&&\\
\hline
&&&&\\
2.5 GeV  &$6.14$ &$4.21 \pm .05$&3.39 &$2.91 \pm .03$ \\
&&&&\\
\hline
\end{tabular}
\end{center}
\caption{\it Variation of the d-d $\gamma$-jet cross section in pbarns with $E_{\bot cut}^*$ in two $Q^2$ ranges. The isolation and jet criteria are implemented in the CM$^*$.}
\label{table1}
\end{table}

\subsection{Resolved-direct contribution}
\hspace*{\parindent}
The r-d contribution that we consider in this subsection is made up of two terms, the Born cross section and the HO
corrections to the latter. Here the Born cross section is given by the convolution of the parton distributions in the virtual
photon with Born subprocesses. In the preceding subsection we found the lowest order expression of this distribution. Here we
use the resummed expression calculated at NLO is the $\overline{\rm MS}$ factorization scheme~\cite{f}. We can compare the resummed
Born contribution of this subsection $\sigma^{Born}$(r-d) with the lowest order one by considering the unsubtracted  HO
contribution and the subtracted $d$-$d$ contribution HO$_s$ found in the preceeding subsection (integrated over $y_\gamma$).

$$\begin{array}{ll}
\sigma^{HO} - \sigma^{{HO}_s} &= 6.13 - 4.21 = 1.92\ \mbox{pb}\\
\sigma^{Born} \hbox{(r-d)} &=  2.12\ \mbox{pb}\\
\end{array}
$$

\noindent} \def\beeq{\begin{eqnarray} The slight difference can be attributed to the difference between the lowest order $\gamma^*$ structure function and the resummed one (which also contains gluons). HO corrections for the r-d contribution can be borrowed from prompt photon production in hadronic collision, by using the code JETPHOX \cite{k)} in which a hadronic parton distribution is replaced by the virtual photon distribution function. We find a large effect $(E_{\bot cut}^* = 2.5$~GeV)~:
$$\begin{array}{l}
\hbox{$\sigma^{Born}$(r-d) = 2.12}\ \mbox{pb}\\
\\
\hbox{$\sigma^{NLO}$(r-d) = 3.30}\ \mbox{pb}\\
\end{array}$$
\noindent} \def\beeq{\begin{eqnarray} which illustrates the interest to consider the HO corrections in the r-d contribution. Here also the $E_{\bot cut}^*$ dependence is large. For $E_{\bot cut}^* = 1.5$ GeV we obtain $\sigma^{Born}$ = 5.04 pb and $\sigma^{NLO}$ = 7.24\ {pb}.\par

The Born and NLO cross sections as function of $y_\gamma$ are displayed in Fig. \ref{fig:ygam-res-CM*}. Unlike in the d-d case the cross section is rather flat in rapidity and even slightly decreasing at large rapidity: this is understood because the photon can now also be emitted by a quark in the $\gamma^*$, $i.e.$ in the backward direction. Concerning the HO corrections we see that they are not negligible.
\begin{figure}[h]
\centering
\includegraphics[scale=.75]{ygam-res-CM.eps}
\caption{\it The rapidity distribution for the resolved-direct (upper two curves, black) and resolved-fragmented (lower two curves, colored) terms at the leading order and the next-to-leading order}
\label{fig:ygam-res-CM*}
\end{figure}

\subsection{Direct-fragmentation contribution}
\hspace*{\parindent}
The direct-fragmentation contribution, obtained with the BGF fragmentation functions, is considerably reduced by the isolation requirement: no parton in the photon cone carrying more than 10$\%$ of the total photon $+$ parton energy. It is roughly 15\% of the inclusive d-f cross section. We obtain, always with $E_{\bot cut}^* = 2.5$~GeV, the following results
$$\begin{array}{l}
\hbox{$\sigma^{Born}$(d-f) = .33 pb}\\
\\
\hbox{$\sigma^{NLO}$(d-f) = .78$\ \pm .01\ $} \mbox{pb}\\
\end{array}$$

\noindent which are one order of magnitude smaller than the direct-direct contribution. The $y_\gamma$ rapidity spectrum is shown is Fig. \ref{fig:ygam-dir-CM}. It is relatively flat. This is related to the fact that the photon can now be radiated by a parton in the backward direction ($\widehat u$ channel pole). This new channel which populates a different region of phase-space, compared to the d-d term, receives large HO corrections associated to diagrams involving the triple gluon coupling. Not unexpectedly, we observed the same behavior as for the inclusive cross section \cite{g}.

\subsection{Resolved-fragmentation contribution}
\hspace*{\parindent}
The r-f contribution is, after isolation, the smallest of the four contributions. We have:
$$\begin{array}{l}
\hbox{$\sigma^{Born}$(r-f) = .19 pb}\\
\\
\hbox{$\sigma^{NLO}$(r-f) = .50$\ \pm .04\ $} \mbox{pb}\\
\end{array}$$
The photon rapidity distribtion is shown in Fig. \ref{fig:ygam-res-CM*}. The large HO corrections are due to many new processes. This process is in fact similar to a pure hadronic one such as $p + p \rightarrow \pi^0 + jet + X$ which is known to receive large higher order corrections \cite{k1)}.

\section{Laboratory  Frame}
\hspace*{\parindent}
The definition of the photon-jet cross section in the laboratory frame
introduces several new features not present previously. All these features come from the fact that a large-$p_\bot$ parton in the laboratory does not necessarily correspond to a large-$p_\bot$ parton in the CM$^*$. Therefore the simple picture of two initial collinear partons scattering into two large-$p_\bot$ final partons and of the associated perturbative HO corrections may break down. The spectator jets, for instance those of the resolved photon, which are low-$p_\bot$ jets in the CM$^*$ can
appear as large-$p_\bot$ jets in the laboratory , and must be included in the
definition of the photon-jet cross section. The jet hierarchy also can be
changed; the highest-$p_\bot$ jet in the CM$^*$ does not necessarily correspond to the highest one in the laboratory. \par

A more adapted approach for a laboratory frame calculation is that of \cite{e}
involving no $E_{\bot cut}^*$. But this approach leads to a new singularity in the
perturbative calculations, that of the final collinear contribution of the
subprocess $\gamma^* + q \to q + \gamma$. Therefore at lowest $O(\alpha^2)$  order this  calculation requires the introduction of a fragmentation function to absorb the
final state singularity. At present there is no $O(\alpha^2 \alpha_s)$ calculation available analogous to that performed in the $\gamma^* \to q+\overline{q} + \gamma$ channel  \cite{l)}. Therefore we continue our CM$^*$ approach adapted to the laboratory frame which implies a cut $E_{\bot cut}^*$. \par

In this section we study the photon-jet cross section measured in the laboratory. This means that isolation and jet algorithms are defined in terms of parton momenta in the laboratory frame. The jet is the jet of highest-$p_{\bot}$ in the laboratory. Moreover if the highest-$p_{\bot}$ jet is outside the acceptance in rapidity we take into account the smaller one. For each of the four topologies there are specific features that we discuss in the following subsections.

\subsection{Direct-direct contribution}
\hspace*{\parindent}
We start this section by discussing two algorithms used to define isolated
photons. They are the cone algorithm, already used in the CM$^*$ calculation, and the democratic $k_\perp$-algorithm \cite{glover} used, for instance, in the ZEUS experiment \cite{c}. For the definition of jets we use the longitudinal $k_\perp$ algorithm~\cite{b)}. All momenta are measured in the laboratory.\par

In our case we have at most two partons besides the photon in the final state~: in the direct-direct case the photon is (in the theoretical sense) isolated while in the direct-fragmented case it is accompanied by a collinear parton. The cone algorithm is the simplest one to implement. One calculates the distance between the photon and each parton ($i = 1,2$)~:
\begin{equation}}   \def\eeq{\end{equation}
\label{1e}
R_{\gamma i} = \sqrt{\delta \eta_{\gamma i}^2 + \delta \phi_{\gamma i}^2} \ ,
\eeq
where the quantities under the $\sqrt{}$ are respectively the difference in (pseudo-)rapidities and in azimuthal angles of the photon and parton $i$. Then if $R_{\gamma i} < 1$, the parton is in the photon cone and we have to test if the total transverse hadronic energy in the cone $E_{\bot i}$ (including also in the d-f case the energy of the fragment collinear to the photon)
\begin{equation}}   \def\eeq{\end{equation}
\label{2e}
E_{\bot i} < \varepsilon \left ( E_{\bot i} + E_{\bot \gamma} \right )
\eeq
with $\varepsilon = .1$ as in the case of ZEUS experiment. If both partons are outside the photon cone, then one tests if they form one or two jets depending on whether their distance $R_{12} =  \sqrt{\delta \eta_{12}^2 + \delta \phi_{12}^2}$ is smaller or larger than $1.$ If $R_{12} < 1$ they form one jet with coordinates:
\begin{eqnarray}}  \def\eea{\end{eqnarray}} \def\nn{\nonumber
\label{3e}
E_{\bot jet} &=& E_{\bot i} + E_{\bot j} \nn \\
\eta_{jet} &=& \left ( E_{\bot i} \ \eta_i + E_{\bot j} \ \eta_j \right )/E_{\bot jet}\nn \\
\phi_{jet} &=& \left ( E_{\bot i} \ \phi_i + E_{\bot j} \ \phi_j \right )/E_{\bot jet} \ .
\eea
If this jet falls within the detector acceptance we keep the event. In the case of two jets,  we test for the small $E_\bot$  jet if the largest one does not fall in the acceptance. It may also happen that both partons satisfy the criterium $R_{\gamma i}  < 1$ in which case we, of course, drop the event since there is no visible jet in that case.\par

In the democratic-$k_\bot$ algorithm case we treat the photon as an ordinary parton $i = \gamma , 1, 2$ and we order the distances defined in the following way~:
\begin{equation}}   \def\eeq{\end{equation}
\label{4e}
d_i = E_{\bot i} \ , \quad d_{ij} = \ {\rm min} \left ( E_{\bot i}, E_{\bot j}\right ) \sqrt{\delta \eta_{ij}^2 + \delta \phi_{ij}^2} /R \ ,
\eeq

\noindent} \def\beeq{\begin{eqnarray} with $R = 1$ as in Zeus case. If the smallest of these variables is a $d_i$ we remove it and call it a jet or an isolated photon, provided that, in the fragmentation case the parton collinear to the photon satisfies the condition (\ref{2e}). We then continue the procedure with the remaining  distances. If the smallest variable is a $d_{ij}$ with $i, j = 1, 2$ we combine the partons to form a jet with the coordinates as in eq. (\ref{3e}) and we perform, with this jet, the isolation tests as above. If the smallest distance is a $d_{\gamma i}$, $i = 1,2$, we test for the isolation condition (\ref{2e})~: if it is satisfied we calculate the coordinates of this ``isolated photon jet'' as in (\ref{3e}) and test whether or not the remaining jet falls within its cone.\par

The two algorithms should lead to very similar results~\cite{d}. In fact, in case there are only two large $E_\bot$ objects they are identical. However when there are three or more objects there appears some differences. For example, consider the hierarchy $d_{12} < d_{\gamma 1} < d_\gamma < d_{\gamma 2} , d_1, d_2$. In the cone algorithm, parton 1 is in the photon cone and the photon appears non-isolated because $E_{\bot\gamma} < E_{\bot 1}$, thus the energy fraction criterium is not satisfied~: the event would be rejected. In the $k_\bot$ algorithm the two partons would form a jet and the photon would appear isolated. Such occurences are rare however. In the exemple above, the conditions $d_{12} < d_{\gamma 1} <  d_\gamma $ mean that the photon and both partons are "close" to one another which is possible only if there is a large transverse boost from the CM$^*$ frame to the LAB one.\par

\begin{table}
\begin{center}
\begin{tabular}{|l|c|c|}
\hline
&&\\
&Cone algor. &Democratic algor. \\
&& \\
\hline
&& \\
{Born} &6.44 &6.44 \\
&& \\
\hline
&& \\
{NLO} &$4.22 \pm .03$ &$4.35 \pm .03$ \\
&& \\
\hline
\end{tabular}
\end{center}
\caption{\it{The d-d $\gamma$-jet cross section calculated with the cone and the democratic algorithms, in pbarns. The isolation and jet criteria are implemented in the laboratory.}}
\label{table2}
\end{table}
We obtain quasi identical results for the cross sections calculated with the two algorithms. They are displayed in table 2. We used the parameters and proton distribution functions defined in section 2.
Unlike in the analysis in the CM$^*$ of sub-section \ref{sec:dir-dir-CM} the d-d NLO cross section is insensitive to the $E_{\bot cut}^*$ cut-off :
the cross section is reduced by 1\% to 2.5\% at negative $y_\gamma$ and unchanged at positive $y_\gamma$ when varying the cut-off from 0 to 2.5 GeV. The fact that the cross sections are not divergent is due to the photon isolation and the requirement of a jet in addition to the isolated photon.
Therefore in the direct-direct case we are able to take the limit $E_{\bot cut}^* \to 0$ since the experimental requirements forbid the final collinear $q - \gamma$ configuration. This independence of the cross section on the cut-off means that the ZEUS cuts are sufficient to constrain the d-d term to remain in the perturbative regime where the HO$_{s}$ corrections to the Born term are under control.\par
\begin{figure}[b!]
\centering
\includegraphics[scale=.75]{ygam-dir-res-LAB.eps}
\caption{\it The photon rapidity distribution for the direct and resolved  terms at the next-to-leading order, with photon isolation and jets defined in the laboratory; the lower two curves are the fragmentation components. For all components the constraint $E^*_{\perp cut} = 2.5$ GeV is implemented.}
\label{fig:ygam-res-LAB}
\end{figure}

In Fig. \ref{fig:ygam-res-LAB} we display the d-d contribution at NLO (solid line) to the cross section $d\sigma^{LAB}/dy_\gamma$ calculated with $E_{\bot cut}^* = 2.5$ GeV and the democratic $k_\bot$- algorithm. \\

Let us note that the laboratory isolation criteria, without imposing an $E_{\bot cut}^*$ condition, lead to a cross section very similar that of table 1 where the constraint $E_{\bot cut}^*> 2.5$ GeV was imposed and jet and isolation defined in the center of mass frame (a cross section of 4.21 $\pm$ 0.05 pb was found in that case). \par

\subsection{Resolved-direct contribution}
\hspace*{\parindent}
The structure of the resolved-direct contribution defined in the laboratory frame is more complicated than the direct-direct one. The complication arises from the fragments of the $\gamma^*$ structure function. These fragments may go into the final photon isolation cone or may be seen as a jet. Moreover, in the higher order contributions we also have configurations with the low $p^*_\perp$ photon in the CM$^*$ collinear to a parton of the $\gamma^*$ structure function, which appears at large transverse momentum in the laboratory. This configuration is divergent (in the collinear limit) and is forbidden in the CM$^*$ frame by the fact that only large $p^*_\perp$ photons are observed. In the laboratory this configuration is forbidden by the condition $E_{\bot cut}^* > 0$. Therefore we expect a strong dependence on $E_{\bot cut}^*$ of the resolved-direct contribution. This dependence is shown in table 3.
\begin{table}[b!]
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
 &\multicolumn{2}{|c|}{} &\multicolumn{2}{|c|}{}  \\
$E_{\bot cut}^*$  [GeV] &\multicolumn{2}{|c|}{$10 < Q^2 < 350$ GeV$^2$} &\multicolumn{2}{|l|}{$10 < Q^2 < 50$ GeV$^2$}  \\
 &\multicolumn{2}{|c|}{} &\multicolumn{2}{|c|}{}  \\
\cline{2-5}
&&&&\\
 &Born &NLO &Born &NLO \\
&&&&\\
\hline
&&&&\\
.5 &2.07 &5.02 &.96 &2.17  \\
&&&&\\
\hline
&&&&\\
1.5 &2.06 &4.41 &.96 &2.06\\
&&&&\\
\hline
&&&&\\
2.5 &1.70 &3.40 &.92 &1.81  \\
&&&&\\
\hline
\end{tabular}
\end{center}
\caption{\it{Variation with $E_{\bot cut}^*$ of the r-d $\gamma$-jet cross section in pbarns, in various phase space domains. The isolation and jet criteria are implemented in the laboratory.}}
\label{table3}
\end{table}
\noindent
However we note that this dependence is weaker when $Q^2 < 50$~GeV$^2$. With this kinematical requirement we obtain a more stable cross section. \par

The r-d contribution at NLO (long-dash-dotted line) to the cross section $d\sigma^{LAB}/dy_\gamma$ is displayed in Fig.~\ref{fig:ygam-res-LAB} for $E_{\bot cut}^* = 2.5$~GeV: it has the same features as in Fig. \ref{fig:ygam-res-CM*}, namely very slightly decreasing with $y_{\gamma}$ and one finds large HO corrections throughout the whole range (about a factor 2).

\subsection{Direct-fragmentation contribution}
\hspace*{\parindent}
The $y_\gamma$ distribution of the d-f component, with $E_{\bot cut}^* = 2.5$ GeV, is shown in Fig.~\ref{fig:ygam-res-LAB}. It is essentially flat and rather small, the same features as in Fig.~\ref{fig:ygam-res-CM*}. The HO contribution is roughly independent of $y_\gamma$ and doubles the Born term. The distribution is relatively stable under the $E_{\perp cut}$ parameter: if taken to zero the d-f component is 13\% larger in the backward bin decreasing to no variation in the most forward bin.

\subsection{Resolved-fragmentation contribution}
\hspace*{\parindent}
We have in the r-f HO contribution a piece similar to that in the r-d HO one. A large-$p_\bot$ parton (in the LAB) can be emitted collinearly with an initial parton in the resolved virtual photon and then fragments into a photon. Again this corresponds to a collinear configuration in the CM$^*$ frame that we cut by the requirement $E_{\bot cut}^* > 0$. Therefore this contribution has a strong dependence on this cut-off parameter.
However, as seen in Fig. \ref{fig:ygam-res-LAB} it is the smallest of all four components and will give a negligible contribution to the full isolated $\gamma$-jet cross section.

\section{Comparison to ZEUS data}
After this lengthy discussion on each of the components which build the $\gamma$-jet cross section we are now ready to compare the NLO calculation to the most recent ZEUS data. It is worth stressing that only the sum of all
\begin{figure}[!t]
\centering
\null\vspace{-2.cm}
\includegraphics[scale=.75]{ygam-ZEUS.eps}
\caption{\it The photon rapidity distribution: comparison of the full NLO calculation to ZEUS data  \cite{c}. The leptonic contribution is as quoted in \cite{c}.}
\label{fig:ygam-ZEUS-LAB}
\end{figure}
\begin{figure}[!h]
\centering
\includegraphics[scale=.75]{PTGam-ZEUS.eps}
\caption{\it The photon transverse momentum distribution: comparison of the full NLO calculation to ZEUS data  \cite{c}. The leptonic contribution is as quoted in \cite{c}.}
\label{fig:PT-ZEUS-LAB}
\end{figure}
four components have a physical meaning and can be compared to data as the relative  weight of each component depends on the unphysical scales. It has been stressed above that measuring the transverse components in the laboratory frame rather than the CM$^*$ frame does not garantee the perturbative stability of the calculation: indeed it appears from the above discussion that, if the direct components are rather stable under the $E^*_{\perp cut}$ parameter, this is not the case for the resolved ones because the ZEUS phase space does not garantee that the CM$^*$ momenta in the hard subprocesses remain large and also does not eliminate all the collinear singularities associated to the photon radiation from a quark at large laboratory transverse momentum. For these reasons we will bracket the theoretical predictions
\begin{figure}[!t]
\centering
\null\vspace{-2.cm}
\includegraphics[scale=.75]{Q2-ZEUS.eps}
\caption{\it The $Q^2$ distribution: comparison of the full NLO calculation to ZEUS data  \cite{c}. The leptonic contribution is as quoted in \cite{c}.}
\label{fig:Q2-ZEUS-LAB}
\end{figure}
by two cross sections: one obtained with $E^*_{\perp cut} = 2.5$ GeV, which garantees the perturbative stability but excludes some $\gamma$-jet configurations included in the data, the other with $E^*_{\perp cut} = 0.5$ GeV which accounts for a larger phase space at the cost of letting the theoretical predictions err in the non-perturbative regime.
The results of our approach are compared with data in Figs. \ref{fig:ygam-ZEUS-LAB}-\ref{fig:PTjet-ZEUS-NORES-LAB}. In all plots we include the contribution from the leptonic radiation of the photon ($e\rightarrow e + \gamma$) based on the DJANGOH~\cite{djangoh} generator, as estimated in \cite{c}. We add it to the hadronic results obtained in this work, with a numerical accuracy of better than 2\%, to obtain cross sections comparable to the data. The interference contribution between leptonic and hadronic emissions is negligible~\cite{c}. Furthermore no hadronization corrections are applied to our estimates. \\

In Fig. \ref{fig:ygam-ZEUS-LAB}  we display the photon rapidity spectrum and we note the very good agreement with the data when the cutoff $E^*_{\perp cut} = 2.5$ GeV is selected. Using the lower cut-off uniformely increases the predictions by about 12\%. In contrast, the predictions of \cite{d}, as quoted in ref. \cite{c}, where the resolved component is treated at lowest order, systematically underestimate the photon rapidity spectrum by about 20\%. \\

\begin{figure}[!t]
\centering
\null\vspace{-2.cm}
\includegraphics[scale=.75]{PTjet-ZEUS.eps}
\caption{\it The $p_\perp^{jet}$ distribution: comparison of the full NLO calculation to ZEUS data  \cite{c}. The leptonic contribution is as quoted in \cite{c}.}
\label{fig:PTjet-ZEUS-LAB}
\end{figure}
\begin{figure}[!h]
\centering
\includegraphics[scale=.75]{PTjet-ZEUS-NORES.eps}
\caption{\it The $p_\perp^{jet}$ distribution: comparison of the partial NLO calculation, with the unresummed resolved component, to ZEUS data. The data and the leptonic contribution are as quoted in \cite{c}.}
\label{fig:PTjet-ZEUS-NORES-LAB}
\end{figure}

The same pattern is found in Fig. \ref{fig:PT-ZEUS-LAB} displaying the photon transverse momentum spectrum: very good agreement with $E^*_{\perp cut} = 2.5$ GeV, overestimate with $E^*_{\perp cut} = 0.5$ GeV. The interesting feature however is that both cut-offs lead to similar results in the high $p_\perp^\gamma$ tail where we expect the NLO resummed treatment of the resolved component to be most appropriate ($p_\perp^{*\gamma} \ge \sqrt{Q^2}$). There, our predictions can be taken as solid predictions from NLO perturbative QCD as all relevant scales are large in the CM$^*$ frame. Comparing to the estimates based on \cite{d} and quoted in \cite{c} we are above~: in fact they systematically underestimate the data while still being compatible with them at large $p_\perp^\gamma$.  \\

Turning to the $Q^2$ distribution in Fig. \ref{fig:Q2-ZEUS-LAB}, our results confirm the discussion above: excellent agreement and stability under a change of the cut-off at small $Q^2$, overestimate of the data at the larger values. Finally we conclude this phenomenological discussion with the $p_\perp^{jet}$ spectrum, in Fig. \ref{fig:PTjet-ZEUS-LAB}, where
we notice a small excess
 in the predictions for the smallest two bins, $p_\perp^{jet} < 6$ GeV, with a large instability under change of cut-off in the first bin. In relation with this observation one notes a large higher correction (up to a factor 2 compared to the Born term)
to the resolved component.
The origin of this is the fact that the collinear fragments of the virtual photon, which would be rejected by a cut-off in the CM$^*$ frame  can be seen as jets in the laboratory. In contrast, for  $p_\perp^{jet} > 6$~GeV we observe good agreement with data as well as a very good stability under change of the cut-off which indicates that NLO perturbation theory is valid. To further explore the small $p_\perp^{jet}$ regime we calculate the cross section without resummation on the resolved component (see Fig. \ref{fig:PTjet-ZEUS-NORES-LAB})~: agreement with data is achieved for the first two bins while above 6 GeV the cross section is systematically underestimated. A last remark concerning the comparison between theory and experiment at small $p_\perp$ is of a more practical nature~: the theoretical jets constructed at the partonic level are compared with the experimental ones at the hadronic level and  hadronization corrections not taken into account at NLO QCD must be important.

\section{Conclusions}
We have discussed at length the full NLO QCD predictions for $\gamma$-jet final states in deep-inelastic scattering at HERA and compared with ZEUS data where transverse momenta are defined in the laboratory frame. The motivation for studying these final states is to avoid the photon-quark final state collinear singularity  present in the Born term $\gamma^*\,q\rightarrow \gamma\,q$ when the photon, produced longitudinally in the CM$^*$ frame, is detected at large transverse momentum in the laboratory frame due to the transverse boost of the virtual photon. We have seen that the full NLO QCD calculation, taking into account the HO corrections to the resummed resolved component, again hits this collinear singularity problem which occurs in the large $Q^2$, low
$p_\perp^\gamma$ or $p_\perp^{jet}$ regions. So, in deep inelastic scattering, doing large $p_\perp$ phenomenology with momenta defined in the laboratory is not enough to cure this collinear problem since it re-enters through the back door when considering higher order diagrams as are needed for precision calculations. Of course, working with CM$^*$ coordinates, or with a cut-off in the CM$^*$ frame, one would not have encountered this difficulty.
Nevertheless, in some well identified kinematical regions in the laboratory (low $Q^2$ or large $p_\perp$) comparaison between experiment and the full NLO theory is astonishingly good unlike the case when considering partial NLO calculation where the resolved component is treated at lowest order. Of course further data involving a cut in the CM$^*$ frame should permit a sounder comparison between theory and experiment.
To be complete a study of the scale dependence of the theoretical estimates should have been done. However in view of the problems discussed  above this is not justified at this stage. It is enough to remember that the choice of scales used in this work ($M^2 = Q^2+p_T^{*2}$) gave very good agreement with data for related processes, namely $\pi^0$ production in DIS~\cite{e)} and photoproduction ($Q^2=0$) of isolated photons~\cite{zeus-photpro} (see \cite{fgh} for the theoretical discussion).
In this respect, we are not as pessimistic as the authors of \cite{dis-review} who observe, based on comparison of older data with previous theoretical calculations,  that isolated photon production both in DIS and photoproduction is underestimated in the NLO QCD approach.

\section{Acknowledgement}
We would like to thank Peter Bussey for carefully reading the manuscript and for his useful remark on the $p_T^{jet}$ spectrum.

redpajama_set_name: RedPajamaArXiv


We know that many respiratory illnesses are caused by bacteria or viruses. There are steps you can take to help the spread of these pathogens, and also to prevent you from catching one. Furthermore, many respiratory illnesses are caused by poor habits, such as smoking. But you can make healthy choices instead.
How can you prevent yourself from getting respiratory system diseases?


Hey Everyone!! Candace here from Candi O. Designs and it's my day over at the SVG Cutting Files Blog and I'm showcasing a new file that will be available tomorrow ~ Lion Heart Standing Box. He's too cute!! This file can be used a few different ways too!! I cut the head twice, put one on the large box and then glued one to the front of the standing cut out. For the final one, I attached the large head box to the standing cut out, then decorated with ribbon and the perfect sentiment!!


text:
Kevin Iole
UFC fighter Walt Harris, wife, believe missing daughter was set up to be kidnapped
Jason Owens
November 14, 2019, 11:20 PM UTC
Aniah Blanchard/Auburn Police
Police arrested a suspect in the case of missing 19-year-old Alabama woman Aniah Blanchard last week.
Blanchard's whereabouts remain unknown, and her stepfather — UFC fighter Walt Harris — and mother Angela Harris believe that she was set up by someone she knew.
The couple appeared on daytime TV show "Dr. Phil" to discuss the case on an episode that aired Thursday.
"I totally believe that there were other people involved, multiple people involved," Angela Harris said. "Personally, I feel like it was someone that, if it was a setup, that it was somebody who knew Aniah and that knew her well."
Angela Harris clarified that she based her belief on knowledge that police are working on a lead that points to a friend or acquaintance connecting Blanchard with 30-year-old suspect Ibraheem Yazeed of Montgomery, Alabama.
Suspect was out on bond on attempted murder charge
Police arrested Yazeed last Thursday in Escambia County, Florida, near the Alabama border. Yazeed fled into the woods when law enforcement approached before he was apprehended. He's being held without bond on a charge of first-degree kidnapping.
Yazeed was free on bond on charges of attempted murder, kidnapping and first-degree robbery when Blanchard disappeared.
Police arrested Yazeed last Thursday in Escambia County, Florida, near the Alabama border in connection with the disappearance of Aniah Blanchard.
Foul play suspected
According to an affidavit, a witness claims to have seen Yazeed "forcing Blanchard into a vehicle against her will and then leaving with her in the vehicle" from an Auburn convenience store where Blanchard was last seen on Oct. 23.
Blanchard's car was recovered days later, 55 miles away at a Montgomery apartment complex. The affidavit states that blood "indicative of someone suffering a life-threatening injury" was found in her car.
Holding out hope
The Harrises remain hopeful that Blanchard is still alive.
"We're hoping that somebody has her and they're just holding her," Angela Harris told Dr. Phil. "That's just what we're holding onto. ... We're trying to keep the hope that even though she had an injury that she is still alive. We have got to keep believing that."
Walt Harris had a message for Blanchard.
"I love you baby girl. We're looking for you. We're doing everything that we can. We're going to get you. I promise I won't stop until we do. We love you."
Officials eject college player after dirty hit
Niners star Sherman warns NFL players of likely strike
Trainer says Brady wants to play until he's 46 or 47
Wetzel: Blame Hardaway, not Wiseman in NCAA case

redpajama_set_name: RedPajamaCommonCrawl


text:
Virgin to construction Hyperloop train in India
By Sophie Chapman
Richard Branson's Virgin Hyperloop One is set to be constructed in India, connecting 26mn people. The British conglomerate will build the Hyperloop t...
Richard Branson's Virgin Hyperloop One is set to be constructed in India, connecting 26mn people.
The British conglomerate will build the Hyperloop train between Pune with Mumbai, linking the new Navi Mumbai International Airport.
The journey is anticipated to be reduced by three hours, taking only 25 minutes to travel almost 100 miles, at speeds of up to 240mph.
A preliminary agreement was signed by Brandon in Mumbai on Monday for a broad hyperloop framework.
Virgin aims for a demonstration track is set to be completed within three years, with construction of the full route to be completed in five to seven years.
"I believe Virgin Hyperloop One could have the same impact upon India in the 21st century as trains in the 20th century," commented Richard Branson, Founder of Virgin Group.
"The Pune-Mumbai route is an ideal first corridor as part of a national hyperloop network," he added.
High Speed Two receives UK's first BREEAM certificate for infrastructure
Carillion was working on 57 projects at time of collapse
Virgin Hyperloop One sets new speed record, brings commercial construction closer
Construction is currently undergoing for the new airport, located 22 miles southeast of Mumbai's existing airport.
The airport is expected to be partially operational by December 2019 – with one runway serving around 10mn passengers.
When the airport is at full capacity, it is designed to host approximately 60mn passenger per year.
In a recent study, Virgin Hyperloop One stated the new route could result in $55bn worth of socio economic benefits over 30 years.
The transport system uses magnetic levitation in low pressure tubes for high speed transportation.
As it is powered by electricity and aims to effectively reduce car travel, it is believed it could reduce greenhouse gas emissions by 15,000 tonnes per year.
"Globalisation is the reality of our times. To keep pace with globalisation, we need top-quality infrastructure," stated Narendra Modi, India's Prime Minister.
Virgin groupHyperloop OneIndiaMumbai
UPC-ACEN begin 420MWp solar build in Madhya Pradesh
RMZ Corp and CPP Investments sign office space JV in India
India's L&T secures order for Uttarakhand rail line
India's Larsen & Toubro secures cross-sector orders


I had the rare pleasure, Dear Reader, of recently investigating several claims made by one Toby Hardy* who, if you were to believe the version of events as depicted by him, would have to be the Unluckiest Boy in the Whole Wide World.
If only he could be believed.
Some six months ago his landlady, the indomitable Mrs Wang*, phoned Hardy at work to tell him that her house had been burgled and that many of his electronic possessions (computer, camera, hard drive etc) had also been taken.
No worries, Hardy phones his insurer who replace the stolen items tout de suite. All well and good except that the replacement laptop, couriered from a computer store, does not arrive. Hardy calls the store to follow the matter up and they despatch a second laptop.
Which also does not arrive.
Finally, Hardy goes to the store in person and is given a different model as they had run out of the previous.
A few short months later, Hardy parks his vehicle up on a major road with the intention of selling it. He sets off to work on foot, is picked up by a colleague 'Bill', and returns in the evening to find that his vehicle has been stolen.
The insurer pays out around $30,000.
Then, another few months later, and somewhat reminiscent of the first event, Hardy is again phoned by Mrs Wang while he is at work as the house has been burgled for a second time. But this time Mrs Wang went into Hardy's room to survey the loss for herself and noted that while major items like the 42" TV had been taken, his camera and external hard drive were still lying around.
So it came as a complete surprise to her when she overheard Hardy include the camera and hard drive when reporting the loss to the police and, later, the insurer. Mrs Wang phoned the police and told them that there was something amiss in Hardy's story and she went back into his room and found the items, which he had since packed away in a suitcase.
Well, Hardy was arrested on charges of making a false complaint and spent the night in the cells before being released and finding out he'd been turfed out onto the street by Mrs Wang. She also found a large quantity of needles, point bags containing a white powder residue, and bottles and bottles of methadone pills (prescripted by a number of different doctors) and was not amused.
The insurer was subsequently informed of this turn of events and decided to look into Hardy's previous claims given the apparant dishonesty, which is where my involvement begins.
Firstly, that she purchased a laptop from Hardy after the first buglary in lieu of rent. He had an identical second laptop and had told her that they were replacements for the stolen computer. This laptop was still in her possession.
Secondly, Mrs Wang was unaware that Hardy's vehicle had been stolen. He had told her, over a month after the alleged theft, that he had sold it and he said the same to several family members. Also, she is adamant that the vehicle had been still parked up at home for several weeks until she went away for a birthday holiday weekend, several weeks after the date of reported theft.
I also confirmed with Hardy's employers that he wasn't working on the day his vehicle was stolen.
And then there was the other revelation that Toby Hardy was also known as Toby Gray*, under which name he had several prior criminal convictions.
Convictions not disclosed to the insurer at time of taking out the policy or when making the three claims, when specifically asked.
Okay, so I arranged an interview with Hardy. Naturally, I did not tell him about what information I already possessed and allowed him to take me through the events in his own words. He reiterated the story about both burglaries and the vehicle theft, also commented on not receiving the first two replacement laptops sent out after the first burglary. He also confirmed parking his vehicle up prior to going to work and also that he had no prior criminal convictions or was currently on any active charges. I couldn't help but notice, he also left out filling in the part of the disclosure form asking for any previously known names or aliases.
I have to admit that I thoroughy enjoyed the rest of the interview where I slowly turned Hardy's own words against him, asking him to clarify or explain previous statements that he had just provided with the information that I had to the contrary.
His sliences grew longer as he struggled to come up with explanations and his fidgeting more pronounced.
Apparantly the police had it all wrong - he found the hard drive and camera after he'd made the complaint and insurance claim but didn't get the opportunity to inform them of this before he was arrested. But he couldn't explain why he had been still maintaining, some twenty minutes earlier, that those very items had been stolen.
And when confronted about telling me he'd gone to work the day of the vehicle theft - but his employer confirmed he didn't work that day at all - he then stated he sometimes did gardening work for cash and that 'Bill' was the person he worked for that day but he couldn't recall where he did this work, or have any contact details for Bill.
However, he did finally come clean about receiving one of the replacement laptops. I told him that I'd traced the serial number of that laptop and asked him to guess where that led me? A small lie of my own, I'll have to admit, as the retail outlet did not record the serials of goods shipped. He continued to deny receiving the first laptop though, and accused Mrs Wang of making things up.
Then he finally admitted that he did have another name, Gray, and that yes he did have criminal convictions under that name but he didn't disclose them out of 'embarrasment' not because he was trying to obfuscate his criminal past.
Makes no difference, buddy, it's still fraud. And I just don't believe you.
I don't know what has become of Hardy. The last I heard, he was due in Court on a number of charges relating to this, but that was before the insurer had his later admissions. I'm asuming further charges will be pending and that he will be asked to repay all monies previously paid out to him earlier as he had failed to disclose his convictions when asked.
So it wasn't so much a case of being the unluckiest, but rather the stupidest, boy in the whole wide world.


Florida Super Senior Grand Prix Circuit Begins in Jan.
The 2014 Florida Super Senior Grand Prix will kick off on Jan. 6 with 11 tournaments slated for January through March on the East and West coasts of Florida. The tournaments will feature some of the top players in the U.S ages 55 to 90.
"The circuit has over a 20-year history and features many of the best players in the U.S.," says Florida Super Senior Grand Prix Director Larry Turville. "New sites this year are the Sanchez-Casals Academy in Naples, and Palm Aire Country Club in Sarasota. The circuit also includes two National Super Cat II events, one at Sterling Oaks Country Club in Naples, and the other at St. Pete Country Club."
The Florida Super Senior Grand Prix Circuit was originated in 1993 in partnership with the USTA Florida Section. The circuit annually attracts more than 200 players per event. For full information on the circuit, including specific event deadlines and contacts, go to www.flsupersenior.com.